Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 928932, 19 pages
Research Article

Optimal Inventory Policy Involving Ordering Cost Reduction, Back-Order Discounts, and Variable Lead Time Demand by Minimax Criterion

1Department of Applied Mathematics, National Chiayi University, Chiayi City 60004, Taiwan
2Department of International Business, Chang Jung Christian University, Tainan 71101, Taiwan
3Graduate Institute of Management Sciences, Tamkang University, Tamsui, Taipei 25137, Taiwan

Received 24 December 2008; Revised 20 April 2009; Accepted 24 May 2009

Academic Editor: Wei-Chiang Hong

Copyright © 2009 Jong-Wuu Wu 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.


This paper allows the backorder rate as a control variable to widen applications of a continuous review inventory model. Moreover, we also consider the backorder rate that is proposed by combining Ouyang and Chuang (2001) (or Lee (2005)) with Pan and Hsiao (2001) to present a new form. Thus, the backorder rate is dependent on the amount of shortages and backorder price discounts. Besides, we also treat the ordering cost as a decision variable. Hence, we develop an algorithmic procedure to find the optimal inventory policy by minimax criterion. Finally, a numerical example is also given to illustrate the results.