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8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
1
ACKNOWLEDGEMENT
I express my sincere gratitude to Dr Hitesh Arora Department of Quantitative Techniques
and Operations FORE School of Management for his encouragement constant support and
guidance His support has been invaluable in completion of the project I would also like to
place on record the sincere efforts taken by him in giving all minor details about the subject
I also thank FORE School of Management New Delhi for providing me with an opportunity
to work on this great learning I would also like to thank my respondent Mr Kunal Mehta
Director of Srikant Industries Pvt Ltd without whom the project would have been
incomplete
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FORE School of Management Decision Making Models
2
Contents
1 Executive Summary 3
2 Introduction 4
21 About The Company 4
22 Objective of the Project 4
3 Methodology 5
31 Data Collection 5
32 Data Analysis 5
4 Problem Description and Formulation 6
41 Problem Description 6
42 Problem Formulation 8
5 Conclusion 12
51 Final Result 12
52 Limitations 13
6 References 14
7 Appendix i
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FORE School of Management Decision Making Models
4
2 Introduction
21 About The Company
Srikant Industries Pvt Ltd Jodhpur is the leader of lime world It also has a subsidiary plant
for Dye manufacturing It is amongst the leading manufacturers of Calcium Hydro-Oxide and
Calcium Oxide and manufactures various Dye products to cater to the tye and dye industry of
Rajasthan
It is in this line of manufacturing lime and dye products for the last 20 years and has
established vast client network all over the country Itrsquos client list includes Nitrex Chemicals
(I) Ltd (Valsad) Shriram Vinyl amp Chemicals Industries Ltd (Kota) Shree Shyam Pulp amp
Board Mills Ltd (Kashipur) Sesa Industries Ltd (Goa) Shree Rayalseema Hi-Strength Hypo
Ltd (Kurrnool) etc
Itrsquos product finds use in Paint Industry Chemical Industry Paper Industry Plastic Industry ampmany more
22 Objective of the Project
The objective of this problem is to determine the maximum profit that can be made
considering the overall sales generated negated by the total expenditure including the
advertising costs
The chemicals need to be optimized keeping the constraints in check with its effective
allocation in forming the dyes
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FORE School of Management Decision Making Models
5
3 Methodology
31 Data Collection
Primary Sources Mr Kunal Mehta Director of Srikant Industries Pvt Ltd Jodhpur provided
the data
Secondary Sources The secondary sources referred to were the companyrsquos books
32 Data AnalysisThe collected data was first transformed into a tabular format for formulation of the linear
programming problem It was then solved through MS Excel Solver
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FORE School of Management
4 Proble
4
Srikant Industries Pvt Ltd as pa
(Dye1 Dye 2 and Dye 3)
Each dye is produced by blendi
Chemical 3) Table 1 Illustrates t
chemicals
It can purchase up to 5000 litres
The three types of dyes differ in t
Dye 1 - The chemicals blendedcontain at most 1 sulphur
Dye 2 - The chemicals blended
contain at most 2 sulphur
Dye 3 - The chemicals blended
contain at most 1 sulphur
Decisi
Description and Formulatio
1 Problem Description
rt of its subsidiary division manufactures thr
g of three types of chemicals (Chemical 1
e sales price per litre of dye and the purcha
Table1 Price Details
f each type of chemicals daily
heir Organic-Content rating (OCR) and sulp
or making dye 1 must have an average OC
for making dye 2 must have an average O
or making dye 3 must have an average OC
Table 2 Dyes for Customers
on Making Models
6
n
e types of dyes
Chemical 2 and
se price per litre of
ur content
of at least 10 and
R of atleast 8 and
of at least 6 and
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FORE School of Management
The average OCR and the sulph
2
It costs Rs 4 to covert 1 litre of s
can produce up to 14000 litres o
Srikant Industries Pvt Ltdrsquos cus
Dye 1 - at 3000 litres per day
Dye 2 - at 2000 litres per day
Dye 3 - at 1000 litres per day
Meeting these demands is a nece
Srikant Industries Pvt Ltd also
For every 1 rupee spent the dem
The problem is to maximize dail
Decisi
r content of the three types of chemicals are
able 3 Chemicals for Blending
nthetics into one litre of dye amp Srikant Ind
dyes daily
tomers require dye in the following amounts
sity
dvertise to stimulate demand for the product
nd for that particular dye increases by 10 lit
profits under given the conditions
on Making Models
7
illustrated in Table
stries Pvt Ltd
s
es
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FORE School of Management Decision Making Models
9
Daily Revenues
Dye Sales
70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
Daily Costs
Purchasing Cost of Chemicals
45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 )
Advertising Cost
a1 + a2 + a3
Production Cost
4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
Daily Profit
Dye Sales ndash [Purchasing costs of Chemicals + Production Cost + Advertising Cost ]
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FORE School of Management Decision Making Models
10
Objective Function
Maximize z = 70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
- [45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 ) + 4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
+ a1 + a2 + a3]
z max= 21 x11 + 11 x12 + x13 + 31x21 + 21x22 + 11 x23 + 41 x31 + 31 x32 + 21 x33 - a1 - a2 - a3
Subject to
(1) Demand constraints
Dye 1 2 and 3 produced daily should equal its daily demand
x11 + x21 + x31 - 10 a1 = 3000 (Dye 1 Demand Constraint)
x12 + x22 + x32 - 10 a2 = 2000 (Dye 2 Demand Constraint)
x13 + x23 + x33 - 10 a3 = 1000 (Dye 3 Demand Constraint)
(2) Usage constraints
At most 5000 litres of each chemical type can be purchased daily
x11 + x12 + x13 le 5000 (Chemical 1 Usage Constraint)
x21 + x22 + x23 le 5000 (Chemical 2 Usage Constraint)x31 + x32 + x33 le 5000 (Chemical 3 Usage Constraint)
(3) Production capacity constraint
Production capacity is 14000 litres of Dye per day
x11 + x21 + x31 + x12 + x22 + x32 + x13 + x23 + x33 le 14000 (ProductionCapacity Constraint)
(4) Average OCR limitation
Chemical blended to make Dye 1 must have an average OCR of at least 10
(12 x11 + 6 x21 + 8 x31) (x11 + x21 + x31) ge 10
2 x11 - 4 x21 - 2 x31 ge 0 (Dye 1 OCR Constraint)
Chemical blended to make Dye 2 must have an average OCR of at least 8
(12 x12 + 6 x22 + 8 x32) (x12 + x22 + x32) ge 8
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FORE School of Management Decision Making Models
11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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FORE School of Management Decision Making Models
i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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FORE School of Management Decision Making Models
ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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FORE School of Management Decision Making Models
iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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FORE School of Management Decision Making Models
2
Contents
1 Executive Summary 3
2 Introduction 4
21 About The Company 4
