The stage shop scheduling problem: Lower bound and metaheuristic

Abstract

Remarkable efforts have been made to develop the job shop scheduling problem up to now. As a novel generalization, the stage shop can be defined as an environment in which each job is composed of some stages and each stage may include one operation or more. A stage can be defined as a subset of operations of a job such that these operations can be done in any arbitrary relative order while the stages should be processed in a predetermined order. In other words, the operations of a stage cannot be initiated until all operations of the prior stage are completed. In this paper, an innovative lower bound by solving the preemptive open shop (using a linear programming model in polynomial time) is devised for the makespan in a stage shop problem. In addition, three metaheuristics, namely firey (FF), Harmony Search (HS), and Water Wave Optimization (WWO) algorithms, are applied to the problem. The results of the algorithms are compared with each other with the proposed lower bound and a commercial solver.