Problems Network Flow Programming Models
 Network Flow Programming Models - Production Scheduling with Two Machines

Company ABC has a production line that produces a product from two raw materials. To make a unit of product, one unit of raw material A is processed in machine A, and one unit of raw material B is processed in machine B. The outputs of these two machines are combined at machine C to produce the finished good. The production process is shown in the figure. Note that the finished product contains one unit each of raw materials A and B.

Due to variability, the capacities of the machines change from time to time. The capacities of the machines (expressed in units per day) together with the demands and unit profits for the next six days are shown in the table. The profits include both revenue and raw material costs, but do not include the inventory costs.

Data for the Problem

 Day Machine A Capacity (Units/Day) Machine B Capacity (Units/Day) Machine C Capacity (Units/Day) Finished Goods Demand (Units) Finished Goods Unit Profit (\$/Unit) 1 100 90 60 50 100 2 80 100 100 80 110 3 100 90 150 70 100 4 90 100 90 260 90 5 100 90 100 70 105 6 90 100 50 60 110

You are to find the amounts each machine should process for the next six days. Because demand may exceed capacity at any time, the owner is willing to build inventory. The cost of storing inventory for one day at A is \$1 per unit, the cost at B is \$2 per unit, and the cost at C is \$4 per unit. The maximum inventory that can be carried at each of the machines is 10 units. The goal is to maximize net profit less inventory cost. The demand in a day is an upper bound to sales. If it is impossible to meet demand, sales may be lost.

Use a network model to solve this problem. Use side constraints if necessary.

Operations Research Models and Methods
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by Paul A. Jensen