The Cash Flow
SOLUTION TO ANDREW–CARTER, INC., CASE
This case presents some of the basic concepts of aggregate planning by the transportation method. The case involves solving a rather complex set of transportation problems. Four different configurations of operating plants have to be tested. The solutions, although requiring relatively few iterations to optimality, involve degeneracy if solved manually. The costs are:
[pic]
The lowest weekly total cost, operating plants 1 and 3 with 2 closed, is $217,430. This is $3,300 per week ($171,600 per year) or 1.5% less than the next most economical solution, operating all three plants. Closing a plant without expanding the capacity of the remaining plants means unemployment. The optimum solution, using plants 1 and 3, indicates overtime production of 4,000 units at plant 1 and 0 overtime at plant 3. The all-plant optima have no use of overtime and include substantial idle regular time capacity:
11,000 units (55%) in plant 2 and either 5,000 units in plant 1
(19% of capacity) or 5,000 in plant 3 (20% of capacity). The idled capacity versus unemployment question is an interesting, nonquantitative aspect of the case and could lead to a discussion of the forecasts for the housing market and thus the plant’s product.
The optimum producing and shipping pattern is
[pic]
There are three alternative optimal producing and shipping patterns, where R.T. _ regular time, O.T. _ overtime, and W _warehouse.
Getting the solution manually should not be attempted using the northwest corner rule. It will take eight tableaux to do the “all plants” configuration, with degeneracy appearing in the seventh tableau; the “1 and 2” configuration takes five tableaux; and so on.
It is strongly suggested that software be
This case presents some of the basic concepts of aggregate planning by the transportation method. The case involves solving a rather complex set of transportation problems. Four different configurations of operating plants have to be tested. The solutions, although requiring relatively few iterations to optimality, involve degeneracy if solved manually. The costs are:
[pic]
The lowest weekly total cost, operating plants 1 and 3 with 2 closed, is $217,430. This is $3,300 per week ($171,600 per year) or 1.5% less than the next most economical solution, operating all three plants. Closing a plant without expanding the capacity of the remaining plants means unemployment. The optimum solution, using plants 1 and 3, indicates overtime production of 4,000 units at plant 1 and 0 overtime at plant 3. The all-plant optima have no use of overtime and include substantial idle regular time capacity:
11,000 units (55%) in plant 2 and either 5,000 units in plant 1
(19% of capacity) or 5,000 in plant 3 (20% of capacity). The idled capacity versus unemployment question is an interesting, nonquantitative aspect of the case and could lead to a discussion of the forecasts for the housing market and thus the plant’s product.
The optimum producing and shipping pattern is
[pic]
There are three alternative optimal producing and shipping patterns, where R.T. _ regular time, O.T. _ overtime, and W _warehouse.
Getting the solution manually should not be attempted using the northwest corner rule. It will take eight tableaux to do the “all plants” configuration, with degeneracy appearing in the seventh tableau; the “1 and 2” configuration takes five tableaux; and so on.
It is strongly suggested that software be