MAT500 Assignment 4 - Running head: STATELINE SHIPPING AND...

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Running head: STATELINE SHIPPING AND TRANSPORT COMPANY 1 Stateline Shipping and Transport Company Strayer University MAT540 – Quantitative Methods September 1, 2011
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STATELINE SHIPPING AND TRANSPORT COMPANY 2 Stateline Shipping and Transport Company 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 Stateline Shipping and Transport Company wanted to transport chemical wastes from the six plants to the three waste disposal sites. The six pants and their capacity for wastes generated are shown below. Also shown are the three waste disposal sites and their demand requirements. Plants Supply (barrels) 1. Kingsport 35 2. Danville 26 3. Macon 42 4. Selma 53 5. Columbus 29 6. Allentown 38 Waste Disposal Sites Demand (barrels) A. Whitewater 65 B. Los Canos 80 C. Duras 105 Shown below are the shipping costs ($/bbl) from each waste disposal site to each plants. Plants Waste Disposal Sites A. Whitewater B. Los Canos C. Duras 1. Kingsport $12 $15 $17 2. Danville 14 9 10 3. Macon 13 20 11 4. Selma 17 16 19 5. Columbus 7 14 12 6. Allentown 22 16 18
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STATELINE SHIPPING AND TRANSPORT COMPANY 3 Mathematical Formulation The objective of the problem is to develop a shipping schedule that minimizes the total cost of transportation. The objective function Z represents the cost. In this transportation model the decision variables, Xij, represent the quantity of waste transported from the i-th plant (where i=1,2,3,4,5,6) to the j-th waste disposal site (where j= A,B,C). The linear programming model for this problem can be written as follows. minimize Z=$12X 1A +15X 1B +17X 1C +14X 2A +9X 2B +10X 2C +13X 3A +20X 3B +11X 3C + 17X 4A +16X 4B +19X 4C +7X 5A +14X 5B +12X 5C +22X 6A +16X 6B +18X 6C subject to X 1A +X 1B +X 1C = 35 X 2A +X 2B +X 2C = 26 X 3A +X 3B +X 3C = 42 X 4A +X 4B +X 4C = 53 X 5A +X 5B +X 5C = 29 X 6A +X 6B +X 6C = 38 X 1A +X 2A +X 3A +X 4A +X 5A +X 6A <= 65 X 1B +X 2B +X 3B +X 4B +X 5B +X 6B <= 80 X 1C +X 2C +X 3C +X 4C +X 5C +X 6C <= 105 Xij >= 0, i=1,2,3,4,5,6; j=A,B,C. Note that the objective function is the sum of the individual shipping costs from each plant to each waste disposal site. The first six constraints represent the supply at each plant; the last three constraints represent the demand at each waste disposal site. The demand constraints are inequalities because the total demand, 250 barrels (= 65+80+105), exceeds the total supply,
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STATELINE SHIPPING AND TRANSPORT COMPANY 4 223 barrels (=35+26+42+53+29+38). If demand exceeds supply, then the demand constraints will be <=. Solve the Model You Developed in #1 (Above) and Clearly Describe the Results The transportation problem described above can be solved mathematically using a computer package. Following is the steps of computer solution with Excel and model solution for this case. Computer Solution with Excel
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MAT500 Assignment 4 - Running head: STATELINE SHIPPING AND...

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