Risk-averse Newsvendor Research Articles

Supply option purchasing decisions via mismatch cost minimization

In this paper, the optimal purchasing decisions of the option procurement of newsvendor-type commodities are studied. Based on the mismatch cost minimization criterion, the present study analyzes the option purchasing decisions of a risk-averse newsvendor under the measure of Conditional Value-at-Risk (CVaR). For the purpose of controlling the procurement risk, it is found that a newsvendor’s optimal option purchasing decision under the CVaR measure increases at the quantile level under certain conditions. The result provides alternative explanations for a newsvendor’s over-purchasing behaviors in reality. To mitigate the conservativeness of the CVaR measure, a combined objective defined as the mean-CVaR on mismatch cost is introduced, and the optimal option purchasing decision of a newsvendor minimizing the combined objective is derived. The combined objective can strike a balance between the minimization of CVaR of mismatch cost as well as the minimization of expected mismatch cost. In addition, a sensitivity analysis is performed to exhibit the results and managerial insights are presented to hedge against the potential risks for newsvendors in the option purchasing decision-making.

Data-driven risk-averse newsvendor problems: developing the CVaR criteria and support vector machines

Incorporating decision-makers' risk preferences into data-driven newsvendor models and developing machine learning methods to solve the models are the challenging problems addressed in this study. To consider different distributions and decision-makers' different risk preferences for the two losses of the total cost newsvendor model, the symmetrical, the partial symmetrical and the asymmetrical CVaR criteria are introduced. The regularisation, the primal-dual approach and the kernels in support vector machines are used to transform the data-driven risk-averse newsvendor problems under the CVaR criterion into the convex quadratic programming problems with good theoretical properties. Computational experiments are conducted on a real-world dataset. The models under the partial symmetrical and the asymmetrical CVaR criteria obtained good performances, but that under the symmetrical CVaR criterion suffered the underfitting problem. Two factors including the degrees of risk aversion for the two losses in the total cost newsvendor model and the empirical errors of data-driven models affect order decisions. The degrees of risk aversion for the two losses have anti-directional effects on order quantities. The introduction of asymmetrical CVaR criterion paves a new way to reveal the effects of different risk references for different losses on order decisions, and has the potential to improve newsvendor decisions.

A comparative study to find the optimal ordering quantity of the risk-neutral and risk-averse newsvendor

In the classical newsvendor problem, it is considered that the newsvendor is risk-neutral and the Optimal Ordering Quantity (OOQ) was found which maximizes the newsvendor expected profit. In the real world, different investors have different attitudes towards risk. Accordingly, this paper considers the utility function which is commonly being used to model the attitude of the investor who makes the investment decision to maximize his expected utility instead of expected profit. This study considers the quadratic utility function and demonstrates that it can be used to describe the riskaverse as well as a risk-neutral investor with some conditions. Finally, by considering the risk profile of the investor at different levels of investor initial wealth, we have developed a method to determine the OOQ which maximizes the expected utility. From the numerical examples, it is clear that the OOQ and hence the expected utility varies depending on an investor?s attitude toward the risk and investment decision. At different levels of initial wealth, the attitudes toward the risk of the investors are different and the sensitivity analysis demonstrates how an investor can choose the initial wealth and OOQ to maximize his expected utility.

Dynamic coordinated maintenance of wind-farms with risk-averse agents under CVaR criterion

We study a coordinated maintenance problem for multi-turbine offshore wind-farms. The deterioration of the turbines follows a Poisson process and the optimal order quantity for a single wind-farm, as well as for a coalition of wind-farms, is obtained using the analogy with the risk-averse newsvendor model considering the conditional value at risk (CVaR) criterion. We apply the theory of robust dynamic coalitional games to design a stable allocation mechanism that distributes the cost of the coalition among all the participants in a fair and stable way.

A Risk-Averse Newsvendor Model under Stochastic Market Price

The optimal inventory control is closely related to an enterprise’s operational efficiency, survival, and development. Market price uncertainty is introduced into the newsvendor model and the uncertainty’s impact on the firm's optimal stocking quantity is discussed. The results show that the impact of stochastic market price on the optimal stocking quantity under a given condition mainly depends on the magnitude of inventory cost. When the inventory cost is low, the market price’s uncertainty leads the firm to increase the stocking quantity. In contrast, when the inventory cost is high, market price uncertainty leads the firm to decrease inventory. Besides, the risk-averse behaviour leads the firm to reduce its stocking quantity.

Replenishment decisions for complementary components with supply capacity uncertainty under the CVaR criterion

In this paper we consider a risk-averse newsvendor to assemble a final product that is made up of multiple complementary components, where both the product demand and the supply capacity of each component are random. A novel approach is proposed to derive the first-order condition for the optimal order quantity under the Conditional Value-at-Risk (CVaR) criterion. A comprehensive comparative statics analysis is conducted. The basic model is also extended to allow dependence among the random demand and supply capacities. We show that the objective function remains to be quasi-concave if those random variables are negatively dependent, and that the positive (negative) dependence of those random variables increases (decreases) the optimal order quantity and objective value. Numerical examples are provided to illustrate some of the main results.

