Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs
讨论如何为实际批量问题建立紧的混合整数规划模型，涵盖安全库存、多层级、启动、切换、最小批量等特征，并通过案例展示预处理和聚合不等式的效果。
In spite of the remarkable improvements in the quality of general purpose mixed-integer programming software, the effective solution of a variety of lot-sizing problems depends crucially on the development of tight formulations for the special problem features occurring in practice. After reviewing some of the basic preprocessing techniques for handling safety 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 period, etc. A set of applications is described that contains one or more of these special features, and some indicative computational results are presented. Finally, to show another technique that is useful, a slightly different (supply chain) application is presented, for which the a priori addition of some simple mixed-integer inequalities, based on aggregation, leads to important improvements in the results.