22 Objective of the Project 4
3 Methodology 5
31 Data Collection 5
32 Data Analysis 5
4 Problem Description and Formulation 6
41 Problem Description 6
42 Problem Formulation 8
5 Conclusion 12
51 Final Result 12
52 Limitations 13
6 References 14
7 Appendix i
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FORE School of Management Decision Making Models
4
2 Introduction
21 About The Company
Srikant Industries Pvt Ltd Jodhpur is the leader of lime world It also has a subsidiary plant
for Dye manufacturing It is amongst the leading manufacturers of Calcium Hydro-Oxide and
Calcium Oxide and manufactures various Dye products to cater to the tye and dye industry of
Rajasthan
It is in this line of manufacturing lime and dye products for the last 20 years and has
established vast client network all over the country Itrsquos client list includes Nitrex Chemicals
(I) Ltd (Valsad) Shriram Vinyl amp Chemicals Industries Ltd (Kota) Shree Shyam Pulp amp
Board Mills Ltd (Kashipur) Sesa Industries Ltd (Goa) Shree Rayalseema Hi-Strength Hypo
Ltd (Kurrnool) etc
Itrsquos product finds use in Paint Industry Chemical Industry Paper Industry Plastic Industry ampmany more
22 Objective of the Project
The objective of this problem is to determine the maximum profit that can be made
considering the overall sales generated negated by the total expenditure including the
advertising costs
The chemicals need to be optimized keeping the constraints in check with its effective
allocation in forming the dyes
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FORE School of Management Decision Making Models
5
3 Methodology
31 Data Collection
Primary Sources Mr Kunal Mehta Director of Srikant Industries Pvt Ltd Jodhpur provided
the data
Secondary Sources The secondary sources referred to were the companyrsquos books
32 Data AnalysisThe collected data was first transformed into a tabular format for formulation of the linear
programming problem It was then solved through MS Excel Solver
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FORE School of Management
4 Proble
4
Srikant Industries Pvt Ltd as pa
(Dye1 Dye 2 and Dye 3)
Each dye is produced by blendi
Chemical 3) Table 1 Illustrates t
chemicals
It can purchase up to 5000 litres
The three types of dyes differ in t
Dye 1 - The chemicals blendedcontain at most 1 sulphur
Dye 2 - The chemicals blended
contain at most 2 sulphur
Dye 3 - The chemicals blended
contain at most 1 sulphur
Decisi
Description and Formulatio
1 Problem Description
rt of its subsidiary division manufactures thr
g of three types of chemicals (Chemical 1
e sales price per litre of dye and the purcha
Table1 Price Details
f each type of chemicals daily
heir Organic-Content rating (OCR) and sulp
or making dye 1 must have an average OC
for making dye 2 must have an average O
or making dye 3 must have an average OC
Table 2 Dyes for Customers
on Making Models
6
n
e types of dyes
Chemical 2 and
se price per litre of
ur content
of at least 10 and
R of atleast 8 and
of at least 6 and
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FORE School of Management
The average OCR and the sulph
2
It costs Rs 4 to covert 1 litre of s
can produce up to 14000 litres o
Srikant Industries Pvt Ltdrsquos cus
Dye 1 - at 3000 litres per day
Dye 2 - at 2000 litres per day
Dye 3 - at 1000 litres per day
Meeting these demands is a nece
Srikant Industries Pvt Ltd also
For every 1 rupee spent the dem
The problem is to maximize dail
Decisi
r content of the three types of chemicals are
able 3 Chemicals for Blending
nthetics into one litre of dye amp Srikant Ind
dyes daily
tomers require dye in the following amounts
sity
dvertise to stimulate demand for the product
nd for that particular dye increases by 10 lit
profits under given the conditions
on Making Models
7
illustrated in Table
stries Pvt Ltd
s
es
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FORE School of Management Decision Making Models
9
Daily Revenues
Dye Sales
70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
Daily Costs
Purchasing Cost of Chemicals
45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 )
Advertising Cost
a1 + a2 + a3
Production Cost
4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
Daily Profit
Dye Sales ndash [Purchasing costs of Chemicals + Production Cost + Advertising Cost ]
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FORE School of Management Decision Making Models
10
Objective Function
Maximize z = 70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
- [45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 ) + 4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
+ a1 + a2 + a3]
z max= 21 x11 + 11 x12 + x13 + 31x21 + 21x22 + 11 x23 + 41 x31 + 31 x32 + 21 x33 - a1 - a2 - a3
Subject to
(1) Demand constraints
Dye 1 2 and 3 produced daily should equal its daily demand
x11 + x21 + x31 - 10 a1 = 3000 (Dye 1 Demand Constraint)
x12 + x22 + x32 - 10 a2 = 2000 (Dye 2 Demand Constraint)
x13 + x23 + x33 - 10 a3 = 1000 (Dye 3 Demand Constraint)
(2) Usage constraints
At most 5000 litres of each chemical type can be purchased daily
x11 + x12 + x13 le 5000 (Chemical 1 Usage Constraint)
x21 + x22 + x23 le 5000 (Chemical 2 Usage Constraint)x31 + x32 + x33 le 5000 (Chemical 3 Usage Constraint)
(3) Production capacity constraint
Production capacity is 14000 litres of Dye per day
x11 + x21 + x31 + x12 + x22 + x32 + x13 + x23 + x33 le 14000 (ProductionCapacity Constraint)
(4) Average OCR limitation
Chemical blended to make Dye 1 must have an average OCR of at least 10
(12 x11 + 6 x21 + 8 x31) (x11 + x21 + x31) ge 10
2 x11 - 4 x21 - 2 x31 ge 0 (Dye 1 OCR Constraint)
Chemical blended to make Dye 2 must have an average OCR of at least 8
(12 x12 + 6 x22 + 8 x32) (x12 + x22 + x32) ge 8
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FORE School of Management Decision Making Models
11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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FORE School of Management Decision Making Models
i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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FORE School of Management Decision Making Models
ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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FORE School of Management Decision Making Models
iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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FORE School of Management Decision Making Models
4
2 Introduction
21 About The Company
Srikant Industries Pvt Ltd Jodhpur is the leader of lime world It also has a subsidiary plant
for Dye manufacturing It is amongst the leading manufacturers of Calcium Hydro-Oxide and
Calcium Oxide and manufactures various Dye products to cater to the tye and dye industry of
Rajasthan
It is in this line of manufacturing lime and dye products for the last 20 years and has
established vast client network all over the country Itrsquos client list includes Nitrex Chemicals
(I) Ltd (Valsad) Shriram Vinyl amp Chemicals Industries Ltd (Kota) Shree Shyam Pulp amp
Board Mills Ltd (Kashipur) Sesa Industries Ltd (Goa) Shree Rayalseema Hi-Strength Hypo
Ltd (Kurrnool) etc
Itrsquos product finds use in Paint Industry Chemical Industry Paper Industry Plastic Industry ampmany more
22 Objective of the Project
The objective of this problem is to determine the maximum profit that can be made
considering the overall sales generated negated by the total expenditure including the
