Tight mixed-integer programming formulations for multi-item discrete lot-sizing problems

This paper discusses mixed-integer programming formulations of variants of the discrete lot-sizing problem. Our approach is to identify simple mixed-integer sets within these models and to apply tight formulations for these sets. This allows us to define integral linear programming formulations for the discrete lot-sizing problem in which backlogging and/or safety stocks are present, and to give extended formulations for other cases. The results help significantly to solve test cases arising from an industrial application motivating this research.