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MS 3053 Logistics Management 3 Distribution System Design: An Application of Integer Programming In the previous lectures, we examined the conceptual...

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1 Leung/MS3053/Fall2012 MS 3053 Logistics Management 3 Distribution System Design: An Application of Integer Programming In the previous lectures, we examined the conceptual background of logistics management. Then, we learned how to formulate and interpret the results (solutions) of the transportation and the transshipment problems. In this class, we look at how to design a distribution system through the use of binary integer programming. Much of the modeling flexibility provided by integer programming is due to the use of 0- 1 variables. In many scenarios, 0-1 variables provide selections or choices with the value of the variable equal to 1 if a corresponding activity is undertaken and equal to 0 if the corresponding activity is not undertaken. For example, variable y is equal to 1 if a distribution center is constructed in the north side of San Antonio. Variable y is equal to 0 if the center is not constructed. Please keep in mind that not all decision variables in the logistic model are binary. Some of them are pure integers (0, 1, 2, 3, ….) Example GE operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated demand, GE plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity (units) Detroit \$175,000 10,000 Toledo \$300,000 20,000 Denver \$375,000 30,000 Kansas City \$500,000 40,000 The company’s sales department developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand (units) Boston 30,000 Atlanta 20,000 Houston 20,000
2 Leung/MS3053/Fall2012 Question: how is this design problem different from the transportation problem presented in the last two classes? The shipping cost per unit from each plant to each distribution center is shown below in the network diagram. Please be aware that only St Louis plant is an existing one in operation whereas all other plants are proposed facilities to be built. Decision regarding which one(s) to be built has not been made yet. It is part of your decision to this logistic distribution problem!! A. Construct a distribution network diagram for this problem. B. Set up the variables for the design of this distribution network.
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