Embed Size (px)
Citation preview
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 1/20
Solution of Ques 2
SUPPLY SOUTH MIDWEST EAST WEST FIXED CO CAPACITY FIXED CO CAPACITY
NEWYORK 232 240 211 300 6000000 200000 10000000 400000
ATLANTA 212 230 232 280 5500000 200000 9200000 400000
CHICAGO 230 215 238 270 5600000 200000 9300000 400000
SAN DIEGO 280 270 299 225 6100000 200000 10200000 400000
DEMAND 180000 120000 110000 100000
DECISION VARIABLES PLANT PLANTSUPPLY SOUTH MIDWEST EAST WEST (1=OPEN0 (1=OPEN)
NEWYORK 0 85000 110000 5000 1 0
ATLANTA 180000 20000 0 0 1 0
CHICAGO 0 0 0 0 0 0
SAN DIEGO 0 15000 0 95000 1 0
CONSTRAINTS
SUPPLY EXCESS Supply
NEWYORK 0
ATLANTA 0
CHICAGO 0
SAN DIEGO 90000
DEMAND
SOUTH MIDWEST EAST WEST
UNMET DEMAND -2.54E-07 2.62E-10 -7.45E-07 2.53E-07
OBJECTIVE FUNCTION
COST 130895028
DRY ICE
DEMAND
DEMAND
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 2/20
ALL THE THINGS ARE IN DOLLARS
DEMAND
SUPPLY N.A S.A EUROPE JAPAN ASIA CAPACITY PRODUCTION
U.S 600 1200 1300 2000 1700 185 10000
GERMANY 1300 1400 600 1400 1300 475 7530
JAPAN 2000 2100 1400 300 900 50 16740BRAZIL 1200 800 1400 2100 2100 200 7306
INDIA 2200 2300 1300 1000 800 80 9200
DEMAND 270 190 200 120 100
DECISION VARIABLE DEMAND PLANT
SUPPLY N.A S.A EUROPE JAPAN ASIA (1=OPEN)
U.S 185 0 0 0 5.72E-09 1
GERMANY 75 0 200 70 20 1
JAPAN 0 0 0 50 0 1
BRAZIL 10 190 0 0 5.72E-09 1
INDIA 0 0 0 0 80 1
CONSTRAINTS
SUPPLY EXCESS CAPACITY
U.S -9.5E-08
GERMANY 110
JAPAN -9.5E-08
BRAZIL 0
INDIA -9.3E-08
DEMAND
N.A S.A EUROPE JAPAN ASIA
UNMET
DEMAND 6.68E-07 6.68E-07 0 0 0
OBJECTIVE FUNCTION
COST 746276
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 3/20
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 4/20
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 5/20
STURDYFON DEMAND ALLOCATION
ALL COST ARE INCLUDED IN THE PRODUCTION MA
production cost matrix
demand
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 12.875 15.24 12.48 14.03 13.312
N AMERICA 11.845 14.4 12.48 14.145 12.688REST OF ASIA 12.36 14.64 12.168 13.34 11.648
DEMAND 12 1 4 8 7
DECISION VARIABLES demand
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 0 0 1 8 0
N AMERICA 12 1 3 0 0
REST OF ASIA 0 0 0 0 7
EXCESS
CONSTRAINTS CAPACITY
SUPPLY
EUROPE 9.616671855
N AMERICA 4.383328139
S AMERICA 0
demand
N,A S,A EUROPE NON EUROPE JAPAN
UNMET DEMAND -5.96046E-09 0 0 0 0
OBJECTIVE EQUATION
COST 455.9960001
SLEEKFON DEMAND ALLOCATION
ALL COST ARE INCLUDED IN THE PRODUCTION MA
production cost matrix
demand
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 12.875 15.24 12.48 14.03 13.312
N AMERICA 11.84 14.4 12.48 14.145 12.688
S AMERICA 13.184 14.76 13.52 15.295 13.728DEMAND 10 4 20 3 2
DECISION VARIABLES demand
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 0 0 16 3 0
N AMERICA 10 2 4 0 2
S AMERICA 0 2 0 0 0
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 6/20
EXCESS
CONSTRAINTS CAPACITY
