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Hybrid MIP-CP Techniques to Solve a Multi-Machine Assignment and Scheduling Problem in Xpress-CP

  • Alkis Vazacopoulos
  • Nitin Verma
Part of the Applied Optimization book series (APOP, volume 98)

Abstract

In this paper we introduce Xpress-CP—a Constraint Programming tool-and demonstrate its modeling and solving capabilities. We consider the multi-machine assignment and scheduling problem (Hooker et al. (1999)), where jobs, with release dates and deadlines, have to be processed on parallel unrelated machines (where processing times depend on machine assignment). Given a job/machine assignment cost matrix, the objective is to minimize the total cost while keeping all machine schedules feasible. We show that by deriving the benefits of MIP and CP techniques simultaneously this problem can be modeled and solved efficiently in a hybrid fashion using Xpress Optimization suite.

Keywords

Schedule Problem Assignment Problem Constraint Programming Master Problem Total Processing Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aggoun, A. and Vazacopoulos, A. 2004. Solving Sports Scheduling and Time tabling Problems with Constraint Programming, in Economics, Management and Optimization in Sports, Edited by S. Butenko, J. Gil-Lafuente and P.M. Pardalos, Springer.Google Scholar
  2. Baptiste, P., Le Pape, C. and Nuijten, W. 2001. Constraint Based Scheduling. Kluwer.Google Scholar
  3. Bockmayr, A. and Kasper, T. 2003. Branch-and-infer: A framework for combining CP and IP. In Constraint and Integer Programming (Ed. M. Milano), Chapter 3, 59–87, Kluwer.Google Scholar
  4. Bockmayr, A. and Hooker, J.N. 2003. Constraint programming. In Handbooks in Operations Research and Management Science: Discrete Optimization (Eds. K. Aardal, G. Nemhauser, and R. Weismantel), Elsevier, To appear.Google Scholar
  5. Bockmayr, A. and Pisaruk, N. 2003. Detecting Infeasibility and Generating Cuts for MIP using CP. 5th International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR’03, Montreal, May 2003.Google Scholar
  6. Brucker, P. 2001. Scheduling Algorithms. Third Edition, Springer.Google Scholar
  7. Carlier, J. and Pinson., E. 1990. A Practical Use of Jackson’s Preemptive Schedule for Solving the Job-Shop Problem. Annals of Operations Research 26, 269–287.MathSciNetzbMATHGoogle Scholar
  8. Colombani, Y and Heipcke, S. 2002. Mosel: An Overview. May 2002, available at http://www.dashoptimization.com/home/downloads/pdf/mosel.pdf.Google Scholar
  9. Easton, K., Nemhauser, G. and Trick, M. 2003. CP Based Branch-and-Price. In Constraint and Integer Programming (Ed. M. Milano), Chapter 7, 207–231, Kluwer.Google Scholar
  10. Hooker, J.N., Ottosson, G., Thorsteinsson, E.S. and Kim, H.J. 1999. On integrating constraint propagation and linear programming for combinatorial optimization. Proceedings of the Sixteenth National Conference on Artificial Intelligence (AAAI-99), AAAI, The AAAI Press/MIT Press, Cambridge, MA. 136–141.Google Scholar
  11. Jain, V. and Grossmann, I.E. 2001. Algorithms for hybrid MIP/CP models for a class of optimization problems. INFORMS J. Computing, 13(4), 258–276, 2001.MathSciNetCrossRefGoogle Scholar
  12. Peter, B. 2001. Scheduling Algorithms. Springer Lehrbuch.Google Scholar
  13. Pritsker, A., Watters, L. and Wolfe, P. 1969. Multi-project scheduling with limited resources: a zero-one programming approach. Management Science, 16:93–108.CrossRefGoogle Scholar
  14. Pinedo, M. 1995. Scheduling: Theory, Algorithms and Systems. Prentice-Hall, NJ.zbMATHGoogle Scholar
  15. Pinedo, M. and Chao, X. 1998. Operations Scheduling with Applications in Manufacturing and services. McGraw-Hill/Irwin.Google Scholar
  16. Sadykov, R. and Wolsey, L. 2003. Integer programming and constraint programming in solving a multi-machine assignment scheduling problem with deadlines and release dates. CORE discussion paper, Nov 2003.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Alkis Vazacopoulos
    • 1
  • Nitin Verma
    • 1
  1. 1.Dash Optimization, IncEnglewood CliffsUSA

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