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Procurement strategies with quantity-oriented reference point and loss aversion
Abstract
This paper considers a single-product, single-period inventory management problem in which the retailer is loss averse with adaptive quantity-oriented reference points. The impact of the loss degree and the quantity-oriented reference point is investigated jointly on the optimal ordering quantity and the profit maximization of the retailer. It shows that there exists a unique optimal order quantity while maximizing the expected utility. The optimal solution can be readily determined via a numerical approach, and it has explicit forms for some special distribution functions. The loss-averse retailer's order quantity is always less than loss-neutral decision maker's when the reference dependency is under consideration. However, the optimal order quantity of the loss-averse system with quantity-oriented reference point is more than, equal to or less than that of the classical system. Furthermore, the structural properties and sensitivity analysis of the optimal solution are addressed. Several important managerial insights are presented by extensive numerical experiments, and finally, some conclusions and future work are given.
... The study of decision-maker's risk behaviour is another growing research stream in the NV problem. In this stream, scholars adopt four risk analysis methods: the expected utility theory (EUT) (Keren & Pliskin, 2006), mean-variance analysis (Rubio-Herrero et al., 2015), conditional value-at-risk (CVaR) criteria (Xinsheng et al., 2015) and prospect theory (PT) and reference point method (R. Wang & Wang, 2018). In our research, we work on the risk behaviour of the decision-maker using PT with reference point analysis. ...
... Apparently, although the risk-based NV model has attracted attention in the past decade, most studies focus only on characterising the reference point concerning the risk-averse NV model, e.g., Wang and Wang (2018). Furthermore, most studies deal with quantity ordering and stocking biases because of decision-makers' risk preferences (Vipin & Amit, 2019). ...
... Furthermore, most studies deal with quantity ordering and stocking biases because of decision-makers' risk preferences (Vipin & Amit, 2019). The models are formulated only for one of the expected penalty costs: shortage or overstocking (R. Wang & Wang, 2018). Jammernegg et al. (2022) investigated the asymmetry and heterogeneity of quantity orders. ...
This study examines the risk behaviour of a decision-maker regarding pricing decisions with the aid of the newsvendor model. In this regard, prospect theory and reference point concept are adopted to formulate the value function of the decision-maker. Unlike the traditional reference points (quantity-based), a reference point is deemed a function of the price. It is proved that a convex combination of the maximum-expected profits and expected losses represents the reference point. Closed-form solutions for the optimum price and quantity orders are obtained under uniformly and exponentially distributed demand. Moreover, the risk when the ordering quantity does not match the actual demand is discussed. The results-based numerical experiments reveal that the risk-averse decision-maker manages to increase the price to evade different expected costs, such as shortages and overstocking. Finally, for the same risk aversion level, the maximum reduction percentage of the optimal quantity concerning the price reaches approximately 8% in the exponential distribution, whereas it decreases by approximately 30% under the uniform distribution.
... It is well known that bounded rationality includes loss aversion (Vipin and Amit 2017, Xu et al. 2017, Hu et al. 2016, anchoring (Wang and Wang 2018, Wu et al. 2018, Charles-Cadogan 2018, fairness concern (Sharma et al. 2019, Wei et al. 2022, overconfidence (Bai et al. 2021, Li et al. 2017, disappointment aversion Shum 2013, Xu andDuan 2020), etc. When faced with uncertainty, individuals may have different attitudes toward risks: risk averse, risk neutral, and risk seeking. ...
... People with bounded rationality are usually characterized by behavior preferences. The most widely-held behavior preferences include but are not limited to loss aversion (Vipin and Amit 2017, Xu et al. 2017, Hu et al. 2016, anchoring (Wang and Wang 2018, Wu et al. 2018, Charles-Cadogan 2018, fairness concern (Sharma et al. 2019, Wei et al. 2022, overconfidence (Bai et al. 2021, Li et al. 2017) and disappointment aversion Shum 2013, Xu andDuan 2020). Owing to the presence of behavior preferences, the total utility could be expressed as "economic outcome + psychological payoff" (Liu and Shum 2013). ...
... For example, Long and Nasiry (2015) introduce a new term "optimism level" to target a newsvendor's best-and worst-sales and construct an anchor's expression that is connected to the newsvendor's optimism level, order quantity and selling price. This setting is very prevailing and appears in lots of top papers (Bai et al. 2021, Kirshner and Ovchinnikov 2019, Bai et al. 2019, Wu et al. 2018, Wang and Wang 2018. We follow this approach to set an anchor and construct the supplier's utility function. ...
