A company currently ships its product from 5 plants to 4 warehouses. It is considering closing one or more plants to reduce cost. What plant(s) should the company close, in order to minimize transportation and fixed costs? Transportation Costs (per 1000 products) Plant 1 Plant 2 Plant 3 Plant 4 Plant 5 Warehouse 1 \$4,000 \$2,000 \$3,000 \$2,500 \$4,500 Warehouse 2 \$2,500 \$2,600 \$3,400 \$3,000 \$4,000 Warehouse 3 \$1,200 \$1,800 \$2,600 \$4,100 \$3,000 Warehouse 4 \$2,200 \$2,600 \$3,100 \$3,700 \$3,200 Open/close decision variables Plant 1 Plant 2 Plant 3 Plant 4 Plant 5 Decision 0 0 0 0 0 Number of products to ship (per 1000) Plant 1 Plant 2 Plant 3 Plant 4 Plant 5 Total Demand Warehouse 1 0 0 0 0 0 0 15 Warehouse 2 0 0 0 0 0 0 18 Warehouse 3 0 0 0 0 0 0 14 Warehouse 4 0 0 0 0 0 0 20 Total 0 0 0 0 0 Capacity 0 0 0 0 0 Distr. Cost \$0 \$0 \$0 \$0 \$0 Fixed Cost \$0 \$0 \$0 \$0 \$0 Total Cost \$0 \$0 \$0 \$0 \$0 \$0 Problem A company currently ships products from 5 plants to 4 warehouses. The company is considering the option of closing down one or more plants. This would increase distribution cost but perhaps lower overall cost. What plants, if any, should the company close? Solution 1) The variables are the decisions to open or close the plants, and the number of products that should be shipped from the plants that are open to the warehouses. In worksheet Facility these are given the names Open_or_close and Products_shipped. 2) The logical constraints are Products_shipped >= 0 via the Assume Non-Negative option Open_or_close = binary The products made can not exceed the capacity of the plants and the number shipped should meet the demand. This gives Products_made <= Capacity Total_shipped >= Demand 3) The objective is to minimize cost. This is given the name Total_cost on the worksheet. Remarks It is often possible to increase the capacity of a plant. This could be worked into the model with additional 0-1 or binary integer variables. The Solver would find out if it would be profitable to extend the capacity of a plant. It could also be interesting to see if it would be profitable to open another warehouse. An example of this can be found, in somewhat modified form, in the capacity planning model in the Finance Examples workbook.