advertising costs
The chemicals need to be optimized keeping the constraints in check with its effective
allocation in forming the dyes
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FORE School of Management Decision Making Models
5
3 Methodology
31 Data Collection
Primary Sources Mr Kunal Mehta Director of Srikant Industries Pvt Ltd Jodhpur provided
the data
Secondary Sources The secondary sources referred to were the companyrsquos books
32 Data AnalysisThe collected data was first transformed into a tabular format for formulation of the linear
programming problem It was then solved through MS Excel Solver
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FORE School of Management
4 Proble
4
Srikant Industries Pvt Ltd as pa
(Dye1 Dye 2 and Dye 3)
Each dye is produced by blendi
Chemical 3) Table 1 Illustrates t
chemicals
It can purchase up to 5000 litres
The three types of dyes differ in t
Dye 1 - The chemicals blendedcontain at most 1 sulphur
Dye 2 - The chemicals blended
contain at most 2 sulphur
Dye 3 - The chemicals blended
contain at most 1 sulphur
Decisi
Description and Formulatio
1 Problem Description
rt of its subsidiary division manufactures thr
g of three types of chemicals (Chemical 1
e sales price per litre of dye and the purcha
Table1 Price Details
f each type of chemicals daily
heir Organic-Content rating (OCR) and sulp
or making dye 1 must have an average OC
for making dye 2 must have an average O
or making dye 3 must have an average OC
Table 2 Dyes for Customers
on Making Models
6
n
e types of dyes
Chemical 2 and
se price per litre of
ur content
of at least 10 and
R of atleast 8 and
of at least 6 and
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FORE School of Management
The average OCR and the sulph
2
It costs Rs 4 to covert 1 litre of s
can produce up to 14000 litres o
Srikant Industries Pvt Ltdrsquos cus
Dye 1 - at 3000 litres per day
Dye 2 - at 2000 litres per day
Dye 3 - at 1000 litres per day
Meeting these demands is a nece
Srikant Industries Pvt Ltd also
For every 1 rupee spent the dem
The problem is to maximize dail
Decisi
r content of the three types of chemicals are
able 3 Chemicals for Blending
nthetics into one litre of dye amp Srikant Ind
dyes daily
tomers require dye in the following amounts
sity
dvertise to stimulate demand for the product
nd for that particular dye increases by 10 lit
profits under given the conditions
on Making Models
7
illustrated in Table
stries Pvt Ltd
s
es
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FORE School of Management Decision Making Models
9
Daily Revenues
Dye Sales
70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
Daily Costs
Purchasing Cost of Chemicals
45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 )
Advertising Cost
a1 + a2 + a3
Production Cost
4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
Daily Profit
Dye Sales ndash [Purchasing costs of Chemicals + Production Cost + Advertising Cost ]
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FORE School of Management Decision Making Models
10
Objective Function
Maximize z = 70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
- [45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 ) + 4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
+ a1 + a2 + a3]
z max= 21 x11 + 11 x12 + x13 + 31x21 + 21x22 + 11 x23 + 41 x31 + 31 x32 + 21 x33 - a1 - a2 - a3
Subject to
(1) Demand constraints
Dye 1 2 and 3 produced daily should equal its daily demand
x11 + x21 + x31 - 10 a1 = 3000 (Dye 1 Demand Constraint)
x12 + x22 + x32 - 10 a2 = 2000 (Dye 2 Demand Constraint)
x13 + x23 + x33 - 10 a3 = 1000 (Dye 3 Demand Constraint)
(2) Usage constraints
At most 5000 litres of each chemical type can be purchased daily
x11 + x12 + x13 le 5000 (Chemical 1 Usage Constraint)
x21 + x22 + x23 le 5000 (Chemical 2 Usage Constraint)x31 + x32 + x33 le 5000 (Chemical 3 Usage Constraint)
(3) Production capacity constraint
Production capacity is 14000 litres of Dye per day
x11 + x21 + x31 + x12 + x22 + x32 + x13 + x23 + x33 le 14000 (ProductionCapacity Constraint)
(4) Average OCR limitation
Chemical blended to make Dye 1 must have an average OCR of at least 10
(12 x11 + 6 x21 + 8 x31) (x11 + x21 + x31) ge 10
2 x11 - 4 x21 - 2 x31 ge 0 (Dye 1 OCR Constraint)
Chemical blended to make Dye 2 must have an average OCR of at least 8
(12 x12 + 6 x22 + 8 x32) (x12 + x22 + x32) ge 8
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FORE School of Management Decision Making Models
11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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FORE School of Management Decision Making Models
i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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FORE School of Management Decision Making Models
4
2 Introduction
21 About The Company
Srikant Industries Pvt Ltd Jodhpur is the leader of lime world It also has a subsidiary plant
for Dye manufacturing It is amongst the leading manufacturers of Calcium Hydro-Oxide and
Calcium Oxide and manufactures various Dye products to cater to the tye and dye industry of
Rajasthan
It is in this line of manufacturing lime and dye products for the last 20 years and has
established vast client network all over the country Itrsquos client list includes Nitrex Chemicals
(I) Ltd (Valsad) Shriram Vinyl amp Chemicals Industries Ltd (Kota) Shree Shyam Pulp amp
Board Mills Ltd (Kashipur) Sesa Industries Ltd (Goa) Shree Rayalseema Hi-Strength Hypo
Ltd (Kurrnool) etc
Itrsquos product finds use in Paint Industry Chemical Industry Paper Industry Plastic Industry ampmany more
22 Objective of the Project
The objective of this problem is to determine the maximum profit that can be made
considering the overall sales generated negated by the total expenditure including the
advertising costs
The chemicals need to be optimized keeping the constraints in check with its effective
allocation in forming the dyes
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
5
3 Methodology
31 Data Collection
Primary Sources Mr Kunal Mehta Director of Srikant Industries Pvt Ltd Jodhpur provided
the data
Secondary Sources The secondary sources referred to were the companyrsquos books
32 Data AnalysisThe collected data was first transformed into a tabular format for formulation of the linear
programming problem It was then solved through MS Excel Solver
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FORE School of Management
4 Proble
4
Srikant Industries Pvt Ltd as pa
(Dye1 Dye 2 and Dye 3)
Each dye is produced by blendi
Chemical 3) Table 1 Illustrates t
chemicals
It can purchase up to 5000 litres
The three types of dyes differ in t
Dye 1 - The chemicals blendedcontain at most 1 sulphur
Dye 2 - The chemicals blended
contain at most 2 sulphur
Dye 3 - The chemicals blended
contain at most 1 sulphur
Decisi
Description and Formulatio
1 Problem Description
rt of its subsidiary division manufactures thr
g of three types of chemicals (Chemical 1
e sales price per litre of dye and the purcha
Table1 Price Details
f each type of chemicals daily
heir Organic-Content rating (OCR) and sulp
or making dye 1 must have an average OC
for making dye 2 must have an average O
or making dye 3 must have an average OC
Table 2 Dyes for Customers
on Making Models
6
n
e types of dyes
Chemical 2 and
se price per litre of
ur content
of at least 10 and
R of atleast 8 and
of at least 6 and