... Bai et al. [1] also use this anchor to study the jointly pricing and ordering problem in the case of additive demand and multiplicative demand. Long and Nasiry [19], Wang and Wang [32] and Mandal et al. [22] all adopt a convex combination of the newsvendor's maximum possible payoff and minimum possible payoff as the reference point. Long and Nasiry [19] show that prospect theory can explain the newsvendor's ordering behavior without relying on risk attitudes if a proper reference point is chosen. ...
... Long and Nasiry [19] show that prospect theory can explain the newsvendor's ordering behavior without relying on risk attitudes if a proper reference point is chosen. Wang and Wang [32] point out that the loss-averse newsvendor's optimal order quantity is always less than the loss-neutral newsvendor's, whereas may be larger than, equal to or less than the classical newsvendor solution. Mandal et al. [22] study the newsvendor's pricing and stocking decisions, and analyze the impacts of reference point on them. ...
... π 0 is the newsvendor's reference point. Although there are multiple methods for setting reference point such as social preferences, mean demand and target profit ( [1]), target profit is widely adopted in the newsvendor models with reference dependence (see e.g., [1,19,22,32,33]). Since the manager usually has a clear and definite target in practice while the target gross profit depends on the order quantity, it may be more realistic for him to choose a target unit profit instead of target gross profit as an anchor. ...
This paper studies a single-period inventory problem with quantity-oriented reference point, where the newsvendor has loss-averse preferences and conditional value-at-risk (CVaR) measure is introduced to hedge against his risk. It is shown there exists a unique optimal order quantity maximizing the CVaR of utility. Moreover, it is decreasing in loss aversion level, confidence level and target unit profit, respectively. Then we establish the sufficient conditions under which the newsvendor's optimal order quantity may be larger than, equal to or less than the classical newsvendor solution. In particular, when the target unit profit is a convex combination of the maximum and minimum, the optimal order quantity is independent of price and cost parameters. Numerical experiments are conducted to illustrate our results and present some managerial insights.
... They showed that the total inventory level in the decentralized case may be lower than that in the centralized case. Wang and Wang [24] proposed a reference dependence utility function to study the newsvendor problem, and showed that the loss-averse newsvendor may order more than the classical one. Mandal et al. [25] investigated the joint pricing and ordering problem under an inventory-dependent demand. ...
... When λ = 1 and π 0 = 0, our model reduces to the risk-neutral one. Note that although multiple forms of loss aversion utility function are presented (e.g., [15,24,35,36]), among them this piecewise-linear one is most widely used in the economics, finance (e.g., [37,38]) and operations management literature (e.g., [15][16][17][18][19][20][21]23,24,26]) because of its simplicity. Nevertheless, π 0 is generally set to zero in (2), and we will consider the non-zero case. ...
... When λ = 1 and π 0 = 0, our model reduces to the risk-neutral one. Note that although multiple forms of loss aversion utility function are presented (e.g., [15,24,35,36]), among them this piecewise-linear one is most widely used in the economics, finance (e.g., [37,38]) and operations management literature (e.g., [15][16][17][18][19][20][21]23,24,26]) because of its simplicity. Nevertheless, π 0 is generally set to zero in (2), and we will consider the non-zero case. ...
This paper studies a loss-averse newsvendor problem with reference dependence, where both demand and yield rate are stochastic. We obtain the loss-averse newsvendor’s optimal ordering policy and analyze the effects of loss aversion, reference dependence, random demand and yield on it. It is shown that the loss-averse newsvendor’s optimal order quantity and expected utility decreases in loss aversion level and reference point. Then, that this order quantity may be larger than the risk-neutral one’s if the reference point is less than a negative threshold. In addition, although the effect of random yield leads to an increase in the order quantity, the loss-averse newsvendor may order more than, equal to or less than the classical one, which significantly depends on loss aversion level and reference point. Numerical experiments were conducted to demonstrate our theoretical results.
... This decision-making bias behavior is incentivized by the firms' loss-averse attitude (Wei et al. 2019). The notion of loss aversion originated from prospect theory and states that people prefer avoiding losses to making gains (Wang and Wang 2018;Abdellaoui et al. 2007;Kőszegi and Rabin 2006). Meanwhile, the perception of losses and gains depends on a specific reference point, which is referred to as reference dependence (Wei et al. 2019). ...
