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The EOQ with defective items and partially permissible delay in payments linked to order quantity derived algebraically

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  • Liang-Yuh Ouyang
  • Chun-Tao Chang
  • Philip Shum

Abstract

Most researchers established their inventory lot-size models under trade credit financing by assuming that the supplier offers the retailer fully permissible delay in payments and the products received are all non-defective. However, in the real business environment, it often can be observed that the supplier offers the retailer a fully permissible delay in payments only when the order quantity is greater than or equal to the predetermined quantity Q d . In addition, an arriving order lot usually contains some defective items due to imperfect production processes or other factors. To capture this reality, the paper extends Huang (2007) economic order quantity (EOQ) model with partially permissible delay in payments to consider defective items. We formulate the proposed problem as a profit maximization EOQ model in which the replenishment cycle time is the decision variable. Then we use the arithmetic-geometric mean inequality approach to determine the optimal solution under various situations. An algorithm to obtain the optimal solution is also provided. Finally, the numerical examples and sensitivity analysis are given to illustrate the results. Copyright Springer-Verlag 2012

Suggested Citation

  • Liang-Yuh Ouyang & Chun-Tao Chang & Philip Shum, 2012. "The EOQ with defective items and partially permissible delay in payments linked to order quantity derived algebraically," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(1), pages 141-160, March.
    • Handle: RePEc:spr:cejnor:v:20:y:2012:i:1:p:141-160
    DOI: 10.1007/s10100-010-0160-9
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    References listed on IDEAS

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    1. Papachristos, S. & Konstantaras, I., 2006. "Economic ordering quantity models for items with imperfect quality," International Journal of Production Economics, Elsevier, vol. 100(1), pages 148-154, March.
    2. Petersen, Mitchell A & Rajan, Raghuram G, 1997. "Trade Credit: Theories and Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 661-691.
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    4. Teng, Jinn-Tsair, 2009. "Optimal ordering policies for a retailer who offers distinct trade credits to its good and bad credit customers," International Journal of Production Economics, Elsevier, vol. 119(2), pages 415-423, June.
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    6. Chang, Chun-Tao, 2004. "An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity," International Journal of Production Economics, Elsevier, vol. 88(3), pages 307-316, April.
    7. J-T Teng, 2002. "On the economic order quantity under conditions of permissible delay in payments," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(8), pages 915-918, August.
    8. Huang, Yung-Fu, 2007. "Economic order quantity under conditionally permissible delay in payments," European Journal of Operational Research, Elsevier, vol. 176(2), pages 911-924, January.
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    Cited by:

    1. Ping Ruan & Yung-Fu Huang & Ming-Wei Weng, 2022. "Impact of COVID-19 on Supply Chains: A Hybrid Trade Credit Policy," Mathematics, MDPI, vol. 10(8), pages 1-22, April.
    2. Vedran Kojić & Zrinka Lukač, 2014. "Solving the production cost minimization problem with the Cobb – Douglas production function without the use of derivatives," EFZG Working Papers Series 1403, Faculty of Economics and Business, University of Zagreb.
    3. Wu, Chengfeng & Liu, Xin & Li, Annan, 2021. "A loss-averse retailer–supplier supply chain model under trade credit in a supplier-Stackelberg game," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 353-365.
    4. Liang-Yuh Ouyang & Cheng-Ju Chuang & Chia-Huei Ho & Chien-Wei Wu, 2014. "An integrated inventory model with quality improvement and two-part credit policy," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1042-1061, October.
    5. József Vörös, 2013. "Economic order and production quantity models without constraint on the percentage of defective items," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 867-885, December.
    6. Vedran Kojić & Zrinka Lukač, 2018. "An alternative approach to solving cost minimization problem with Cobb–Douglas technology," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 629-643, September.

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