The One-Machine Problem with Earliness and Tardiness Penalties

Authors:
Francis Sourd;Safia Kedad-Sidhoum
Affiliations:
Laboratoire LIP6, 4, place Jussieu, 75 252 Paris, Cedex 05, France;Laboratoire LIP6, 4, place Jussieu, 75 252 Paris, Cedex 05, France/ E-mail: Safia.Kedad-Sidhoum@lip6.fr
Venue:
Journal of Scheduling
Year:
2003

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Abstract

We address the one-machine problem in which the jobs have distinct due dates, earliness costs, and tardiness costs. In order to determine the minimal cost of such a problem, a new lower bound is proposed. It is based on the decomposition of each job in unary operations that are then assigned to the time slots, which gives a preemptive schedule. Assignment costs are defined so that the minimum assignment cost is a valid lower bound. A branch-and-bound algorithm based on this lower bound and on some new dominance rules is experimentally tested.