An EPQ model for deteriorating items with inventory-level-dependent demand and permissible delay in payments

Abstract

This article develops an inventory model for exponentially deteriorating items under conditions of permissible delay in payments. Unlike the existing related models, we assume that the items are replenished at a finite rate and the demand rate of the items is dependent on the current inventory level. The objective is to determine the optimal replenishment policies in order to maximise the system's average profit per unit of time. A simple method is shown for finding the optimal solution of the model based on the derived properties of the objective function. In addition, we deduce some previously published results as the special cases of the model. Finally, numerical examples are used to illustrate the proposed model. Some managerial insights are also inferred from the sensitive analysis of model parameters.

Keywords:

• inventory
• EPQ
• inventory-level-dependent demand
• deteriorating items
• delay in payments

Acknowledgements

The authors greatly appreciate the editor, associate editor and anonymous referees for their insightful comments and suggestions that have significantly improved this article. This research has been supported by the Natural Science Foundation of China (71101002, 71131003, 71072165, 71171071), Anhui Provincial Natural Science Foundation (10040606Q10), the Key Project of Natural Scientific Research of Universities in Anhui Province (KJ2010A063), the Key Projects of the Foundation for Young Talents in Universities of Anhui (2011SQRL113ZD, 2011SQRW033ZD) and the 2010 annual Doctoral Science Foundation of Anhui University of Architecture.