Risk preferences, newsvendor orders and supply chain coordination using the Mean-CVaR model

The standard newsvendor model assumes that decision-makers in the supply chain are risk-neutral. This paper explores the newsvendor problem using risk measures building on the classical normative definition of risk preferences by certainty equivalents to model risk-averse, risk-neutral, and risk-taking decision-makers. We suggest the Mean-CVaR model based on the popular risk measures Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). The objective function is characterized by a tolerance level differentiating between low and high profits and by a pessimism level representing the weight of low profits. For the first time, we prove that the optimal order quantity is higher (lower) than the risk-neutral order quantity if and only if the newsvendor is risk-taking (risk-averse). The equivalence of product-specific risk preferences and the size of the order quantity enables the determination of the Mean-CVaR parameters from given order quantities or from a target profit. Further, based on supply chain's objective maximization criterion, we discuss supply chain coordination with Mean-CVaR decision-makers. We show that a simple wholesale price contract can coordinate the supplier–buyer supply chain and completely characterize the decision makers’ risk preferences under supply chain coordination. For example, if the coordinator (supplier) is risk-averse, a coordinating wholesale price exists for a less risk-averse buyer as well as for a risk-neutral and risk-taking buyer. We also determine the Mean-CVaR parameters if the coordinator specifies a target for the supply chain profit and the buyer communicates a target profit. In this case, the coordinating wholesale price depends on the ratio of the target profits and we show the impact on supply chain efficiency.