Asymmetry and Ambiguity in Newsvendor Models

Abstract

The traditional decision-making framework for newsvendor models is to assume a distribution of the underlying demand. However, the resulting optimal policy is typically sensitive to the choice of the distribution. A more conservative approach is to assume that the distribution belongs to a set parameterized by a few known moments. An ambiguity-averse newsvendor would choose to maximize the worst-case profit. Most models of this type assume that only the mean and the variance are known, but do not attempt to include asymmetry properties of the distribution. Other recent models address asymmetry by including skewness and kurtosis. However, closed-form expressions on the optimal bounds are difficult to find for such models. In this paper, we propose a framework under which the expectation of a piecewise linear objective function is optimized over a set of distributions with known asymmetry properties. This asymmetry is represented by the first two moments of multiple random variables that result from partitioning the original distribution. In the simplest case, this reduces to semivariance. The optimal bounds can be solved through a second-order cone programming (SOCP) problem. This framework can be applied to the risk-averse and risk-neutral newsvendor problems and option pricing. We provide a closed-form expression for the worst-case newsvendor profit with only mean, variance and semivariance information.

Distribution-free Inventory Risk Pooling in a Multi-location Newsvendor

“…Since inventory risk is not shared between locations, additional correlation information does not reduce the worst-case expected cost, which from the figure, we surmise to occur for a set of demand distributions whose correlation coefficient is greater than −0.55. This is consistent with the observation from Figure 9 of Natarajan et al (2018) that having additional covariance information does not significantly change the robust inventory levels since there is no pooling.…”

“…As previously illustrated in the Example 1, if the firm assumes a particular distribution for the demand vector, say a multivariate normal distribution with parameters (m, Σ), then the optimal decision resulting from the stochastic program (3) may be suboptimal with a high expected cost under the true (unknown) demand distribution. To protect against such cases, we adapt a minmax distributionally robust approach (Scarf 1958, Gallego and Moon 1993, Hanasusanto et al 2015, Natarajan et al 2018) that aims to choose inventory levels y to minimize the maximal expected cost over all demand distributions consistent with the information known to the firm.…”

Robust Vehicle Pre‐Allocation with Uncertain Covariates

“…, Natarajan et al. ). It would be a promising future research direction to incorporate the covariate information into the more sophisticated ambiguity sets considered in those works.…”

Closed-Form Solutions for Robust Inventory Management

“…Note that these models utilize a minmax approach to differing degrees, which implies that the models result in decisions that are risk averse, in contrast to the risk neutrality of stochastic models that optimize expected values. Other examples of this min-max style of research include Ehrhardt (1979) and Natarajan et al (2008). For other examples of riskaverse decision making in inventory management, see Lau (1980), Eeckhoudt et al (1995), Chen et al (2007b), Van Mieghem (2007, and the references therein.…”