Complex dynamic analysis of risk-averse newsvendor models with buyback guarantee financing

In the framework of the newsvendor model, both single- and multi-period models are proposed to investigate the ordering strategy of a risk-averse retailer under buyback guarantee financing (BGF) and stochastic demand. In the single-period model, the classical newsvendor is extended by introducing risk aversion and capital constraints simultaneously. It is found that the optimal ordering quantity is a monotonic function in some parameters, such as increasing in the retailer's risk aversion and salvage value, while decreasing in the initial capital and wholesale price. The multi-period model is a dynamical model described by the bounded rationality decision adjustment rules. We then investigate the complex dynamics they admit, such as period-doubling bifurcation and chaotic phenomena, and have found that the dynamical models experience more complex behaviour than their static counterpart. Furthermore, in the dynamical case, we could see periodic, bifurcating or chaotic changes in ordering quantity. We also investigate the influence of BGF on ordering quantity, which may lead to a risk-averse retailer to order aggressively. Finally, some numerical simulations are given to illustrate the theoretical results and some suggestions are also provided.

Stochastic sensitivity and dynamical complexity of newsvendor models subject to trade credit

To describe the dynamical ordering behaviour of a risk-averse newsvendor with trade credit in supply chain, two models are formulated for two scenarios based on the bounded rationality rule. Assuming the newsvendor chooses the ordering quantity by adaptively adjusting the choice of previous period, we first develop a deterministic model. Then, mathematical analysis of the model is provided, such as the stability of equilibrium points, Neimark–Sacker bifurcation and normal form. Besides, the diagrams such as bifurcation to chaos, Lyapunov exponent, attractors and time series are illustrated numerically. It is then followed by a stochastic model to reflect the unexpected random noises from external operational environment and the perturbation on the newsvendor behaviour. The sensitivity of equilibria, the confidence ellipse and the confidence band are investigated by utilising Stochastic Sensitivity Function technique. Analysis on stochastic sensitivity shows that the retailer’s dynamical ordering exhibits more complex behaviour than the deterministic counterpart.

The optimal order decisions of a risk-averse newsvendor under backlogging

In this paper, we are concerned with the optimal order quantities for a risk-averse newsvendor with backlogging, where it is assumed that all or part of the unsatisfied demands can be fullfilled by backordering. The optimal order quantities are derived under the famous conditional value-at-risk (CVaR) criterion and mean-CVaR criterion on controlling the profit loss due to the uncertainty of market demands. With the optimal order quantities to the proposed models, several important monotone properties are obtained and their relationships with the existing results are discussed. Moreover, it is shown in this paper that low risk means low expected profit while high expected profit comes with high risk. Finally, we present some managerial insights for the risk-averse newsvendor model under backlogging.

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.

Dynamics of a risk-averse newsvendor model with continuous-time delay in supply chain financing

In this paper, delay differential equations are adopted to describe the ordering performance of the risk-averse newsvendor with supply chain financing. Firstly, authors theoretically explore the local asymptotical stability for equilibrium point, and also the conditions and directions for Hopf bifurcation of the ordering quantity for risk-averse retailer. Secondly, they investigate the influence of important parameters on the bifurcation, and find that the initial capital, risk aversion and friction coefficient can make the Hopf bifurcation undergo a long time, but the adjustment speed induces the inverse effect. Then phase diagram, stable region, bifurcation to chaos, time series and CVaR profit are illustrated by means of numerical simulation. It is found that the upstream supplier can share the risk from market uncertain with stochastic demand under supply chain financing. The results also indicate that the optimal ordering quantity placed by risk-averse newsvendor is smaller than the risk-neutral ordering quantity. Furthermore, the less initial capital may cause the CVaR profit to increase steadily or drop sharply, which exhibits complex dynamical behaviour in the presence of the time delay. Finally, the stability and bifurcation analysis of a fractional delay ordering model has also been proposed and studied. It is worth pointing out that in this study authors assume there is only one retailer who is risk-averse. Therefore, it will be more interesting and meaningful to consider the scenario having multiple retailers and to incorporate the upstream supplier’s optimal decision into the dynamical decision model.

