Chapter 8, Problem 20P

Refer to the Calhoun Textile Mill production problem described in Problem 19. Use the procedure described in Section 11.7 to try to find an alternative optimal solution. If you are successful, discuss the differences in the solution you found versus that found in Problem 19.

19. The Calhoun Textile Mill is in the process of deciding on a production schedule. It wishes to know how to weave the various fabrics it will produce during the coming quarter. The sales department has confirmed orders for each of the 15 fabrics produced by Calhoun. These demands are given in the following table. Also given in this table is the variable cost for each fabric. The mill operates continuously during the quarter: 13 weeks, 7 days a week, and 24 hours a day.

There are two types of looms: dobbie and regular. Dobbie looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids. The rate of production for each fabric on each type of loom is also given in the table. Note that if the production rate is zero, the fabric cannot be woven on that type of loom. Also, if a fabric can be woven on each type of loom, then the production rates are equal. Calhoun has 90 regular looms and 15 dobbie looms. For this problem, assume that the time requirement to change over a loom from one fabric to another is negligible.

Management would like to know how to allocate the looms to the fabrics and which fabrics to buy on the market so as to minimize the cost of meeting demand.