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.

Solving a Multi-Level Capacitated Lot Sizing Problem with Multi-Period Setup Carry-Over via a Fix-and-Optimize Heuristic

This paper presents a new algorithm for the dynamic Multi-Level Capacitated Lot Sizing Problem with Setup Carry-Overs (MLCLSP-L). The MLCLSP-L is a big-bucket model that allows the production of any number of products within a period, but it incorporates partial sequencing of the production orders in the sense that the first and the last product produced in a period are determined by the model. We solve a model which is applicable to general bill-of-material structures and which includes minimum lead times of one period and multi-period setup carry-overs. Our algorithm solves a series of mixed-integer linear programs in an iterative so-called Fix-and-Optimize approach. In each instance of these mixed-integer linear programs a large number of binary setup variables is fixed whereas only a small subset of these variables is optimized, together with the complete set of the inventory and lot size variables. A numerical study shows that the algorithm provides high-quality results and that the computational effort is moderate.Lot Sizing, MIP, Decomposition, MLCLSP-L, Fix-and-Optimize heuristic.