The Martin-Beck Company 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 increase in demand, Martin-Beck 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:

The company€™s long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows:
Distribution Center Annual Demand
Boston€¦€¦€¦€¦€¦€¦€¦€¦ 30,000
Atlanta€¦€¦€¦€¦€¦€¦€¦€¦ 20,000
Houston€¦€¦€¦€¦€¦€¦€¦€¦ 20,000
The shipping cost per unit from each plant to each distribution center is as follows:

a. Formulate a mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in order to satisfy anticipated demand.
b. Solve the model you formulated in part a. What is the optimal cost? What is the optimal set of plants to open?

Transcribed Image Text:

Proposed Plant Detroit Toledo Denver Kansas City Annual Fixed Cost $175,000 $300,000 $375,000 $500,000 Annual Capacity 10,000 20,000 30,000 40,000 Distribution Centers Atlanta Plant Site Detroit Toledo Denver Kansas City St. Louis Boston Houston 4 10 4