Annals of Operations Research

, Volume 118, Issue 1–4, pp 49–71 | Cite as

A Hybrid Approach to Scheduling with Earliness and Tardiness Costs

  • J. Christopher Beck
  • Philippe Refalo
Article

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.

constraints scheduling mixed integer programming hybrid algorithms linear programming 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [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.Google Scholar
  2. [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. [3]
    P. Baptiste, C. Le Pape and W. Nuijten, Constraint-Based Scheduling (Kluwer Academic, Dordrecht, 2001).Google Scholar
  4. [4]
    J.C. Beck, Texture measurements as a basis for heuristic commitment techniques in constraintdirected scheduling, Ph.D. thesis, University of Toronto (1999).Google Scholar
  5. [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. [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. [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).Google Scholar
  8. [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. [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. [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. [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. [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).Google Scholar
  13. [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).Google Scholar
  14. [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. [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. [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).Google Scholar
  17. [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).Google Scholar
  18. [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).Google Scholar
  19. [19]
    T. Morton and D. Pentico, Heuristic Scheduling Systems (Wiley, New York, 1993).Google Scholar
  20. [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).Google Scholar
  21. [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. [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. [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. [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. [25]
    Scheduler, ILOG Scheduler 5.2 user's manual and reference manual, ILOG, SA (2001).Google Scholar
  26. [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.Google Scholar
  27. [27]
    F. Sourd, Study about solving disjunctive scheduling problems, Ph.D. thesis, Université Paris VI (2000).Google Scholar
  28. [28]
    E. Taillard, Benchmarks for basic scheduling problems, European Journal of Operational Research 64 (1993) 278–285.Google Scholar
  29. [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. [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.Google Scholar
  31. [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).Google Scholar

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

Personalised recommendations