Advertisement

Constraints

, Volume 24, Issue 2, pp 183–209 | Cite as

The item dependent stockingcost constraint

  • Vinasetan Ratheil HoundjiEmail author
  • Pierre Schaus
  • Laurence Wolsey
Article
  • 26 Downloads

Abstract

In a previous work we introduced a global StockingCost constraint to compute the total number of periods between the production periods and the due dates in a multi-order capacitated lot-sizing problem. Here we consider a more general case in which each order can have a different per period stocking cost and the goal is to minimise the total stocking cost. In addition the production capacity, limiting the number of orders produced in a given period, is allowed to vary over time. We propose an efficient filtering algorithm in O(n log n) where n is the number of orders to produce. On a variant of the capacitated lot-sizing problem, we demonstrate experimentally that our new filtering algorithm scales well and is competitive wrt the StockingCost constraint when the stocking cost is the same for all orders.

Keywords

StockingCost constraint Production planning Lot-sizing Scheduling Constraint programming Global constraint Optimization contraint Cost-based filtering 

Notes

References

  1. 1.
    Armentano, V.A., Franca, P.M., de Toledo, F.M.B. (1999). A network flow model for the capacitated lot-sizing problem. Omega, 27, 275–284.CrossRefGoogle Scholar
  2. 2.
    Barany, I., Roy, T.J.V., Wolsey, L.A. (1984). Strong formulations for multi-item capacitated lot sizing. Management Science, 30, 1255–1261.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Belvaux, G., & Wolsey, L.A. (2001). Modelling practical lot-sizing problems as mixed integer programs. Management Science, 47, 724–738.CrossRefzbMATHGoogle Scholar
  4. 4.
    Demassey, S., Pesant, G., Rousseau, L.M. (2006). A cost-regular based hybrid column generation approach. Constraints, 4(11), 315–333.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Drexl, A., & Kimms, A. (1997). Lot sizing and scheduling - survey and extensions. European Journal of Operational Research, 99, 221–235.CrossRefzbMATHGoogle Scholar
  6. 6.
    Ducomman, S., Cambazard, H., Penz, B. (2016). Alternative filtering for the weighted circuit constraint: Comparing lower bounds for the tsp and solving tsptw. In 13th AAAI conference on artificial intelligence.Google Scholar
  7. 7.
    Focacci, F., Lodi, A., Milano, M. (1999). Cost-based domain filtering. In Principles and practice of constraint programming–CP’99 (pp. 189–203). Springer.Google Scholar
  8. 8.
    Gay, S., Hartert, R., Lecoutre, C., Schaus, P. (2015). Conflict ordering search for scheduling problems. In Principles and practice of constraint programming - CP 2015 (pp. 144–148). Springer.Google Scholar
  9. 9.
    German, G., Cambazard, H., Gayon, J.P., Penz, B. (2015). Une contrainte globale pour le lot sizing. In Journée francophone de la programation par contraintes - JFPC 2015 (pp. 118–127).Google Scholar
  10. 10.
    Ghomi, S.M.T.F., & Hashemin, S.S. (2001). An analytical method for single level-constrained resources production problem with constant set-up cost. Iranian Journal of Science and Technology, 26(B1), 69–82.Google Scholar
  11. 11.
    Gicquel, C. (2008). Mip models and exact methods for the discrete lot-sizing and scheduling problem with sequence-dependent changeover costs and times. Paris: Ph.D. thesis, Ecole centrale.Google Scholar
  12. 12.
    Harris, F.W. (1913). How many parts to make at once. Factory, The magazine of management, 10(2), 135–136.Google Scholar
  13. 13.
    Houndji, V.R., Schaus, P., Wolsey, L. Cp4pp: Constraint programming for production planning. https://bitbucket.org/ratheilesse/cp4pp.
  14. 14.
    Houndji, V.R., Schaus, P., Wolsey, L., Deville, Y. (2014). The stockingcost constraint. In Principles and practice of constraint programming–CP 2014 (pp. 382–397). Springer.Google Scholar
  15. 15.
    Jans, R., & Degraeve, Z. (2006). Modeling industrial lot sizing problems: A review. International Journal of Production Research.Google Scholar
  16. 16.
    Karimi, B., Ghomi, S.M.T.F., Wilson, J. (2003). The capacitated lot sizing problem: a review of models. Omega, The international Journal of Management Science, 31, 365–378.CrossRefGoogle Scholar
  17. 17.
    Leung, J.M.Y., Magnanti, T.L., Vachani, R. (1989). Facets and algorithms for capacitated lot sizing. Mathematical Programming, 45, 331–359.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    López-Ortiz, A., Quimper, C.G., Tromp, J., van Beek, P. (2003). A fast and simple algorithm for bounds consistency of the alldifferent constraint. In International joint conference on artificial intelligence – IJCAI03.Google Scholar
  19. 19.
    Pesant, G. (2004). A regular language membership constraint for finite sequences of variables. In International conference on principles and practice of constraint programming (pp. 482–495). Springer.Google Scholar
  20. 20.
    Pesant, G., Gendreau, M., Potvin, J.Y., Rousseau, J.M. (1998). An exact constraint logic programming algorithm for the traveling salesman problem with time windows. Transportation Science, 32(1), 12–29.CrossRefzbMATHGoogle Scholar
  21. 21.
    Pochet, Y., & Wolsey, L. (2005). Production planning by mixed integer programming. Springer.Google Scholar
  22. 22.
    Quimper, C.G., Van Beek, P., López-Ortiz, A., Golynski, A., Sadjad, S.B. (2003). An efficient bounds consistency algorithm for the global cardinality constraint. In Principles and practice of constraint programming–CP 2003 (pp. 600–614). Springer.Google Scholar
  23. 23.
    Régin, J.C. (1996). Generalized arc consistency for global cardinality constraint. In Proceedings of the 13th national conference on artificial intelligence-Volume 1 (pp. 209–215). AAAI Press.Google Scholar
  24. 24.
    Régin, J.C. (2002). Cost-based arc consistency for global cardinality constraints. Constraints, 7(3–4), 387–405.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Shaw, P. (1998). Using constraint programming and local search methods to solve vehicle routing problems. In International conference on principles and practice of constraint programming (pp. 417–431). Springer.Google Scholar
  26. 26.
    Oscar Team (2012). Oscar: Scala in or https://bitbucket.org/oscarlib/oscar.
  27. 27.
    Ullah, H., & Parveen, S. (2010). A literature review on inventory lot sizing problems. Global Journal of Researches in Engineering, 10, 21–36.Google Scholar
  28. 28.
    Van Cauwelaert, S., Lombardi, M., Schaus, P. (2015). Understanding the potential of propagators. In Integration of AI and OR techniques in constraint programming for combinatorial optimization problems - CPAIOR 2015 (pp. 427–436). Springer.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut de Formation et de Recherche en Informatique (IFRI)Université d’Abomey-Calavi (UAC)Abomey-CalaviBenin
  2. 2.Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM)Université catholique de Louvain (UCL)Louvain la NeuveBelgium
  3. 3.Institute for Multidisciplinary Research in Quantitative Modelling and Analysis (IMMAQ)Université catholique de Louvain (UCL)Louvain la NeuveBelgium

Personalised recommendations