# Cassimy_Evan_Homework 5.docx - Evan Cassimy MGMT 651...

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Evan Cassimy MGMT 651 2/9/2020 Professor Avijit Sarkar Homework 5 1. (10 points) Chapter 6 Problem 28 Let x ij be the number of units that flow from node i to node j. Only one unit can flow from node 1 to node 4, the value of x ij either be 1 or 0. Let x ij = 1 be the arc from the node i to node j is the shortest route. Let x ij = 0 be the arc from the node i to node j is not the shortest route 34
Submit your homework as one single attachment. Include POM-QM input and output screenshots wherever applicable. If you submit your homework as an MS-Excel document, make sure that it is properly formatted to 8.5x11 page size!! 1 of 13
2. (15 points) A company is considering 4 locations to open warehouses: New York , Los Angeles Chicago and Atlanta . Each warehouse can ship up to 100 units per week. The weekly fixed cost of keeping each warehouse open is \$400 for NY, \$500 for LA, \$300 for Chicago, and \$150 for Atlanta. The company’s customers are spread across three well-defined regions across the country. Region 1 requires 80 units per week, region 2 requires 70 units per week and region 3 requires 40 units per week. The unit transportation costs for each warehouse to a region are shown in the following table: Table of Unit Transportation Costs FROM TO Region 1 Region 2 Region 3 New York \$20 \$40 \$50 Los Angeles 48 15 26 Chicago 26 35 18 Atlanta 24 50 35 The company wants to meet weekly demands at minimum cost, subject to the preceding information and he following strategic criteria: If the NY warehouse is opened, then the LA warehouse must be opened. At most two warehouses can be opened. Either the Atlanta or LA warehouse must be opened. Formulate a mixed integer linear program (MILP) for this problem and solve using POM/QM (Integer and Mixed Integer Programming) . Interpret your results: (a) which warehouse locations are selected? (b) What is the transportation schedule and what is the total transportation cost? , i j j