A scheduling in flexible flow shop problem with unrelated parallel machines and sequence-dependent setup times

Abstract

To study a scheduling problem of flexible flow shop, where at least one production stage is made up of unrelated parallel machines, and setup times are sequence- and machine-dependent. The objective is to find a schedule that minimizes the makespan and the number of tardy jobs in a static scheduling environment. For this problem, a 0-1 mixed integer programming is formulated. The model is, however, a combinatorial optimization problem which is too difficult to be solved for large-sized problems, and hence, a heuristic is developed to obtain good solutions in reasonable time. The heuristic has three phases. The first phase uses a constructive algorithm. It starts with the generation of the operating time representative for each operation. Then, it uses a dispatching rule or a simple flow shop makespan heuristic to determine an initial solution. The improvement algorithm based on shift moves or pairwise interchanges of jobs is applied to improve the solution in the second phase. After that, a metaheuristic is used to refine the solution in the final phase. Several well-known heuristics are tested in each phase. The performances of the heuristics are compared to one another based on a set of test problems with up to 50 jobs and 20 stages and with an optimal solution for small-sized problems. The computational results indicate that the Nawaz, Enscore, and Ham (NEH) algorithm is most suitable for determining the initial solution, the all-pairwise-interchange approach is good for improving the solution, and the simulated annealing algorithm is best metaheuristic for refining the solution.