An Exact Method to Minimize the Number of Tardy Jobs in Single Machine Scheduling

Authors:
Stéphane Dauzère-Pérès;Marc Sevaux
Affiliations:
Ecole des Mines de Saint-Etienne, CMP Georges Charpak, Avenue des Anémones, Quartier Saint-Pierre, F-13541 Gardanne, France. Dauzere-Peres@emse.fr;University of Valenciennes, Dept. Production Systems, UMR CNRS 8530, LAMIH-SP, Mont-Houy, F-59313 Valenciennes Cedex, France. Marc.Sevaux@univ-valenciennes.fr
Venue:
Journal of Scheduling
Year:
2004

Citing 1
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Abstract

This paper considers the problem of scheduling n jobs on a single machine to minimize the number of tardy (or late) jobs. Each job has a release date, a processing time and a due date. The general case with non-equal release dates and different due dates is considered. Using new and efficient lower bounds and several dominance rules, a branch and bound scheme is proposed based on the definition of a master sequence, i.e. a sequence containing at least one optimal sequence. With this procedure, 95% of 140-job instances are optimally solved in a maximum of one-hour CPU time.