A Decentralized Scheduling Method for Flowshop Problems with Resource Constraints

In this paper, we propose a decentralized scheduling method for flowshop scheduling problems with resource constraints using the Lagrangian decomposition and coordination approach. When a flowshop scheduling problem with resource constraints is decomposed into machine-level sub-problems, the decomposed problem becomes very difficult to be solved to obtain the optimal solution even when the production sequence of operations is given. In this study, the decomposed sub-problems. are solved by a simulated annealing algorithm combined with dynamic programming. By decomposing the problem into single machine sub-problems, the changeover cost can easily be incorporated in the objective function. In order to reduce the computation time, a heuristic algorithm for calculating the starting times of operations is also proposed. The performance of the proposed method is compared with that of the simulated annealing method in which a schedule of the entire machine is successively improved. Numerical results have shown that the proposed method can generate better solutions than those generated by the conventional method.