Optimal (R,S) Inventory Policy Under Non-Stationary Demand

This prototype computes optimal replenishment periods and corresponding order-up-to-levels under the assumption that the demand is non-stationary, and we incur fixed ordering cost and linear holding cost under a service level constraint.

The prototype is limited to 15 periods.

Fixed ordering cost		the fixed procurement cost that is incurred each time a replenishment order is placed
Variable holding cost		the linear holding cost that is incurred on any unit carried over in inventory from one period to the next
Service level (%)		the probability that at the end of each and every time period the net inventory will not be negative
Coefficient of variation		the coefficient of variation of the demand, which is assumed to be normally distributed, in each period of the planning horizon that is considered (i.e., stdev_i / mean_i)
Expected demands		the expected demand values, assumed to be normally distributed, for the planning horizon
Lead-time length		the deterministic lead-time length (in periods)

Relevant Publications

R. Rossi, S. A. Tarim, B. Hnich and S. Prestwich, "Computing Replenishment Cycle Policy under Non-stationary Stochastic Lead Time", International Journal of Production Economics, Elsevier, Vol. 127(1):180-189, 2010
R. Rossi, S. A. Tarim, B. Hnich and S. Prestwich, "A State Space Augmentation Algorithm for the Replenishment Cycle Inventory Policy", International Journal of Production Economics, Elsevier, forthcoming
B. Hnich, R. Rossi, S. A. Tarim and S. Prestwich, "A Survey on CP-AI-OR Hybrids for Decision Making under Uncertainty", Lecture Notes in Computer Science, Springer-Verlag, to appear
S. A. Tarim, B. Hnich, R. Rossi and S. Prestwich, "A Decision Support System for Computing Optimal (R,S) Policy Parameters", In proceedings of the 19th Irish Conference on Artificial Intelligence and Cognitive Science (AICS 2008), pp.301-302, Aug. 27, 2008, Cork, Ireland
S. A. Tarim, B. Hnich, R. Rossi and S. Prestwich, "Cost-based Filtering Techniques for Stochastic Inventory Control under Service Level Constraints", Constraints, Springer-Verlag, Vol. 14(2):137-176, 2009
R. Rossi, S. A. Tarim, B. Hnich and S. Prestwich, "A Global Chance-Constraint for Stochastic Inventory Systems under Service Level Constraints", Constraints, Springer-Verlag, Vol. 13(4):490-517, 2008
S. A. Tarim and B. M. Smith, "Constraint Programming for Computing Non-Stationary (R,S) Policy", European Journal of Operational Research, Elsevier, Vol. 189(3):1004-1021, 2008.
S. A. Tarim, B. Hnich, R. Rossi and S. Prestwich, "Cost-based Filtering for Stochastic Inventory Control", Recent Advances in Constraints: 11th Annual ERCIM International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2006 Caparica, Portugal, June 26-28, 2006 Revised Selected and Invited Papers, Lecture Notes in Computer Science, Springer-Verlag, LNCS 4651, pp.169-183, 2007
R. Rossi, S. A. Tarim, B. Hnich and S. Prestwich, "Replenishment Planning for Stochastic Inventory Systems with Shortage Cost", In proceedings of The Fourth International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR 07) May 23-26, 2007, Brussels, Belgium, Lecture Notes in Computer Science, Springer-Verlag, LNCS 4510, pp.229-243, 2007
R. Rossi, S. A. Tarim, B. Hnich and S. Prestwich, ""Cost-based Filtering for Stochastic Inventory Systems with Shortage Cost", Thirteenth International Conference on Principles and Practice of Constraint Programming, Doctoral Program Proceedings, Providence (RI), 2007
R. Rossi, S. Prestwich, "A Global Constraint for Computing Exact Buffer Stock Levels in Stochastic Inventory Control", Twelfth International Conference on Principles and Practice of Constraint Programming, Doctoral Program Proceedings, Nantes, 2006
Tarim, S. A. and B. G. Kingsman, "Modelling and Computing (Rn,Sn) Policies for Inventory Systems with Non-Stationary Stochastic Demand", European Journal of Operational Research, 174, pp.581-599, 2006.
Tarim, S. A. and B. G. Kingsman, "The Stochastic Dynamic Production/Inventory Lot-Sizing Problem with Service-Level Constraints", International Journal of Production Economics, 88, pp.105-119, 2004.

Awards

The project has been selected as one of the four Most Commercially Viable Softwares at ISA Student Medal Award 2006

S. Armagan Tarim
Hacettepe University, Ankara, Turkey

Roberto Rossi
Wageningen UR, the Netherlands

Brahim Hnich
Izmir University of Economics, Turkey

Steven D. Prestwich
University College Cork, Ireland

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