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Case Problem: Stateline Shipping And Transport Company

1087 words - 5 pages

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

...view middle of the document...

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 to recalculate the transportation cost considering all possibilities.

For this, we are given transportation costs from various plants to plants and sites to sites in attached MS Excel Spreadsheet.

Solve the model you developed in #3 (above) and clearly describe the results.

Plants were labeled 1 through 6, waste facilities labeled A through C.

Problem was set up in 2 Stages: Stage 1 = shipment from plants to intermediate/final location; Stage 2 = shipment from intermediate to final location.

Objective function:
Minimize Z = Total Stage 1 Cost + Total Stage 2 Cost =
[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) +
12(6) + 13(4) + 14(9) + 15(7) + 16(8) + 21(6) + 23(11) + 24(10) + 25(12) + 26(7) +
31(5) + 32(11) + 34(3) + 35(7) + 36(15) + 41(9) + 42(10) + 43(3) + 45(3) + 46(16) +
51(7) + 52(12) + 53(7) + 54(3) + 56(14) + 61(8) + 62(7) + 63(15) + 64(16) +
65(14)] + [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) + AB(12) + AC(10) + BA(12) + BC(15) + CA(10) + CB(15)] ;

Subject to:
Stage 1
12 + 13 + 14 + 15 + 16 + 1A + 1B + 1C = 35
21 + 23 + 24 + 25 + 26 + 2A + 2B + 2C = 26
31 + 32 + 34 + 35 + 36 + 3A + 3B + 3C = 42
41 + 42 + 43 + 45 + 46 + 4A + 4B + 4C = 53
51 + 52 + 53 + 54 + 55 + 56 + 5A + 5B + 5C = 29
61 + 62 + 63 + 64 + 65 + 6A + 6B + 6C = 38

Stage 2
1A + 2A + 3A + 4A + 5A + 6A + AA + BA + CA ≤ 65
1B + 2B + 3B + 4B + 5B + 6B + AB + BB + CB ≤ 80
1C + 2C + 3C + 4C + 5C + 6C + AC + BC + CC ≤ 105

All Combinations ≥ 0
Solver add-on solution in MS Excel yielded the following results:
19 bbl of wastes shipped from Kingsport to Macon to Duras,
16 bbl of wastes shipped from Kingsport to Los Canos,
26 bbl of wastes shipped from Danville to Los Canos,
42 bbl of wastes shipped from Macon to Duras,
17 bbl of wastes shipped from Selma to Macon to Duras,
36 bbl of...

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