Optimal spare ordering policy under a rebate warranty

Abstract

This paper develops, from the customer’s perspective, the optimal spare ordering policy for a non-repairable product with a limited-duration lifetime and under a rebate warranty. The spare unit for replacement is available only by order and the lead time for delivery follows a specified probability distribution. Through evaluation of gains due to the rebate and the costs due to ordering, shortage, and holding, we derive the expected cost per unit time and cost effectiveness in the long run and examine the optimal ordering time by minimizing or maximizing these cost expressions. We show that there exists a unique optimum solution under mild assumptions. We provide a numerical example and illustrate sensitivity analysis.