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: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 20,000 Toledo $300,000 30,000 Denver $375,000 40,000 Kansas City $500,000 10,000 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 20,000 Atlanta 30,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is as follows: Distribution Centers Plant Site Boston Atlanta Houston Detroit 5 2 3 Toledo 4 3 4 Denver 9 7 5 Kansas City 10 4 2 St. Louis 8 4 3 (a) Develop 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. Solve the model and answer the following questions. What is the optimal cost?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

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:

Proposed Plant	Annual Fixed Cost	Annual Capacity
Detroit	$175,000	20,000
Toledo	$300,000	30,000
Denver	$375,000	40,000
Kansas City	$500,000	10,000

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	20,000
Atlanta	30,000
Houston	20,000

The shipping cost per unit from each plant to each distribution center is as follows:

	Distribution Centers
Plant Site	Boston	Atlanta	Houston
Detroit	5	2	3
Toledo	4	3	4
Denver	9	7	5
Kansas City	10	4	2
St. Louis	8	4	3

(a)

Develop 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. Solve the model and answer the following questions. What is the optimal cost?

b. Using the equation in the image, find a second best solution. What is the optimal set of plants to open?

What is the increase in cost versus the best solution part from (a)?