C07 E11 - Chapter 7 Transportation Assignment and...

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ference between the total supply and the total demand. Dummy origin An origin added to a transportation problem in order to make the total supply equal to the total demand. The supply assigned to the dummy origin is the differ- ence between the total demand and the total supply. Hungarian method A special-purpose solution procedure for solving an assignment problem. Opportunity loss For each cell in an assignment matrix, the difference between the largest value in the column and the value in the cell. The entries in the cells of an assign- ment matrix must be converted to opportunity losses to solvemaximization problems using the Hungarian method. PROBLEMS Note: For Problems 1-32 a variety of solution methods can be used. In many cases, we ask you to formulate and solve the problem as a linear program. Where the solution method is not spec- ified, you may also use the transportation or assignment modules of The Management Scientist or some other software package. Problems 33-45 are intended to be solved using the special- purpose algorithms of Sections 7.5 and 7.6. These special-purpose algorithms could also be used for many of the first 32 problems. 1. A company imports goods at two ports: Philadelphia and New Orleans. Shipments of one of its products are made to customers in Atlanta, Dallas, Columbus, and Boston. For the next planning period, the supplies at each port, customer demands, and the shipping costs per case from each port to each customer are as follows: Develop a network model of the distribution system for this problem. Customers Port Port Atlanta Dallas Columbus Boston Supply Philadelphia 2 6 6 2 5000 New Orleans 1 2 5 7 3000 Demand 1400 3200 2000 1400 PDF processed with CutePDF evaluation edition www.CutePDF.com
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356 INTRODUCTION TOMANAGEMENTSCIENCE 2. Consider the following network representation of a transportation problem: 30 10 25 15 20 t t Supplies Demands The supplies, dem?U\ds,?U\dtr?U\.'io~rta.tion costs Qer unit are shown on the network. a. Develop a linear programming model for this problem; be sure to define the varici:::= in your Qlodel. b. Solve the linear program to detennine the optimal solution. 3. Reconsider the distribution system described in Problem I. a. Develop a linear programming model for minimizing transportation costs. b. Solve the linear program to detennine the minimum cost shipping schedule. 4. A product is produced at three plants and shipped to three warehouses (the transport-.. - costs per unit are shown in the following table). a. Show a network representation of the problem. b. Develop a linear programming model for minimizing transportation costs; soh'~ ;..- model to detennine the minimum cost solution. c. Suppose that the entries in the table represent profit per unit produced at plan~ _. sold to warehousej. How does the.model change from that in part (b)?
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