Risk-averse Retailer Research Articles

Impact of Risk Aversion on Optimal Decisions in Supply Contracts with Bidirectional Options

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.

Loss-averse newsvendor model with two ordering opportunities and market information updating

A fashion supply chain characterized by a long lead time and a short selling season is considered in this paper. Facing demand uncertainty, the risk averse retailer has two opportunities to make order decisions before the demand is realized. The risk aversion is modelled as a penalty to the decision maker (the retailer) if a target profit is not attained. We derive the retailer's optimal ordering decisions and analyze the monotonicity behaviours of the critical market signal, the optimal first-stage order quantity, and the optimal expected payoff with respect to the penalty coefficient. We also examine the impact of demand forecast quality on the retailer's decisions and extend the study to the case where order cancellation is allowed.

The Effect of Risk Aversion on Manufacturer Advertising in a Two-Stage Supply Chain

Abstract We consider a supply chain system with a risk-neutral manufacturer as the leader and a risk-averse retailer as the follower with uncertain demand. At the beginning of the game, the manufacturer makes efforts on advertising and then the retailer decides its order quantity before demand realization. The retailer's risk aversion is modeled by the Value-at-Risk (VaR) approach with the downside risk constraint. The analysis of equilibrium strategies indicates some characteristics of the game are different from those under risk-neutral assumptions. We find that the manufacturer can effectively prevent the risk-averse retailer from downsizing the order quantity through advertising. In order to explain the difference, we investigate the impacts of risk aversion on the manufacturer's advertising decision and the retailer's ordering decision. We find that the retailer with moderate degree of risk aversion orders a larger volume and receives greater advertising support from the manufacturer. Moreover, the feasible combinations of target profit and downside risk for moderate risk aversion are discussed to derive the relationship of the two parameters. In addition, we make a simple analysis of the situation with two independent retailers who have heterogeneous degrees of risk aversion.

Product Portfolio Evaluation and Differentiated Pricing: A Risk Management Perspective

We consider a retailer that sells a product line to a market with multiple segments. The risk neutral or averse retailer can tailor product assortment and differentiate product prices to each submarket, in which heterogenous customer demand takes a logit form. We derive the optimal pricing operator, which is increasing and concave in a product line power index and determines the optimal product prices in each submarket. From a risk management perspective, we evaluate the product line performance as a financial portfolio problem, in which the optimal pricing operator can be viewed as a utility function, each product variant as a stock with random payoff and each submarket as a state of nature. First, we calculate and characterize the risk aversion coefficient of the optimal pricing operator. Second, we obtain managerial insights for product portfolio evaluation via mean-variance analysis and using stochastic orders. The principles of forming an efficient product line are to select products with high average popularity, low heterogeneity risk across submarkets and low/negative correlation among each other. Selecting products that are popular in separate submarkets generates low/negative correlation among the products.

CHANNEL BARGAINING WITH RISK-AVERSE RETAILER UNDER THE MULTIPLICATIVE DEMAND MODEL

We consider a channel bargaining problem.The channel is made up with a riskneutral manufacturer and a risk-averse retailer who faces a stochastic price-dependent demand in this paper.Using the Conditional Value-at-Risk(CVaR) as the risk measure,we investigate the optimal equilibrium wholesale price,selling price and order quantity and find a sufficient condition for the equilibria of the unequal bargaining problem under the multiplicative demand model.Furthermore,when the demand noise follows a uniform distribution,it is shown that the manufacturer's profit share of the supply chain is the same as the general demand situation, and it is increasing with respect to the retailer's risk attitude and unrelated to the form of the mean demand function.

