LOT-SIZING WITH CONSTANT BATCHES - FORMULATION AND VALID INEQUALITIES

We consider the classical lot-sizing problem with constant production capacities (LCC) and a variant in which the capacity in each period is an integer multiple of some basic batch size (LCB). We first show tha t the classical dynamic program for LCC simplifies for LCB leading to an O(n2 min{n, C}) algorithm (where n is the number of periods and C t he batch size). Using this new algorithm, we show how to formulate bot h problems as linear programs with O(n3) variables and constraints. A class of so-called (k, l, S, I) inequalities are described for LCB whi ch capture both the dynamic nature of the problem as well as the capac ity aspects. For LCB, we prove that these inequalities are the only fa cet-defining inequalities of a certain form. For LCC, we show that the se inequalities include all the known classes of valid inequalities. F inally, we discuss several open questions and possible extensions.