Model 2: Transportation Problem

Roshnika Fernando

Model 2 Summary

Dealerships

1 2 3 4 5 6 7 8 9 10 11 12 supply

Manufacturers

1 25 36 31 20 27 33 27 21 24 35 21 24 100

2 37 23 28 35 19 31 23 25 28 27 19 31 90

3 26 19 17 28 27 36 31 24 21 27 17 30 120

4 42 25 15 33 23 28 29 33 26 29 20 27 80

5 19 31 45 37 31 34 27 31 32 30 22 25 90

demand 35 42 28 52 17 33 62 61 43 37 28 42

Goal

Minimize cost of shipping cars from car manufacturer to dealership 5 12

z = Σ Σ cij xij i = 1,2,…,5 ; j = 1, 2,…, 12 i=1 j=1 x ≥ 0, integer

Subject to supply and demand constraints 12 5

Σ xij = si and Σ xij = dj

j=1 i=1

Linear Equation

5 12

min: z = Σ Σ cij xij i = 1,2,…,5 ; j = 1, 2,…, 12 i=1 j=1 x ≥ 0, integers.t. : 12 5

Σ xij = si and Σ xij = dj

j=1 i=1

Supply equals demand for Model 2 5 12

Σ si = 480 = Σ dj

i=1 j=1

MatLab Solution: $10,427

Dealers  

Manufacturers

 1 2 3 4 5 6 7 8 9 10 11 12 Supply

125   36   31   20   27   33   27   21   24   35   21   24

100      52       48        

237   23 28   35 19   31 23 25 28   27 19 31  

90        17   62 4   7    

326   19   17  28   27   36   31   24   21   27   17 30  

120  42           9 43   26  

442   25 15   33 23   28 29   33 26   29 20 27  

80    28     33       17 2  

519   31   45   37   31   34   27   31   32   30   22   25  

9035                 13   42

Demand 35 42 28 52 17 33 62 61 43 37 28 42 480

Management Scientist Program Solution: $10,427

Dealers  

Manufacturers

 1 2 3 4 5 6 7 8 9 10 11 12 Supply

125   36   31   20   27   33   27   21   24   35   21   24

100      52       48        

237   23 28   35 19   31 23 25 28   27 19 31  

90        17   62 6   5    

326   19   17  28   27   36   31   24   21   27   17 30  

120  42           7 43   28  

442   25 15   33 23   28 29   33 26   29 20 27  

80    28     33       19  

519   31   45   37   31   34   27   31   32   30   22   25  

9035                 13   42

Demand 35 42 28 52 17 33 62 61 43 37 28 42 480

Analysis of Solutions

Minimum cost of shipping is $10,427

Multiple solutions exist

Sensitivity Analysis

Demand > Supply? No optimal solution – need more information (i.e. level of priority for each dealer) or more

constraints.

Demand < Supply? Optimal solution exists

Questions?

Citation

Kolman, Bernard, and Robert E. Beck. Elementary Linear Programming with Applications. 2nd ed. New York: Academic Press, 1995. Print.