Annals of Operations Research

, Volume 118, Issue 1–4, pp 49–71

A Hybrid Approach to Scheduling with Earliness and Tardiness Costs

  • J. Christopher Beck
  • Philippe Refalo


A hybrid technique using constraint programming and linear programming is applied to the problem of scheduling with earliness and tardiness costs. The linear model maintains a set of relaxed optimal start times which are used to guide the constraint programming search heuristic. In addition, the constraint programming problem model employs the strong constraint propagation techniques responsible for many of the advances in constraint programming for scheduling in the past few years. Empirical results validate our approach and show, in particular, that creating and solving a subproblem containing only the activities with direct impact on the cost function and then using this solution in the main search, significantly increases the number of problems that can be solved to optimality while significantly decreasing the search time.

constraints scheduling mixed integer programming hybrid algorithms linear programming 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • J. Christopher Beck
    • 1
  • Philippe Refalo
    • 2
  1. 1.Cork Constraint Computation CentreUniversity College CorkCorkIreland
  2. 2.ILOG, SA, Les TaissounièresValbonneFrance

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