Distributed Flow Shop Scheduling Problem With Learning Effect, Setups, Non-Identical Factories, and Eligibility Constraints

Abstract

In the flow shop scheduling, the route of each job is the same, and the order of the jobs on the machines is determined. In the distributed flow shop scheduling (DFSS) problem, on the other hand, the assignment of jobs to factories is carried out in addition to the determination of the order of the jobs. Therefore, the DFSS problem is both an assignment and a sequencing problem. This study considers machine factory-dependent setup times, non-identical factories, position-based learning effects on processing times and setup times, and factory eligibility constraints for the DFSS problem. The study is the first to consider all these real-life features encountered in the DFSS problem. The addressed problem is defined considering the scheduling problem of Enterprise Resource Planning (ERP) projects. A mathematical model is proposed for the solution of the problem. Since the problem is NP-hard, a multi-start iterative tabu search (ITS) algorithm is proposed to solve large-scale problems. An encoding schema, decoding algorithm, and multi-start strategy are proposed to solve the problem with the ITS algorithm. The parameters of the proposed algorithm are determined by the Taguchi experimental design method. The success of the proposed multi-start ITS algorithm is demonstrated by comparing it with the state-of-the-art genetic algorithm (GA), simulated annealing (SA) algorithm, and tabu search (TS) algorithm through test problems and a real-world application. Statistical analysis is performed to determine the performance of the proposed heuristic. As a result, the proposed heuristic algorithm is found to be more successful than other algorithms in the literature.