Journal of Global Optimization

, Volume 34, Issue 2, pp 245–271

Optimal Ordering Policy for Deteriorating Items with Partial Backlogging under Permissible Delay in Payments


DOI: 10.1007/s10898-005-2604-7

Cite this article as:
Ouyang, LY., Teng, JT. & Chen, LH. J Glob Optim (2006) 34: 245. doi:10.1007/s10898-005-2604-7


In 1985, Goyal developed an Economic order quantity (EOQ) model under conditions of permissible delay in payments. Jamal et al. then generalized Goyal’s model for deteriorating items with completely backlogging. However, they only ran several simulations to indicate that the total relevant cost may be convex. Recently, Teng amended Goyal’s model by considering the difference between unit price and unit cost, and provided an alternative conclusion that it makes economic sense for some retailers to order less quantity and take the benefits of the permissible delay more frequently. However, he did not consider deteriorating items and partial backlogging. In this paper, we establish a general EOQ model for deteriorating items when the supplier offers a permissible delay in payments. For generality, our model allows not only the partial backlogging rate to be related to the waiting time but also the unit selling price to be larger than the unit purchase cost. Consequently, the proposed model includes numerous previous models as special cases. In addition, we mathematically prove that the total relevant cost is strictly pseudo-convex so that the optimal solution exists and is unique. Finally, our computational results reveal six managerial phenomena.


deteriorating itemsfinanceinventorypartial backlogging

Copyright information

© Springer 2006

Authors and Affiliations

  • Liang-Yuh Ouyang
    • 1
  • Jinn-Tsair Teng
    • 2
  • Liang-Ho Chen
    • 1
    • 3
  1. 1.Graduate Institute of Management SciencesTamkang UniversityTamsui, TaipeiRepublic of China
  2. 2.Department of Marketing and Management Sciences, Cotsakos College of BusinessWilliam Paterson University of New JerseyWayneUSA
  3. 3.Department of Industry ManagementTung-Nan Institute of TechnologyShenKeng, TaipeiRepublic of China