On the first come–first served rule in multi‐echelon inventory control

A two-echelon distribution inventory system with a central warehouse and a number of retailers is considered. The retailers face stochastic demand and replenish from the warehouse, which, in turn, replenishes from an outside supplier. The system is reviewed continuously and demands that cannot be met directly are backordered. Standard holding and backorder costs are considered. In the literature on multi-echelon inventory control it is standard to assume that backorders at the warehouse are served according to a first come-first served policy (FCFS). This allocation rule simplifies the analysis but is normally not optimal. It is shown that the FCFS rule can, in the worst case, lead to an asymptotically unbounded relative cost increase as the number of retailers approaches infinity. We also provide a new heuristic that will always give a reduction of the expected costs. A numerical study indicates that the average cost reduction when using the heuristic is about two percent. The suggested heuristic is also compared with two existing heuristics.

[1]  Sven Axsäter,et al.  Exact Analysis of Continuous Review (R, Q) Policies in Two-Echelon Inventory Systems with Compound Poisson Demand , 2000, Oper. Res..

[2]  Sven Axsäter,et al.  Chapter 4 Continuous review policies for multi-level inventory systems with stochastic demand , 1993, Logistics of Production and Inventory.

[3]  Fangruo Chen,et al.  Lower Bounds for Multi-Echelon Stochastic Inventory Systems , 1994 .

[4]  Eb Erik Diks,et al.  Stock allocation in general multi-echelon distribution systems with (R, S) order-up-to-policies , 1997 .

[5]  Paul H. Zipkin,et al.  Approximations of Dynamic, Multilocation Production and Inventory Problems , 1984 .

[6]  P. Jackson Stock allocation in a two-echelon distribution system or “What to do until your ship comes in” , 1988 .

[7]  W. Zijm,et al.  European Journal of Operational Research Materials Coordination in Stochastic Multi-echelon Systems , 2022 .

[8]  Sven Axsäter,et al.  Supply Chain Operations: Serial and Distribution Inventory Systems , 2003, Supply Chain Management.

[9]  Stephen C. Graves,et al.  A Multi-Echelon Inventory Model for a Repairable Item with One-for-One Replenishment , 1985 .

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

[11]  Özalp Özer,et al.  Bounds, Heuristics, and Approximations for Distribution Systems , 2007, Oper. Res..

[12]  S. Graves A multiechelon inventory model with fixed replenishment intervals , 1996 .

[13]  P. Jackson,et al.  Risk pooling in a two‐period, two‐echelon inventory stocking and allocation problem , 1989 .

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

[15]  Sven Axsäter,et al.  Heuristic Methods for Centralized Control of One-Warehouse, N-Retailer Inventory Systems , 2001, Manuf. Serv. Oper. Manag..

[16]  Paul H. Zipkin,et al.  Foundations of Inventory Management , 2000 .

[17]  G. Houtum,et al.  A numerical study on the effect of the balance assumption in one-warehouse multi-retailer inventory systems , 2009 .

[18]  A. Federgruen Chapter 3 Centralized planning models for multi-echelon inventory systems under uncertainty , 1993, Logistics of Production and Inventory.