Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 867847, 16 pages
Research Article

Distribution-Free Continuous Review Inventory Model with Controllable Lead Time and Setup Cost in the Presence of a Service Level Constraint

School of Economics and Management, Tongji University, Shanghai 200092, China

Received 15 March 2012; Revised 3 June 2012; Accepted 4 July 2012

Academic Editor: Jun Hu

Copyright © 2012 Wei-Min MA and Bing-Bing QIU. 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.


Based on the mean and the standard deviation of lead time demand, and also taking the difficulty in measuring shortage cost into consideration, we investigate the joint decision problem of continuous review inventory in which a service level constraint should be satisfied. Under the assumption of controllable lead time and setup cost, a mathematical programming model is established. The objective function of the proposed model is the total expected annual cost and the constraint guarantees that the service level requirement can be satisfied at the worst case. Subsequently, an equivalent nonlinear programming model is derived. By constructing Lagrange function, the analysis regarding the solution procedure is conducted, and a solution algorithm is then provided. Moreover, a numerical example is introduced to illustrate the proposed model and solution algorithm. Through sensitivity analysis, some observations and managerial implications are provided.