Scheduling flexible flow shops with sequence-dependent setup effect

This paper presents an optimization model-based approach for production scheduling of flexible flow shops where sequence-dependent setup effect is significant. The scheduling problem is formulated as an integer programming problem. In the presence of setup effect, individual machine setup status must be scheduled in accordance with part processing schedule. A Lagrangian relaxation method is adopted to solve the problem in dual space, where the synchronization constraint between machine setup and part processing is relaxed. An efficient heuristic is developed to adjust the dual solution to primal feasibility. Network flow structures of both machine status change and part flow balance equations are exploited for algorithm development. Numerical results demonstrate that our methodology generates an optimal schedule on a small example and a near-optimal solution on a multi-stage and multi-machine example using a reasonable amount of CPU time