A model for optimal base stock system for patient customers with lead time satisfying scbz property

A new type of Inventory model using the so-called setting the clock back to zero (SCBZ) property is analyzed in this paper. Base stock system for patient customers is a special type of ordering mechanism in inventory control theory. The inventory process begins with an initial inventory of B units. Whenever a customer order for ‘r’ units is received, an inventory replenishment order of ‘r’ units is replaced. Replenishment orders are filled after the lead time L. The customer order is filled as far as possible for the supply on hand. If the total unfilled customer demand exceeds the supply on hand, then assume that the customer will not cancel the order but await the arrival of sufficient stock. It follows from our assumption that the sum of inventory on the ground and an order is constant in time and equal to 8, known as base stock. In this problem it is assumed that the lead time is a random variable and it satisfies the SCBZ property. In the sense that before a truncation point, it has a distribution and after the truncation point, it undergoes a parametric change. Assuming that the truncation point itself a random variable, the optimal value of base stock is derived.