Comparing Modeling Approaches for the Multi-Level Capacitated Lot-Sizing and Scheduling Problem

Determining lot sizes is an essential step during the material requirements planning phase influencing total production cost and total throughput time of a production system. It is well-known that lot-sizing and scheduling decisions are intertwined. Neglecting this relation, as it is done in the classical hierarchical planning approach, leads to inefficient and sometimes infeasible plans. In this work we compare different approaches for integrating the lot-sizing and the scheduling decisions in multi-stage systems. We show their abilities and limitations in describing relevant aspects of a production environment. By applying the models to benchmark instances we analyze their computational behavior. The structural and numerical comparisons show that there are considerable differences between the approaches although all models aim to describe the same planning problem. The results provide a guideline for selecting the right modeling approach for different planning situations.