Optimizing inventory levels in a two-echelon retailer system with partial lost sales

This paper considers a retailer inventory system with N first-echelon stores and a single second-echelon distribution center DC. Customer demands at the stores are assumed to be random. When a stockout occurs, customers are willing to wait for their order to be filled with a known probability. Customers who are unwilling to wait result in lost sales. The first and second echelons are both restocked at fixed, equally spaced time points, where the store restocking frequency is an integer multiple of the DC restocking frequency. We also assume that replenishment quantities at both echelons can be adjusted up to the time of delivery, resulting in replenishment lead times equal to zero. This simplification allows us to determine optimal solutions for the partial lost sales case, which has proven intractable for two-echelon formulations with lead times. Computational results are given for illustrative examples.

[1]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[2]  Kenneth F. Simpson.  A Theory of Allocation of Stocks to Warehouses , 1959 .

[3]  A. F. Veinott,et al.  Optimal policy for a dynamic multi‐echelon inventory model , 1966 .

[4]  C. Das.  Supply and Redistribution Rules for Two-Location Inventory Systems: One-Period Analysis , 1975 .

[5]  D. Heyman,et al.  A two‐echelon inventory model with purchases, dispositions, shipments, returns and transshipments , 1977 .

[6]  R. Ehrhardt.  The Power Approximation for Computing (s, S) Inventory Policies , 1979 .

[7]  G. D. Eppen.  Note---Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem , 1979 .

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

[9]  Leroy B. Schwarz,et al.  Multi-level production/inventory control systems : theory and practice , 1981 .

[10]  Awi Federgruen,et al.  Allocation policies and cost approximations for multilocation inventory systems , 1984 .

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

[12]  L. B. Schwarz,et al.  Fill-Rate Optimization in a One-Warehouse N-Identical Retailer Distribution System , 1985 .

[13]  Edward A. Silver,et al.  Analysis of a two-echelon inventory control system with complete redistribution , 1987 .

[14]  E. Silver,et al.  Stock allocation among a central warehouse and identical regional warehouses in a particular push inventory control system , 1987 .

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

[16]  Paul H. Zipkin,et al.  Estimating the Performance of Multi-Level Inventory Systems , 1988, Oper. Res..

[17]  Stephen C. Graves,et al.  A multi-echelon inventory model with fixed reorder intervals , 1989 .

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

[19]  W. H. Hausman,et al.  Optimal centralized ordering policies in multi-echelon inventory systems with correlated demands , 1990 .

[20]  S. Nahmias,et al.  Mathematical Models of Retailer Inventory Systems: A Review , 1993 .