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# Mat540 Assignment 4

706 words - 3 pages

Plants were labeled 1 through 6, 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);
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

35 bbl shipped from Kinsport to Whitewater
26 bbl shipped from Danville to Duras
42 bbl shipped from Macon to Duras
1 bbl shipped from Selma to Whitewater
52 bbl shipped from Selma to Los Canos
29 bbl shipped from Columbus to Whitewater
28 bbl shipped from Allentown to Los Canos
10 bbl shipped from Allentown to Duras
Assignment #4 – Helen Davenport – Math 540
Total Cost = \$2,822

Solver add-on solution in MS Excel yielded the following results:
19 bbl shipped from Kingsport to Macon to Duras
16 bbl shipped from Kingsport to Los Canos
26 bbl shipped from Danville to Los Canos
42 bbl shipped from Macon to Duras
17 bbl shipped from Selma to Macon to Duras
36 bbl shipped from Selma to Columbus to Whitewater
29 bbl shipped from Columbus to Whitewater
38 bbl shipped from Allentown to Danville to Los Canos
Total Cost = \$2,630

Rachel can save a few hundred dollars each week by using a few routes that involve intermediate points. However, this cost analysis fails to consider the actual physical risks of dealing with potentially hazardous industrial waste. The dropping off and picking up of waste at intermediate sites may cause a time delay, which may impact the risk of the waste becoming a potential hazard. Also, the additional handling of the waste associated with loading and unloading at intermediate sites may cause increased risk of a problem. Even though Polychem has agreed to handle the wastes at no additional cost, there may be additional risk that has not been evaluated. In summary, a cost savings would be one factor to consider in a more complete analysis of all the risk factors involved in evaluating the use of intermediate locations for the shipping routes.

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