Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - The Price-Setting Newsvendor with Poisson Demand
AU - Schulte, Benedikt
AU - Sachs, Anna-Lena
PY - 2020/5/16
Y1 - 2020/5/16
N2 - 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.
AB - 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.
KW - Inventory
KW - Newsvendor model
KW - Pricing
KW - Poisson demand
U2 - 10.1016/j.ejor.2019.10.039
DO - 10.1016/j.ejor.2019.10.039
M3 - Journal article
VL - 283
SP - 125
EP - 137
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
IS - 1
ER -