Conterserver

IIE Transactions (2010) 42, 812–824
Copyright C “IIE”
ISSN: 0740-817X print / 1545-8830 online
DOI: 10.1080/0740817X.2010.491499

A centralized ordering and allocation system with
backorders and strategic lost sales
YANYI XU1 , ARNAB BISI2,∗ and MAQBOOL DADA3
1

School of Management, Shanghai University, Shanghai 200444, People’s Republic of China
E-mail: yxu@shu.edu.cn
2
Krannert School of Management, Purdue University, West Lafayette, IN 47907, USA
E-mail: abisi@purdue.edu
3
Johns Hopkins Carey Business School, Baltimore, MD 21201, USA
E-mail: mdada1@jhu.edu
Received August 2008 and accepted April 2010

This article considers a multi-retailer distribution system that is managed by a central decision maker who, at the start of each
period, determines how much to order to replenish the system stock. The decision maker also determines how to allocate incoming
pipeline inventory to maintain inventory balance among the retailers. It has been noted in the literature that balancing inventories
can equalize service levels among retailers. To improve the efficacy of the allocation, this article allows some demand to be rejected to
keep inventories in balance. Consequently, depending on the realized pattern of demand during the delivery lead time, the inventory is
dynamically allocated to each of the retailers. For the model with two retailers, an exact representation of the infinite-horizon long-run
average cost function is developed. This exact expression is used to develop conditions for the unique solution for the two-retailer
case. The presented analysis holds for a wide class of continuously and discretely distributed demand.
Keywords: Stochastic inventory models, base stock systems, backorders, lost sales

1. Introduction
In many large-scale distribution systems, inventory is procured and periodically distributed to the distribution centers of the network by a centralized decision maker. In some
applications, such as distribution of...