[SOLVED] Annual fixed cost
Annual fixed cost 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 | 10,000 |
| Toledo | $300,000 | 20,000 |
| Denver | $375,000 | 30,000 |
| Kansas City | $500,000 | 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 Demand |
|---|---|
| Boston | 30,000 |
| Atlanta | 20,000 |
| Houston | 20,000 |
The shipping cost per unit from each plant to each distribution center is shown in table below.
A network representation of the potential Martin-Beck supply chain is shown in figure below.
Each potential plant location is shown; capacities and demands are shown in thousands of units. This network representation is for a transportation problem with a plant at St. Louis and at all four proposed sites. However, the decision has not yet been made as to which new plant or plants will be constructed. Annual fixed cost Annual fixed cost Annual fixed costAnnual fixed cost
- Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that a plant must be located either in Detroit or in Toledo, but not both. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)
Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3 Min x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33 + x41 + x42 + x43 + x51 + x52 + x53 + y1 + y2 + y3 + y4 s.t. x11 + x12 + x13 + y1 Detriot capacity x21 + x22 + x23 + y2 Toledo capacity x31 + x32 + x33 + y3 Denver capacity x41 + x42 + x43 + y4 Kansas City capacity x51 + x52 + x53 St. Louis capacity x11 + x21 + x31 + x41 + x51 Boston demand x12 + x22 + x32 + x42 + x52 Atlanta demand x13 + x23 + x33 + x43 + x53 Houston demand xij ≥ for all i and j; y1 , y2
, y3
, y1 + y2
- Formulate a model that could be used for choosing the best plant locations and for determining how much to ship from each plant to each distribution center. There is a policy restriction that no more than two plants can be located in Denver, Kansas City, and St. Louis. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)
Let y1 = 1 if a plant is constructed in Detroit; 0 if not y2 = 1 if a plant is constructed in Toledo; 0 if not y3 = 1 if a plant is constructed in Denver; 0 if not y4 = 1 if a plant is constructed in Kansas City; 0 if not xij = the units shipped in thousands from plant i to distribution center j i= 1,2,3,4,5, and j = 1,2,3 Min x11 + x12 + x13 + x21 + x22 + x23 + x31 + x32 + x33 + x41 + x42 + x43 + x51 + x52 + x53 + y1 + y2 + y3 + y4 s.t. x11 + x12 + x13 + y1 Detriot capacity x21 + x22 + x23 + y2 Toledo capacity x31 + x32 + x33 + y3 Denver capacity x41 + x42 + x43 + y4 Kansas City capacity x51 + x52 + x53 St. Louis capacity x11 + x21 + x31 + x41 + x51 Boston demand x12 + x22 + x32 + x42 + x52 Atlanta demand x13 + x23 + x33 + x43 + x53 Houston demand xij ≥ for all i and j; y1 , y2
, y3
, y3 + y4
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