Constraint-Based Local Search for Inventory Control Under Stochastic Demand and Lead Time

In this paper, we address the general multiperiod production/inventory problem with nonstationary stochastic demand and supplier lead time under service-level constraints. A replenishment cycle policy is modeled. We propose two hybrid algorithms that blend constraint programming and local search for computing near-optimal policy parameters. Both algorithms rely on a coordinate descent local search strategy; what differs is the way this strategy interacts with the constraint programming solver. These two heuristics are first, compared for small instances against an existing optimal solution method. Second, they are tested and compared with each other in terms of solution quality and run time on a set of larger instances that are intractable for the exact approach. Our numerical experiments show the effectiveness of our methods.

[1]  A. Charnes,et al.  Chance-Constrained Programming , 1959 .

[2]  Christopher S. Tang.  Perspectives in supply chain risk management , 2006 .

[3]  François Laburhe.  CHOCO: implementing a CP kernel , 2007 .

[4]  James H. Bookbinder,et al.  Strategies for the Probabilistic Lot-Sizing Problem with Service-Level Constraints , 1988 .

[5]  Kok de Ag,et al.  Nervousness in inventory management : comparison of basic control rules , 1997 .

[6]  Armagan Tarim,et al.  Constraint programming for computing non-stationary (R, S) inventory policies , 2008, Eur. J. Oper. Res..

[7]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[8]  Roberto Rossi,et al.  Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints , 2009, Constraints.

[9]  Roberto Rossi,et al.  A Global Chance-Constraint for Stochastic Inventory Systems Under Service Level Constraints , 2008, Constraints.

[10]  M. Fu,et al.  Optimization of( s, S ) inventory systems with random lead times and a service level constraint , 1998 .

[11]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[12]  Toby Walsh,et al.  Stochastic Constraint Programming: A Scenario-Based Approach , 2009, Constraints.

[13]  Michel Gendreau,et al.  A View of Local Search in Constraint Programming , 1996, CP.

[14]  J. Riezebos.  Inventory order crossovers , 2006 .

[15]  J. C. Hayya,et al.  On static stochastic order crossover , 2008 .

[16]  Andrea Lodi,et al.  Cost-Based Domain Filtering , 1999, CP.

[17]  Patrick Prosser,et al.  Solving Vehicle Routing Problems Using Constraint Programming and Metaheuristics , 2000, J. Heuristics.

[18]  R. Kaplan.  A Dynamic Inventory Model with Stochastic Lead Times , 1970 .

[19]  Toby Walsh,et al.  Handbook of Constraint Programming (Foundations of Artificial Intelligence) , 2006 .

[20]  Gerald Heisig,et al.  Planning Stability in Material Requirements Planning Systems , 2002 .

[21]  Toby Walsh,et al.  Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming , 2001 .

[22]  Ş. Tarim,et al.  The stochastic dynamic production/inventory lot-sizing problem with service-level constraints , 2004 .

[23]  Christian Blum,et al.  Metaheuristics in combinatorial optimization: Overview and conceptual comparison , 2003, CSUR.

[24]  G. D. Eppen,et al.  Determining Safety Stock in the Presence of Stochastic Lead Time and Demand , 1988 .

[25]  Amedeo Cesta,et al.  A Constraint-Based Architecture for Flexible Support to Activity Scheduling , 2001, AI*IA.

[26]  Roberto Rossi,et al.  Computing the non-stationary replenishment cycle inventory policy under stochastic supplier lead-times , 2010 .

[27]  Jean-Charles Régin,et al.  Global Constraints and Filtering Algorithms , 2004 .

[28]  Paul H. Zipkin,et al.  Stochastic leadtimes in continuous‐time inventory models , 1986 .

[29]  D. Clay Whybark,et al.  MATERIAL REQUIREMENTS PLANNING UNDER UNCERTAINTY , 1976 .

[30]  Y. Dallery,et al.  Dynamic re-order point inventory control with lead-time uncertainty: analysis and empirical investigation , 2009 .

[31]  Joseph A. Hunt.  Balancing Accuracy and Simplicity in Determining Reorder Points , 1965 .

[32]  Brian G. Kingsman,et al.  Production, Manufacturing and Logistics Modelling and computing (R n ,S n ) policies for inventory systems with non-stationary stochastic demand , 2005 .

[33]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[34]  Roberto Rossi,et al.  A state space augmentation algorithm for the replenishment cycle inventory policy , 2011 .

[35]  Christopher H. Nevison,et al.  The Dynamic Lot-Size Model with Stochastic Lead Times , 1984 .

[36]  Susan H. Xu,et al.  Order crossover in inventory systems , 1995 .

[37]  Andrea Lodi,et al.  Local Search and Constraint Programming , 2003, Handbook of Metaheuristics.

[38]  David F. Pyke,et al.  Inventory management and production planning and scheduling , 1998 .

[39]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[40]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[41]  Krzysztof R. Apt,et al.  Principles of constraint programming , 2003 .

[42]  Horst Tempelmeier,et al.  On the stochastic uncapacitated dynamic single-item lotsizing problem with service level constraints , 2007, Eur. J. Oper. Res..

[43]  A. G. de Kok.  Basics of inventory management (Part 6): The (R,s,S)-model) , 1991 .