The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units....
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 | 30,000 |
| Toledo | $300,000 | 40,000 |
| Denver | $375,000 | 10,000 |
| Kansas City | $500,000 | 20,000 |
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? |
| $ | |
| What is the optimal set of plants to open? | |
| - Select your answer -Kansas CityDetroit & ToledoToledoDetroitItem 2 | |
| (b) | Using equation 12.1, find a second-best solution. What is the optimal set of plants to open? |
| - Select your answer -DetroitDetroit & DenverDenverDetroit & ToledoItem 3 | |
| What is the increase in cost versus the best solution from part (a)? | |
| $ |
Homework Answers
a)
The model is shown below. Since the plant in St. Louis is already operational we will only consider the transportation cost for St. Louis and not the fixed cost.
The formulas are shown below
The solver parameters are shown below
The result is shown below
The optimal cost is = 540000
The optimal set of plants to open = Only Toledo
b)
Now, modify the solver parameter so that Toledo is not selected.
The result is shown below
The next best solution is to open = Detroit & Kansas City
The increase in cost is = 830000 – 540000 = 290000
Add Answer to:
The Martin-Beck Company operates a plant in St. Louis with an
annual capacity of 30,000 units....
The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units....
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...
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A company that manufactures compressors has plants in three locations: Cleveland, Chicago, and Boston. During a...
A company that manufactures compressors has plants in three
locations: Cleveland, Chicago, and Boston. During a week, the total
capacity of each plant to produce one type of special compressor is
25, 45, and 35 units, respectively. The company wants to ship at
least 40, 10, 20 and 30 units to distribution centers in Dallas,
Atlanta, San Francisco, and Philadelphia respectively. The unit
production and distribution costs from each plant to each
distribution center are given in the table below....
Use the table below to answer the following question(s). The Riviera Transport Company (RTC) produces car...
Use the table below to answer the following question(s). The Riviera Transport Company (RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces...
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...
Problem 7-13 Recall the Martin-Beck Company distribution system problem shown below. Use a software package LINGO. Min 5x1u + 2x12 +3x13 +4221 3x22 + 4x23 + 9x31 732 5x33 + 104 4x42 S 10y Detroit capacity 20y Toledo capacity 30y3 Denver capacity S 40y4 Kansas City capacity K 30 - 30 - 20 St. Louis capacity Boston demand Atlanta demand Houston demand 11 + 21 + 31 +41 51 12 + 22 + 32 +42 52 rij 20 for all...
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2. A company that manufactures compressors has plants in three locations: Cleveland, Chicago, and Boston. During a week, the total capacity of each plant to produce one type of special compressor is 25, 45, and 35 units, respectively. The company wants to ship at least 40, 10, 20 and 30 units to distribution centers in Dallas, Atlanta, San Francisco, and Philadelphia respectively. The unit production and distribution costs from each plant to each distribution center are given in the table...
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A company that manufactures compressors has plants in three
locations: Cleveland, Chicago, and Boston. During a week, the total
capacity of each plant to produce one type of special compressor is
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least 40, 10, 20 and 30 units to distribution centers in Dallas,
Atlanta, San Francisco, and Philadelphia respectively. The unit
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distribution center are given in the table below....
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