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FORE School of Management
The average OCR and the sulph
2
It costs Rs 4 to covert 1 litre of s
can produce up to 14000 litres o
Srikant Industries Pvt Ltdrsquos cus
Dye 1 - at 3000 litres per day
Dye 2 - at 2000 litres per day
Dye 3 - at 1000 litres per day
Meeting these demands is a nece
Srikant Industries Pvt Ltd also
For every 1 rupee spent the dem
The problem is to maximize dail
Decisi
r content of the three types of chemicals are
able 3 Chemicals for Blending
nthetics into one litre of dye amp Srikant Ind
dyes daily
tomers require dye in the following amounts
sity
dvertise to stimulate demand for the product
nd for that particular dye increases by 10 lit
profits under given the conditions
on Making Models
7
illustrated in Table
stries Pvt Ltd
s
es
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FORE School of Management Decision Making Models
9
Daily Revenues
Dye Sales
70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
Daily Costs
Purchasing Cost of Chemicals
45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 )
Advertising Cost
a1 + a2 + a3
Production Cost
4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
Daily Profit
Dye Sales ndash [Purchasing costs of Chemicals + Production Cost + Advertising Cost ]
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FORE School of Management Decision Making Models
10
Objective Function
Maximize z = 70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
- [45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 ) + 4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
+ a1 + a2 + a3]
z max= 21 x11 + 11 x12 + x13 + 31x21 + 21x22 + 11 x23 + 41 x31 + 31 x32 + 21 x33 - a1 - a2 - a3
Subject to
(1) Demand constraints
Dye 1 2 and 3 produced daily should equal its daily demand
x11 + x21 + x31 - 10 a1 = 3000 (Dye 1 Demand Constraint)
x12 + x22 + x32 - 10 a2 = 2000 (Dye 2 Demand Constraint)
x13 + x23 + x33 - 10 a3 = 1000 (Dye 3 Demand Constraint)
(2) Usage constraints
At most 5000 litres of each chemical type can be purchased daily
x11 + x12 + x13 le 5000 (Chemical 1 Usage Constraint)
x21 + x22 + x23 le 5000 (Chemical 2 Usage Constraint)x31 + x32 + x33 le 5000 (Chemical 3 Usage Constraint)
(3) Production capacity constraint
Production capacity is 14000 litres of Dye per day
x11 + x21 + x31 + x12 + x22 + x32 + x13 + x23 + x33 le 14000 (ProductionCapacity Constraint)
(4) Average OCR limitation
Chemical blended to make Dye 1 must have an average OCR of at least 10
(12 x11 + 6 x21 + 8 x31) (x11 + x21 + x31) ge 10
2 x11 - 4 x21 - 2 x31 ge 0 (Dye 1 OCR Constraint)
Chemical blended to make Dye 2 must have an average OCR of at least 8
(12 x12 + 6 x22 + 8 x32) (x12 + x22 + x32) ge 8
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FORE School of Management Decision Making Models
11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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FORE School of Management Decision Making Models
i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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FORE School of Management Decision Making Models
ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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FORE School of Management Decision Making Models
iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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FORE School of Management Decision Making Models
5
3 Methodology
31 Data Collection
Primary Sources Mr Kunal Mehta Director of Srikant Industries Pvt Ltd Jodhpur provided
the data
Secondary Sources The secondary sources referred to were the companyrsquos books
32 Data AnalysisThe collected data was first transformed into a tabular format for formulation of the linear
programming problem It was then solved through MS Excel Solver
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FORE School of Management
4 Proble
4
Srikant Industries Pvt Ltd as pa
(Dye1 Dye 2 and Dye 3)
Each dye is produced by blendi
Chemical 3) Table 1 Illustrates t
chemicals
It can purchase up to 5000 litres
The three types of dyes differ in t
Dye 1 - The chemicals blendedcontain at most 1 sulphur
Dye 2 - The chemicals blended
contain at most 2 sulphur
Dye 3 - The chemicals blended
contain at most 1 sulphur
Decisi
Description and Formulatio
1 Problem Description
rt of its subsidiary division manufactures thr
g of three types of chemicals (Chemical 1
e sales price per litre of dye and the purcha
Table1 Price Details
f each type of chemicals daily
heir Organic-Content rating (OCR) and sulp
or making dye 1 must have an average OC
for making dye 2 must have an average O
or making dye 3 must have an average OC
Table 2 Dyes for Customers
on Making Models
6
n
e types of dyes
Chemical 2 and
se price per litre of
ur content
of at least 10 and
R of atleast 8 and
of at least 6 and
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FORE School of Management
The average OCR and the sulph
2
It costs Rs 4 to covert 1 litre of s
can produce up to 14000 litres o
Srikant Industries Pvt Ltdrsquos cus
Dye 1 - at 3000 litres per day
Dye 2 - at 2000 litres per day
Dye 3 - at 1000 litres per day
Meeting these demands is a nece
Srikant Industries Pvt Ltd also
For every 1 rupee spent the dem
The problem is to maximize dail
Decisi
r content of the three types of chemicals are
able 3 Chemicals for Blending
nthetics into one litre of dye amp Srikant Ind
dyes daily
tomers require dye in the following amounts
sity
dvertise to stimulate demand for the product
nd for that particular dye increases by 10 lit
profits under given the conditions
on Making Models
7
illustrated in Table
stries Pvt Ltd
s
es
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FORE School of Management Decision Making Models
9
Daily Revenues
Dye Sales
70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
Daily Costs
Purchasing Cost of Chemicals
45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 )
Advertising Cost
a1 + a2 + a3
Production Cost
4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
Daily Profit
Dye Sales ndash [Purchasing costs of Chemicals + Production Cost + Advertising Cost ]
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FORE School of Management Decision Making Models
10
Objective Function
Maximize z = 70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
- [45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 ) + 4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
+ a1 + a2 + a3]
z max= 21 x11 + 11 x12 + x13 + 31x21 + 21x22 + 11 x23 + 41 x31 + 31 x32 + 21 x33 - a1 - a2 - a3
Subject to
(1) Demand constraints
Dye 1 2 and 3 produced daily should equal its daily demand
x11 + x21 + x31 - 10 a1 = 3000 (Dye 1 Demand Constraint)
x12 + x22 + x32 - 10 a2 = 2000 (Dye 2 Demand Constraint)
x13 + x23 + x33 - 10 a3 = 1000 (Dye 3 Demand Constraint)
(2) Usage constraints
At most 5000 litres of each chemical type can be purchased daily
x11 + x12 + x13 le 5000 (Chemical 1 Usage Constraint)
x21 + x22 + x23 le 5000 (Chemical 2 Usage Constraint)x31 + x32 + x33 le 5000 (Chemical 3 Usage Constraint)
(3) Production capacity constraint
Production capacity is 14000 litres of Dye per day
x11 + x21 + x31 + x12 + x22 + x32 + x13 + x23 + x33 le 14000 (ProductionCapacity Constraint)
(4) Average OCR limitation
Chemical blended to make Dye 1 must have an average OCR of at least 10
(12 x11 + 6 x21 + 8 x31) (x11 + x21 + x31) ge 10
2 x11 - 4 x21 - 2 x31 ge 0 (Dye 1 OCR Constraint)
