# Stateline Shipping and Transport

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Date Submitted: 11/16/2012 09:04 AM

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1. Check attached MS Excel Spreadsheet for Question 1.

2. Model was solved as follows:

I. The six Plants were labeled 1 through 6, while the three waste facilities labeled A through C.

II. 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);

III. 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

IV. 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

3. Check attached MS Excel Spreadsheet for Question 3.

4. Model was solved as follows:

V. 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.

VI. 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) +...