MAT Assignment

# MAT Assignment - Running head STATELINE SHIPPING AND...

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Running head: STATELINE SHIPPING AND TRANSPORT COMPANY “Stateline Shipping and Transport Company” Strayer University Quantitative Methods – MAT 540 Dr Alexander Thomas December 10, 2011 1) In Excel, or other suitable program, develop a model for shipping the waste directly from the 6 plants to the 3 waste disposal sites. The model for the transportation problem consists of 18 decision variables, representing the number of barrels of wastes transported from each of the 6 plants to each of the 3 waste disposal sites: = Number of Barrels transported per week from plant ‘ i ’ to the j - waste disposal site, where i = 1, 2, 3, 4, 5, 6 and j = A, B, C.

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The objective function of the manager is to minimize the total transportation cost for all shipments. Thus the objective function is the sum of the individual shipping costs from each plant to each waste disposal site: Minimize Z = 12+ 15+ 17+ 14+ 9+ 10+ 13+ 20 +11 +17 +16 +19 +7 +14 +12 +22 +16 +18 The constraints in the model are the number of barrels of wastes available per week at each plant and the number of barrels of wastes accommodated at each waste disposal site. There are 9 constraints- one for each plant supply and one for each waste disposal site’s demand. The six supply constraints are: + + = 35 + + = 26 + + = 42 + + = 53 + + = 29 + + = 38 The three demand constraints are: + + ++ + ≤ 65 + + + + + ≤ 80 + ++ + + ≤ 105 The demand constraints are ≤ inequalities because the total demand (65+80+105) = 250 exceeds the total supply (26+42+53+29+38) = 223. The linear programming model for the transportation problem is summarized as follows: Minimize Z = 12+ 15+ 17+ 14+ 9+ 10+ 13+ 20 +11 +17 +16 +19 +7 +14 +12 +22 +16 +18 Subject to + + = 35 + + = 26 + + = 42 + + = 53 + + = 29 + + = 38 + + ++ + ≤ 65 + + + + + ≤ 80 + ++ + + ≤ 105
2) Solve the model you developed in #1 (above) and clearly describe the results. Because the transportation model is formulated as a linear programming model. Plant Whitewater Los Canos Duras Waste Shipped Kingsport 35 0 0 35 Danville 0 0 26 26 Macon 0 0 42 42 Selma 1 52 0 53 Columbus 29 0 0 29 Allentown 0 28 10 38 ---------------------------------------------------------------------- Received Waste 65 80 105 223 Waste Disposed 65 80 78 Total Cost: \$ 2, 822 Thus the optimum solution of the transportation problem is given in the following table. From

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## This note was uploaded on 02/10/2012 for the course MAT 540 taught by Professor Dralexander during the Spring '11 term at Strayer.

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MAT Assignment - Running head STATELINE SHIPPING AND...

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