Customer and retailer rebates under risk aversion

This article develops a game theoretic model of a supply chain with one supplier and two risk-averse retailers competing in price, service and lot size, where the Economic Order Quantity (EOQ) production-inventory policy is adopted. After studying the existence of EOQ equilibrium, we investigate how to adjust their decisions when the economic environment changes. We find that one retailer will decrease its optimal lot size, retail price and service level when it becomes more risk averse or its service investment efficiency decreases. When the supplier's capacity increases, the retailers will reduce retail price and increase service level, which in turn results in a higher lot size. The effect of the risk sensitivity of one retailer on the rival retailer's decisions depends on the relative service cost efficiency of the retailer. When the absolute risk aversion and service investment efficiency of one retailer increase, the supplier's profitability will increase due to a higher total expected demand. We further give the managerial insights for practitioners, which helps managers to make right decisions in an uncertain environment.

This paper investigates a dual-channel supply chain with one risk-neutral manufacturer and one risk-averse retailer where there is only one perishable product with price-dependent stochastic demand. We choose Conditional Value-at-Risk criterion to measure the retailer’s risk-averse level, and assume that the manufacturer’s direct sales channel and the retailer’s traditional channel adopt a consistent pricing strategy. The model explores a Nash bargaining problem where the manufacturer and the retailer negotiate with each other on the wholesale price, the retail price and the order quantity when they have equal bargaining power. It is found that when demand uncertainty follows a uniform distribution, a Nash bargaining equilibrium exists and the retail price will decrease as the retailer becomes more risk averse. However, when the risk-averse indicator increases, the manufacturer’s profit on his direct channel will decrease, increase or first increase and then decrease, depending on the values of the related parameters. The profit shares of the manufacturer and the retailer under the Nash equilibrium model are related to the risk-averse indicator of the retailer. Furthermore, we perform three sets of numerical experiments to verify the effects of the retailer’s risk-averse indicator on decision-making and profit allocations under the different environmental parameters and gain several meaningful managerial insights.

Supply contracts with options have been proposed to provide flexibility in supply chains with high demand uncertainties. In this paper, we consider a flexible supply contract model with bidirectional options in which a risk-averse retailer subject to high uncertain market demand and ordering decisions. We use the Conditional Value-at-Risk, a risk measure commonly used in finance, as a decision criterion and derive the retailer's optimal ordering decisions equations. In particular, we obtain closed-form formulae to describe the retailer's optimal behavior when the demand is uniformly distributed. Numerical examples analyze that how the risk aversion and contract parameters affect the retailer's optimal decisions. We also numerically prove that bidirectional options improve the retailer's profit under risk aversions, compared with the wholesale price contract.

We use household survey data to construct a direct measure of absolute risk aversion based on the maximum price a consumer is willing to pay for a risky security. We relate this measure to consumer's endowments and attributes and to measures of background risk and liquidity constraints. We find that risk aversion is a decreasing function of the endowment—thus rejecting CARA preferences. We estimate the elasticity of risk aversion to consumption at about 0.7, below the unitary value predicted by CRRA utility. We also find that households' attributes are of little help in predicting their degree of risk aversion, which is characterized by massive unexplained heterogeneity. We show that the consumer's environment affects risk aversion. Individuals who are more likely to face income uncertainty or to become liquidity constrained exhibit a higher degree of absolute risk aversion, consistent with recent theories of attitudes toward risk in the presence of uninsurable risks.

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

In this study, we conduct a comprehensive literature review on the inventory and pricing decisions under the supply chain coordination. To be specific, we review the publications from 1997 to 2017 and divide the papers into six areas for discussion, they are: decisions under integrated supply chain, supply contract, capital-constrained, competition, risk aversion, and information asymmetry. After reviewing the literature, we identify three major future research directions. First, we propose to explore different real world industrial supply contracts and the forms of demand function. Second, limited studies consider risk aversion behaviour of the supply chain members; hence, we also propose to examine the inventory and pricing decisions under supply chain coordination with risk-averse retailer and risk-averse supplier, respectively. Finally, it is also interesting to investigate different types of information asymmetry.