Chemical blended to make Dye 2 must have an average OCR of at least 8
(12 x12 + 6 x22 + 8 x32) (x12 + x22 + x32) ge 8
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FORE School of Management Decision Making Models
11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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FORE School of Management Decision Making Models
i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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FORE School of Management Decision Making Models
ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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FORE School of Management Decision Making Models
iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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FORE School of Management
4 Proble
4
Srikant Industries Pvt Ltd as pa
(Dye1 Dye 2 and Dye 3)
Each dye is produced by blendi
Chemical 3) Table 1 Illustrates t
chemicals
It can purchase up to 5000 litres
The three types of dyes differ in t
Dye 1 - The chemicals blendedcontain at most 1 sulphur
Dye 2 - The chemicals blended
contain at most 2 sulphur
Dye 3 - The chemicals blended
contain at most 1 sulphur
Decisi
Description and Formulatio
1 Problem Description
rt of its subsidiary division manufactures thr
g of three types of chemicals (Chemical 1
e sales price per litre of dye and the purcha
Table1 Price Details
f each type of chemicals daily
heir Organic-Content rating (OCR) and sulp
or making dye 1 must have an average OC
for making dye 2 must have an average O
or making dye 3 must have an average OC
Table 2 Dyes for Customers
on Making Models
6
n
e types of dyes
Chemical 2 and
se price per litre of
ur content
of at least 10 and
R of atleast 8 and
of at least 6 and
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FORE School of Management
The average OCR and the sulph
2
It costs Rs 4 to covert 1 litre of s
can produce up to 14000 litres o
Srikant Industries Pvt Ltdrsquos cus
Dye 1 - at 3000 litres per day
Dye 2 - at 2000 litres per day
Dye 3 - at 1000 litres per day
Meeting these demands is a nece
Srikant Industries Pvt Ltd also
For every 1 rupee spent the dem
The problem is to maximize dail
Decisi
r content of the three types of chemicals are
able 3 Chemicals for Blending
nthetics into one litre of dye amp Srikant Ind
dyes daily
tomers require dye in the following amounts
sity
dvertise to stimulate demand for the product
nd for that particular dye increases by 10 lit
profits under given the conditions
on Making Models
7
illustrated in Table
stries Pvt Ltd
s
es
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FORE School of Management Decision Making Models
9
Daily Revenues
Dye Sales
70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
Daily Costs
Purchasing Cost of Chemicals
45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 )
Advertising Cost
a1 + a2 + a3
Production Cost
4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
Daily Profit
Dye Sales ndash [Purchasing costs of Chemicals + Production Cost + Advertising Cost ]
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FORE School of Management Decision Making Models
10
Objective Function
Maximize z = 70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
- [45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 ) + 4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
+ a1 + a2 + a3]
z max= 21 x11 + 11 x12 + x13 + 31x21 + 21x22 + 11 x23 + 41 x31 + 31 x32 + 21 x33 - a1 - a2 - a3
Subject to
(1) Demand constraints
Dye 1 2 and 3 produced daily should equal its daily demand
x11 + x21 + x31 - 10 a1 = 3000 (Dye 1 Demand Constraint)
x12 + x22 + x32 - 10 a2 = 2000 (Dye 2 Demand Constraint)
x13 + x23 + x33 - 10 a3 = 1000 (Dye 3 Demand Constraint)
(2) Usage constraints
At most 5000 litres of each chemical type can be purchased daily
x11 + x12 + x13 le 5000 (Chemical 1 Usage Constraint)
x21 + x22 + x23 le 5000 (Chemical 2 Usage Constraint)x31 + x32 + x33 le 5000 (Chemical 3 Usage Constraint)
(3) Production capacity constraint
Production capacity is 14000 litres of Dye per day
x11 + x21 + x31 + x12 + x22 + x32 + x13 + x23 + x33 le 14000 (ProductionCapacity Constraint)
(4) Average OCR limitation
Chemical blended to make Dye 1 must have an average OCR of at least 10
(12 x11 + 6 x21 + 8 x31) (x11 + x21 + x31) ge 10
2 x11 - 4 x21 - 2 x31 ge 0 (Dye 1 OCR Constraint)
Chemical blended to make Dye 2 must have an average OCR of at least 8
(12 x12 + 6 x22 + 8 x32) (x12 + x22 + x32) ge 8
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FORE School of Management Decision Making Models
11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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FORE School of Management Decision Making Models
i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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FORE School of Management Decision Making Models
ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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FORE School of Management Decision Making Models
iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
8132019 Decision Making Models Project Report
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FORE School of Management
The average OCR and the sulph
2
It costs Rs 4 to covert 1 litre of s
can produce up to 14000 litres o
Srikant Industries Pvt Ltdrsquos cus
Dye 1 - at 3000 litres per day
Dye 2 - at 2000 litres per day
Dye 3 - at 1000 litres per day
Meeting these demands is a nece
Srikant Industries Pvt Ltd also
For every 1 rupee spent the dem
The problem is to maximize dail
Decisi
r content of the three types of chemicals are
able 3 Chemicals for Blending
nthetics into one litre of dye amp Srikant Ind
dyes daily
tomers require dye in the following amounts
sity
dvertise to stimulate demand for the product
nd for that particular dye increases by 10 lit
profits under given the conditions
on Making Models
7
illustrated in Table
stries Pvt Ltd
s
es
8132019 Decision Making Models Project Report
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8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
9
Daily Revenues
Dye Sales
70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
Daily Costs
Purchasing Cost of Chemicals
45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 )
Advertising Cost
a1 + a2 + a3
Production Cost
4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
Daily Profit
Dye Sales ndash [Purchasing costs of Chemicals + Production Cost + Advertising Cost ]
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FORE School of Management Decision Making Models
10
Objective Function
Maximize z = 70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
- [45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 ) + 4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
+ a1 + a2 + a3]
z max= 21 x11 + 11 x12 + x13 + 31x21 + 21x22 + 11 x23 + 41 x31 + 31 x32 + 21 x33 - a1 - a2 - a3
Subject to
(1) Demand constraints
Dye 1 2 and 3 produced daily should equal its daily demand
x11 + x21 + x31 - 10 a1 = 3000 (Dye 1 Demand Constraint)
x12 + x22 + x32 - 10 a2 = 2000 (Dye 2 Demand Constraint)
x13 + x23 + x33 - 10 a3 = 1000 (Dye 3 Demand Constraint)
(2) Usage constraints
At most 5000 litres of each chemical type can be purchased daily
x11 + x12 + x13 le 5000 (Chemical 1 Usage Constraint)
x21 + x22 + x23 le 5000 (Chemical 2 Usage Constraint)x31 + x32 + x33 le 5000 (Chemical 3 Usage Constraint)
