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 Detroit 10,000 Toledo 20,000 Denver 30,000 Kansas City 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Fixed Cost $175,000 $300,000 $375,000 $500,000 Boston Atlanta Plant Site Detroit Toledo Denver Kansas City St. Louis Houston Boston The shipping cost per unit from each plant to each distribution center is as follows: 5 4 9 10 8 Annual Capacity Annual Demand Atlanta 2 3 7 4 30,000 20,000 20,000 Distribution Centers Houston 3 4 5 2 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? $ 695000 X What is the optimal set of plants to open? Kansas City (b) Using equation 13.1, find a second-best solution. What is the optimal set of plants to open? Detroit & Denver What is the increase in cost versus the best solution from part (a)? $ 145000
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 Detroit 10,000 Toledo 20,000 Denver 30,000 Kansas City 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Fixed Cost $175,000 $300,000 $375,000 $500,000 Boston Atlanta Plant Site Detroit Toledo Denver Kansas City St. Louis Houston Boston The shipping cost per unit from each plant to each distribution center is as follows: 5 4 9 10 8 Annual Capacity Annual Demand Atlanta 2 3 7 4 30,000 20,000 20,000 Distribution Centers Houston 3 4 5 2 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? $ 695000 X What is the optimal set of plants to open? Kansas City (b) Using equation 13.1, find a second-best solution. What is the optimal set of plants to open? Detroit & Denver What is the increase in cost versus the best solution from part (a)? $ 145000
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 100P
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Transcribed Image Text: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
Detroit
Toledo
Denver
Kansas City
The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows:
Distribution Center
Plant Site
Detroit
Toledo
Denver
Annual Fixed Cost
$175,000
$300,000
$375,000
$500,000
Boston
Kansas City
St. Louis
Atlanta
Houston
The shipping cost per unit from each plant to each distribution center is as follows:
Annual Capacity
Boston
10,000
20,000
30,000
40,000
8
Annual Demand
Distribution Centers
Atlanta
Houston
5
2
3
4
3
4
111
9
7
5
10
4
2
4
3
$ 695000
What is the optimal set of plants to open?
30,000
20,000
20,000
(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?
Kansas City
(b) Using equation 13.1, find a second-best solution. What is the optimal set of plants to open?
Detroit & Denver
What is the increase in cost versus the best solution from part (a)?
$ 145000
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