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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
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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### Martin-Beck Company Plant Expansion Analysis The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Products are shipped to distribution centers located in Boston, Atlanta, and Houston. Due to an expected increase in demand, the company plans to expand by constructing a new plant in one or more of these cities: Detroit, Toledo, Denver, or Kansas City. Below is a breakdown of estimated annual fixed costs and capacities for these proposed plants: #### Proposed Plant Details | Proposed Plant | Annual Fixed Cost | Annual Capacity | |----------------|-------------------|-----------------| | Detroit | $175,000 | 10,000 units | | Toledo | $300,000 | 20,000 units | | Denver | $375,000 | 30,000 units | | Kansas City | $500,000 | 40,000 units | #### Distribution Center Demand Forecasts for annual demand at each distribution center are as follows: | Distribution Center | Annual Demand | |---------------------|---------------| | Boston | 30,000 units | | Atlanta | 20,000 units | | Houston | 20,000 units | #### Shipping Costs The cost to ship each unit from a plant to a distribution center is provided below: | 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 | ### Optimization Problems **(a) Optimization Model:** A mixed-integer programming model should be developed to identify which new plant or plants provide the lowest cost to meet the anticipated demand. The optimal set of plants to open needs to be determined. - The optimal cost found is **$695,000**. - The best option is to open a plant in **Kansas City**. **(b) Alternative Solution:** Using equation 13.1, a second-best solution should be explored, identifying the optimal set of plants to open. - The alternative solution is to open plants in
Transcribed Image Text:### Martin-Beck Company Plant Expansion Analysis The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Products are shipped to distribution centers located in Boston, Atlanta, and Houston. Due to an expected increase in demand, the company plans to expand by constructing a new plant in one or more of these cities: Detroit, Toledo, Denver, or Kansas City. Below is a breakdown of estimated annual fixed costs and capacities for these proposed plants: #### Proposed Plant Details | Proposed Plant | Annual Fixed Cost | Annual Capacity | |----------------|-------------------|-----------------| | Detroit | $175,000 | 10,000 units | | Toledo | $300,000 | 20,000 units | | Denver | $375,000 | 30,000 units | | Kansas City | $500,000 | 40,000 units | #### Distribution Center Demand Forecasts for annual demand at each distribution center are as follows: | Distribution Center | Annual Demand | |---------------------|---------------| | Boston | 30,000 units | | Atlanta | 20,000 units | | Houston | 20,000 units | #### Shipping Costs The cost to ship each unit from a plant to a distribution center is provided below: | 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 | ### Optimization Problems **(a) Optimization Model:** A mixed-integer programming model should be developed to identify which new plant or plants provide the lowest cost to meet the anticipated demand. The optimal set of plants to open needs to be determined. - The optimal cost found is **$695,000**. - The best option is to open a plant in **Kansas City**. **(b) Alternative Solution:** Using equation 13.1, a second-best solution should be explored, identifying the optimal set of plants to open. - The alternative solution is to open plants in
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