Simpufied Production-inventory Control Chart

This paper is concerned witl). "a problem in which a firm is engaged in manufacturing a number of types and sizes of goods at equal intervals, e. g. monthly, and the production is forced to fulfill the customer's demand immediately. In general the products are subject to considerable variations in demands. Let us assume that the amount demanded is uncertain but has a certain probability distribution. If inventory remains after the orders have been filled in any period, it is carried over into the next period. But, in case where the order can not be delivered from available inventory, the difference should not be filled in by the production of the next period because of the needs of immediate delivery. In this situation, it may be appropriate to consider only the shortage cost, and neglect the other costs. The shortage cost, however, may be obscure in most cases, then we discuss the probability which the shortage occurs. The model used in this paper is a production process with a lag time. We define a lag time as the time between the issuance of production order and the arrival of finished goods into stock. We assume that the lag time is equal to the production period. Then the production schedules are to be made for the future production periods. The list of symbols used in this paper is: F(q) ==the probability distribution function for the sales demand in each period. qk==the actual demand in the k-th period. xk=the initial stock at the beginning of the k-th period. Yk=the size of the scheduled prodUction at the beginning of the k-