Parallel machine scheduling with nested processing set restrictions

Document Type

Article

Publication Date

7-16-2010

Abstract

We consider the problem of scheduling a set of n independent jobs on m parallel machines, where each job can only be scheduled on a subset of machines called its processing set. The machines are linearly ordered, and the processing set of job j is given by two machine indexes aj and bj; i.e., job j can only be scheduled on machines aj, aj + 1, ..., bj. Two distinct processing sets are either nested or disjoint. Preemption is not allowed. Our goal is to minimize the makespan. It is known that the problem is strongly NP-hard and that there is a list-type algorithm with a worst-case bound of 2 - 1 / m. In this paper we give an improved algorithm with a worst-case bound of 7/4. For two and three machines, the algorithm gives a better worst-case bound of 5/4 and 3/2, respectively. © 2009 Elsevier B.V. All rights reserved.

Identifier

71649097955 (Scopus)

Publication Title

European Journal of Operational Research

External Full Text Location

https://doi.org/10.1016/j.ejor.2009.10.025

ISSN

03772217

First Page

229

Last Page

236

Issue

2

Volume

204

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