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

Article

Abstract

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.

Keywords

deteriorating items finance inventory partial backlogging 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abad, P.L. 1996Optimal pricing and lot sizing under conditions of perishability and partial backorderingManagement Science4210931104Google Scholar
  2. 2.
    Aggarwal, S.P., Jaggi, C.K. 1995Ordering policies of deteriorating items under permissible delay in paymentsJournal of the Operational Research Society46658662Google Scholar
  3. 3.
    Bazarra, M., Sherali, H., Shetty, C.M. 1993Nonlinear Programming2WileyNew YorkGoogle Scholar
  4. 4.
    Brigham, E.F. 1995Fundamentals of Financial ManagementThe Dryden PressFloridaGoogle Scholar
  5. 5.
    Chang, C.T., Ouyang, L.Y., Teng, J.T. 2003An EOQ model for deteriorating items under supplier credits linked to ordering quantityApplied Mathematical Modelling27983996CrossRefGoogle Scholar
  6. 6.
    Chang, C.T. and Teng, J.T. (2004), Retailer’s optimal ordering policy under supplier credits, to appear in Mathematical Methods of Operations Research.Google Scholar
  7. 7.
    Chang, H.J., Dye, C.Y. 1999An EOQ model for deteriorating items with time varying demand and partial backloggingJournal of the Operational Research Society5011761182Google Scholar
  8. 8.
    Chang, H.J., Dye, C.Y. 2001An inventory model for deteriorating items with partial backlogging and permissible delay in paymentsInternational Journal of Systems Science32345352Google Scholar
  9. 9.
    Dave, U. 1985On “economic order quantity under conditions of permissible delay in payments”Journal of the Operational Research Society361069Google Scholar
  10. 10.
    Goyal, S.K. 1985Economic order quantity under conditions of permissible delay in paymentsJournal of the Operational Research Society36335338Google Scholar
  11. 11.
    Hwang, H., Shinn, S.W. 1997Retailer’s pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in paymentsComputers and Operations Research24539547CrossRefGoogle Scholar
  12. 12.
    Jamal, A.M.M., Sarker, B.R., Wang, S. 1997An ordering policy for deteriorating items with allowable shortage and permissible delay in paymentJournal of the Operational Research Society48826833CrossRefGoogle Scholar
  13. 13.
    Jamal, A.M.M., Sarker, B.R., Wang, S. 2000Optimal payment time for a retailer under permitted delay of payment by the wholesalerInternational Journal of Production Economics665966CrossRefGoogle Scholar
  14. 14.
    Liao, H.C., Tsai, C.H., Su, C.T. 2000An inventory model with deteriorating items under inflation when a delay in payment is permissibleInternational Journal of Production Economics63207214CrossRefGoogle Scholar
  15. 15.
    Sharker, B. R., Jamal, A.M.M., Wang, S. 2000Optimal payment time under permissible delay for products with deteriorationProduction Planning & Control11380390Google Scholar
  16. 16.
    Papachristos, S., Skouri, K. 2000An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential type-backloggingOperations Research Letters27175184CrossRefGoogle Scholar
  17. 17.
    Teng, J.T. 2002On the economic order quantity under conditions of permissible delay in paymentsJournal of the Operational Research Society53915918CrossRefGoogle Scholar
  18. 18.
    Teng, J.T., Chern, M.S., Yang, H.L., Wang, Y.J. 1999Deterministic lot-size inventory models with shortages and deterioration for fluctuating demandOperations Research Letters246572CrossRefGoogle Scholar
  19. 19.
    Teng, J.T., Chang, H.J., Dye, C.Y., Hung, C.H. 2002An optimal replenishment policy for deteriorating items with time-varying demand and partial backloggingOperations Research Letters30387393CrossRefGoogle Scholar
  20. 20.
    Teng, J.T., Yang, H.L., Ouyang, L.Y. 2003On an EOQ model for deteriorating items with time-varying demand and partial backloggingJournal of the Operational Research Society54432436CrossRefGoogle Scholar

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

Personalised recommendations