Discrete-Time Spare Ordering Policy with Discounting and Two Types of Lead Times

摘要

In this paper, a discrete-time order-replacement model is considered for a single-unit which is supplied by a regular order with a deterministic lead time. When in service, the unit is subject to random failure. If the unit fails before a pre-specified time then the spare is delivered by an expedited order with a deterministic lead time; otherwise, the spare is supplied by a regular order. If the original unit fails before the spare arrives by regular order then the spare is taken into service from the delivery point. Otherwise, the spare is put into inventory until the unit fails or passes a predetermined critical age called the inventory time limit, whichever occurs first. We consider the total discounted cost over an infinite time span as a criterion of optimality and analyze the model taking the inventory time limit and regular ordering time as decision variables. A numerical example is adopted to determine the optimal ordering policy numerically and perform the sensitivity analysis. The model is also extended to the case of a negative ordering time.