Decision Making models project

SUBMITTED TO:

Dr. HITESH ARORA

SUBMITTED BY:

VARUN KABARIA

221061

FMG 22 B

DECISION MAKING MODELS PROJECT

Preferred Plant Site Based on Raw material Procurement Cost


ABSTRACT

ABC LIMITED is a HDPP (High Density Polypropylene) woven sack manufacturing company which caters to the need of cement, sugar and fertilizer producing companies. Due to its increasing market share, the company intends to open up a new manufacturing plant. The company is contemplating over two site options available.

The major raw material that the company utilises is HDPP i.e. High Density Polypropylene which it acquires from various refineries. These are granule shaped substances extracted from petroleum.

Thus depending upon the procurement cost of this raw material for all the operating plants, including the new plant turn by turn, a consensus can be reached upon as to which site would be more profitable.

FORE SCHOOL OF MANAGEMENTPage 2


TABLE OF CONTENTS

Abstract ................................................................. 2

Acknowledgement ................................................................. 3

Problem at hand ................................................................. 5

Solution to the problem ................................................................. 7

Excel solver ................................................................. 16

Recommendation ................................................................. 20

Bibliography ................................................................. 21



PROBLEM AT HAND

The company mentioned has 3 manufacturing sites in Ahmedabad, Mumbai & Jhansi. It purchases the raw material from 3 petrochemical industries located in Jamnagar, Mathura & Manali.

SUPPLY LOCATION DESTINATION LOCATION

Jamnagar AhmedabadMathura MumbaiManali Jhansi

Looking at the increasing demand, the company intends to expand its output. Though the company has options to expand its facilities at the present location itself, it intends to be a leader in the western region of the country and hence is contemplating over the site options available other than ones operating.

PROPOSED SITE OPTIONS

Udaipur

Kota

Thus the company plans to choose the best alternative and it intends to do so by looking over the procurement cost of the raw material for all the plant sites including the new one. One should not forget that just the inclusion of a new plant may also change the supply proportions to other plants in a way to arise at the minimum procurement cost. Thus the total procurement cost will be taken into consideration rather than just for the new plant.



The following table enlists the demand of the raw material by various sites:

PLANT DEMAND (tonnes / month)

Ahmedabad 600Mumbai 500

Jhansi 550Latest plant 750

Total Demand 2400

The following table enlists the supply strength from each source:

SOURCE SUPPLY CAPACITY (tonnes / month)

Jamnagar 1000Mathura 800Manali 600

Total Supply 2400

The cost of procuring HDPP raw material for each plant, including the new ones, is enlisted in the following table:

Cost per unit procurement (Rupees in Lakhs per tonne)

Ahmedabad Mumbai Jhansi Udaipur KotaJamnagar 2 4 5 1 3Mathura 5 5 3 3 1Manali 5 7 3 5 4



SOLUTION TO THE PROBLEM

We will start by taking the proposed plant sites one by one.

POSSIBILITY 1:

Ahmedabad Mumbai Jhansi Udaipur SupplyJamnagar 2 4 5 1 1000Mathura 5 5 3 3 800Manali 5 7 3 5 600

Demand 600 500 550 750 2400

Solving the above mentioned balanced transportation problem by Vogel’s Approximation Method (VOM), we get the IBFS (Initial Basic Feasible Solution) as follows:

IBFS

600 - - 400

- 450 - 350

- 50 550 -

Here as m+n-1 = 6 = No. of occupied cells, the solution is NON-DEGENERATE



Now using Modified Distribution Method (MODI) to check the optimality of this IBFS, we follow the method shown below:

COST OF OCCUPIED CELLS

Ui2 - - 1 1- 5 - 3 3- 7 3 - 5

Vj 1 2 -2 0

COST OF UNOCCUPIED CELLS

Ui- 4 5 - 15 - 3 - 35 - - 5 5

Vj 1 2 -2 0

NET EVALUATION TABLE

- 1 6 -1 - 2 --1 - - 0

Here, the appearance of ‘-1’ is indicative of the fact the IBFS obtained is not optimal.

Thus to further optimize the solution, we insert a THETA value in the solution table corresponding to the negative value in the net evaluation table and follow the following method:



600 -ᶿ

- -

400+ᶿ

-450+ᶿ

- 350-ᶿ

ᶿ50-ᶿ 550 -

Here we take ᶿ = 50, minimum of all the values in the loop, so that the basic variables does not take negative values.

