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
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 the table below.
A network representation of the potential Martin-Beck supply chain is shown in the 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.
- 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 fill in the blank 1x11 + fill in the blank 2x12 + fill in the blank 3x13 + fill in the blank 4x21 + fill in the blank 5x22 + fill in the blank 6x23 + fill in the blank 7x31 + fill in the blank 8x32 + fill in the blank 9x33 + fill in the blank 10x41 + fill in the blank 11x42 + fill in the blank 12x43 + fill in the blank 13x51 + fill in the blank 14x52 + fill in the blank 15x53 + fill in the blank 16y1 + fill in the blank 17y2 + fill in the blank 18y3 + fill in the blank 19y4 s.t. fill in the blank 20x11 + fill in the blank 21x12 + fill in the blank 22x13 + fill in the blank 23y1 ≥ fill in the blank 25 Detriot capacity fill in the blank 26x21 + fill in the blank 27x22 + fill in the blank 28x23 + fill in the blank 29y2 ≥ fill in the blank 31 Toledo capacity fill in the blank 32x31 + fill in the blank 33x32 + fill in the blank 34x33 + fill in the blank 35y3 ≥ fill in the blank 37 Denver capacity fill in the blank 38x41 + fill in the blank 39x42 + fill in the blank 40x43 + fill in the blank 41y4 ≥ fill in the blank 43 Kansas City capacity fill in the blank 44x51 + fill in the blank 45x52 + fill in the blank 46x53 ≥ fill in the blank 48 St. Louis capacity fill in the blank 49x11 + fill in the blank 50x21 + fill in the blank 51x31 + fill in the blank 52x41 + fill in the blank 53x51 = fill in the blank 55 Boston demand fill in the blank 56x12 + fill in the blank 57x22 + fill in the blank 58x32 + fill in the blank 59x42 + fill in the blank 60x52 = fill in the blank 62 Atlanta demand fill in the blank 63x13 + fill in the blank 64x23 + fill in the blank 65x33 + fill in the blank 66x43 + fill in the blank 67x53 = fill in the blank 69 Houston demand xij ≥ for all i and j; y1 fill in the blank , y2 fill in the blank, y3 fill in the blank, y1 + y2 fill in the blank
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Project Management A Systems Approach to Planning Scheduling and Controlling
Authors: Harold Kerzner
10th Edition
978-047027870, 978-0-470-5038, 470278706, 978-0470278703
