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Confidence-based optimisation for the newsvendor problem under binomial, Poisson and exponential demand

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  • Rossi, Roberto
  • Prestwich, Steven
  • Tarim, S. Armagan
  • Hnich, Brahim

Abstract

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach produces an upper and a lower bound for the associated cost. We apply this approach to three demand distributions in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist—e.g. based on maximum likelihood estimators—or Bayesian strategies.

Suggested Citation

  • Rossi, Roberto & Prestwich, Steven & Tarim, S. Armagan & Hnich, Brahim, 2014. "Confidence-based optimisation for the newsvendor problem under binomial, Poisson and exponential demand," European Journal of Operational Research, Elsevier, vol. 239(3), pages 674-684.
  • Handle: RePEc:eee:ejores:v:239:y:2014:i:3:p:674-684
    DOI: 10.1016/j.ejor.2014.06.007
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    6. Mare, Davide Salvatore & Moreira, Fernando & Rossi, Roberto, 2017. "Nonstationary Z-Score measures," European Journal of Operational Research, Elsevier, vol. 260(1), pages 348-358.
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    9. Wang, Daao & Dimitrov, Stanko & Jian, Lirong, 2020. "Optimal inventory decisions for a risk-averse retailer when offering layaway," European Journal of Operational Research, Elsevier, vol. 284(1), pages 108-120.
    10. Afshar-Nadjafi, Behrouz, 2016. "The influence of sale announcement on the optimal policy of an inventory system with perishable items," Journal of Retailing and Consumer Services, Elsevier, vol. 31(C), pages 239-245.
    11. 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.
    12. Guo, Min & Chen, Yu-wang & Wang, Hongwei & Yang, Jian-Bo & Zhang, Keyong, 2019. "The single-period (newsvendor) problem under interval grade uncertainties," European Journal of Operational Research, Elsevier, vol. 273(1), pages 198-216.
    13. Abu Hashan Md Mashud & Hui-Ming Wee & Chiao-Ven Huang & Jei-Zheng Wu, 2020. "Optimal Replenishment Policy for Deteriorating Products in a Newsboy Problem with Multiple Just-in-Time Deliveries," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    14. 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.
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