Multi‐stage simultaneous lot‐sizing and scheduling for flow line production

This paper addresses the simultaneous lot‐sizing and scheduling of several products in multi‐stage flow line production systems consisting of heterogeneous parallel production lines per stage. The limited capacity of the production lines may be further reduced by sequence dependent setup times. Deterministic, dynamic demand of standard products has to be met without backlogging with the objective of minimizing sequence dependent setup, holding and production costs as well as costs for external purchase, overtime, and standby. Different mixed‐integer programming (MIP) model formulations are proposed and tested using a standard MIP‐solver. Furthermore, construction heuristics like LP‐and‐Fix and Relax‐and‐Fix are designed and applied. The solution quality and computational performance of these approaches are examined in several test scenarios.