This paper investigates the impacts of bilateral asymmetric information in a supply chain. More specifically, we consider a supply chain consisting of one risk-neural manufacturer and one risk-averse retailer who have their private information regarding the manufacturing cost and risk aversion degree, respectively. We first construct a model under the bilateral asymmetric information case using M-V approach. There exists a pair of threshold values of cost and risk aversion degree such that the optimal trading quantity holds. We then give a wholesale price contract under bilateral asymmetric information case to examine the information revealing. We find that the manufacturer and the retailer both announce a lower information type to gain more opportunistically individual profit. This damages the supply chain’s performance.

Supply chain contract mechanism under bilateral information asymmetry

The expected utility hypothesis predicts that, when the price of insurance is actuarially fair to the consumer, a risk-averse consumer will choose to fully insure against a potential loss. The only role that income can play in affecting the amount of insurance demanded at the actuarially fair price is to affect the size of the potential loss. This result is independent of the consumer's degree of risk aversion or how it varies with income. However, at a price of insurance above or below the actuarially fair level the consumer's degree of risk aversion and its relation to the consumer's income level must be considered if we are to usefully describe consumer behavior.' Mossin [10] showed, for a consumer with declining absolute risk aversion and at a price of insurance above the actuarially fair level but below the price at which no insurance will be purchased, the optimal amount of insurance demanded against a loss of a given size is inversely related to the consumer's income. Chesney and Louberge [2] noted that Mossin's result does not take into account the empirically plausible situation in which higher income consumers may have greater potential losses to insure against. They present results concerning the relationship between risk aversion and the level and composition of income (in terms of the proportion of income subject to loss) and the maximum premium the consumer would be willing to pay for full insurance coverage. Since their results are in terms of the maximum willingness to pay for full insurance,

For instance, one suspects that risk-averse farmers should be willing to pay more for improved weather forecasts than risk-neutral ones. Similarly defensive medicine (i.e., the excess ordering of almost useless diagnostic tests) is often attributed to a risk-averse behavior by physicians. This widespread belief about a monotone relationship between the value of information and the degree of risk aversion has resisted accepting important theoretical contributions that have shown the possibility of a reverse relationship. Gould (1974) established the lack of unambiguous relationship between the degree of risk and information value. Freixas and Kihlstrom (1984) showed that information demand may decrease with the degree of risk aversion, and their result was reiterated in a different context by Willinger (1989). Unfortunately these important contributions did not have a wide impact because they were rather technical. The exception is a survey paper by Hilton (1981) who examined properties of information value. Among many other results, he showed, with the help of a very short numerical example, that an increase in risk aversion may indeed lead to a lower information value. However, he did not give the intuitive reason that justifies this surprising result. Our purpose is to explain precisely, in as simple terms as possible, why more risk aversion does not always induce a greater information value. We present the basic model, and we define the concept of (perfect) information value. A detailed numerical illustration is provided.

Risk Aversion Behavior of Farm Households and the Role of Credit Service in Kobbo District, North Wollo Zone of Ethiopia

Risk aversion and asymmetry in procurement auctions: Identification, estimation and application to construction procurements

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 need for low-carbon development has become a social consensus. Increasing numbers of enterprises implement carbon emission reduction by using carbon cap-and-trade mechanisms to cater to consumers and practice social responsibility. From the manufacturer’s perspective, they can implement carbon emission reduction investment by themselves or outsource it to the retailer or energy service company (referred as ESCO). To explore the best carbon emission reduction mode selection strategy, we built and compared three carbon emission reduction modes—manufacturer emission reduction, retailer emission reduction, and ESCO emission reduction—by using Stackelberg game models. The joint decisions of operation, finance, and environment were obtained by using the backward induction approach. The impacts of key parameters were analyzed, such as the retailer’s initial capital amount and the decision-makers’ risk aversion degree on the low carbon supply chain operation. Our results show that the optimal carbon emission reduction mode for the manufacturer is changed as the retailer’s initial capital amount changes. Carbon emission reduction by the ESCO (retailer) becomes the dominant strategy for both the economy and environment when the cost advantage (cash investment ratio) of the ESCO (retailer) carbon emission reduction mode is sufficiently high (low). Overall, decision-makers’ risk aversion is detrimental to both the economic and environmental developments of the supply chain. We also designed contracts to realize the coordination of risk-neutral, risk-averse, capital-adequate, and capital-constrained low-carbon supply chains. These results give guidance for decision-makers to better manage the low-carbon supply chain in the context of fully considering the influential factors of risk aversion and capital constraint.

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.