Customer and retailer rebates under risk aversion

In a supply chain setting, we analyze a manufacturer's customer and retailer rebates, which are sales incentives offered to the end buyers and retailers, respectively. The performance of both rebates is influenced by the retailer's objective and response to the promotion due to his intermediary position in the channel. Earlier studies investigating rebates in distribution channels have traditionally assumed that the retailer is risk neutral with the objective of maximizing expected profits. In our paper, we consider a risk-averse retailer. We formally model risk aversion by adopting the Conditional-Value-at-Risk ( CVaR) decision criterion. Using a stochastic and (effective) price dependent demand, we analyze the manufacturer's rebate amount decisions and the retailer's joint inventory and pricing decisions in a game theoretical framework. We provide several structural properties of the objective functions and show monotonicity of the retailer's decisions in the degree of risk aversion. For the case of retailer rebates, we characterize the unique equilibrium, and for the case of customer rebates, we prove the existence of an equilibrium. Using numerical examples, we provide further insights on the impact of risk aversion. For example, given an exogenous wholesale price, we observe a threshold value on the retailer's risk-aversion parameter below (above) which the manufacturer is better off with retailer rebates (customer rebates); implying that the manufacturer's preferred rebate type can be different depending on whether the retailer is risk neutral or sufficiently risk averse.

Supply chain coordination with risk sensitive retailer under target sales rebate

Target sales rebate (TSR) contracts have been shown to be useful in coordinating supply chains with risk-neutral agents. However, there have been few studies on the cases with risk sensitive agents. As a result, based on the classic Markowitz portfolio theory in finance, we carry out in this paper a mean–variance (MV) analysis of supply chains under TSR contracts. We study a supply chain with a single supplier and a single risk averse retailer. We propose TSR contracts for achieving coordination. We demonstrate how TSR contracts can coordinate the supply chain which takes into consideration the degree of risk aversion of the retailer. We find that the supplier can coordinate the channel with flexible TSR contracts. In addition, we extend the supply chain model to include sales effort decision of the retailer. Conditions for TSR contracts to coordinate the supply chain with sales effort of retailer are also derived.

Supply Chain Competition with Multiple Manufacturers and Retailers

We study competition in a supply chain where multiple manufacturers compete in quantities to supply a set of products to multiple risk-averse retailers who compete in quantities to satisfy the uncertain consumer demand. For the symmetric supply chain, we give closed-form expressions for the unique equilibrium. We find that, provided there is a sufficiently large number of manufacturers and retailers, the supply chain efficiency (the ratio of the aggregate utility in the decentralized and centralized chains) can be raised to 1 by inducing the right degree of retailer differentiation. Also, risk aversion results in triple marginalization: retailers require a strictly positive margin to distribute even when they are perfectly competitive, because otherwise they are unwilling to undertake the risk associated with the uncertainty in demand. For the asymmetric supply chain, we show how numerical optimization can be used to compute the equilibria, and we find that the supply chain efficiency may drop sharply with the asymmetry of either manufacturers or retailers. We also find that the introduction of asymmetric product assortment reduces the degree of competition among retailers and thus has an effect similar to that of reducing the number of retailers. We show that, unlike in the symmetric chain, the asymmetric chain efficiency depends on product differentiation and risk aversion because of the interaction between these features and the asymmetry of manufacturers and retailers.

Manufacturer’s return policy in a two-stage supply chain with two risk-averse retailers and random demand

This paper studies the manufacturer’s return policy and the retailers’ decisions in a supply chain consisting of one manufacturer and two risk-averse retailers under a single-period setting with price-sensitive random demand. We characterize each retailer’s risk-embedded objective via conditional value-at-risk, and construct manufacturer-Stackelberg games with and without horizontal price competition between the retailers. We explore, through numerical studies, the effects of the retailers’ aversion to risk and other parameters on the manufacturer’s return policy and profit and the retailers’ decisions. We further investigate the effect of distribution asymmetry by comparing the results with normal and lognormal demand.

Managing inventory with two suppliers under yield uncertainty and risk aversion

In this paper, we consider a single-product single-period inventory model in which the retailer can source from two suppliers. The primary supplier is cheaper but unreliable in the sense that it generates supply yield uncertainty, whereas the secondary supplier is perfectly reliable but more expensive. The reliable supplier's capacity is fixed and the retailer cannot order more than the quantity reserved in advance. We study the problem in the context of a risk-averse retailer who has to determine the optimal order quantity from the primary supplier and the optimal reserved quantity from the secondary supplier. We develop the model in the perspective of a low risk averse retailer and quantify the risk via an exponential utility function. We show by numerical experiments how the resulting dual sourcing strategies differ from those obtained in the risk-neutral analysis. We also examine the sensitivity of some model-parameters on the optimal decisions.

