Case Problem: Stateline Shipping and Transport Company

Assignment #4

Case Problem: Stateline Shipping and Transport Company

MAT540: Quantitative Methods

Vargha Azad

09/08/13

In Excel, or other suitable program, develop a model for shipping the waste directly from the 6 plants to the 3 waste disposal sites.

Solve the model you developed in #1 (above) and clearly describe the results. In Excel, or other suitable program. Develop a transshipment model in which each of the plants and disposal sites can be used as intermediate points.

6 Plants labeled 1 through 6, 3 waste facilities labeled A through C

Objective function:

Minimize Z = 1A(12) + 1B(15) + 1C(17) + 2A(14) + 2B(9) + 2C(10) + 3A(13) + 3B(20) + 3C(11) + 4A(17) + 4B(16) + 4C(19) + 5A(7) + 5B(14) + 5C(12) + 6A(22) + 6B(16) + 6C(18);

Subject to:

1A + 1B + 1C = 35

2A + 2B + 2C = 26

3A + 3B + 3C = 42

4A + 4B + 4C = 53

5A + 5B + 5C = 29

6A + 6B + 6C = 38

1A + 2A + 3A + 4A + 5A + 6A ≤ 65

1B + 2B + 3B + 4B + 5B + 6B ≤ 80

1C + 2C + 3C + 4C + 5C + 6C ≤ 105

All Combinations ≥ 0

Solver add-on solution in MS Excel yielded the following results:

35 bbl of wastes shipped from Kingsport to Whitewater,

26 bbl of waste shipped from Danville to Duras,

42 bbl of wastes shipped from Macon to Duras,

1 bbl of wastes shipped from Selma to Whitewater,

52 bbl of wastes shipped from Selma to Los Canos,

29 bbl of wastes shipped from Columbus to Whitewater,

28 bbl of wastes shipped from Allentown to Los Canos,

10 bbl of wastes shipped from Allentown to Duras.

Total Cost = $2,822

Rachel is considering using each of the plant and waste disposal sites as intermediate shipping points. Now, there is a possibility to reduce the transportation coat by utilizing alternative routes. For example, as per the given cost table, cost to transport from Kingsport to Duras is $17. Instead of this route, if we transport first from Kingsport to Macon and then from Macon to Duras the cost is only $15 (4 + 11). We have...