A review of single item lot sizing problems

In this paper, a literature review of a particular planning problem, the single item lot sizing problem (SILSP), is given for both its uncapacitated and capacitated versions. We first present a summary of the different classes of lot sizing problems. We then review solution methods being proposed for the uncapacitated single item lot sizing problem (USILSP) from the time the Wagner-Whitin method was developed. The USILSP is solved efficiently in polynomial time using dynamic programming. This is why we focus on the real application extensions which have appeared mainly in the past few years. For the capacitated single item lot sizing problem (CSILSP), we give a survey of its complexity results, the different formulations and exact and heuristic approaches to solve it.