|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.