A company needs to establish a shipping schedule for the next two months. The demands for each customer are 15 units in the first month and 20 units in the second month. These demands must be met. The warehouses are really manufacturing plants where the products are made. Plant A has a manufacturing capacity of 30 in each month, while plant B has a capacity of 50 in each month. In the first month the cost of manufacture at A is $8 per unit and the cost of manufacture at B is $10 per unit. In the second month the cost of manufacture is $9 at both plants. Products can be stored at the customer sites from one month to the next. The storage cost is $1 per unit. Products cannot be stored at the plants. Shipping costs are as given in the previous example except that the shipping company is giving a discount of $1 per unit on all routes during the first month. The goal is to minimize total production, shipping and inventory costs over the two months. Not all production capacity need be utilized by the solution.

The network model for this case is shown in Fig. 20. A transportation network represents each period. Arcs that go from one period to the next represent inventories. With this construction, the size of the network is proportional to the number of periods. This same approach is useful for a variety of multiperiod situations.Figure 20. Two period network model.

Figure 20. Two period network model.