Bidirectional Flow Shop Scheduling with Multi-Machine Capacity and Critical Operation Sequencing (original) (raw)

We study a special bidirectional flow shop problem with multi-machine capacity and sequencing constraints on critical operations. A formulation is proposed in continuous time domain and compared with a mixed integer programming (MIP) formulation in discrete time domain. Of particular interest to us is the formulation of the machine utilization function -both in continuous time and in discrete time domain. Fast heuristics are proposed with the relaxation of the machine capacity. A Lagrangian-based heuristic procedure is used to further reduce the duality gap. The performance of the heuristic and Lagrangian relaxation is compared with optimal solutions experimentally.