Exponential neighborhood search for a parallel machine scheduling problem

• Published in: Computers & operations research Vol. 35; no. 5; pp. 1697 - 1712
• Main Authors: Rios-Solis, Y.A., Sourd, F.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-05-2008; Elsevier Science; Pergamon Press Inc; Elsevier
• Subjects: Algorithms; Applied sciences; Computer Science; Dynamic programming; Earliness-tardiness penalties; Exact sciences and technology; Job shops; Large neighborhood search; Neighborhoods; Operational research and scientific management; Operational research. Management science; Parallel machine scheduling; Parallel processing; Polynomials; Production scheduling; Scheduling, sequencing; Studies; Earliness-tardiness penalties; Parallel machine scheduling; Dynamic programming; Large neighborhood search; Neighborhood search; NP hard problem; Task scheduling; Parallel machines; Scheduling; Polynomial method; Due date; Workload
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2006.10.008

We consider the parallel machine scheduling problem where jobs have different earliness-tardiness penalties and a restrictive common due date. This problem is NP-hard in the strong sense. In this paper we define an exponential size neighborhood for this problem and prove that finding the local minimum in it is an NP-hard problem. The main contribution of this paper is to propose a pseudo-polynomial algorithm that finds the best solution of the exponential neighborhood. Additionally, we present some computational results.