The item dependent stockingcost constraint
- 28 Downloads
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.
KeywordsStockingCost constraint Production planning Lot-sizing Scheduling Constraint programming Global constraint Optimization contraint Cost-based filtering
- 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.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.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.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.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.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.Harris, F.W. (1913). How many parts to make at once. Factory, The magazine of management, 10(2), 135–136.Google Scholar
- 13.Houndji, V.R., Schaus, P., Wolsey, L. Cp4pp: Constraint programming for production planning. https://bitbucket.org/ratheilesse/cp4pp.
- 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.Jans, R., & Degraeve, Z. (2006). Modeling industrial lot sizing problems: A review. International Journal of Production Research.Google Scholar
- 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.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
- 21.Pochet, Y., & Wolsey, L. (2005). Production planning by mixed integer programming. Springer.Google Scholar
- 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.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
- 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.Oscar Team (2012). Oscar: Scala in or https://bitbucket.org/oscarlib/oscar.
- 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.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