OPTIMAL PRODUCTION PLANNING AND INVENTORY CONTROL*

This paper is concerned with the optimal production planning and inventory control. The first problem is a multiperiod production scheduling problem in which the objective is to minimize the operating cost for a planning period. This cost is composed principally of the sum of the production cost and inventory carrying cost. The second problem considers an inventory system with two decision variables in each planning period. These are the production schedule and work force which are to be determined so as to minimize the operating cost which includes the costs of changing the production rate, of changing the work force and of carrying the inventory. The maximum principle in the discrete form is used to reduce both the first problem which has N decision variables and the second problem which has 2N decision variables respectively to a series of two decision variables problems. The so-called sequential simplex pattern search technique is used to determine the optimal values of these two decision variables. Numerical examples are given to demonstrate the method.