Yield and demand randomness are common in the industry, and loss aversion has been regarded as an inherent behavior for decision-makers. We combine these two factors and investigate a retailer’s ordering decisions under both yield and demand randomness with loss aversion. Before the selling season, the demand is unknown and the loss-averse retailer places an order from an unreliable supplier with an uncertain yield rate. After the demand and supply from the unreliable supplier are known, the retailer can carry out emergency replenishment from a spot market during the selling season. We characterize the retailer’s optimal ordering decisions in three scenarios: (1) the retailer is risk-neutral; (2) the retailer is loss-averse and has a zero reference profit; (3) the retailer is loss-averse and has a nonzero fixed reference profit (FRP). We compare the retailer’s order quantities in the three scenarios and find that the order quantity of the loss-averse retailer with a zero reference profit is always lower than that of the risk-neutral retailer. However, the order quantity of the loss-averse retailer with a nonzero fixed reference profit is higher than that of the risk-neutral retailer when the salvage value is sufficiently large. Interestingly, we find that the loss-averse retailer’s optimal order quantity decreases with the reference profit and increases with the loss-averse degree and the maximum fulfillment rate from the unreliable supplier under some conditions. We investigate these conditions under a uniform demand distribution. We further study the ordering quantity of the retailer with a prospect-dependent reference point (PRP) and compare the results under FRP and PRP.
... The EOQ is used to develop an optimal inventory model to reduce costs and maximize orders [6]. The EOQ method can balance supply and demand to maximize the companies procurement function, but the order trend is flat every period [7]. The SAFEA application can determine orders according to fluctuating actual conditions. ...
span>The availability of stock in the chicken egg supply chain is influenced by the ability of egg Agents to determine the optimal orders to suppliers. The optimal number of orders is very important to manage for the Bogor City Egg Agent Indonesia because the stock capacity reaches 340 crates. The optimal number of orders for eggs at the Egg Agent is influenced by input variables, namely final stock (crate), selling price (crate), and consumer demand (crate) so that the inventory is under control. The three input variables have fuzzy values that must be processed using fuzzy logic to get the optimal number of orders to suppliers so that the egg stock in the warehouse is well maintained. The optimal order model for eggs in the smart application for egg agent (SAFEA) was developed using a fuzzy logic approach with the triangular and trapezoidal membership function. Based on the optimal order model in the SAFEA application, the optimal order to the supplier is 100-104 crates per day.</span
... A detailed review on this topic is presented by Tang [41]. Mean-variance method is a commonly used method to explore the impact of risk on operational decisions, such as order quantity [42,43], price [44][45][46], service levels [45], and supply chain contracts design [6,47]. Xiao and Yang [45] analyze the impact of competition and the retailer's risk aversion on the equilibrium results in two supply chains with one risk-neutral supplier and one risk-averse, respectively. ...
Motivated by the prevailing green product design and the different supply chain power structures, this paper aims to analyse the role of power relationship and risk-aversion in economic and environmental performance of sustainable supply chain. Three game theory models, including the manufacturer Stackelberg (MS) model, retailer Stackelberg (RS) model, and vertical Nash (VN) model, are developed to study the pricing and greenness level decisions in a two-echelon sustainable supply chain, where one risk-averse manufacturer sells green products through one risk-averse retailer. This paper shows that when selling through a more risk-averse retailer, the risk-averse manufacturer prefers to provide a product with a higher level of greenness and achieve a greater utility regardless of the power structure. A manufacturer as a follower may have stronger motivation to increase the product’s level of greenness than one in a more balanced supply chain when the green technology investment coefficient is sufficiently low. With regard to the power structure, the channel leadership is not necessary to for the manufacturer to achieve higher utility, which depends on the green technology investment coefficient, greenness level sensitivity, and players’ risk aversion.
... Most studies on the loss-averse newsvendor with reference point effects simply focused on inventory control (Vipin & Amit, 2019;Wei, Xiong, & Li, 2019) and aimed to obtaining ordering decisions (Kirshner & Ovchinnikov, 2019;Uppari & Hasija, 2018;Wang & Wang, 2018). However, price is also an important factor that cannot be ignored especially when the retailer faces a competitive market. ...
This study investigates the joint pricing and stocking decisions for a loss‐averse retailer with reference point effect under stochastic demand. By solving an expected utility maximization model developed based on the prospect theory, the optimal pricing and stocking decisions are derived and compared with those of the classical newsvendor. The results show that the optimal decisions significantly depend on the loss aversion coefficient, optimism level, and reference effect strength. Smaller loss aversion coefficient and lower optimism level lead to higher expected utilities. In particular, a loss‐averse retailer with a smaller loss aversion coefficient benefits from a higher reference effect strength and vice versa.
