The economic lot-sizing problem with lost sales and bounded inventory

This article considers an economic lot-sizing problem with lost sales and bounded inventory. The structural properties of optimal solutions under different assumptions on the cost functions are proved. Using these properties, new and improved algorithms for the problem are presented. Specifically, the first polynomial algorithm for the general lot-sizing problem with lost sales and bounded inventory is presented, and it is shown that the complexity can be reduced considerably in the special case of non-increasing lost sales costs. Moreover, with the additional assumption that there is no speculative motive for holding inventory, an existing result is improved by providing a linear time algorithm.