Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 90873, 18 pages
Research Article

Retailer's EOQ Model with Limited Storage Space Under Partially Permissible Delay in Payments

Yung-Fu Huang,1 Chih-Sung Lai,2 and Maw-Liann Shyu2

1Department of Marketing and Logistics Management, Chaoyang University of Technology, Wufong Township, Taichung County 41349, Taiwan
2Department of Business Administration, Chaoyang University of Technology, Wufong Township, Taichung County 41349, Taiwan

Received 6 September 2006; Revised 5 April 2007; Accepted 1 July 2007

Academic Editor: Jingshan Li

Copyright © 2007 Yung-Fu Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The main purpose of this paper wants to investigate the optimal retailer's lot-sizing policy with two warehouses under partially permissible delay in payments within the economic order quantity (EOQ) framework. In this paper, we want to extend that fully permissible delay in payments to the supplier would offer the retailer partially permissible delay in payments. That is, the retailer must make a partial payment to the supplier when the order is received. Then the retailer must pay off the remaining balance at the end of the permissible delay period. In addition, we want to add the assumption that the retailer's storage space is limited. That is, the retailer will rent the warehouse to store these exceeding items when the order quantity is larger than retailer's storage space. Under these conditions, we model the retailer's inventory system as a cost minimization problem to determine the retailer's optimal cycle time and optimal order quantity. Three theorems are developed to efficiently determine the optimal replenishment policy for the retailer. Finally, numerical examples are given to illustrate these theorems and obtained a lot of managerial insights.