Textile Mill Scheduling
Above solution shows that production quantity for all fabric types except for Fabric3 are same in Profit maximization and Cost minimization model. All Fabric 3 should be purchased in Profit maximization model while in Cost minimization model, almost all of the Fabric3 should be produced by Regular loom and a small quantity (about 10%) should be purchased. Cost contribution of Fabric one on the dobbie loom can ranges from 0. 64425 to 0. 67 for the cost minimization model.
Note here that since demand for the fabrics is fixed, both the profit maximization and cost minimization models will provide the same optimal solution. However, the interpretation of the ranges for the objective function coefficients differ for the two models.
In the profit maximization case, the coefficients are profit contributions. Thus, the range information indicates how price per unit and cost per unit may vary simultaneously. That is, as long as the net changes in price per unit and cost per unit keep the profit contributions within the ranges, the solution will remain optimal. In the cost minimization model, the coefficients are costs per unit. Thus, the range information indicates how much the cost per unit may vary to maintain the same optimal solution.