Modelling practical lot-sizing problems as mixed-integer programs

In spite of the remarkable improvements in the quality of general purpose m ixed-integer programming software, the effective solution of a variety of l ot-sizing problems depends crucially on the development of tight formulatio ns for the special problem features occurring in practice. After reviewing some of the basic preprocessing techniques for handling saf ety stocks and multilevel problems, we discuss a variety of aspects arising particularly in small and large bucket (time period) models such as start- ups, changeovers, minimum batch sizes, choice of one or two set-ups per per iod, etc. A set of applications is described that contains one or more of t hese special features, and some indicative computational results are presen ted. Finally, to show another technique that is useful, a slightly differen t (supply chain) application is presented, for which the a priori addition of some simple mixed-integer inequalities, based on aggregation, leads to i mportant improvements in the results.