Bi-criteria scheduling problems: Number of tardy jobs and maximum weighted tardiness

Document Type

Article

Publication Date

2-16-2007

Abstract

Consider a single machine and a set of n jobs that are available for processing at time 0. Job j has a processing time pj, a due date dj and a weight wj. We consider bi-criteria scheduling problems involving the maximum weighted tardiness and the number of tardy jobs. We give NP-hardness proofs for the scheduling problems when either one of the two criteria is the primary criterion and the other one is the secondary criterion. These results answer two open questions posed by Lee and Vairaktarakis in 1993. We consider complexity relationships between the various problems, give polynomial-time algorithms for some special cases, and propose fast heuristics for the general case. The effectiveness of the heuristics is measured by empirical study. Our results show that one heuristic performs extremely well compared to optimal solutions. © 2006 Elsevier B.V. All rights reserved.

Identifier

33750471582 (Scopus)

Publication Title

European Journal of Operational Research

External Full Text Location

https://doi.org/10.1016/j.ejor.2005.06.067

ISSN

03772217

First Page

116

Last Page

134

Issue

1

Volume

177

Grant

SBR-421350

Fund Ref

National Science Foundation

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