Advances in Decision Sciences
Volume 2011 (2011), Article ID 745896, 9 pages
Research Article

Using Complete Squares Method to Optimize Replenishment Policies in a Four-Stage Supply Chain with Planned Backorders

Department of Information Systems, College of Computer Science and Information Technology, King Faisal University, Alhsaa 3198, Saudi Arabia

Received 1 January 2011; Revised 16 May 2011; Accepted 1 June 2011

Academic Editor: Roger Z. Ríos-Mercado

Copyright © 2011 M. E. Seliaman. 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.


We develop a four-stage, serial supply chain inventory model with planned backorders. This supply chain model is formulated for the integer multipliers coordination mechanism, where firms at the same stage of the supply chain use the same cycle time and the cycle time at each stage is an integer multiplier of the cycle time used at the adjacent downstream stage. We develop an optimal replenishment policy using a simple algebraic method to solve the problem without the use of differential calculus.