SUPPLY
EUROPE 0
N AMERICA 0
S AMERICA 8
demandN,A S,A EUROPE NON EUROPE JAPAN
UNMET DEMAND 0 0 0 0 0
OBJECTIVE EQUATION
COST 539.786
DEMAND
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 12.875 15.24 12.48 14.03 13.312
N AMERICA 11.84 14.4 12.48 14.145 12.688
S AMERICA 13.184 14.76 13.52 15.295 13.728
REST OF ASIA 12.36 14.64 12.168 13.34 11.648
DEMAND(SUM) 22 5 24 11 9
DECISION VARIABLES DEMAND
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 1.70299E-07 0 15 11 0
N AMERICA 21.99999949 5 9.000001 0 3.999999
S AMERICA 0 0 0 0 7.31E-07
REST OF ASIA 1.70299E-07 0 0 0 5
CONSTRAINTS EXCESS
supply CAPACITY
EUROPE 12.0000009
N AMERICA 8.17856E-10
S AMERICA 9.999999269
REST OF ASIA -3.75637E-09
DEMAND
N,A S,A EUROPE NON EUROPE JAPAN
UNMET DEMAND 1.70299E-07 0 0 0 0
OBJECTIVE FUNCTION
COST 993.4219992
D)
STURDYFON DEMAND ALLOCATION
AFTER MERGER - SLEEKFON &STURDYFON
WHEN ALL THE DUTIES ARE REDUCED TO ZERO
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 7/20
ALL COST ARE INCLUDED IN THE PRODUCTION MA
production cost matrix
demand
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 12.5 12.7 12 12.2 12.8
N AMERICA 11.5 12 12 12.3 12.2
REST OF ASIA 12 12.2 11.7 11.6 11.2DEMAND 12 1 4 8 7
DECISION VARIABLES demand
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 0 0 2 8 0
N AMERICA 12 1 2 0 0
REST OF ASIA 0 0 0 0 7
EXCESS
CONSTRAINTS CAPACITYSUPPLY
EUROPE 9.450003882
N AMERICA 4.549995829
S AMERICA -5.78824E-07
demand
N,A S,A EUROPE NON EUROPE JAPAN
UNMET DEMAND 0 0 0 0 0
OBJECTIVE EQUATION
COST 419.4000102
SLEEKFON DEMAND ALLOCATION
ALL COST ARE INCLUDED IN THE PRODUCTION MA
production cost matrix
demand
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 12.5 12.7 12 12.2 12.8
N AMERICA 11.5 12 12 12.3 12.2
S AMERICA 12.8 12.3 13 13.3 13.2
DEMAND 10 4 20 3 2
DECISION VARIABLES demand
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 10 4 2 0 2
N AMERICA 0 0 9 2 0
S AMERICA 0 0 9 1 0
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 8/20
EXCESS
CONSTRAINTS CAPACITY
SUPPLY
EUROPE -4.92919E-09
N AMERICA 8.000000005
S AMERICA 0
demandN,A S,A EUROPE NON EUROPE JAPAN
UNMET DEMAND 0 0 0 0 0
OBJECTIVE EQUATION
COST 526.4
E) NO DUTIES ARE CHARGED THEN MERGED NETWORK CONFIGURATION
STURDY FON &SLEEKFON DEMAND ALLOCATION
ALL COST ARE INCLUDED IN THE PRODUCTION MA
production cost matrix
demand
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 12.5 12.7 12 12.2 12.8
N AMERICA 11.5 12 12 12.3 12.2
S AMERICA 12.8 12.3 13 13.3 13.2
REST OF ASIA 12 12.2 11.7 11.6 11.2
DEMAND 22 5 24 11 9
DECISION VARIABLES demand
supply N,A S,A EUROPE NON EUROPE JAPAN
EUROPE 0 0 15 11 0
N AMERICA 22 5 9 0 4
S AMERICA 0 0 0 0 0
REST OF ASIA 0 0 0 0 5
EXCESS
CONSTRAINTS CAPACITY
SUPPLY
EUROPE 12
N AMERICA 1.77872E-09
S AMERICA 10
REST OF ASIA -3.40918E-09 demand
N,A S,A EUROPE NON EUROPE JAPAN
UNMET DEMAND 0 0 0 0 0
OBJECTIVE EQUATION
COST 919.8
