A Linear Decision Rule for Production and Employment Scheduling

The decision problems involved in setting the aggregate production rate of a factory and setting the size of its work force are frequently both complex and difficult. The quality of these decisions can be of great importance to the profitability of an individual company, and when viewed on a national scale these decisions have a significant influence on the efficiency of the economy as a whole. This paper reports some of the findings of a research team that has been developing new methods to enable production executives to make better decisions and to make them more easily than they can with prevailing procedures. With the cooperation of a manufacturing concern, the new methods have been developed in the context of a set of concrete production scheduling problems that were found in a factory operated by the company. The new method which is presented in this paper, involves: (1) formalizing and quantifying the decision problem (using a quadratic approximation to the criterion function) and (2), calculating a generalized optimal solution of the problem in the form of a (linear) decision rule. Like a rule of thumb, an optimal decision rule prescribes a course of action when it is applied to a particular set of circumstances; but, unlike most rules of thumb, an optimal decision rule prescribes courses of action for which the claim can be made that the decisions are "the best possible," the meaning of "best" being clearly specified. The ultimate test, of course, must be whether the new decision methods do or do not outperform prevailing decision methods when full allowance is made for the cost of obtaining the optimal decisions.