In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences for example, chi-squared, Hellinger, Kullback--Leibler. We show how uncertainty regions based on φ-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with φ-divergence uncertainty is tractable for most of the choices of φ typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach.

This paper was accepted by Gerard P. Cachon, optimization.

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Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

Samenvatting	In this paper we focus on robust linear optimization problems with uncertainty regions defined by o-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on o-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with o-divergence uncertainty is tractable for most of the choices of o typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach.

Supply chain operations have entered the digital era with the emergence of blockchain technology. In this paper, we discuss how the mean–variance (MV) approach can be applied to explore global supply chain operations risk with air logistics in the blockchain technology era. To be specific, we examine the related literature from four areas, namely air-logistics operations, demand management, supply management, and supply-demand coordination. We propose how the blockchain technology can be applied to facilitate the implementation of mean-variance risk analysis for global supply chain operations. We then highlight several promising areas for further studies. A future research agenda is developed.

The mean-variance approach for global supply chain risk analysis with air logistics in the blockchain technology era

Pioneered by Nobel laureate Harry Markowitz in the 1950s, the mean-variance (MV) formulation is a fundamental theory for risk management in finance. Over the past decades, there is a growing popularity of applying this ground breaking theory in analyzing stochastic supply chain management problems. Nowadays, there is no doubt that the mean-variance (MV) theory is a well-proven approach for conducting risk analysis in stochastic supply chain operational models. In view of the growing importance of MV approach in supply chain management, we review a selection of related papers in the literature that focus on MV analytical models. By classifying the literature into three major areas, namely, single-echelon problems, multi-echelon supply chain problems, and supply chain problems with information updating, we derive insights into the current state of knowledge in each area and identify some associated challenges with a discussion of some specific models. We also suggest future research directions on topics such as information asymmetry, supply networks, and boundedly rational agents, etc. In conclusion, this paper provides up-to-date information which helps both academicians and practitioners to better understand the development of MV models for supply chain risk analysis.

Supply chain risk analysis with mean-variance models: a technical review

Pricing strategy and coordination in a dual channel supply chain with a risk-averse retailer

The classical risk-neutral newsvendor problem is to decide the order quantity that maximizes the one-period expected profit. In this note, we consider a risk-averse newsvendor with stochastic price-dependent demand. We adopt Conditional Value-at-Risk ( CVaR ), a risk measure commonly used in finance, as the decision criterion. The aim of our study is to investigate the optimal pricing and ordering decisions in such a setting. For both additive and multiplicative demand models, we provide sufficient conditions for the uniqueness and existence of the optimal policy. Comparative statics show the monotonicity properties and other characteristics of the optimal pricing and ordering decisions. We also compare our results with those of the newsvendor with a risk-neutral attitude and a general utility function.

Minghui Xu

Papers

Technical Note---A Risk-Averse Newsvendor Model Under the CVaR Criterion