Computers & Operations Research 32 (2005) 2905 – 2917 www.elsevier.com/locate/dsw An exact approach to early/tardy scheduling with release dates Jorge M.S. Valente * , Rui A.F.S. Alves Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-464 Porto, Portugal Available online 9 June 2004 Abstract In this paper, we consider the single machine earliness/tardiness scheduling problem with dierent release dates and no unforced idle time. The problem is decomposed into weighted earliness and weighted tardiness subproblems. Lower bounding procedures are proposed for each of these subproblems, and the lower bound for the original problem is the sum of the lower bounds for the two subproblems. The lower bounds and several versions of a branch-and-bound algorithm are then tested on a set of randomly generated problems, and instances with up to 30 jobs are solved to optimality. To the best of our knowledge, this is the rst exact approach for the early/tardy scheduling problem with release dates and no unforced idle time. ? 2004 Elsevier Ltd. All rights reserved. Keywords: Scheduling; Early/tardy; Release dates; Branch-and-bound 1. Introduction In this paper, we consider a single-machine scheduling problem with early and tardy costs, dierent release dates and no unforced machine idle time. Scheduling models with both earliness and tardiness costs are compatible with the philosophy of just-in-time production, which emphasizes producing goods only when they are needed, since jobs are scheduled to complete as close as possible to their due dates. It is assumed that no unforced machine idle time is allowed, and therefore the machine is only idle when no jobs are available for processing. This assumption represents a type of production environment where the machine idleness cost is higher than the cost incurred by completing a job early, or the machine is heavily loaded, so it must be kept running in order to satisfy the demand. Korman [1] and Landis [2] give some specic examples of production settings with these characteristics. The existence of dierent release dates is compatible with the assumption of no unforced idle time, as long as the forced idle time caused by the distinct release dates is inexistent * Corresponding author. Fax: +351-22-550-50-50. E-mail address: jvalente@fep.up.pt (J.M.S. Valente). 0305-0548/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2004.04.016