Assignment #4: Case Problem “Stateline Shipping and Transport Company”

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Assignment #4: Case Problem “Stateline Shipping and Transport Company”

1) This transportation model problem consists of 18 decision variables, representing the number of barrels of wastes product transported from each of the 6 plants to each of the 3 waste disposal sites: [pic]= Number of Barrels transported per week from plant ‘i’ to the j-th waste disposal site, where i = 1, 2, 3, 4, 5, 6 and j = A, B, C.
The objective function is to minimize the total transportation cost for all shipments. So the objective function is the sum of the individual shipping costs from each plant to each waste disposal site:
Minimize Z = 12[pic]+ 15[pic]+ 17[pic]+ 14[pic]+ 9[pic]+ 10[pic]+ 13[pic]+ 20[pic] +11[pic] +17[pic] +16[pic] +19[pic]
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]+ [pic]+[pic]) – ([pic]+ [pic]+ [pic]+ [pic]+ [pic]) [pic]+ [pic]+ [pic] = 26 + ([pic]+ [pic]+ [pic]+ [pic]+[pic]) – ([pic]+[pic]+[pic] +[pic]+ [pic]) [pic]+ [pic] +[pic] = 42 + ([pic]+ [pic]+ [pic]+ [pic]+[pic]) – ([pic]+[pic]+[pic]+[pic]+[pic]) [pic] + [pic] +[pic] = 53 + ([pic]+ [pic]+ [pic]+ [pic]+[pic]) – ([pic]+[pic]+[pic] + [pic]+[pic]) [pic] +[pic] +[pic] = 29 + ([pic]+ [pic]+ [pic]+ [pic]+[pic]) – ([pic]+[pic]+[pic]+[pic]+[pic]) [pic] + [pic] +[pic] = 38 + ([pic]+ [pic]+ [pic]+ [pic]+[pic]) – ([pic]+[pic]+[pic] + [pic]+[pic])
The number of barrels that can accommodate in the i-th waste disposal site is given by (Number of barrels transported from the six plants to the i-th waste disposal site)
+ (Number of barrels shipped from other waste disposal sites to i-th waste disposal site)
– (Number of barrels shipped to other waste disposal sites from i-th waste disposal site)

Thus the three demand constraints now become: ([pic]+ [pic]+ [pic]+[pic]+ [pic]+[pic]) + ([pic]+[pic]) – ([pic]+[pic]) ≤ 65 ([pic]+ [pic]+ [pic]+ [pic]+[pic] +[pic]) + ([pic]+[pic]) – ([pic]+[pic]) ≤ 80 ([pic]+ [pic]+[pic]+ [pic]+[pic] +[pic]) + ([pic]+[pic]) – ([pic]+[pic]) ≤ 105
Thus the linear programming model for the transshipment problem is summarized as follows:
Minimize Z = 12[pic]+ 15[pic]+ 17[pic]+ 14[pic]+ 9[pic]+ 10[pic]+ 13[pic]+ 20[pic] +11[pic] + 17[pic] +16[pic] +19[pic] +7[pic] +14[pic] +12[pic] +22[pic] +16[pic] +18[pic] + 6[pic]+ 4[pic]+ 9[pic]+

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