(3) Production capacity constraint
Production capacity is 14000 litres of Dye per day
x11 + x21 + x31 + x12 + x22 + x32 + x13 + x23 + x33 le 14000 (ProductionCapacity Constraint)
(4) Average OCR limitation
Chemical blended to make Dye 1 must have an average OCR of at least 10
(12 x11 + 6 x21 + 8 x31) (x11 + x21 + x31) ge 10
2 x11 - 4 x21 - 2 x31 ge 0 (Dye 1 OCR Constraint)
Chemical blended to make Dye 2 must have an average OCR of at least 8
(12 x12 + 6 x22 + 8 x32) (x12 + x22 + x32) ge 8
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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FORE School of Management Decision Making Models
ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
8132019 Decision Making Models Project Report
httpslidepdfcomreaderfulldecision-making-models-project-report 1718
FORE School of Management Decision Making Models
iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
8132019 Decision Making Models Project Report
httpslidepdfcomreaderfulldecision-making-models-project-report 1818
FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
8132019 Decision Making Models Project Report
httpslidepdfcomreaderfulldecision-making-models-project-report 818
8132019 Decision Making Models Project Report
httpslidepdfcomreaderfulldecision-making-models-project-report 918
FORE School of Management Decision Making Models
9
Daily Revenues
Dye Sales
70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
Daily Costs
Purchasing Cost of Chemicals
45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 )
Advertising Cost
a1 + a2 + a3
Production Cost
4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
Daily Profit
Dye Sales ndash [Purchasing costs of Chemicals + Production Cost + Advertising Cost ]
8132019 Decision Making Models Project Report
httpslidepdfcomreaderfulldecision-making-models-project-report 1018
FORE School of Management Decision Making Models
10
Objective Function
Maximize z = 70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
- [45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 ) + 4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
+ a1 + a2 + a3]
z max= 21 x11 + 11 x12 + x13 + 31x21 + 21x22 + 11 x23 + 41 x31 + 31 x32 + 21 x33 - a1 - a2 - a3
Subject to
(1) Demand constraints
Dye 1 2 and 3 produced daily should equal its daily demand
x11 + x21 + x31 - 10 a1 = 3000 (Dye 1 Demand Constraint)
x12 + x22 + x32 - 10 a2 = 2000 (Dye 2 Demand Constraint)
x13 + x23 + x33 - 10 a3 = 1000 (Dye 3 Demand Constraint)
(2) Usage constraints
At most 5000 litres of each chemical type can be purchased daily
x11 + x12 + x13 le 5000 (Chemical 1 Usage Constraint)
x21 + x22 + x23 le 5000 (Chemical 2 Usage Constraint)x31 + x32 + x33 le 5000 (Chemical 3 Usage Constraint)
(3) Production capacity constraint
Production capacity is 14000 litres of Dye per day
x11 + x21 + x31 + x12 + x22 + x32 + x13 + x23 + x33 le 14000 (ProductionCapacity Constraint)
(4) Average OCR limitation
Chemical blended to make Dye 1 must have an average OCR of at least 10
(12 x11 + 6 x21 + 8 x31) (x11 + x21 + x31) ge 10
2 x11 - 4 x21 - 2 x31 ge 0 (Dye 1 OCR Constraint)
Chemical blended to make Dye 2 must have an average OCR of at least 8
(12 x12 + 6 x22 + 8 x32) (x12 + x22 + x32) ge 8
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
8132019 Decision Making Models Project Report
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
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52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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9
Daily Revenues
Dye Sales
70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
Daily Costs
Purchasing Cost of Chemicals
45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 )
Advertising Cost
a1 + a2 + a3
Production Cost
4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
Daily Profit
Dye Sales ndash [Purchasing costs of Chemicals + Production Cost + Advertising Cost ]
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Objective Function
Maximize z = 70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
- [45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 ) + 4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
+ a1 + a2 + a3]
z max= 21 x11 + 11 x12 + x13 + 31x21 + 21x22 + 11 x23 + 41 x31 + 31 x32 + 21 x33 - a1 - a2 - a3
Subject to
(1) Demand constraints
Dye 1 2 and 3 produced daily should equal its daily demand
x11 + x21 + x31 - 10 a1 = 3000 (Dye 1 Demand Constraint)
x12 + x22 + x32 - 10 a2 = 2000 (Dye 2 Demand Constraint)
x13 + x23 + x33 - 10 a3 = 1000 (Dye 3 Demand Constraint)
(2) Usage constraints
At most 5000 litres of each chemical type can be purchased daily
x11 + x12 + x13 le 5000 (Chemical 1 Usage Constraint)
x21 + x22 + x23 le 5000 (Chemical 2 Usage Constraint)x31 + x32 + x33 le 5000 (Chemical 3 Usage Constraint)
(3) Production capacity constraint
Production capacity is 14000 litres of Dye per day
x11 + x21 + x31 + x12 + x22 + x32 + x13 + x23 + x33 le 14000 (ProductionCapacity Constraint)
(4) Average OCR limitation
Chemical blended to make Dye 1 must have an average OCR of at least 10
(12 x11 + 6 x21 + 8 x31) (x11 + x21 + x31) ge 10
2 x11 - 4 x21 - 2 x31 ge 0 (Dye 1 OCR Constraint)
Chemical blended to make Dye 2 must have an average OCR of at least 8
(12 x12 + 6 x22 + 8 x32) (x12 + x22 + x32) ge 8
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11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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FORE School of Management Decision Making Models
ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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10
Objective Function
Maximize z = 70(x11 + x21 + x31) + 60 (x12+ x22 + x32 ) + 50(x13+ x23 + x33 )
- [45(x11 + x12 + x13) + 35(x21 + x22 + x23 ) + 25(x31 + x32 + x33 ) + 4(x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33)
+ a1 + a2 + a3]
z max= 21 x11 + 11 x12 + x13 + 31x21 + 21x22 + 11 x23 + 41 x31 + 31 x32 + 21 x33 - a1 - a2 - a3
Subject to
(1) Demand constraints
Dye 1 2 and 3 produced daily should equal its daily demand
x11 + x21 + x31 - 10 a1 = 3000 (Dye 1 Demand Constraint)
x12 + x22 + x32 - 10 a2 = 2000 (Dye 2 Demand Constraint)
x13 + x23 + x33 - 10 a3 = 1000 (Dye 3 Demand Constraint)
(2) Usage constraints
At most 5000 litres of each chemical type can be purchased daily
x11 + x12 + x13 le 5000 (Chemical 1 Usage Constraint)
x21 + x22 + x23 le 5000 (Chemical 2 Usage Constraint)x31 + x32 + x33 le 5000 (Chemical 3 Usage Constraint)
(3) Production capacity constraint
Production capacity is 14000 litres of Dye per day
x11 + x21 + x31 + x12 + x22 + x32 + x13 + x23 + x33 le 14000 (ProductionCapacity Constraint)
(4) Average OCR limitation
Chemical blended to make Dye 1 must have an average OCR of at least 10
(12 x11 + 6 x21 + 8 x31) (x11 + x21 + x31) ge 10
2 x11 - 4 x21 - 2 x31 ge 0 (Dye 1 OCR Constraint)
Chemical blended to make Dye 2 must have an average OCR of at least 8
(12 x12 + 6 x22 + 8 x32) (x12 + x22 + x32) ge 8
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FORE School of Management Decision Making Models
11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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FORE School of Management Decision Making Models
i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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FORE School of Management Decision Making Models
ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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FORE School of Management Decision Making Models