Channel bargaining with risk-averse retailer

Abstract We first consider a supply chain with one manufacturer and one retailer where there is only one product with stochastic demand. The retailer is risk averse with Conditional Value-at-Risk (CVaR) as her risk measure and the manufacturer is a risk-neutral agent. We model the problem as a Nash-bargaining problem where the manufacturer and the retailer negotiate about the wholesale price and order quantity. We show that there exists a Nash-bargaining equilibrium for the wholesale price and order quantity with equal and unequal bargaining power. We also find that even for the equal bargaining power between the two agents, the retailer's bargaining power for the supply chain profit increases as she becomes more risk averse. We then extend the model to the case where demand is endogenous and can be manipulated by setting the retail price. We show that there exists a Nash-bargaining equilibrium for the wholesale price, retail price and the order quantity under equal bargaining power.

Optimization of Electricity Retailer's Contract Portfolio Subject to Risk Preferences

When an electricity retailer faces volume risk in meeting load and spot price risk in purchasing from the wholesale market, conventional risk management optimization methods can be quite inefficient. For the management of an electricity contract portfolio in this context, we develop a multistage stochastic optimization approach which accounts for the uncertainties of both electricity prices and loads, and which permits the specification of conditional-value-at-risk requirements to optimize hedging across intermediate stages in the planning horizons. Our experimental results, based on real data from Nordpool, suggest that the modeling of price and load correlations is particularly important. The sensitivity analysis is extended to characterize the behavior of retailers with different risk attitudes. Thus, we observe that a risk neutral retailer is more susceptible to price-related than load-related uncertainties in terms of the expected cost of satisfying the load, and that a risk averse retailer is especially sensitive to the drivers of the forward risk premium.

Risk sharing and information revelation mechanism of a one-manufacturer and one-retailer supply chain facing an integrated competitor

This paper develops an information revelation mechanism model of a one-manufacturer and one-retailer supply chain facing an outside integrated-competitor under demand uncertainty. We investigate how the manufacturer designs a wholesale price-order quantity contract to induce the retailer to report his risk sensitivity information truthfully. We try to explore the effects of the outside competitor and the risk-sharing rule on the optimal price-service level decisions of the retailer and the optimal wholesale prices of the manufacturer. We find that the strategic interaction plays an important role in the effect of risk sensitivity on the order quantity for the retailer. When the fraction of the risk cost shared by the manufacturer is sufficiently large (small), the optimal wholesale price for the high risk-averse retailer is higher (lower) than that for the low risk-averse retailer.

Pricing, service level and lot size decisions of a supply chain with risk-averse retailers: implications to practitioners

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.

SUPPLY CHAIN COORDINATION WITH CVaR CRITERION

We study the coordination of supply chains with a risk-neutral supplier and a risk-averse retailer. Different from the downside risk setting, in a conditional value-at-risk (CVaR) framework, we show that the supply chain can be coordinated with the revenue-sharing, buy-back, two-part tariff and quantity flexibility contracts. Furthermore the revenue-sharing contracts are still equivalent to the buy-back contracts when the retail price is fixed. At the same time, it is shown that the risk-averse retailer of the coordinated supply chain can increase its profit by raising its risk-averse degree under mild conditions.

