Dynamic multi-machine lotsizing and sequencing with simultaneous scheduling of a common setup resource

In this paper we propose a new solution approach to a lotsizing and scheduling problem which explicitly includes the simultaneous consideration of a common setup operator. This type of problem has been observed in several industries. We propose a model formulation of this dynamic capacitated multi-item multi-machine one-setup-operator lotsizing problem that is based on the proportional lotsizing and scheduling problem (PLSP) of Haase [1994. Lotsizing and Scheduling for Production Planning. Springer, Berlin]. In addition, we propose a model reformulation that is based on the simple plant location analogy. Finally, we extend the model for the case of a special type of sequence-dependent setup times. The different models are applied in an industrial planning environment and it is shown that good solutions are found within a few minutes of CPU time with a standard solver. Compared to the planning procedure used in the company up to now significant reductions in setup costs as well as feasible production schedules without backorders are achievable.