(tp, S) inventory policy for returnable item

Abstract

This study is concerned with analyzing the so-called ($t_p$,S) Inventory system for a single returnable item. Under the ($t_p$,S) policy, the associated inventory system cost function is formulated for three cases of returnable item which are related to demand rate and return rate. The first case is for the inventory system in which both demand rate and returned rate are constant, and also for the inventory system with constant demand rate and normally distributed return rate. The second case is for the inventory system in which demand rate is constant but return rate is represented as a function of procurement price. The last case is for the inventory system constrained by a minimum specified service level, in which demand rate is constant and return rate is normally distributed. The system models for both the first case and the last case are shown to be in convex form, while the model for the second case is not in convex form and so is solved by the false position method. Numerical examples for the above three cases are given.