Mathematical Programming

, Volume 82, Issue 1–2, pp 255–271 | Cite as

Approximation algorithms for two-machine flow shop scheduling with batch setup times

  • Bo Chen
  • Chris N. Potts
  • Vitaly A. Strusevich
Article

Abstract

In many practical situations, batching of similar jobs to avoid setups is performed while constructing a schedule. This paper addresses the problem of non-preemptively scheduling independent jobs in a two-machine flow shop with the objective of minimizing the makespan. Jobs are grouped into batches. A sequence independent batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. Besides its practical interest, this problem is a direct generalization of the classical two-machine flow shop problem with no grouping of jobs, which can be solved optimally by Johnson's well-known algorithm. The problem under investigation is known to be NP-hard. We propose two O(n logn) time heuristic algorithms. The first heuristic, which creates a schedule with minimum total setup time by forcing all jobs in the same batch to be sequenced in adjacent positions, has a worst-case performance ratio of 3/2. By allowing each batch to be split into at most two sub-batches, a second heuristic is developed which has an improved worst-case performance ratio of 4/3. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

Keywords

Scheduling Flow shop Batch setup times Approximation algorithm Performance analysis 

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Copyright information

© The Mathematical Programming Society, Inc. 1998

Authors and Affiliations

  • Bo Chen
    • 1
  • Chris N. Potts
    • 2
  • Vitaly A. Strusevich
    • 3
  1. 1.Warwick Business SchoolUniversity of WarwickCoventryUK
  2. 2.Faculty of Mathematical StudiesUniversity of SouthamptonSouthamptonUK
  3. 3.School of Computing and Mathematical SciencesUniversity of GreenwichLondonUK

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