Single-machine scheduling with an availability constraint to minimize the weighted sum of the completion times

Authors:
Imed Kacem;Chengbin Chu;Ahmed Souissi
Affiliations:
Université de Technologie de Troyes, ICD, LOSI FRE CNRS 2848, 12 rue Marie Curie, BP 2060, Troyes, France;Université de Technologie de Troyes, ICD, LOSI FRE CNRS 2848, 12 rue Marie Curie, BP 2060, Troyes, France;Université de Technologie de Troyes, ICD, LOSI FRE CNRS 2848, 12 rue Marie Curie, BP 2060, Troyes, France
Venue:
Computers and Operations Research
Year:
2008

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Abstract

In this article, we consider a single-machine scheduling problem with one unavailability period, with the aim of minimizing the weighted sum of the completion times. We propose three exact methods for solving such a problem: a branch-and-bound method based on new properties and lower bounds, a mixed integer programming model, and a dynamic programming method. These methods were coded and tested on randomly generated instances, and their performances were analyzed. Our numerical experiments show that the branch-and-bound method and the dynamic programming method are complementary. Using these approaches, we are able to solve problems with up to 3000 jobs within a reasonable computation time.