... Different from likelihood measures such as probability of loss, the expected loss beyond a threshold can serve as a useful performance-benchmarking tool as it measures the magnitude of exceeding the threshold, which is particularly suitable for lossaverse managers (Abeler et al., 2011;Herweg, 2013) and managers with a cost target in mind (Lim and Wang, 2017). Various supply chain management studies consider expected losses due to loss aversion (Vipin and Amit, 2017;Wang and Wang, 2018). In particular, Fleischhacker and Fok (2015) prove that reducing demand uncertainty can reduce expected loss in an inventory system. ...
Achieving cost targets is a major concern for business managers. In this paper, we consider two risk management criteria for a production-inventory system under a cost target: Probability of Loss and Expected Loss. We study two models with stochastic demand and production: The unit stockout cost model and the backlogging cost rate model. We analyze a limited-information setting that is an excellent approximation to a full-information setting. We discimal inventory decisions for minimizing probability of loss are identical for both models, and that the optimal inventory decisions for minimizing expected loss share a similar structure for both models. In addition, we investigate inventory decisions when minimizing the expected cost subject to a probability of loss constraint. Extension to a generally-distributed unit production time is also explored. We provide comparative statics and managerial insights of value to loss-aware managers.
... Wang and Wang investigated the inventory management problem, the impact of the loss degree and the quantity-oriented reference point is investigated jointly on the optimal ordering quantity and the profit maximization of the retailer has been studied by a numerical approach. It has found that there exists a unique optimal order quantity while maximizing the expected utility [4]. ...
... Becker-Peth & Thonemann (2016) analyzed how contractual reference points affect inventory decision making in a revenue-sharing contract. Wang & Wang (2017) investigated how an adaptive quantity-oriented reference point affects the retailer's procurement decision. Chen & Sheu (2017) proposed a model in which a green product's quality reference point was incorporated into the gain and loss value functions. ...
We examine the impact of the stochastic and multiple-variable dependent reference point, under which the members of a dyadic supply chain decide on a product's green level, wholesale price, and order quantity to improve greening performance. The supply chain consists of a dominant manufacturer and a newsvendor retailer, both of whom may be inequity-averse. Their utility function involves disadvantageous inequity aversion when their trade partner's profit is regarded as the reference point. Considering the availability of information on the distribution function of market demand, we build an analytical model to derive equilibrium results in three scenarios and then compare them with the results obtained in a normative retailer situation. We show that, in the absence of information on the distribution, for any given wholesale price, the retailer will choose to "under-order" as long as disadvantageous inequity occurs. If the environmental constraint is not binding, the risk-neutral manufacturer will keep the green level unchanged, whereas the inequity-averse manufacturer will reduce it. If the constraint is binding, the manufacturer will increase the green level in response to the reduction of order quantities. As a result, the equilibrium-expected profit of the manufacturer may decrease. The manufacturer can control the impact of the retailer's inequity aversion by selecting an appropriate combination of wholesale price and green effort level.
... A variety of research on ordering decision bias with reference effects continues to grow; to name a few, joint stocking and pricing decisions( Mandal et al. 2018), a loss-averse newsvendor with recourse option(Vipin and Amit 2017), and quantity-oriented reference points( Wang and Wang 2018), consumers with preference uncertainty and loss aversion (Chen and Sheu 2017), as well as consumers with environmental awareness and reference behaviour ( Hong et al. 2018). This paper differs from the extant literature by examining the impacts of multiple reference points on a newsvendor ordering quantity as well as supply chain contracting. ...
This paper studies a newsvendor’s ordering decision with two exogenous reference points: industry benchmark and a minimum requirement on profit, based on which the psychological values are divided into gains, losses, and failures. With the objective to maximise the total expected value, the order quantity is to balance the marginal values of underage and overage costs, losses, and failures. The decision bias relative to a risk-neutral or a loss-averse newsvendor could be positive or negative and significantly determined by the reference profits and the shortage cost. In addition, a wholesale price contract may coordinate the supply chain under certain circumstances.
... Wakker (2005),and Masatlioglu and Uler(2013). In reference effect modeling, the gain and loss value function may take different forms according to specific situations as illustrated in Chen and Sheu(2017), Becker-Peth and Thonemann (2016), and Wang and Wang(2017). Analogously, we assume that the loss aversion index is infinity in the cost-reduction function (Eq.1). ...