Hedging and Vertical Integration in Electricity Markets

This paper analyzes the interactions between competitive (wholesale) spot, retail, and forward markets and vertical integration in electricity markets. We develop an equilibrium model with producers, retailers, and traders that enables us to quantify the impact of forward markets and vertical integration on prices, risk premia and retail market shares. We point out that forward hedging and vertical integration are two separate mechanisms for demand and spot price risk diversification that both reduce the retail price and increase retail market shares. We show that they are imperfect substitutes as to their impact on prices and firms' utility because of the asymmetry between production and retail segments. Vertical integration restores the symmetry between producers' and retailers' exposure to demand risk while linear forward contracts do not. Vertical integration is superior to forward hedging in presence of highly risk averse retailers. We illustrate our analysis with data from the French electricity market.

Price and service competition of supply chains with risk-averse retailers under demand uncertainty

We develop a price–service competition model of two supply chains to investigate the optimal decisions of players under demand uncertainty. Each supply chain consists of one risk-neutral supplier and one risk-averse retailer. We analyze the effects of the retailers’ risk sensitivity on the players’ optimal strategies. We find that the higher the risk sensitivity of one retailer, the lower his optimal service level and retail price will be, while the effects of the rival's risk sensitivity on his decisions depend on the substitutability of the two products. The optimal wholesale price of one supplier is first increasing and then decreasing with the risk sensitivity of the two retailers if the substitutability is sufficiently low, otherwise decreasing with the risk sensitivity. The expected equilibrium order quantity of one retailer is often increasing with his risk sensitivity. We also study the effects of the wholesale prices and the service investment efficiencies on the retail price–service level decisions of the retailers. We find that the higher the service investment efficiency of one retailer, the lower the optimal retail price and service level of his rival will be.

Channel coordination in supply chains with agents having mean-variance objectives

This paper investigates the issues of channel coordination in a supply chain when the individual supply chain decision makers take mean-variance (MV) objectives. We propose an MV formulation to capture the risk preference of each individual supply chain agent. Through the studies of a wholesale pricing policy, we find that the incorporation of risk concerns into the setting of supply chain coordinating policy is very important because it can substantially affect the achievability of channel coordination. It is also interesting to find that channel coordination depends on how big the net difference between the risk preferences of the supply chain coordinator and the retailer is. Thus, a slightly risk averse supply chain coordinator can successfully coordinate with a slightly risk prone retailer but not a very risk averse retailer. Numerical analyses are included and managerial insights are developed.

Supply chain structure and demand risk

V. Agrawal and S. Seshadri (2000) [Risk intermediation in supply chains. IIE Transactions, 32, 819–831] considered a problem in which a single risk neutral distributor supplies a short-lifecycle, long-leadtime product to several retailers that are identical except in their attitudes towards risk. They proved that the distributor should not offer the same terms to every retailer but instead offer less risky (from the demand risk perspective) contracts to more risk averse retailers. They did not prove the optimality of their menu. In this paper we reconstruct their results when the number of retailers is infinite and their coefficient of risk aversion is drawn from a continuous distribution. We use optimal control theory to solve this problem. We show that this distribution uniquely determines the channel structure. Moreover, the optimal contract menu not only has the same structure as in Agrawal and Seshadri but is also optimal among nearly all contracts. The implications of these findings for channel design are discussed.

Impact of Uncertainty and Risk Aversion on Price and Order Quantity in the Newsvendor Problem

We consider a single-period inventory model in which a risk-averse retailer faces uncertain customer demand and makes a purchasing-order-quantity and a selling-price decision with the objective of maximizing expected utility. This problem is similar to the classic newsvendor problem, except: (a) the distribution of demand is a function of the selling price, which is determined by the retailer; and (b) the objective of the retailer is to maximize his/her expected utility. We consider two different ways in which price affects the distribution of demand. In the first model, we assume that a change in price affects the scale of the distribution. In the second model, a change in price only affects the location of the distribution. We present methodology by which this problem with two decision variables can be simplified by reducing it to a problem in a single variable. We show that in comparison to a risk-neutral retailer, a risk-averse retailer in the first model will charge a higher price and order less; where as, in the second model a risk-averse retailer will charge a lower price. The implications of these findings for supply-chain strategy and channel design are discussed. Our research provides a better understanding of retailers' pricing behavior that could lead to improved price contracts and channel-management policies.