A forward recursive algorithm for inventory lot-size models with power-form demand and shortages

Barbosa and Friedman establish an optimal replenishment policy for power-form demand rate. In this paper, we extend their inventory lot-size model to allow for shortages. The goal is to find the optimal number and time of replenishments in order to keep the total relevant cost as low as possible during a finite planning horizon. We develop a simple forward recursive algorithm to determine the optimal replenishment timing. Furthermore, we propose an intuitively accurate estimate for the optimal number of replenishments, which significantly reduces computational complexity in finding the optimal replenishment number. A numerical example is provided to illustrate the solution procedure.