A newsvendor model with autocorrelated demand under a time-consistent dynamic CVaR measure

As a result of autocorrelation, static risk measures such as value at risk and Conditional Value at Risk (CVaR) are time inconsistent and can thus result in inconsistent decisions over time. In this article, we present a time-consistent dynamic CVaR measure and examine it in the context of a newsvendor problem with autocorrelated demand. Due to the concavity of our CVaR measure, the dynamic program formulation associated with our dynamic newsvendor problem is not immediately separable. However, by exploring certain properties of the dynamic CVaR measure and underlying profit function, our dynamic program can be transformed into a sequence of (single-period) risk-averse newsvendor problems that depend on the observed demand history. By examining the structure of the optimal order quantities, we find both intuitive and counterintuitive results. When demands are positively correlated, the optimal order quantity is monotonically increasing in the degree of risk aversion. However, when demands are negatively correlated and the underlying cost structure satisfies certain conditions, the optimal order quantity is no longer monotonically increasing in the degree of risk aversion. Instead, the optimal order quantity is a decreasing (increasing) function of the degree of risk aversion when it is below (above) a certain threshold. We also show that these results continue to hold when demands follow a general ARMA process, and when inventory carryover is considered.

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.

Pricing and ordering decisions of risk-averse newsvendors: Expectile-based value at risk (E-VaR) approach

Pricing and ordering decisions of risk-averse newsvendors: Expectile-based value at risk (E-VaR) approach

Comparing validity of risk measures on newsvendor models in open innovation perspective

In the era of Industry 4.0, firms are facing with greater uncertainty. Accordingly, it is important to select quality risk measures to analyze newsvendor problems under risk. Then, open innovation can be a good remedial option for such risk-averse newsvendors because open innovation can offset the profit losses from risk aversion by sharing revenues in supply chains. To find such risk measures in newsvendor problems, we review various risk measures of risk-averse inventory models and existing articles in inventory management literature. Then we provide a logical reasoning and axiomatic framework to evaluate validity of each risk measure in newsvendor problems - consistency to the four axioms in coherent risk measures. In this framework, the underlying assumptions and managerial insights to the newsvendor problems are examined for each risk measure. Consequently, exponential utility function and coherent measures of risk are selected as two plausible risk measures to analyze multi-product risk-averse newsvendor models.

Optimal Policies of Newsvendor Model Under Inventory-Dependent Demand

This paper aims to give the newsvendor’s unique optimal order quantity in two forms of models under inventory-dependent demand: the linear model and the non-linear model (e.g. exponential function), and study differences caused by different effects of the inventory level on the consumer demand. Finally, we provide optimal order policies and find the risk-averse newsvendor’s optimal order quantity always decreases in the risk aversion and is still lower than that of the risk-neutral newsvendor no matter how the inventory level affects the consumer demand. Moreover, effects of parameters on optimal order quantities have been proved through numerical studies.

Inventory centralization with risk-averse newsvendors

In the paper, we study the inventory centralization problem with risk-averse newsvendors using cooperative game theory. Pareto-optimality and collective rationality conditions are adopted to characterize the stable profit allocations among coalition members. Pareto-optimal profit allocation rules are derived for exponential and power utilities while the necessary and sufficient conditions are shown for stable profit allocations. We also show that the game model has a nonempty core when the exponential and power utilities are adopted to describe the risk-averse behavior.

A Risk-Averse Newsvendor Model Under Trade Credit Contract with CVaR

A supply chain with a supplier and a risk-averse retailer is considered in the paper under trade credit contract. The retailer as newsvendor faces a non-negative random demand and the supplier provides the trade credit for the risk-averse retailer with budget constraints. Different from the existing research, in a conditional value-at-risk (CVaR) framework, the optimal ordering quantity and wholesale price are obtained. Analytical results are obtained for the newsvendor retailer’s optimal ordering quantity and supplier’s optimal wholesale price under CVaR measure. Sensitivity analysis is also yielded. It is found that the optimal ordering quantity decreases as the degree of risk aversion increases. Furthermore, we analyze the effect of the initial budget of retailer and the wholesale price on the order quantity decision. This paper also finds that the trade credit contract could create value for a risk-averse supply chain with budget constraints. Finally, to compare with the existing results the theoretical analysis and numerical examples are illustrated.

The Optimal Strategies of Risk-Averse Newsvendor Model for a Dyadic Supply Chain with Financing Service

This paper studies the budget-constrained newsvendor problem under risk aversion with financing service and builds a two-stage supply chain decision model on the order quantity and wholesale price. The budget-constrained retailer as a newsvendor faces a nonnegative random demand and the financial institution provides the loan service for the retailer who is risk-averse. This paper first explores the impact of risk aversion on the decisions in financial supply chain. Different from the existing research, we analyze how the financing service of bank loan impacts the risk-averse newsvendor’s decision and how the risk-averse behavior of the retailer influences the optimal strategies in supply chain with CVaR risk measure criterion. It is found that the order quantity decreases in the degree of risk aversion. The optimal order quantity is decreasing in initial budget, wholesale price, and interest rate. It is worth noting that the financing service can improve the profit of the supply chain system when the retailer has a low initial wealth. Finally, to compare with the existing results the theoretical analysis and numerical examples are also illustrated.

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.