Constraints

pp 1–14 | Cite as

Modeling uncertainties with chance constraints

Article
  • 23 Downloads
Part of the following topical collections:
  1. Topical Collection on 20th Anniversary Issue

Abstract

Chance constraints are a major modeling tool for problems under uncertainty. We summarize the basic modeling ingredients of uncertain combinatorial problems and show how the Stochastic Constraint Satisfaction Problems formalism is able to support high-level declarative constructs that allow for ease of modeling of such problems in general. Then, we outline the different propagation methods for chance constraints. Finally, we identify some modeling subtleties that might arise when modeling with chance constraints.

Keywords

Uncertainty Chance constraints Stochastic constraint satisfaction problems 

References

  1. 1.
    Balafoutis, T., & Stergiou, K. (2006). Algorithms for stochastic csps. In Principles and Practice of Constraint Programming, CP 2006 (pp. 44–58): Proceedings.Google Scholar
  2. 2.
    Bessiere, C., Hebrard, E., Hnich, B., Walsh, T. (2007). The complexity of reasoning with global constraints. Constraints, 12(2), 239–259.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bessiėre, C., & Van Hentenryck, P. (2003). To be or not to be ... a global constraint. In Principles and Practice of Constraint Programming - CP 2003, 9th International Conference, CP 2003 (pp. 789–794). Kinsale: Proceedings.Google Scholar
  4. 4.
    Birge, J.R., & Louveaux, F. (1997). Introduction to Stochastic Programming. New York: Springer Verlag.MATHGoogle Scholar
  5. 5.
    Brown, K.N., & Miguel, I. (2006). Uncertainty and change. In Rossi, F., van Beek, P., Walsh, T. (Eds.) Handbook of Constraint Programming, chapter 21: Elsevier.Google Scholar
  6. 6.
    Charnes, A., & Cooper, W.W. (1959). Chance-constrainted programming. Management Science, 6(1), 73–79.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Cire, A.A., Coban, E., van Hoeve, W.-J. (2012). Flow-Based Combinatorial Chance Constraints, (pp. 129–145). Berlin: Springer Berlin Heidelberg.Google Scholar
  8. 8.
    Fargier, H., Lang, J., Martin-Clouaire, R., Schiex, T. (1995). A constraint satisfaction framework for decision under uncertainty. In Besnard, P., & Hanks, S. (Eds.) UAI ’95: Proceedings of the Eleventh Annual Conference on Uncertainty in Artificial Intelligence (pp. 167–174). Montreal: Morgan Kaufmann.Google Scholar
  9. 9.
    Hnich, B., Rossi, R., Tarim, S.A., Prestwich, S. (2011). A survey on CP-AI-OR hybrids for decision making under uncertainty. In van Hentenryck, P., & Milano, M. (Eds.) Hybrid Optimization, volume 45 of Springer Optimization and Its Applications, chapter 7 (pp. 227–270). New York: Springer.Google Scholar
  10. 10.
    Hnich, B., Rossi, R., Armagan Tarim, S., Prestwich, S.D. (2012). Filtering algorithms for global chance constraints. Artificial Intelligence, 189, 69–94.MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Kall, P., & Wallace, S.W. (1994). Stochastic Programming. Hoboken: Wiley.MATHGoogle Scholar
  12. 12.
    Regin, J.-C. (1994). A filtering algorithm for constraints of difference in csps. In Proceedings of the 12th National Conference on Artifcial Intelligence, (Vol. 1 pp. 362–367). Seattle: AAAI Press.Google Scholar
  13. 13.
    Rossi, R., Tarim, S.A., Bollapragada, R. (2012). Constraint-based local search for computing non-stationary replenishment cycle policy under stochastic lead-times. INFORMS Journal on Computing, 24(1), 66–80.MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Rossi, R., Tarim, S.A., Hnich, B., Prestwich, S. (2008). A global chance-constraint for stochastic inventory systems under service level constraints. Constraints, 13(4), 490–517.MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Rossi, R., Tarim, S.A., Hnich, B., Prestwich, S.D. (2008). Cost-based domain filtering for stochastic constraint programming. In Stuckey, P. J. (Ed.) Principles and Practice of Constraint Programming, CP 2008, Proceedings, volume 5202 of LNCS (pp. 235–250): Springer.Google Scholar
  16. 16.
    Rossi, R., Tarim, S.A., Hnich, B., Prestwich, S. (2010). Computing replenishment cycle policy under non-stationary stochastic lead time. International Journal of Production Economics, 127(1), 180–189.CrossRefGoogle Scholar
  17. 17.
    Rossi, R., Hnich, B., Armagan Tarim, S., Prestwich, S. (2015). Confidence-based reasoning in stochastic constraint programming. Artificial Intelligence, 228, 129–152.MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Sahinidis, N.V. (2004). Optimization under uncertainty: State-of-the-art and opportunities. Computers and Chemical Engineering, 28, 971–983.CrossRefGoogle Scholar
  19. 19.
    Tarim, S.A., Hnich, B., Prestwich, S.D., Rossi, R. (2008). Finding reliable solution: Event-driven probabilistic constraint programming. Annals of Operations Research.Google Scholar
  20. 20.
    Tarim, S.A., Hnich, B., Rossi, R., Prestwich, S. (2009). Cost-based filtering techniques for stochastic inventory control under service level constraints. Constraints, 14(2), 137–176.MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Tarim, S.A., Manandhar, S., Walsh, T. (2006). Stochastic constraint programming: A scenario-based approach. Constraints, 11(1), 53–80.MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Walsh, T. (2002). Stochastic constraint programming. In European Conference on Artificial Intelligence, ECAI’2002 (pp. 111–115): Proceedings.Google Scholar
  23. 23.
    Zghidi, I. (2011). Computing optimal (s,s) policy parameters under service level constraints: A stochastic constraint programming approach. Tunisia: Master’s thesis, Sfax University.Google Scholar
  24. 24.
    Zghidi, I. (2016). Towards Statistical Consistency for Stochastic Constraint Programming. Tunisia: PhD thesis, University of Sfax.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.MODILS Research Lab, FSEGSSfax UniversitySfaxTunisia
  2. 2.CES, ENISSfax UniversitySfaxTunisia

Personalised recommendations