11
4 x12 - 2 x22 ge 0 (Dye 2 OCR Constraint)
Chemical blended to make Dye 3 must have an average OCR of at least 6
( 12 x13 + 6 x23 + 8 x33 ) ( x13 + x23 + x33 ) ge 6
6x13 + 2 x33ge 0 (Dye 3 OCR Constraint)
But we also know that x13 and x33 are always ge 0 So we need not consider this
constraints These are called as ldquoRedundant Constraintsrdquo as each type of Chemical
will have OCR as minimum 6
(5) Percentage of sulphur
Chemical blended to make Dye 1 must contain at most 1 sulphur(0005 x11 + 002 x21 + 003 x31) (x11 + x21 + x31) le 001
-0005 x11 + 001 x21 + 002 x31 le 0 (Dye1 Sulphur Constraint)
Chemical blended to make Dye 2 must contain at most 2 sulphur
(0005 x12 + 002 x22 + 003 x32) (x12 + x22 + x32) le 002
-0015 x12 + 001 x32 le 0 (Dye2 Sulphur Constraint)
Chemical blended to make Dye 3 must contain at most 1 sulphur
(0005 x13 + 002 x23 + 003 x33) (x13 + x23 + x33) le 001
-0005 x13 + 001 x23 + 002 x33le 0 (Dye 3 Sulphur Constraint)
(6) Non-negativity constraint
xij ge 0 i =123 and j =123
ai ge 0 i =123
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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FORE School of Management Decision Making Models
i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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FORE School of Management Decision Making Models
ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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FORE School of Management Decision Making Models
iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
8132019 Decision Making Models Project Report
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FORE School of Management
By using the data solver in MS E
Therefore
To produce Dye 1 daily ndash2000 litres of Chemical 1 1000 li
To produce Dye 2 daily ndash233333 litres of Chemical 1 36be used
To produce Dye 3 daily ndash66666 litres of Chemical 1 333used
And
The amount to be spent daily on
The amount to be spent daily onThe amount to be pent daily on a
Decisi
5 Conclusion
51 Final Result
cel 2007 an optimal solution was reached
res of Chemical 2 and 0 litres of Chemical 3
666 litres of Chemical 2 and 3500 litres of
33 litres of Chemical 2 and 0 litres of Ch
advertising Dye 1 is ndash Rs 0
advertising Dye 2 is ndash Rs 750dvertising Dye 3 is ndash Rs 0
on Making Models
12
s stated below
should be used
Chemical 3 should
mical 3 should be
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
13
52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
8132019 Decision Making Models Project Report
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i
7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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52 Limitations
bull OCR (Organic Content Rating) and Sulphur Rating are assumed to the nearest
approximation as per data available However they are subject to change in reality
bull The cost of conversion of chemicals into dye is the nearest approximation as the exact
number could not be obtained
bull Other external factors have not been considered
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6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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14
6 References
bull Problem based on a real life case provided by Mr Kunal Mehta owner of SrikantIndustries Pvt Ltd
bull Frederick S Hillier amp Gerald J Lieberman Introduction to Operations Research
bull AndersonSweeneyWilliamsMartin An Introduction to Management Science
Quantitative Approaches to Decision Making
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7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
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7 Appendix
PAGE
A983152983152983141983150983140983145983160 A 991251 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270 983145983145
A983152983152983141983150983140983145983160 B 991251 A983150983155983159983141983154 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270 983145983145983145A983152983152983141983150983140983145983160 983107 991251 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270991270983145983158
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Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
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Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
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Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
ii
Appendix A - 983123983151983148983157983156983145983151983150 983124983137983138983148983141 983125983155983145983150983143 983109983160983139983141983148 983123983151983148983158983141983154
98316011 98316012 98316013 98316021 98316022 98316023 98316031 98316032 98316033 9831371 9831372 9831373 983116983112983123 983122983112983123
983120983154983151983142983145983156 21 11 1 31 21 11 41 31 21 9830851 9830851 9830851
287750
983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 1 0 0 1 0 0 1 0 0 98308510 0 0 3000 = 3000
983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 1 0 0 1 0 0 1 0 0 98308510 0 2000 = 2000
983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 0 0 1 0 0 1 0 0 1 0 0 98308510 1000 = 1000
983107983144983141983149983145 983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 1 1 1 0 0 0 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 1 1 1 0 0 0 0 0 0 5000 lt= 5000
983107983144983141983149983145 983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 0 0 0 0 0 0 1 1 1 0 0 0 3500 lt= 5000
983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 1 1 1 1 1 1 1 1 1 0 0 0 13500 lt= 14000
983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 2 0 0 9830854 0 0 9830852 0 0 0 0 0 0 gt= 0
983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 4 0 0 9830852 0 0 0 0 0 0 0 2000 gt= 0
983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 0 0 6 0 0 0 0 0 2 0 0 0 4000 gt= 0
9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 9830850005 0 0 001 0 0 002 0 0 0 0 0 0 lt= 0
9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 9830850015 0 0 0 0 0 001 0 0 0 0 0 lt= 0
983108983161983141 3 983123983157983148 983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 0 0 9830850005 0 0 001 0 0 002 0 0 0 0 lt= 0
983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 2000 2333333333 6666666667 1000 3666666667 3333333333 0 3500 0 0 750 0
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
8132019 Decision Making Models Project Report
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FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
8132019 Decision Making Models Project Report
httpslidepdfcomreaderfulldecision-making-models-project-report 1718
FORE School of Management Decision Making Models
iii
Appendix B ndash 983105983150983155983159983141983154 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983105983150983155983159983141983154 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
983124983137983154983143983141983156 983107983141983148983148 (983117983137983160)
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$983118$4 983120983154983151983142983145983156 983116983112983123 287750 287750
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983107983141983148983148 983118983137983149983141 983119983154983145983143983145983150983137983148 983126983137983148983157983141 983110983145983150983137983148 983126983137983148983157983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 2000$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 2333333333
