A new type of model for multi-item capacitated dynamic lotsizing and scheduling

Three types of multi-item capacitated dynamic lotsizing and scheduling models are well established until now: The capacitated lotsizing problem, the discrete lotsizing and scheduling problem as well as the continuous setup lotsizing problem. An analysis of the underlying fundamental assumptions provides the basis for introducing a new model type, the proportional lotsizing and scheduling problem. This model type is well suited for incorporating some of the extensions relevant with respect to practice: Setup times, sequence dependent setup costs (times), multiple machines as well as multiple stages. Last but not least we show how make-or-buy decisions may be modelled within this framework. This is relevant regarding three important aspects: First it is more general, second it is of practical relevance, third it provides the basis for overcoming difficulties associated with feasibility problems. The last fact opens up new avenues especially for the development of efficient local search procedures.