An algorithm to determine the DOQ for deteriorating items with shortage and a linear trend in demand

In 1991, Goswami and Chaudhuri considered the inventory replenishment policy over a fixed planning period for a deteriorating item having a deterministic demand pattern with a linear trend and shortages. Basically, they concentrated on the establishment of the inventory model but did not present a concrete algorithm to solve it. This paper complements the shortcoming of Goswami and Chaudhuri's paper. We first show that the total cost function of Goswami and Chaudhuri is convex. Subsequently, with the convexity, an algorithm to determine the number of reorders, the interval between two successive reorders and the shortage intervals over a finite time-horizon in an optimal manner is developed. Many numerical examples illustrate how the algorithm works.