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

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

Chen, Bo, Potts, Chris N. and Strusevich, Vitaly A. (1998) Approximation algorithms for two-machine flow shop scheduling with batch setup times. Mathematical Programming, 82 (1-2). pp. 255-271. ISSN 0025-5610 (Print), 1436-4646 (Online) (doi:10.1007/BF01585875)

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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.

Item Type: Article
Additional Information: [1] This is the official journal of the Mathematical Optimization Society - now published by Springer-Verlag.
Uncontrolled Keywords: scheduling, flow shop, batch setup times, approximation algorithm, performance analysis
Subjects: Q Science > QA Mathematics
Pre-2014 Departments: School of Computing & Mathematical Sciences
School of Computing & Mathematical Sciences > Department of Mathematical Sciences
School of Computing & Mathematical Sciences > Statistics & Operational Research Group
Last Modified: 14 Oct 2016 08:59
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/102

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