A three-machine permutation flow-shop problem with minimum makespan on the second machine

• Published in: The Journal of the Operational Research Society Vol. 57; no. 4; pp. 460 - 468
• Main Authors: Yanai, S, Fujie, T
• Format: Journal Article
• Language: English
• Published: Basingstoke Taylor & Francis 01.04.2006; Palgrave Macmillan Press; Palgrave; Taylor & Francis Ltd
• Subjects: Algorithms; Applied sciences; branch-and-bound algorithm; Exact sciences and technology; Experiments; flow-shop scheduling; Heuristics; hierarchical criteria; Integer programming; Integers; Job shops; Manufacturing; Mathematical permutation; Mathematical programming; multicriteria scheduling; Objective functions; Operational research and scientific management; Operational research. Management science; Operations research; Optimal solutions; Polynomials; Production scheduling; Ratios; Schedules; Scheduling; Scheduling, sequencing; Simulated annealing; Studies; Theoretical Papers; Branching; hierarchical criteria; Multicriteria analysis; Branch and bound method; Permutation; Dominance; Mixed integer programming; Scheduling; Makespan; Polynomial time; multicriteria scheduling; Minimum time; flow-shop scheduling; branch-and-bound algorithm; NP hard problem; Flow shop; Objective function; Completion time
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/palgrave.jors.2602014

In this paper, we consider a three-machine permutation flow-shop scheduling problem where the criterion is to minimize the total completion time without idle times subject to the minimum makespan on the second machine. This problem is NP-hard while each of the objective functions alone can be optimized in polynomial time. We develop a branch-and-bound algorithm with effective branching rules and dominance properties which help to reduce the search space. By our computational experiments, the branch-and-bound algorithm is comparable to a recent mixed integer programming solver and, for some kinds of problem instances, the branch-and-bound algorithm outperforms the solver. On the other hand, the computational result would indicate that the hierarchical scheduling problems are essentially hard in both theoretical and computational points of view.