A simple approach to an integrated single-vendor single-buyer inventory system with shortage

Abstract

In this article, a simple approach with two basic inequalities (Cauchy–Schwarz inequality and arithmetic–geometric mean inequality) is used to solve the integrated single-vendor single-buyer inventory problem developed by Wu and Ouyang (Wu, K.-S. and Ouyang, L.-Y., 2003. An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Production Planning & Control, 14 (6), 555–561). Without the method of completing perfect square, the proposed approach yields the global minimum of the integrated total cost per year more easily than the algebraic approach used by Wu and Ouyang (2003). In addition, for people without the background of calculus, it is more useful to determine the buyer's economic order quantity and the vendor's optimal number of deliveries.

Keywords:

• without derivatives
• arithmetic–geometric mean inequality
• Cauchy–Schwarz inequality
• single-vendor single-buyer
• shortage

Acknowledgements

We would like to thank the associate editor and two anonymous reviewers for their valuable and constructive comments, which have led to a significant improvement in the manuscript. This research was partially supported by the National Science Council of the Republic of China under Grant NSC-97-2221-E-156-005 and NSC-97-2221-E-366-006-MY2.