Stochastic Inventory Control Models Research Articles

Stochastic material requirements planning for optional parts†

Most procedures in materials management may be grouped into two classes: deterministic material requirements planning with bill of material explosion on the one hand, and usage-oriented stochastic inventory control models on the other. Each approach is also used for optional parts. With the first class of procedures, however, the random aspect of usage ratios is neglected, whereas in the second class of product structure, relations to planned final products are lost sight of. In the following paper, there is first developed a model of usage ratio generation which reveals the factors influencing the parameters of a usage ratio distribution. The model exhibits satisfactory agreement with practical observation. The paper then demonstrates how usage ratios may be included in a material requirements planning procedure despite their stochastic nature

Bounds on the Solution of the Lagged Optimal Inventory Equation with No Demand Backlogging and Proportional Costs

These equations depict the following inventory situation. A nonnegative order for a single product is to be placed at the beginning of each of an infinite sequence of equally spaced periods into the future, labeled 0, 1, 2, .. Demands depleting the inventory form a nonnegative sequence of independent identically distributed random variables 40, 1, '2, * . For analytic convenience the distribution is assumed to possess a continuous positive density function 0(4) on [0, oo). An order zi placed at the beginning of period i arrives after a fixed Aperiod lag at the beginning of period i + A, and is relabeled Y(i + ), which explains (4). The pipeline vector qi at the beginning of period i consists of the inventory on hand at that point xi together with the sequence of outstanding orders to arrive in succeeding periods Y(i+ 1), Y(i+ 2)' ... , Y(i+ -1) If demand in a given period exceeds inventory on hand, two extreme cases are considered. In model I, also called the no backlogging or the lost sales case, no customer will wait, so the inventory level is conveniently thought of as being nonnegative; it is recursively generated by (5a). In model II, also called the backlogging case, all customers