Stochastic Inventory Models

Abstract

In the previous chapters, we discussed models that may be used when demand and lead time are constant. In this chapter, we explore the uncertainty of demand (and lead time) and its effect on order size and replenishment strategies. When demand for an item is uncertain, it becomes difficult for inventory managers to decide the order quantity and the timing of replenishment orders. In some situations, demand could exceed expectations or orders may arrive late. This could result in a stockout – a situation when inventory does not exist on hand to meet the demand. Besides how much and when to order, an additional question becomes important – that of how much to stock in order to offset the uncertainties of demand and lead time. This inventory, held in excess of regular usage quantities, is referred to as safety stock. Carrying safety stock is one of the most popular methods of reducing the effects of demand and lead time uncertainty. Reliable, historical data of demand and lead time is an important factor in the calculation of safety stock. In this chapter, we use historical data and fit it into a probability distribution (discrete as well as continuous) to determine the size of safety stock. (s, Q) and (T, S) models have been discussed.