Proportional lotsizing and scheduling

Two multi-item capacitated dynamic lotsizing and scheduling models with a finite horizon have been established recently: 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, the proportional lotsizing and scheduling problem. The authors present a new backward-oriented regret-based biased random sampling method which solves the new model efficiently. The model is well suited for the incorporation of some of the extensions relevant for practice setup times, sequence-dependent setup costs (times), multiple machines as well as multiple stages.