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

In 1978, Barbosa and Friedman established a ‘general root law’ for power-form demand rate. Shortages are prohibited. However, in reality, shortages may occur and the planning time horizon is usually finite as the product life cycle is short. Therefore, the author here extends their inventory lot-size model to allow for shortages during a finite planning time horizon and propose an alternative algorithm in a backward manner to determine the optimal replenishment timing without using iterative search schemes. The study not only shows that the total relevant cost is a strictly convex function of the replenishment number, but also provides the condition for determining the optimal replenishment number. Finally, a numerical example is given for illustration.