Risk-averse Newsvendor Problem Research Articles

Procurement of New Products: Data-Driven Newsvendor with Profit Risk

We study a risk-averse newsvendor problem where demand distribution is unknown. The focal product is new, and only the historical demand information of related products is available. The newsvendor aims to maximize its expected profit subject to a profit risk constraint. We develop a model with a value-at-risk constraint and propose a data-driven approximation to the theoretical risk-averse newsvendor model. Specifically, based on the covariate information, we use machine learning methods to weight the similarity between the new product and the previous ones. The sample-dependent weights are then embedded to approximate the expected profit and the profit risk constraint. Afterward, we show that the data-driven risk-averse newsvendor solution entails a closed-form quantile structure and can be efficiently computed. Finally, we prove that this data-driven solution is asymptotically optimal. Experiments based on real data and synthetic data demonstrate the effectiveness of our approach. We find that under data-driven decision making, contrary to that in the theoretical risk-averse newsvendor model, the average realized profit may benefit from a stronger risk aversion. It further reveals that under data-driven decision making, even a risk-neutral newsvendor can benefit from incorporating a risk constraint, which plays a regularizing role in mitigating issues of data-driven decision making such as sampling error and model misspecification. The above effects however diminish as the size of the training data set increases, as the asymptotic optimality result implies.

A Risk-Averse Newsvendor Model Under the Framework of Uncertainty Theory

Due to the ever-changing and complex market environment, companies frequently face highly uncertain demand where data are so insufficient that the use of random or fuzzy variables, which are typically assumed in the literature, is impractical. Furthermore, companies are often risk-averse when making decisions. To address these two challenges, in this paper, we present the first study on a risk-averse newsvendor problem using the framework of uncertainty theory. To measure risk aversion, we adopt the measure of tail value-at-risk redefined based on uncertainty theory. We are able to analytically derive the optimal order quantity that maximizes the newsvendor’s expected utility. We find that the optimal order quantity of a risk-averse newsvendor is less than that of a risk-neutral newsvendor. Furthermore, as the degree of risk aversion increases, the optimal order quantity decreases. Also, we show that the optimal order quantity may be independent of the risk confidence level when the degree of risk aversion is below a threshold. Moreover, we use numerical examples to illustrate how various parameters, such as the degree of risk aversion, salvage value, and unit ordering cost, affect the optimal order quantity.

The risk-averse newsvendor problem under spectral risk measures: A classification with extensions

We study the risk-averse newsvendor problem by defining the objective function as a spectral risk measure. We analyze the problem under different types of return formulations, focusing on the impact of risk aversion and cost parameters on the optimal ordering decision. We show that the monotonicity of the return function with respect to random demand determines the structural properties of the problem. When the return function is monotone in demand realization, optimal order quantity does not depend on the return margin but only on the overage and underage costs, and it has a monotone relation to risk aversion. However, if return is non-monotone in demand impact of risk aversion depends on the specific setting and it can also be non-monotone. Additionally, it is non-increasing in the margin which leads to varying impact of selling price under distinct settings.

An empirical analysis of scenario generation methods for stochastic optimization

This work presents an empirical analysis of popular scenario generation methods for stochastic optimization, including quasi-Monte Carlo, moment matching, and methods based on probability metrics, as well as a new method referred to as Voronoi cell sampling. Solution quality is assessed by measuring the error that arises from using scenarios to solve a multi-dimensional newsvendor problem, for which analytical solutions are available. In addition to the expected value, the work also studies scenario quality when minimizing the expected shortfall using the conditional value-at-risk. To quickly solve problems with millions of random parameters, a reformulation of the risk-averse newsvendor problem is proposed which can be solved via Benders decomposition. The empirical analysis identifies Voronoi cell sampling as the method that provides the lowest errors, with particularly good results for heavy-tailed distributions. A controversial finding concerns evidence for the ineffectiveness of widely used methods based on minimizing probability metrics under high-dimensional randomness.

A risk-averse competitive newsvendor problem under the CVaR criterion

We study a risk-averse newsvendor problem with quantity competition and price competition. Under the Conditional Value-at-Risk (CVaR) criterion, we characterize the optimal quantity and pricing decisions under both quantity and price competition. For quantity competition, we consider two demand splitting rules, namely proportional demand allocation and demand reallocation. Although competition always leads to overstocking, interestingly it does not necessarily lead to a profit loss in certain competitive environments, such as demand reallocation, by avoiding/reducing overstocking that results from competition under the risk-neutral criterion. For price competition, we consider both additive and multiplicative demand. We find that the order quantity, sale price, and the expected profit decrease in the degree of risk aversion. Further, both high price sensitivity and competition intensity force decision makers to lower their prices. However, high price sensitivity always reduces the order quantity while competition can have the opposite effect.

The risk averse newsvendor problem from rank-dependent expected utility approach

This paper examines the single-period newsvendor problem where the risk averse newsvendor with rank-dependent expected utility (RDEU) determines the optimal order of newspapers for sale. Compared with the expected-utility (EU) newsvendor model, the effect of risk averse under RDEU on optimal order quantity is more significant and a closed-form solution is derived for dual-utility (DU) theory. The optimal order for RDEU newsvender is less than that for DU one. It follows that the optimal order for EU newsvender is less than that for expected-profit (EP) one. On the other hand, the optimal order for RDEU newsvender is less than that for EU one. In particular, the optimal order for DU newsvender is less than that for EP one. Effect of changes in risk aversion degree is also explored.

The risk-averse newsvendor problem with random capacity

We study the effect of capacity uncertainty on the inventory decisions of a risk-averse newsvendor. We consider two well-known risk criteria, namely Value-at-Risk (VaR) included as a constraint and Conditional Value-at-Risk (CVaR). For the risk-neutral newsvendor, we find that the optimal order quantity is not affected by the capacity uncertainty. However, this result does not hold for the risk-averse newsvendor problem. Specifically, we find that capacity uncertainty decreases the order quantity under the CVaR criterion. Under the VaR constraint, capacity uncertainty leads to an order decrease for low confidence levels, but to an order increase for high confidence levels. This implies that the risk criterion should be carefully selected as it has an important effect on inventory decisions. This is shown for the newsvendor problem, but is also likely to hold for other inventory control problems that future research can address.

A risk-averse newsvendor with law invariant coherent measures of risk

For general law invariant coherent measures of risk, we derive an equivalent representation of a risk-averse newsvendor problem as a mean-risk model. We prove that the higher the weight of the risk functional, the smaller the order quantity. Our theoretical results are confirmed by sample-based optimization.

A benchmark solution for the risk-averse newsvendor problem

In this paper, we derive the first order conditions for optimality for the problem of a risk-averse expected-utility maximizer newsvendor. We use these conditions to solve a special case where the utility function is any increasing differentiable function, and the random demand is uniformly distributed. This special case has a simple closed form solution and therefore it provides an insightful and practical interpretation to the optimal point. We show some properties of the solution and also demonstrate how it can be used for assessing the newsvendor utility function parameters.