Problems Network Flow Programming Models
 Problems for Network Flow Programming Models - Production Scheduling with Two Machines
 The network model is shown below. The gains on the arc entering nodes C1, C2, etc. are equal to 1/2. This causes the amount of flow leaving C1, C2, etc. to be equal to 1 for each unit produced. The arcs entering the nodes labeled A and B are the production capacities in each period. Arcs passing from one period to the next, A1 to A2 for instance, carry inventories. The arcs leaving C limit the production capacity at C. The arc leaving nodes such as C1' describe the demand and net profit in each period. It is necessary to add side constraints so that for every unit of C produced, one unit of each A and B is required. Let x(Ai, Ci) be the flow on arc (Ai, Ci) where i is the period number. Let x(Bi, Ci) be the flow on arc (Bi, Ci) where i is the period number. Side Constraints: x(Ai, Ci) = x(Bi, Ci) for i = 1…6

Operations Research Models and Methods
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by Paul A. Jensen