Question: Q3: Problem Ch6 transportation: Distribution System Design 0,1 variables Binary The DSD Company operates a plant in York with an annual capacity of 2500 units.
Q3: Problem Ch6 transportation: Distribution System Design 0,1 variables Binary
The DSD Company operates a plant in York with an annual capacity of 2500 units. The product is shipped to regional distribution centers located in Boston, Chicago, St. Louis, and Lexington. Because of an anticipated increase in demand, DSD plans to increase capacity by constructing a new plant in one or more of the following cities: Cleveland or Bedford. The estimated annual fixed cost and the annual capacity for the two proposed plants are as follows:
| Proposed Plant | Annual Fixed cost | Annual Capacity |
| Cleveland | $55,000 | 5000 |
| Bedford | $80,000 | 6000 |
The companys long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows:
| Distribution Center | Annual Demand |
| Boston | 6,000 |
| Chicago | 4,000 |
| St. Louis | 2,000 |
| Lexington | 1,500 |
The shipping cost per unit from each plant to each distribution center is shown below.
| Distribution Centers | ||||
| Plant Site | Boston | Chicago | St. Louis | Lexington |
| Cleveland | 3 | 2 | 7 | 6 |
| Bedford | 7 | 5 | 2 | 3 |
| York | 2 | 5 | 4 | 5 |
This network representation is for a transportation problem with a plant at York and at all two proposed sites.
Formulate a linear programming model for minimization to determine for the construction of a new plant. How many units should be shipped to each plant?
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