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A newsboy problem with an emergency order under a general backorder rate function

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  • Pando, Valentín
  • San-José, Luis A.
  • García-Laguna, Juan
  • Sicilia, Joaquín

Abstract

In this paper, a generalization is presented of the newsboy problem where an emergency lot can be ordered to provide for a certain fraction of shortage. This fraction is described by a general backorder rate function which is non-increasing with respect to the unsatisfied demand. An exponential distribution for the demand during the selling season is assumed. An expression is obtained in a closed form for the optimal lot size and the maximum expected profit. A general sensitivity analysis of the optimal policy with respect to the backorder rate function and the parameters of the inventory system is developed. When the backorder rate function is described by some particular functions, its behavior is analyzed with respect to changes in the parameters. To illustrate the theoretical results, some numerical examples are also given.

Suggested Citation

  • Pando, Valentín & San-José, Luis A. & García-Laguna, Juan & Sicilia, Joaquín, 2013. "A newsboy problem with an emergency order under a general backorder rate function," Omega, Elsevier, vol. 41(6), pages 1020-1028.
    • Handle: RePEc:eee:jomega:v:41:y:2013:i:6:p:1020-1028
    DOI: 10.1016/j.omega.2013.01.003
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    2. Marziyeh Karimi & Amir Hossein Niknamfar & Seyed Hamid Reza Pasandideh, 2017. "Two-stage single period inventory management for a manufacturing vendor under green-supplier supply chain," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(4), pages 704-718, December.
    3. Janssen, Larissa & Claus, Thorsten & Sauer, Jürgen, 2016. "Literature review of deteriorating inventory models by key topics from 2012 to 2015," International Journal of Production Economics, Elsevier, vol. 182(C), pages 86-112.
    4. Jingxian Chen & Liang Liang & Dong-Qing Yao, 2017. "Pre-positioning of relief inventories for non-profit organizations: a newsvendor approach," Annals of Operations Research, Springer, vol. 259(1), pages 35-63, December.
    5. V. Pando & L. San-José & J. García-Laguna & J. Sicilia, 2014. "Some general properties for the newsboy problem with an extraordinary order," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 674-693, July.
    6. Xiaoqing Liu & Felix T. S. Chan & Xinsheng Xu, 2019. "Hedging Risks in the Loss-Averse Newsvendor Problem with Backlogging," Mathematics, MDPI, vol. 7(5), pages 1-23, May.
    7. Rung-Hung Su & Dong-Yuh Yang & He-Jhen Lin & Yu-Cheng Yang, 2023. "Estimating conservative profitability of a newsboy-type product with exponentially distributed demand based on multiple samples," Annals of Operations Research, Springer, vol. 322(2), pages 967-989, March.
    8. Li, Yanhai & Ou, Jinwen, 2020. "Optimal ordering policy for complementary components with partial backordering and emergency replenishment under spectral risk measure," European Journal of Operational Research, Elsevier, vol. 284(2), pages 538-549.
    9. Adrián Esteban-Pérez & Juan M. Morales, 2022. "Partition-based distributionally robust optimization via optimal transport with order cone constraints," 4OR, Springer, vol. 20(3), pages 465-497, September.
    10. Roni, Mohammad S. & Jin, Mingzhou & Eksioglu, Sandra D., 2015. "A hybrid inventory management system responding to regular demand and surge demand," Omega, Elsevier, vol. 52(C), pages 190-200.
    11. Fu, Hong & Ma, Yongkai & Cai, Xiaoqiang, 2018. "Downstream firm’s investment with equity holding in decentralized assembly systems," Omega, Elsevier, vol. 75(C), pages 27-56.
    12. Sillanpää, Ville & Liesiö, Juuso & Käki, Anssi, 2021. "Procurement decisions over multiple periods under piecewise-linear shortage costs and fixed capacity commitments," Omega, Elsevier, vol. 100(C).
    13. Irfanullah Khan & Biswajit Sarkar, 2021. "Transfer of Risk in Supply Chain Management with Joint Pricing and Inventory Decision Considering Shortages," Mathematics, MDPI, vol. 9(6), pages 1-20, March.
    14. Khouja, Moutaz & Christou, Eliana & Stylianou, Antonis, 2020. "A heuristic approach to in-season capacity allocation in a multi-product newsvendor model," Omega, Elsevier, vol. 95(C).
    15. Xu, Xinsheng & Wang, Hongwei & Dang, Chuangyin & Ji, Ping, 2017. "The loss-averse newsvendor model with backordering," International Journal of Production Economics, Elsevier, vol. 188(C), pages 1-10.

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