A two-level distribution inventory system with stochastic lead time at the lower echelon

We consider a two-level distribution inventory system with a number of identical retailers at the lower echelon and a single supplier at the upper echelon. The replenishment policy is continuous review policy (R, Q) at all installations. We assume independent Poisson demands with stochastic lead time for the retailers and a constant transportation time for replenishing supplier orders from an external warehouse. Unsatisfied demands are assumed to be lost in the retailers and unsatisfied retailer orders are backordered in the supplier. We develop an approximate cost function to find optimal reorder points for given batch sizes in all installations, and the related accuracy is assessed through simulation. We present numerical examples for the gamma distributed lead time for the retailers orders at the supplier.

[1]  Hui-Ming Wee,et al.  A note on a single-vendor and multiple-buyers production-inventory policy for a deteriorating item , 2007, Eur. J. Oper. Res..

[2]  John A Muckstadt.  Analysis of a Two-Echelon Inventory System in Which All Locations Follow Continuous Review (S,s) Policies , 1977 .

[3]  Sven Axsäter.  A Simple Decision Rule for Decentralized Two-Echelon Inventory Control , 2005 .

[4]  Kamran Moinzadeh,et al.  Operating characteristics of a two‐echelon inventory system for repairable and consumable items under batch ordering and shipment policy , 1987 .

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

[6]  Paul H. Zipkin,et al.  Models for Design and Control of Stochastic, Multi-Item Batch Production Systems , 1986, Oper. Res..

[7]  Jonas Andersson,et al.  A two-echelon inventory model with lost sales , 2001 .

[8]  S. Albin.  On Poisson Approximations for Superposition Arrival Processes in Queues , 1982 .

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

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

[11]  David K. Smith,et al.  A two-echelon inventory model with lost sales , 2007, Eur. J. Oper. Res..

[12]  Roger M. Hill,et al.  A two-echelon base-stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon , 2007, Eur. J. Oper. Res..

[13]  Sven Axsäter,et al.  Evaluation of Installation Stock Based (R, Q)-Policies for Two-Level Inventory Systems with Poisson Demand , 1998, Oper. Res..

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

[15]  Søren Glud Johansen,et al.  Optimal and approximate (Q, r) inventory policies with lost sales and gamma-distributed lead time , 1993 .

[16]  Hui-Ming Wee,et al.  Production , Manufacturing and Logistics The optimal and heuristic solutions of a distribution network , 2004 .

[17]  Craig C. Sherbrooke,et al.  Metric: A Multi-Echelon Technique for Recoverable Item Control , 1968, Oper. Res..

[18]  K. Moinzadeh,et al.  Batch size and stocking levels in multi-echelon repairable systems , 1986 .

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

[20]  Sven Axsäter.  Approximate Optimization of a Two-Level Distribution Inventory System , 2003 .

[21]  Hui-Ming Wee,et al.  Production , Manufacturing and Logistics A single-vendor and multiple-buyers production – inventory policy for a deteriorating item , 2002 .