Exact resolution of the one-machine sequencing problem with no machine idle time

Authors:
Jacques Carlier;Fatma Hermès;Aziz Moukrim;Khaled Ghédira
Affiliations:
Université de Technologie de Compiègne, Centre de Recherches de Royallieu, BP 20529, 60205 Compiègne cedex, France;Faculté des Sciences Mathématiques, Physiques et Naturelles de Tunis, Campus Universitaire, 1060 Tunis, Tunisia;Université de Technologie de Compiègne, Centre de Recherches de Royallieu, BP 20529, 60205 Compiègne cedex, France;Institut Supérieur de Gestion de Tunis, 41, rue de la Liberté, Bouchoucha, 2000 Bardo, Tunisia
Venue:
Computers and Industrial Engineering
Year:
2010

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Abstract

This paper investigates the one-machine sequencing problem in a workshop where the machine has to satisfy the no-idle constraint, that is, the machine must process jobs without interruption. The objective is to minimize the makespan. Each job has a release date for which it is available for processing on the machine and a delivery time during which it must remain in the system after being processed by the machine. This problem has been studied without adding the no-idle constraint. It is solved in polynomial time, when the preemption of jobs is allowed, applying Jackson's rule. But, when the preemption of jobs is not allowed, it becomes strongly NP-hard. Although, it can be solved in a very short time using Carlier's branch and bound algorithm. Below, we propose to adapt Carlier's branch and bound method in order to calculate an optimal nonpreemptive schedule for the problem when adding the no-idle constraint.