Parametric analysis of setup cost in the economic lot-sizing model without speculative motives

In this paper we consider the important special case of the economic lot-sizing problem in which there are no speculative motives to hold inventory. We analyze the effects of varying all setup costs by the same amount. This is equivalent to studying the set of optimal production periods when the number of such periods changes. We show that this optimal set changes in a very structured way. This fact is interesting in itself and can be used to develop faster algorithms for such problems as the computation of the stability region and the determination of all efficient solutions of a lot-sizing problem. Furthermore, we generalize two related convexity results which have appeared in the literature.