Optimal scheduling on parallel machines for a new order class

Authors:
Aziz Moukrim
Affiliations:
Université de Clermont II, LIMOS, Complexe Scientifique des Cézeaux, 63177 Aubière Cedex, France
Venue:
Operations Research Letters
Year:
1999

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Abstract

This paper addresses the problem of scheduling n unit length tasks on m identical machines under certain precedence constraints. The aim is to compute minimal length nonpreemptive schedules. We introduce a new order class which contains properly two rich families of precedence graphs: interval orders and a subclass of the class of series parallel orders. We present a linear time algorithm to find an optimal schedule for this new order class on any number of machines.