A Decomposition Approach for a Class of Capacitated Serial Systems

We study a class of two-echelon serial systems with identical ordering/production capacities or limits for both echelons. Demands are assumed to be integer valued. For the case where the lead time to the upstream echelon is one period, the optimality of state-dependent modified echelon base-stock policies is proved using a decomposition approach. For the case where the upstream lead time is two periods, we introduce a new class of policies called “two-tier base-stock policies,” and prove their optimality. Some insight about the inventory control problem in N echelon serial systems with identical capacities at all stages and arbitrary lead times everywhere is also provided. We argue that a generalization of two-tier base-stock policies, which we call “multitier base-stock policies,” are optimal for these systems; we also provide a bound on the number of parameters required to specify the optimal policy.

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

[2]  Cyrus Derman,et al.  Inventory Depletion Management , 1958 .

[3]  Paul Glasserman,et al.  Sensitivity Analysis for Base-Stock Levels in Multiechelon Production-Inventory Systems , 1995 .

[4]  Sridhar R. Tayur,et al.  A Capacitated Production-Inventory Model with Periodic Demand , 1998, Oper. Res..

[5]  Roman Kapuscinski,et al.  Optimal Policies and Simulation-Based Optimization for Capacitated Production Inventory Systems , 1999 .

[6]  John N. Tsitsiklis,et al.  A Single-Unit Decomposition Approach to Multiechelon Inventory Systems , 2008, Oper. Res..

[7]  Hemant K. Bhargava,et al.  Stockout Compensation: Joint Inventory and Price Optimization in Electronic Retailing , 2006, INFORMS J. Comput..

[8]  Awi Federgruen,et al.  Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model , 1984, Oper. Res..

[9]  Roman Kapuscinski,et al.  Optimal Policies for a Capacitated Two-Echelon Inventory System , 2004, Oper. Res..

[10]  van der J Jan Wal,et al.  The capacitated multi-echelon inventory system with serial structure. 1. The 'push ahead'-effect , 1991 .

[11]  Jing-Sheng Song,et al.  Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand , 2001, Oper. Res..

[12]  Sven Axsäter,et al.  Simple Solution Procedures for a Class of Two-Echelon Inventory Problems , 1990, Oper. Res..

[13]  P. Glasserman,et al.  A simple approximation for a multistage capacitated production-inventory system , 1996 .

[14]  Sridhar Tayur.  Recent developments in single product, discrete-time, capacitated production-inventory systems , 1997 .

[15]  平山 克己.  Sridhar Tayur, Ram Ganeshan, Michael J. Magazine著, Quantitative Models for Supply Chain Management (International Series in Operations Research & Management Science, 17), Kluwer Academic Publishers, 1998年12月,896頁 , 2000 .

[16]  Paul Zipkin,et al.  Evaluation of base‐stock policies in multiechelon inventory systems with compound‐poisson demands , 1991 .

[17]  L. Sennott.  Stochastic Dynamic Programming and the Control of Queueing Systems , 1998 .

[18]  S. Tayur.  Computing the Optimal Policy for Capacitated Inventory Models , 1993 .

[19]  Paul Glasserman,et al.  The Stability of a Capacitated, Multi-Echelon Production-Inventory System Under a Base-Stock Policy , 1994, Oper. Res..

[20]  John A. Muckstadt,et al.  A Decomposition Approach for a Capacitated , Single Stage , Production-Inventory System , 2003 .

[21]  Herbert E. Scarf,et al.  Optimal Policies for a Multi-Echelon Inventory Problem , 1960, Manag. Sci..

[22]  Sven Axsäter,et al.  Exact and Approximate Evaluation of Batch-Ordering Policies for Two-Level Inventory Systems , 1993, Oper. Res..

[23]  Awi Federgruen,et al.  An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion , 1986, Math. Oper. Res..

[24]  John A. Muckstadt,et al.  Inventory Control in Directed Networks: A Note on Linear Costs , 2004, Oper. Res..

[25]  John N. Tsitsiklis,et al.  Appendix for \A Single-Unit Decomposition Approach to Multi-Echelon Inventory Systems" , 2007 .

[26]  Steven Nahmias,et al.  Simple Approximations for a Variety of Dynamic Leadtime Lost-Sales Inventory Models , 1979, Oper. Res..

[27]  Awi Federgruen,et al.  An Inventory Model with Limited Production Capacity and Uncertain Demands I. The Average-Cost Criterion , 1986, Math. Oper. Res..

[28]  Awi Federgruen,et al.  Stochastic Inventory Models with Limited Production Capacity and Periodically Varying Parameters , 1997, Probability in the Engineering and Informational Sciences.