The Permutation Flow Shop Scheduling Problem with Human Resources: MILP Models, Decoding Procedures, NEH-Based Heuristics, and an Iterated Greedy Algorithm

Abstract

In this paper, we address the permutation flow shop scheduling problem with sequence-dependent and non-anticipatory setup times. These setups are performed or supervised by multiple servers, which are renewable secondary resources (typically human resources). Despite the real applications of this kind of human supervision and the growing attention paid in the scheduling literature, we are not aware of any previous study on the problem under consideration. To cover this gap, we start theoretically addressing the problem by: proposing three mixed-integer linear programming models to find optimal solutions in the problem; and proposing different decoding procedures to code solutions in approximated procedures. After that, the best decoding procedure is used to propose a new mechanism that generates 896 different dispatching rules, combining different measures, indicators, and sorting criteria. All these dispatching rules are embedded in the traditional NEH algorithm. Finally, an iterated greedy algorithm is proposed to find near-optimal solutions. By doing so, we provide academics and practitioners with efficient methods that can be used to obtain exact solutions of the problem; applied to quickly schedule jobs and react under changes; used for initialisation or embedded in more advanced algorithms; and/or easily updated and implemented in real manufacturing scenarios.