Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 689061, 15 pages
Research Article

Effective Investment to Reduce Setup Cost in a Mixture Inventory Model Involving Controllable Backorder Rate and Variable Lead Time with a Service Level Constraint

Department of Applied Mathematics, Aletheia University, Tamsui, Taipei 25103, Taiwan

Received 5 August 2011; Revised 21 October 2011; Accepted 22 October 2011

Academic Editor: Wanquan Liu

Copyright © 2012 Hsien-Jen Lin. 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 investigates the impact of setup cost reduction on an inventory policy for a continuous review mixture inventory model involving controllable backorder rate and variable lead time with a service level constraint, in which the order quantity, setup cost, and lead time are decision variables. Our objective is to develop an algorithm to determine the optimal order quantity, setup cost, and lead time simultaneously, so that the total expected annual cost incurred has a minimum value. Furthermore, four numerical examples are provided to illustrate the results, and the effects of system parameters are also included for decision making.