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The price-setting newsvendor with Poisson demand

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  • Schulte, Benedikt
  • Sachs, Anna-Lena

Abstract

The price-setting newsvendor (PSN) model has received considerable attention since it was first introduced by Whitin (1955). However, the existing publications that study this model consistently assume the existence of a continuous density function of demand. In this paper, we study the PSN model with Poisson demand — that is, a discrete demand distribution without density function. The Poisson PSN has an important property, it combines price-dependency of variance and coefficient of variation of the (standard) additive and multiplicative models: demand variance decreases and the coefficient of variation increases in the selling price. We develop an analytical solution approach that covers a broad class of demand models, including linear and logit demand, explain how to apply our approach to more general demand functions via piece-wise linear approximation, and develop analytical and numerical insights. We characterize the behavior of the optimal price and we analyze the performance gap of different price-setting heuristics. Among other insights, we observe some instances in which a significant share of profits would be lost if the discrete nature of demand were not modeled explicitly. To help companies overcome this risk, we present an easily applicable decision rule with which to determine when to use simple heuristics and when to solve the associated discrete optimization problem.

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  • Schulte, Benedikt & Sachs, Anna-Lena, 2020. "The price-setting newsvendor with Poisson demand," European Journal of Operational Research, Elsevier, vol. 283(1), pages 125-137.
    • Handle: RePEc:eee:ejores:v:283:y:2020:i:1:p:125-137
    DOI: 10.1016/j.ejor.2019.10.039
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    2. Xu, Xianhao & Chen, Cheng & Zou, Bipan & Wang, Hongwei & Li, Zhiwen, 2023. "Shipping before order making: Optimal shipping quantity and pricing decisions under uncertain demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 169(C).
    3. Babai, M. Zied & Ivanov, Dmitry & Kwon, Oh Kang, 2023. "Optimal ordering quantity under stochastic time-dependent price and demand with a supply disruption: A solution based on the change of measure technique," Omega, Elsevier, vol. 116(C).
    4. Milena Bieniek, 2021. "Bartering: Price-Setting Newsvendor Problem with Barter Exchange," Sustainability, MDPI, vol. 13(12), pages 1-22, June.

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