A manufacturer produces a product at three plants and distributes the product through four market-service warehouses. The
Question:
A manufacturer produces a product at three plants and distributes the product through four market-service warehouses. The following tables provide data pertinent to the production and distribution for the firm. Table 1 provides the price the warehouses charge their retail customers and the demand (units that can be sold) at each warehouse. Table 2 provides the cost of producing each unit at each plant and the capacity at each plant. Table 3 provides the transportation cost of shipping each unit between the plants and the warehouses.
Table 1: Warehouse Price and Demand
Warehouse | Selling Price per Unit | Annual Demand (units) |
Warehouse 1 | $1.00 | 40,000 |
Warehouse 2 | $1.10 | 10,000 |
Warehouse 3 | $1.00 | 20,000 |
Warehouse 4 | $0.60 | 25,000 |
Table 2: Plant Costs and Capacity
Plant | Unit Variable Production Cost | Annual Capacity |
Plant A | $0.40 | 40,000 |
Plant B | $0.35 | 30,000 |
Plant C | $0.45 | 45,000 |
Table 3: Transportation Cost from Plant to Warehouse
Warehouse 1 | Warehouse 2 | Warehouse 3 | Warehouse 4 | |
Plant A | $0.20 | $0.20 | $0.30 | $0.30 |
Plant B | $0.20 | $0.10 | $0.35 | $0.40 |
Plant C | $0.45 | $0.30 | $0.20 | $0.20 |
- Suppose the production manager wants to meet all demand at the minimum cost. Formulate a linear program that will provide the optimal production and distribution schedule.
- Suppose the group vice president wishes to meet only the demands that will maximize profits. Modify your LP formulation to provide the production and distribution schedule that maximizes profits.
Hint: For #1, you may want to combine the variable production cost with the transportation costs to get one matrix for the unit cost on each distribution route. In part 2, you are maximizing total profit. You can do this by using a per unit profit matrix by subtracting the per unit costs from the selling price per unit.
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman