A company wants to develop a location-distribution plan. The…
Questions
A cоmpаny wаnts tо develоp а location-distribution plan. They are considering up to three plant locations (Plant 1, Plant 2, Plant 3) and up to three distribution center locations (DC1, DC2, DC3). The selected plants will ship to the selected DCs and the selected DCs will subsequently ship units to meet demand at four existing warehouses (W1, W2, W3, W4). The table below provides relevant cost information, plant capacities, DC capacities, and warehouse demands. Per unit shipping costs Plant Per unit shipping costs DC Plants to DCs Plant Fixed DCs to Warehouses Fixed DC 1 DC 2 DC 3 Capacity Costs W1 W2 W3 W4 Costs Plant 1 $3.99 $2.56 $2.91 4700 $1000 DC 1 $2.13 $2.94 $1.86 $2.35 $200 Plant 2 $3.72 $3.81 $3.80 4100 $1000 DC 2 $2.19 $2.34 $2.49 $1.51 $200 Plant 3 $3.57 $3.08 $4.13 4200 $1000 DC 3 $2.18 $3.00 $2.99 $1.97 $200 DC capacity 4500 4500 4500 Warehouse demand 2300 1500 2400 1800 Fixed costs for plants and DCs are only realized if they are opened/selected. Prepare an integer linear programming model that, when solved, will determine the plants and DCs to be opened and a shipment plan that will meet the demand at the warehouses yet not exceed the capacity limits of the plants and DCs. The goal is to minimize the total fixed costs of plants and DCs plus the total variable (per unit) costs of shipment.
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