Case studies

The managing director of a steel plant faces the decision of how much of each raw material to order for the plant for the following month. Due to lower and upper bounds on the amounts of each raw material in a batch and varying amounts of electricity and time consumed for different raw materials, one can't simply use the cheapest raw material. A linear program and the solver optimization function of Excel will provide the optimal amounts that meet the constraints. Interestingly, the best mixture for a batch is not the best mixture for a monthly plan. Shadow prices indicate the value of relaxing constraints. The typical monthly model from a student will be nonlinear, although it can be written as a linear model. This case provides the basis for an introductory class on linear programming and linear versus nonlinear models.