Economic order quantity models for deteriorating items and partial backlogging when demand is quadratic in time

In this paper, we extend the inventory lot-size model introduced in Ghosh and Chaudhuri (2006) to allow for partial backlogging. In addition, we also relax their assumptions of equal replenishment cycles and constant shortage lengths. For any given number of replenishment cycles, we show that the optimal replenishment schedule exists uniquely. We then prove that the total relevant cost is a convex function of the number of replenishments. Consequently, we propose an algorithm to find the optimal replenishment number and schedule. Finally, we run several numerical examples, and obtain some managerial implications by using sensitivity analyses. [Received 18 November 2009; Revised 18 February 2010; Revised 27 April 2010; Accepted 28 April 2010]