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 9/20
TRIX
CAPACITY
REST OF ASIA AFRICA
15.5 15.5 20
15.25 15.875 2013.42 14.75 10
3 1
PLANT
REST OF ASIA AFRICA (1=OPEN)
0 1 1
0 0 1
3 0 1
REST OF ASIA AFRICA
0 0
TRIX
CAPACITY
REST OF ASIA AFRICA
15.5 15.5 20
15.25 15.875 20
16.47 16.875 102 1
PLANT
REST OF ASIA AFRICA (1=OPEN)
0 1 1
2 0 1
0 0 1
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 10/20
REST OF ASIA AFRICA
0 0
REST OF ASIA AFRICA CAPACITY
15.5 15.5 40
15.25 15.875 40
16.47 16.875 10
13.42 14.75 10
5 2
REST OF ASIA AFRICA CAPACITY
0 2 1
0 0 1
0 0 1
5 0 1
REST OF ASIA AFRICA
0 0
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 11/20
TRIX
CAPACITY
REST OF ASIA AFRICA
12.7 12.4 20
12.5 12.7 20
11 11.8 103 1
PLANT
REST OF ASIA AFRICA (1=OPEN)
0 1 1
0 0 1
3 0 1
REST OF ASIA AFRICA
0 -8.7E-07
TRIX
CAPACITY
REST OF ASIA AFRICA
12.7 12.4 20
12.5 12.7 20
13.5 13.5 10
2 1
PLANT
REST OF ASIA AFRICA (1=OPEN)
2 0 1
0 1 1
0 0 1
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 12/20
REST OF ASIA AFRICA
0 0
TRIX
REST OF ASIA AFRICA CAPACITY
12.7 12.4 40
12.5 12.7 40
13.5 13.5 10
11 11.8 10
5 2
PLANT
REST OF ASIA AFRICA (1=OPEN)
0 2 1
0 0 1
0 0 1
5 0 1
REST OF ASIA AFRICA
0 0
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 13/20
DEMAND
supply N,A S,A EUROPE NON EUROPE JAPAN REST OF ASIA
EUROPE 12.875 15.24 12.48 14.03 13.312 15.5
N AMERICA 11.84 14.4 12.48 14.145 12.688 15.25
S AMERICA 13.184 14.76 13.52 15.295 13.728 16.47REST OF ASIA 12.36 14.64 12.168 13.34 11.648 13.42
DEMAND(SUM) 22 6 24 13.2 9 15
DECISION VARIABLES DEMAND
supply N,A S,A EUROPE NON EUROPE JAPAN REST OF ASIA
EUROPE 0 0 24 13.2 0 0.400000191
N AMERICA 22 4.400001 0 0 9 4.599999237
S AMERICA 0 1.599999 0 0 0 0
REST OF ASIA 0 0 0 0 0 10.00000057
CONSTRAINTS EXCESS
supply CAPACITY
EUROPE -2E-07
N AMERICA 1.44E-08
S AMERICA 8.400001
REST OF ASIA -5.7E-07
DEMAND
N,A S,A EUROPE NON EUROPE JAPAN REST OF ASIA
UNMET DEMAND 3.5E-10 0 -8.9E-09 0 -3.9E-08 0
OBJECTIVE FUNCTION
COST 1194.114
supply N,A S,A EUROPE NON EUROPE JAPAN REST OF ASIA
EUROPE 12.5 12.7 12 12.2 12.8 12.7
N AMERICA 11.5 12 12 12.3 12.2 12.5
S AMERICA 12.8 12.3 13 13.3 13.2 13.5
REST OF ASIA 12 12.2 11.7 11.6 11.2 11
DEMAND(SUM) 22 6 24 13.2 9 15
DECISION VARIABLES DEMAND
supply N,A S,A EUROPE NON EUROPE JAPAN REST OF ASIA
EUROPE 0 2.38E-08 24 13.2 0 0.4
AFTER MERGER - SLEEKFON &STURDYFON
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 14/20
N AMERICA 22 4.4 0 0 9 4.600000023
S AMERICA 0 1.6 0 0 0 0
REST OF ASIA 0 0 0 0 0 10
CONSTRAINTS EXCESS
supply CAPACITYEUROPE -1.9E-08
N AMERICA -2.4E-08
S AMERICA 8.4
REST OF ASIA 0
DEMAND
N,A S,A EUROPE NON EUROPE JAPAN REST OF ASIA
UNMET DEMAND 2.86E-07 0 4.37E-09 0 0 -2.31128E-08
OBJECTIVE FUNCTION
COST 1086.66
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 15/20
AFRICA CAPACITY
15.5 40
15.875 40
16.875 1014.75 10
2.4
AFRICA CAPACITY
2.4 1
0 1
