# An open shop scheduling problem with a non-bottleneck machine

Strusevich, V.A. and Hall, L.A.
(1997)
*An open shop scheduling problem with a non-bottleneck
machine.*
Operations Research Letters, 21 (1).
pp. 11-18.
ISSN 0167-6377
(doi:10.1016/S0167-6377(97)00030-8)

## Abstract

This paper considers the problem of processing n jobs in a two-machine non-preemptive open shop to minimize the makespan, i.e., the maximum completion time. One of the machines is assumed to be non-bottleneck. It is shown that, unlike its flow shop counterpart, the problem is NP-hard in the ordinary sense. On the other hand, the problem is shown to be solvable by a dynamic programming algorithm that requires pseudopolynomial time. The latter algorithm can be converted into a fully polynomial approximation scheme that runs in time. An O(n log n) approximation algorithm is also designed whi finds a schedule with makespan at most 5/4 times the optimal value, and this bound is tight.

Item Type: | Article |
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Additional Information: | [1] Available online: 10 June 1998. [2] Published in print: August 1997. |

Uncontrolled Keywords: | open shop, complexity, dynamic programming, fully polynomial approximation scheme, worst-case analysis, approximation |

Subjects: | Q Science > QA Mathematics > QA76 Computer software |

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 |

Related URLs: | |

Last Modified: | 14 Oct 2016 09:00 |

URI: | http://gala.gre.ac.uk/id/eprint/394 |

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