Abstract
An interesting class of production/inventory control problems considers a single product and a single stocking location, given a stochastic demand with a known non-stationary probability distribution. Under a widely-used control policy for this type of inventory system, the objective is to find the optimal number of replenishments, their timings and their respective order-up-to-levels that meet customer demands to a required service level. We extend a known CP approach for this problem using a cost-based filtering method. Our algorithm can solve to optimality instances of realistic size much more efficiently than previous approaches, often with no search effort at all.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Apt, K.: Principles of Constraint Programming. Cambridge University Press, Cambridge, UK (2003)
Askin, R.G.: A Procedure for Production Lot Sizing With Probabilistic Dynamic Demand. AIIE Transactions 13, 132–137 (1981)
Bellman, R.E.: Dynamic Programming. Princeton University Press, Princeton, NJ (1957)
Florian, M., Lenstra, J.K., Rinooy Kan, A.H.G.: Deterministic Production Planning: Algorithms and Complexity. Management Science 26(7), 669–679 (1980)
Bookbinder, J.H., Tan, J.Y.: Strategies for the Probabilistic Lot-Sizing Problem With Service-Level Constraints. Management Science 34, 1096–1108 (1988)
Brailsford, S.C., Potts, C.N., Smith, B.M.: Constraint Satisfaction Problems: Algorithms and Applications. European Journal of Operational Research 119, 557–581 (1999)
Fahle, T., Sellmann, M.: Cost-Based Filtering for the Constrained Knapsack Problem. Annals of Operations Research 115, 73–93 (2002)
Focacci, F., Lodi, A., Milano, M.: Cost-Based Domain Filtering. In: Jaffar, J. (ed.) Principles and Practice of Constraint Programming – CP’99. LNCS, vol. 1713, pp. 189–203. Springer, Heidelberg (1999)
Fortuin, L.: Five Popular Probability Density Functions: a Comparison in the Field of Stock-Control Models. Journal of the Operational Research Society 31(10), 937–942 (1980)
Gartska, S.J., Wets, R.J.-B.: On Decision Rules in Stochastic Programming. Mathematical Programming 7, 117–143 (1974)
Gupta, S.K., Sengupta, J.K.: Decision Rules in Production Planning Under Chance-Constrained Sales. Decision Sciences 8, 521–533 (1977)
Heady, R.B., Zhu, Z.: An Improved Implementation of the Wagner-Whitin Algorithm. Production and Operations Management 3(1) (1994)
Johnson, L.A., Montgomery, D.C.: Operations Research in Production Planning, Scheduling, and Inventory Control. Wiley, New York (1974)
Jussien, N., Debruyne, R., Boizumault, P.: Maintaining Arc-Consistency Within Dynamic Backtracking. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 249–261. Springer, Heidelberg (2000)
Laburthe, F. and the OCRE project team.: Choco: Implementing a CP Kernel. Bouygues e-Lab, France
Lustig, I.J., Puget, J.-F.: Program Does Not Equal Program: Constraint Programming and its Relationship to Mathematical Programming. Interfaces 31, 29–53 (2001)
Peterson, R., Silver, E., Pyke, D.F.: Inventory Management and Production Planning and Scheduling. John Wiley and Sons, New York (1998)
Porteus, E.L.: Foundations of Stochastic Inventory Theory. Stanford University Press, Stanford, CA (2002)
Sedgewick, R.: Algorithms. Addison-Wesley Publishing Company, Reading, Massachusetts (1983)
Silver, E.A.: Inventory Control Under a Probabilistic Time-Varying Demand Pattern. AIIE Transactions 10, 371–379 (1978)
Simchi-Levi, D., Simchi-Levi, E., Kaminsky, P.: Designing and Managing the Supply Chain. McGraw-Hill, New York (2000)
Tan, J.Y.: Heuristic for the Deterministic and Probabilistic Lot-Sizing Problems. Department of Management Sciences, University of Waterloo (1983)
Tarim, S.A., Kingsman, B.G.: The Stochastic Dynamic Production/Inventory Lot-Sizing Problem With Service-Level Constraints. International Journal of Production Economics 88, 105–119 (2004)
Tarim, S.A., Smith, B.: Constraint Programming for Computing Non-Stationary (R,S) Inventory Policies. European Journal of Operational Research (to appear)
Tarim, S.A., Manandhar, S., Walsh, T.: Stochastic Constraint Programming: A Scenario-Based Approach. Constraints 11, 53–80 (2006)
Vajda, S.: Probabilistic Programming. Academic Press, New York (1972)
Wagner, H.M., Whitin, T.M.: Dynamic Version of the Economic Lot Size Model. Management Science 5, 89–96 (1958)
Zipkin, P.H.: Foundations of Inventory Management. McGraw-Hill/Irwin, Boston, Mass (2000)
Silver, E.A., Pyke, D.F., Peterson, R.: Inventory Management and Production Planning and Scheduling. John-Wiley and Sons, New York (1998)
Wemmerlov, U.: The Ubiquitous EOQ - Its Relation to Discrete Lot Sizing Heuristics. Internat. J. of Operations and Production Management 1, 161–179 (1981)
Van Hentenryck, P., Carillon, J.-P.: Generality vs. specificity: an experience with AI and OR techniques. In: AAAI 1988. National Conference on Artificial Intelligence (1988)
Charnes, A., Cooper, W.W.: Chance-Constrainted Programming. Management Science 6(1), 73–79 (1959)
Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer, New York (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tarim, S.A., Hnich, B., Rossi, R., Prestwich, S. (2007). Cost-Based Filtering for Stochastic Inventory Control. In: Azevedo, F., Barahona, P., Fages, F., Rossi, F. (eds) Recent Advances in Constraints. CSCLP 2006. Lecture Notes in Computer Science(), vol 4651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73817-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-73817-6_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73816-9
Online ISBN: 978-3-540-73817-6
eBook Packages: Computer ScienceComputer Science (R0)