Asymmetry and Ambiguity in Newsvendor Models

Karthik Natarajan (), Melvyn Sim () and Joline Uichanco ()
Additional contact information
Karthik Natarajan: Engineering Systems and Design, Singapore University of Technology and Design, Singapore 487372
Melvyn Sim: NUS Business School, National University of Singapore, Singapore 117591
Joline Uichanco: Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109

Management Science, 2018, vol. 64, issue 7, 3146-3167

Abstract: A basic assumption of the classical newsvendor model is that the probability distribution of the random demand is known. But in most realistic settings, only partial distribution information is available or reliably estimated. The distributionally robust newsvendor model is often used in this case where the worst-case expected profit is maximized over the set of distributions satisfying the known information, which is usually the mean and covariance of demands. However, covariance does not capture information on asymmetry of the demand distribution. In this paper, we introduce a measure of distribution asymmetry using second-order partitioned statistics. Semivariance is a special case with a single partition of the univariate demand. With mean, variance, and semivariance information, we show that a three-point distribution achieves the worst-case expected profit and derive a closed-form expression for the distributionally robust order quantity. For multivariate demand, the distributionally robust problem with partitioned statistics is hard to solve, but we develop a computationally tractable lower bound through the solution of a semidefinite program. We demonstrate in numerical experiments that asymmetry information significantly reduces expected profit loss particularly when the true distribution is heavy tailed. In computational experiments on automotive spare parts demand data, we provide evidence that the distributionally robust model that includes partitioned statistics outperforms the model that uses only covariance information.

Keywords: inventory production; approximations; heuristics; uncertainty; stochastic models; programming; nonlinear theory (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (19)

Downloads: (external link)
https://doi.org/10.1287/mnsc.2017.2773 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:64:y:2018:i:7:p:3146-3167

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().