Thus the next Basic Feasible Solution is:

BFS

550 - - 450

- 500 - 300

50 - 550 -

Again applying the MODI method for optimality:


Ui2 - - 1 1



- 5 - 3 35 - 3 - 4

Vj 1 2 -1 0


Ui- 4 5 - 15 - 3 - 3- 7 - 5 4

Vj 1 2 -1 0


- 1 5 -1 - 1 -- 1 - 1

Thus as all the elements of the EVALUATION TABLE are positive, the BFS obtained is the OFS (Optimal Feasible Solution):

OFS

550 - - 450

- 500 - 300

50 - 550 -



Thus,

OBJECTIVE FUNCTION = Min Z = (550*2) + (450*1) + (500*5) + (300*3)

+ (50*5) + (550*3)

= 1100 + 450 + 2500 + 900 + 250 + 1650

= Rs. 6850 (in Lakhs Rupees)

i.e. [68, 50, 00,000 Rupees]



POSSIBILITY 2:

Ahmedabad Mumbai Jhansi Kota SupplyJamnagar 2 4 5 3 1000Mathura 5 5 3 1 800Manali 5 7 3 4 600

Demand 600 500 550 750 2400

Solving the above mentioned balanced transportation problem by Vogel’s Approximation Method (VOM), we get the IBFS (Initial Basic Feasible Solution) as follows:

IBFS

600 400 - -

- 50 - 750

- 50 550 -

Here as m+n-1 = 6 = No. of occupied cells, the solution is NON-DEGENERATE



Now using Modified Distribution Method (MODI) to check the optimality of this IBFS, we follow the method shown below:


Ui2 4 - - 0- 5 - 1 1- 7 3 - 3

Vj 2 4 0 0


Ui- - 5 3 05 - 3 - 15 - - 4 3

Vj 2 4 0 0


- - 5 32 - 2 -0 - - 1



Thus as all the elements of the EVALUATION TABLE are positive, the BFS obtained is the OFS (Optimal Feasible Solution):

OFS

600 400 - -

- 50 - 750

- 50 550 -

Here, the appearance of ‘-1’ is indicative of the fact the IBFS obtained is not optimal.

Thus to further optimize the solution, we insert a THETA value in the solution table corresponding to the negative value in the net evaluation table and follow the following method:

Alternate Solution:

Value ‘0’ appears in the bottom left corner. This is indicative of an alternate solution We insert a THETA value in the solution table corresponding to the zero value

in the net evaluation table and follow the following method:

600-ᶿ 400+ᶿ- -

- 50 - 750

ᶿ50-ᶿ 550 -



Here we take ᶿ = 50, minimum of all the values in the loop, so that the basic variables does not take negative values.

Thus the Alternate Optimal Solution is:

Alternate Optimal Feasible Solution ( AOFS)

550 450 - -0

- 50 - 750

50 - 550 -

Thus, for OFS


+ (50*7) + (550*3)

= 1200 + 1600 + 250 + 750 + 350 + 1650


i.e. [58, 00, 00,000 Rupees]

For AOFS,


+ (50*5) + (550*3)

= 1100 + 1800 + 250 + 750 + 250 + 1650


i.e. [58, 00, 00,000 rupees]



EXCEL SOLVER

The solutions obtained above for the 2 possibilities can also be obtained by using EXCEL SOLVER.

POSSIBILITY 1



ANSWER REPORT



POSSIBILITY 2



ANSWER REPORT



RECOMMENDATIONS

Given the problem, we have evaluated both the possibilities above. Possibility 1, where in Udaipur is selected as the choice for the new

plant, gives out the cost of procurement as Rs. 68.5 Crores Possibility 2, where in Kota is selected as the choice for the new plant,

gives out the cost of procurement as Rs. 58 Crores Given such a large difference in the cost of procurement, the company would

be attracted towards Possibility 2, thus setting up a plant in Kota Moreover this possibility provides you with 2 options of meeting the demand

of the plants which gives the company as well as the supplier the flexibility to operate.



BIBLIOGRAPHY

Inputs from the manager of the company Books & Notes


Documents

Decision Making models project