Problem 11-13
The Martin-Beck Company operates a plant in St. Louis with anannual capacity of 30,000 units. Product is shipped to regionaldistribution centers located in Boston, Atlanta, and Houston.Because of an anticipated increase in demand, Martin-Beck plans toincrease capacity by constructing a new plant in one or more of thefollowing cities: Detroit, Toledo, Denver, or Kansas City. Theestimated annual fixed cost and the annual capacity for the fourproposed 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 ofthe anticipated annual demand at the distribution centers asfollows:
Distribution Center | Annual Demand |
Boston | 30,000 |
Atlanta | 20,000 |
Houston | 20,000 |
The shipping cost per unit from each plant to each distributioncenter is shown in table below.
A network representation of the potential Martin-Beck supplychain is shown in figure below.
Each potential plant location is shown; capacities and demandsare shown in thousands of units. This network representation is fora transportation problem with a plant at St. Louis and at all fourproposed sites. However, the decision has not yet been made as towhich new plant or plants will be constructed.
- Formulate a model that could be used for choosing the bestplant locations and for determining how much to ship from eachplant to each distribution center. There is a policy restrictionthat a plant must be located either in Detroit or in Toledo, butnot both. For those boxes in which you must enter subtractive ornegative 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 KansasCity; 0 if not |
| xij = the units shipped in thousands fromplant 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 | | | | |
- Formulate a model that could be used for choosing the bestplant locations and for determining how much to ship from eachplant to each distribution center. There is a policy restrictionthat no more than two plants can be located in Denver, Kansas City,and St. Louis. For those boxes in which you must enter subtractiveor 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 KansasCity; 0 if not |
| xij = the units shipped inthousands from plant i to distribution centerj |
| 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 | | | | |
Please show how to solve parts a and busing Excel