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 6666666667
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 1000
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 3666666667
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 3333333333
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0
$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 3500
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 0
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 750
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 0
983107983151983150983155983156983154983137983145983150983156983155
983107983141983148983148 983118983137983149983141 983107983141983148983148 983126983137983148983157983141 983110983151983154983149983157983148983137 983123983156983137983156983157983155 983123983148983137983139983147
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 $983118$5=$983120$5 983118983151983156 B983145983150983140983145983150983143 0
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$6=$983120$6 983118983151983156 B983145983150983140983145983150983143 0
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 $983118$7=$983120$7 983118983151983156 B983145983150983140983145983150983143 0
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$8lt=$983120$8 B983145983150983140983145983150983143 0
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 $983118$9lt=$983120$9 B983145983150983140983145983150983143 0
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 $983118$10lt=$983120$10 983118983151983156 B983145983150983140983145983150983143 1500$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 $983118$11lt=$983120$11 983118983151983156 B983145983150983140983145983150983143 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$12gt=$983120$12 B983145983150983140983145983150983143 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 $983118$13gt=$983120$13 983118983151983156 B983145983150983140983145983150983143 2000
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 $983118$14gt=$983120$14 983118983151983156 B983145983150983140983145983150983143 4000
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$15lt=$983120$15 B983145983150983140983145983150983143 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$16lt=$983120$16 B983145983150983140983145983150983143 0
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 $983118$17lt=$983120$17 B983145983150983140983145983150983143 0
8132019 Decision Making Models Project Report
httpslidepdfcomreaderfulldecision-making-models-project-report 1818
FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
8132019 Decision Making Models Project Report
httpslidepdfcomreaderfulldecision-making-models-project-report 1818
FORE School of Management Decision Making Models
iv
Appendix C ndash 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983117983145983139983154983151983155983151983142983156 983109983160983139983141983148 120 983123983141983150983155983145983156983145983158983145983156983161 983122983141983152983151983154983156
983127983151983154983147983155983144983141983141983156 983131983108983117983117983135983120983154983151983146983141983139983156983160983148983155983160983133983123983151983148983157983156983145983151983150
983122983141983152983151983154983156 983107983154983141983137983156983141983140 992013 50741 983120983117
A983140983146983157983155983156983137983138983148983141 983107983141983148983148983155
983110983145983150983137983148 983122983141983140983157983139983141983140 983119983138983146983141983139983156983145983158983141 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983107983151983155983156 983107983151983141983142983142983145983139983145983141983150983156 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$B$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316011 2000 0 21 0 1983109+30
$983107$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316012 2333333333 0 11 1983109+30 0
$983108$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316013 6666666667 0 1000000001 0 1983109+30
$983109$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316021 1000 0 31 627 0
$983110$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316022 3666666667 0 21 0 209
$983111$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316023 3333333333 0 11 1227 0
$983112$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316031 0 0 4100000369 0 4635000411$983113$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316032 3500 0 31 1983109+30 0
$983114$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 98316033 0 0 2099999983 0 1983109+30
$983115$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831371 0 983085209 9830850999999989 209 1983109+30
$983116$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831372 750 0 9830851 0 1045
$983117$19 983123983151983148983157983156983145983151983150 983126983137983148983157983141983155 9831373 0 983085409 9830850999999989 409 1983109+30
983107983151983150983155983156983154983137983145983150983156983155
983110983145983150983137983148 983123983144983137983140983151983159 983107983151983150983155983156983154983137983145983150983156 983105983148 983148983151983159983137983138983148983141 983105983148 983148983151983159983137983138983148983141
983107983141983148983148 983118983137983149983141 983126983137983148983157983141 983120983154983145983139983141 983122983112 983123983145983140983141 983113983150983139983154983141983137983155983141 983108983141983139983154983141983137983155983141
$983118$5 983108983161983141 1 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3000 983085208 3000 1000 500
$983118$6 983108983161983141 2 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 01 2000 7500 1983109+30
$983118$7 983108983161983141 3 983108983141983149983137983150983140 983107983151983150983155983156983154983137983145983150983156 983116983112983123 1000 983085408 1000 1000 500
$983118$8 983107983144983141983149983145983139983137983148 1 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 5725 5000 200 500
$983118$9 983107983144983141983149983145983139983137983148 2 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 5000 209 5000 500 3666666667
$983118$10 983107983144983141983149983145983139983137983148 3 983125983155983137983143983141 983107983151983150983155983156983154983137983145983150983156 983116983112983123 3500 0 5000 1983109+30 1500
$983118$11 983120983154983151983140983157983139983156983145983151983150 983107983137983152983137983139983145983156983161 983107983151983150983155983156983154983137983145983150983156 983116983112983123 13500 0 14000 1983109+30 500
$983118$12 983108983161983141 1 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 0 0 2000000013 0
$983118$13 983108983161983141 2 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 2000 0 0 2000 1983109+30
$983118$14 983108983161983141 3 983119983107983122 983107983151983150983155983156983154983137983145983150983156 983116983112983123 4000 0 0 4000 1983109+30
$983118$15 9831089831619831411 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090000274 0 5000000017 0
$983118$16 9831089831619831412 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 35
$983118$17 983108983161983141 3 983123983157983148983152983144983157983154 983107983151983150983155983156983154983137983145983150983156 983116983112983123 0 3090 0 5 5
