Transformation of Flow
|A company makes three products
in four plants. Because of differences in labor skills,
different times are required to produce the products
in the various plants. The time requirements (minutes
per unit) are shown in the table below. A dash indicates
that the product cannot be made at the plant. The demand
for the products is also shown. The total time available
in each plant is 25 hours per week. The hourly charge
for labor is $10, 12, 9, and 13 for plants 1, 2, 3,
and 4, respectively. Not all the time available at a
plant need be used. There is no labor charge for time
not used. Our problem is to construct and solve the
network model that minimizes the cost of manufacturing
to meet the demand.
The example illustrates the use of gains to transform
one type of flow to another. The situation is like a transportation
problem except the plants have capacities measured in
hours, and demand is in units. We use the gain factor
transform the flow as indicated in Fig. 21.
Figure 21. Using the gain factor to transform
The data for this situation is given in minutes per unit,
so to compute the appropriate gain factors, invert the
quantities and multiply by 60 to find units per hour.
The gain for plant 1 producing product A is 2 units per
hour. The complete network model and the solution are
shown in Fig. 22 and 23.
Figure 22. Model
Figure 23. Solution