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Optimal ordering for a probabilistic one-time discount

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  • Shaposhnik, Yaron
  • Herer, Yale T.
  • Naseraldin, Hussein

Abstract

We develop a model for a one-time special purchasing opportunity where there is uncertainty with respect to the materialization of the discounted purchasing offer. Our model captures the phenomenon of an anticipated future event that may or may not lead to a discounted offer. We analyze the model and show that the optimal solution results from a tradeoff between preparing for the special offer and staying with the regular ordering policy. We quantify the tradeoff and find that the optimal solution is one of four intuitive policies. We present numerical illustrations that provide additional insights on the relationship between the different ordering policies.

Suggested Citation

  • Shaposhnik, Yaron & Herer, Yale T. & Naseraldin, Hussein, 2015. "Optimal ordering for a probabilistic one-time discount," European Journal of Operational Research, Elsevier, vol. 244(3), pages 803-814.
  • Handle: RePEc:eee:ejores:v:244:y:2015:i:3:p:803-814
    DOI: 10.1016/j.ejor.2015.02.020
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    1. Benjamin Lev & Howard J. Weiss, 1990. "Inventory Models with Cost Changes," Operations Research, INFORMS, vol. 38(1), pages 53-63, February.
    2. Hau L. Lee & Kut C. So & Christopher S. Tang, 2000. "The Value of Information Sharing in a Two-Level Supply Chain," Management Science, INFORMS, vol. 46(5), pages 626-643, May.
    3. Basil A. Kalymon, 1971. "Stochastic Prices in a Single-Item Inventory Purchasing Model," Operations Research, INFORMS, vol. 19(6), pages 1434-1458, October.
    4. Taleizadeh, Ata Allah & Pentico, David W. & Aryanezhad, Mirbahador & Ghoreyshi, Seyed Mohammad, 2012. "An economic order quantity model with partial backordering and a special sale price," European Journal of Operational Research, Elsevier, vol. 221(3), pages 571-583.
    5. Robert A. Davis & Norman Gaither, 1985. "Optimal Ordering Policies Under Conditions of Extended Payment Privileges," Management Science, INFORMS, vol. 31(4), pages 499-509, April.
    6. Robin Roundy, 1985. "98%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems," Management Science, INFORMS, vol. 31(11), pages 1416-1430, November.
    7. Robert W. Grubbström & Brian G. Kingsman, 2004. "Ordering and Inventory Policies for Step Changes in the Unit Item Cost: A Discounted Cash Flow Approach," Management Science, INFORMS, vol. 50(2), pages 253-267, February.
    8. Sam G. Taylor & Charles E. Bradley, 1985. "Optimal Ordering Strategies for Announced Price Increases," Operations Research, INFORMS, vol. 33(2), pages 312-325, April.
    9. Chih-Te Yang & Liang-Yuh Ouyang & Kun-Shan Wu & Hsiu-Feng Yen, 2012. "Optimal ordering policy in response to a temporary sale price when retailer's warehouse capacity is limited," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 6(1), pages 26-49.
    10. Kamal Golabi, 1985. "Optimal Inventory Policies When Ordering Prices are Random," Operations Research, INFORMS, vol. 33(3), pages 575-588, June.
    11. Arcelus, F. J. & Shah, Nita H. & Srinivasan, G., 2003. "Retailer's pricing, credit and inventory policies for deteriorating items in response to temporary price/credit incentives," International Journal of Production Economics, Elsevier, vol. 81(1), pages 153-162, January.
    12. Taleizadeh, Ata Allah & Mohammadi, Babak & Cárdenas-Barrón, Leopoldo Eduardo & Samimi, Hadi, 2013. "An EOQ model for perishable product with special sale and shortage," International Journal of Production Economics, Elsevier, vol. 145(1), pages 318-338.
    13. Goyal, S. K. & Srinivasan, G. & Arcelus, F. J., 1991. "One time only incentives and inventory policies," European Journal of Operational Research, Elsevier, vol. 54(1), pages 1-6, September.
    14. Kevin Hsu, Wen-Kai & Yu, Hong-Fwu, 2009. "EOQ model for imperfective items under a one-time-only discount," Omega, Elsevier, vol. 37(5), pages 1018-1026, October.
    15. Peter Chu & Patrick Chen & Thomas Niu, 2003. "Note on supplier-restricted order quantity under temporary price discounts," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(1), pages 141-147, August.
    16. Chang, Horng-Jinh & Lin, Wen-Feng & Ho, Jow-Fei, 2011. "Closed-form solutions for Wee's and Martin's EOQ models with a temporary price discount," International Journal of Production Economics, Elsevier, vol. 131(2), pages 528-534, June.
    17. Andrew Lim & Brian Rodrigues, 2005. "A Note on the Optimal EOQ for Announced Price Increases in the Infinite Horizon," Operations Research, INFORMS, vol. 53(4), pages 731-732, August.
    18. Sarker, Bhaba R. & Al Kindi, Mahmood, 2006. "Erratum to "Optimal ordering policies in response to discount offer" [International Journal of Production Economics 100 (2006) 195-211]," International Journal of Production Economics, Elsevier, vol. 103(2), pages 895-895, October.
    19. Wei Huang & Vidyadhar G. Kulkarni & Jayashankar M. Swaminathan, 2003. "Optimal EOQ for Announced Price Increases in Infinite Horizon," Operations Research, INFORMS, vol. 51(2), pages 336-339, April.
    20. Yu-Shen Zheng, 1994. "Optimal Control Policy for Stochastic Inventory Systems with Markovian Discount Opportunities," Operations Research, INFORMS, vol. 42(4), pages 721-738, August.
    21. Ramasesh, Ranga V., 2010. "Lot-sizing decisions under limited-time price incentives: A review," Omega, Elsevier, vol. 38(3-4), pages 118-135, June.
    22. Ardalan, Alireza, 1994. "Optimal prices and order quantities when temporary price discounts result in increase in demand," European Journal of Operational Research, Elsevier, vol. 72(1), pages 52-61, January.
    23. Kamran Moinzadeh, 1997. "Replenishment and Stocking Policies for Inventory Systems with Random Deal Offerings," Management Science, INFORMS, vol. 43(3), pages 334-342, March.
    24. Sarker, Bhaba R. & Al Kindi, Mahmood, 2006. "Optimal ordering policies in response to a discount offer," International Journal of Production Economics, Elsevier, vol. 100(2), pages 195-211, April.
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    Cited by:

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    2. Yusen Xia, 2016. "Responding to supplier temporary price discounts in a supply chain through ordering and pricing decisions," International Journal of Production Research, Taylor & Francis Journals, vol. 54(7), pages 1938-1950, April.
    3. Yiju Wang & Donglei Du & Jingfu Huang, 2021. "Optimal Replenishment Strategy for Inventory Mechanism with Step-Shaped Demand," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 841-860, September.

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