0 1
0 1
AFRICA
0
AFRICA CAPACITY
12.4 40
12.7 40
13.5 10
11.8 10
2.4
AFRICA CAPACITY
2.4 1
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 16/20
0 1
0 1
0 1
AFRICA
0
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 17/20
SOLUTION 6 COMPONUND GROWTH 20%
DEMAND
NORTH WEST SOUTH EAST
1 100000 150000 150000 50000 TOTAL
2 120000 180000 180000 60000 540000
3 144000 216000 216000 72000 648000
4 172800 259200 259200 86400 7776005 207360 311040 311040 103680 933120
248832 373248 373248 124416 1119744
FOR FIRST YEAR
DEMAND
SUPPLY NORTH EAST WEST SOUTH FIXED COST CAPACITY
CHENNAI 20 19 17 15 4000000000 300000
MUMBAI 17 20 15 17 4000000000 300000
DEMAND 120000 180000 180000 60000
DECISION VARIABLES DEMAND PLANT
SUPPLY NORTH EAST WEST SOUTH (1=OPEN)
CHENNAI 0 180000 0 60000 1
MUMBAI 120000 0 180000 0 1
CONSTRAINTS
SUPPLY EXCESS CAPACITYCHENNAI 60000
MUMBAI 0
DEMAND
UNMET NORTH EAST WEST SOUTH
DEMAND 0 0 0 0
OBJECTIVE FUNCTION
COST 8009060000
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 18/20
Northeast Southeast Midwest South West Annual F.C.
Kentuchy 185 180 175 175 200 150
Pennsyivania 170 190 180 200 220 200
Demand 700000 400000 400000 300000 600000
Decision variables
Supply Region
Northeast Southeast Midwest South West Plants
Kentuchy 394999.9 120000.4 120000.4 70000.4 294999.9 1.000001
Pennsyivania 305000.1 279999.6 279999.6 229999.6 305000.1 0.93333267
Constraints
Supply region Excess capacity
Kentuchy 0
Pennsyivania 0
Northeast Southeast Midwest South West
0 0 0 0 0
Objective Function
Cost 455475321
Northeast Southeast Midwest South West Annual F.C.
Kentuchy 185 180 175 175 200 150
Pennsyivania 170 190 180 200 220 200
N. Carolina 180 180 185 185 215 150
California 220 220 195 195 175 150
Demand 1050000 600000 600000 450000 900000
Decision variables
Supply Region
Northeast Southeast Midwest South West Plants
Kentuchy 271590.871 180303.07 171212.1 145833.4 231060.6 1
Pennsyivania 271590.951 143939.38 146969.7 97348.44 212878.8 0.58181815
N. Carolina 265530.344 150000.03 143939.4 106439.4 215909.1 0.58787885
Demand Region
Unmet demand
Demand Region
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 19/20
California 241287.834 125757.52 137878.8 100378.8 240151.6 0.56363634
Constraints
Supply region Excess capacity
Kentuchy 0Pennsyivania 0
N. Carolina 0
California 0
Northeast Southeast Midwest South West
0 0 0 0 0
Objective Function
Cost 687443612
Unmet demand
8/4/2019 Solutions of Chapter-5
http://slidepdf.com/reader/full/solutions-of-chapter-5 20/20
Supply
1000000
1500000
Supply
1000000
1500000
1500000
1500000
![Chapter 5: Problem Solutions - Naval Postgraduate Schoolfaculty.nps.edu/.../homework/solutions/Solutions_Chapter5[1].pdf · Chapter 5: Problem Solutions Digital Filter Implementation](https://img.dokumen.tips/doc/110x75/5ab6b7c17f8b9a1a048e1795/chapter-5-problem-solutions-naval-postgraduate-1pdfchapter-5-problem-solutions.jpg)
