Bayesian demand updating in lost sales newsvendor: a two moment approximation

Date
2007-10
Authors
Berk, E.
Gürler, Ü.
Levine, R. A.
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Source Title
European Journal of Operational Research
Print ISSN
0377-2217
Electronic ISSN
1872-6860
Publisher
Elsevier
Volume
182
Issue
1
Pages
256 - 281
Language
English
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Abstract

We consider Bayesian updating of demand in a lost sales newsvendor model with censored observations. In a lost sales environment, where the arrival process is not recorded, the exact demand is not observed if it exceeds the beginning stock level, resulting in censored observations. Adopting a Bayesian approach for updating the demand distribution, we develop expressions for the exact posteriors starting with conjugate priors, for negative binomial, gamma, Poisson and normal distributions. Having shown that non-informative priors result in degenerate predictive densities except for negative binomial demand, we propose an approximation within the conjugate family by matching the first two moments of the posterior distribution. The conjugacy property of the priors also ensure analytical tractability and ease of computation in successive updates. In our numerical study, we show that the posteriors and the predictive demand distributions obtained exactly and with the approximation are very close to each other, and that the approximation works very well from both probabilistic and operational perspectives in a sequential updating setting as well.

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