Skip to main content
SpringerLink
Log in

A Hybrid Approach to Scheduling with Earliness and Tardiness Costs

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. Ajili and H. El Sakkout, LP probing for piecewise linear optimization in scheduling, in: Proceedings of the 3rd International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (2001) pp. 189–203.

  2. D. Applegate and W. Cook, A computational study of the job-shop scheduling problem, ORSA Journal on Computing 3 (1991) 149–156.

    Google Scholar 

  3. P. Baptiste, C. Le Pape and W. Nuijten, Constraint-Based Scheduling (Kluwer Academic, Dordrecht, 2001).

    Google Scholar 

  4. J.C. Beck, Texture measurements as a basis for heuristic commitment techniques in constraintdirected scheduling, Ph.D. thesis, University of Toronto (1999).

  5. J.C. Beck, A.J. Davenport, E.D. Davis and M.S. Fox, The ODO project: toward a unified basis for constraint-directed scheduling, Journal of Scheduling 1(2) (1998) 89–125.

    Google Scholar 

  6. J.C. Beck and M.S. Fox, Dynamic problem structure analysis as a basis for constraint-directed scheduling heuristics, Artificial Intelligence 117(1) (2000) 31–81.

    Google Scholar 

  7. J.C. Beck and P. Refalo, Combining local search and linear programming to solve earliness/tardiness scheduling problems, in: Proceedings of the Fourth International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR'02) (2002).

  8. H. Beringer and B. de Backer, Combinatorial problem solving in constraint logic programming with cooperating solvers, in: Logic Programming: Formal Methods and Practical Applications (Elsevier Science, Amsterdam, 1994).

    Google Scholar 

  9. J. Blazewicz, W. Domschke and E. Pesch, The job shop scheduling problem: conventional and new solution techniques, European Journal of Operational Research 93(1) (1996) 1–33.

    Google Scholar 

  10. A. Bockmayer and T. Kasper, Branch and infer: a unifying framework for integer and finite domain constraint programming, INFORMS Journal on Computing 10(3) (1998) 287–300.

    Google Scholar 

  11. A. Cesta, A. Oddi and S. Smith, A constraint-based method for project scheduling with time windows, Journal of Heuristics 8(1) (2002) 109–136.

    Google Scholar 

  12. J.V. den Akker, C. Hurkens and M. Savelsberg, Time-indexed formulations for machine scheduling problems: branch-and-cut, Technical Report COSOR 95–24, Eindhoven University of Technology (1995).

  13. J.V. den Akker, C. Hurkens and M. Savelsberg, Time-indexed formulations for machine scheduling problems: column generation, INFORMS Journal of Computing 12(2) (1998).

  14. H. El Sakkout and M. Wallace, Probe backtrack search for minimal perturbation in dynamic scheduling, Constraints 5(4) (2000) 359–388.

    Google Scholar 

  15. M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NPCompleteness (Freeman, New York, 1979).

    Google Scholar 

  16. J.N. Hooker, G. Ottosson, E.S. Thornsteinsson and H.-J. Kim, A scheme for unifying optimization and constraint satisfaction methods, Knowledge Engineering Review (2000).

  17. P. Laborie, Algorithms for propagating resource constraints in AI planning and scheduling: existing approaches and new results, in: Proceedings of the 6th European Conference on Planning (ECP'01) (2001).

  18. C. Le Pape, P. Couronné, D. Vergamini and V. Gosselin, Time-versus-capacity compromises in project scheduling, in: Proceedings of the Thirteenth Workshop of the UK Planning Special Interest Group (1994).

  19. T. Morton and D. Pentico, Heuristic Scheduling Systems (Wiley, New York, 1993).

    Google Scholar 

  20. W.P.M. Nuijten, Time and resource constrained scheduling: a constraint satisfaction approach, Ph.D. thesis, Department of Mathematics and Computing Science, Eindhoven University of Technology (1994).

  21. M. Queyranne and A. Schulz, Polyhedral approaches to machine scheduling problems, Technical Report 408/1994, Department of Mathematics, Technische Universitat Berlin, Germany (1994), revised in 1996.

    Google Scholar 

  22. P. Refalo, Tight cooperation and its application in piecewise linear optimization, in: Proceedings of Fifth International Conference on Principles and Practice of Constraint Programming (CP'99), Alexandria, VA (Springer, New York, 1999) pp. 369–383.

    Google Scholar 

  23. P. Refalo, Linear formulation of constraint programming models and hybrid solvers, in: Proceedings of Sixth International Conference on Principles and Practice of Constraint Programming (CP 2000), Singapore (Springer, Berlin, 2000) pp. 369–383.

    Google Scholar 

  24. R. Rodosek and M. Wallace, A generic model and hybrid algorithm for hoist scheduling problems, in: Proceedings of the Fourth International Conference on Principles and Practice of Constraint Programming (CP'98), Pisa, Italy, Lecture Notes in Computer Science, Vol. 1520 (Springer, Berlin, 1998) pp. 385–399.

    Google Scholar 

  25. Scheduler, ILOG Scheduler 5.2 user's manual and reference manual, ILOG, SA (2001).

  26. S.F. Smith and C.C. Cheng, Slack-based heuristics for constraint satisfaction scheduling, in: Proceedings of the Eleventh National Conference on Artificial Intelligence (AAAI-93) (1993) pp. 139–144.

  27. F. Sourd, Study about solving disjunctive scheduling problems, Ph.D. thesis, Université Paris VI (2000).

  28. E. Taillard, Benchmarks for basic scheduling problems, European Journal of Operational Research 64 (1993) 278–285.

    Google Scholar 

  29. M. Vazquez and L.D.Whitley, A comparision of genetic algorithms for the dynamic job shop scheduling problem, in: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2000) (Morgan Kaufmann, San Francisco, CA, 2000) pp. 1011–1018.

    Google Scholar 

  30. J.Watson, L. Barbulescu, A. Howe and L. Whitley, Algorithms performance and problem structure for flow-shop scheduling, in: Proceedings of the Sixteenth National Conference on Artificial Intelligence (AAAI-99) (1999) pp. 688–695.

  31. J.-P.Watson, J. Beck, A. Howe and L. Whitley, Problem difficulty for tabu search in job-shop scheduling, Artificial Intelligence, in press (2002).

Download references

Author information

Authors and Affiliations

  1. Cork Constraint Computation Centre, University College Cork, Cork, Ireland

    J. Christopher Beck

  2. ILOG, SA, Les Taissounières, 1681, route des Dolines, Sophia-Antipolis, 06560, Valbonne, France

    Philippe Refalo

Authors
  1. J. Christopher Beck
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Philippe Refalo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beck, J.C., Refalo, P. A Hybrid Approach to Scheduling with Earliness and Tardiness Costs. Annals of Operations Research 118, 49–71 (2003). https://doi.org/10.1023/A:1021849405707

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021849405707

Search

Navigation