We consider consumers' loss aversion in environmental quality and develop a two‐period game theoretical model to investigate the optimal pricing and environmental quality decisions for a green supply chain where a manufacturer sells products to consumers through a retailer. We then introduce a two‐part tariff contract to coordinate the supply chain for both periods. We suggest that optimal decisions in the second period depend on the reference point of the first period in the decentralized supply chain. A higher reference point leads to the increased environmental quality of products, prices, and profits of supply chain members in the second period. However, when the reference point is sufficiently high, the environmental quality will be lower to avoid excessive environmental investment costs. Furthermore, consumers' loss aversion reduces the environmental quality of products when the reference point is low. As consumers' loss aversion increases, the manufacturer's profit rises, while the wholesale and retail prices and the retailer's profit show a decreasing and then increasing trend. Finally, we find that a two‐part tariff contract enables the two‐period supply chain to be coordinated and achieve Pareto improvements in profit and environmental quality. This study sheds valuable light on understanding consumer environmental preferences and irrational behavior for supply chain decision‐making and green product design.
The COVID-19 pandemic has been one of the most severe disruptions to normal life, impacting how businesses operate. The academic literature in the areas of supply chain and operations management has been trying to explain how this has affected decision-making in businesses. However, the existing literature has predominantly overlooked organisational culture and behavioural economic theories. This paper contends that considering the decisions made in supply chain disruption management involve groups and the individuals within them, the relevance of behavioural economic concepts becomes paramount. As such, the objective of this paper is to conduct an integrative literature review, utilising the purposive sampling method to explore the dearth of academic work connecting behavioural economic theories and organisational culture to supply chain disruption management. Additionally, the paper aims to offer guidelines for future research in this domain. Enhancing our comprehension of these domains concerning supply chain disruption management would empower firms to better anticipate their parties’ decisions, refine their decision-making models, and cultivate stronger relationships with suppliers and customers.
This study investigates a retailer's sourcing decisions from two different suppliers (i.e., compliant and substandard suppliers) during environmental enforcement campaigns. The compliant supplier spends more on environmental protection and will supply products stably at a higher price, whereas the substandard supplier is cheaper but less environmentally friendly. Due to environmental issues, the substandard supplier is at risk of production disruption, which makes the supplier partially deliver the order with the quantity related to the disruption time. When the disruption occurs, an emergency ordering opportunity is provided at a cost that increases with the disruption time. We derive optimal order quantities and threshold conditions regarding supplier selection. If the order cost of the substandard supplier (or compliant supplier) is relatively small (or large), the compliant supplier will always be abandoned regardless of the increasing rate of the emergency order cost. Otherwise, the compliant supplier will be selected only if the increasing rate is large. The impacts of loss aversion are also investigated. Loss aversion will inhibit the retailer's willingness to place an emergency order and may increase the retailer's preference for the substandard supplier rather than the compliant supplier. Numerical experiments are conducted based on the sourcing problem of the company Mengniu.
Purpose
This work examines the joint pricing and ordering (JPO) decisions for a loss-averse retailer with quantity-oriented reference point (RP) effect under demand uncertainty.
Design/methodology/approach
The demand is assumed to be uncertain with the mean and variance as the only known information. The prospect theory is used to model the retailer's expected utility. An expected utility maximization model in the distribution-free approach (DFA) is then developed. Using duality theory, the expected utility under the worst-case distribution is transformed into tractable piece-wise functions. To examine the effectiveness of the DFA in coping with the demand uncertainty, a stochastic programming model is developed and its solutions are used as benchmarks.
Findings
The proposed model and solution approach can effectively hedge against the demand uncertainty. The JPO decisions are significantly influenced by the LA coefficient and the reference level. The LA has a stronger influence than the reference level does on the expected utility. An excessive LA is detrimental while an appropriate reference level is beneficial to the retailer.
Practical implications
The results of this work are applicable to loss-averse retailers with the quantity-oriented RP when making JPO decisions with difficulty in predicting the demands.
Originality/value
The demand is assumed to be uncertain in this work, but a certain demand distribution is usually assumed in the existing literature. The DFA is used to study JPO decisions for the loss-averse retailer with quantity-oriented RP effect under the uncertain demand.
This study investigates the coordination problem for a two-tier decentralized supply chain consisting of a supplier and a retailer. The supplier can control and adjust the product quality and the retailer sells the product both offline and online (O2O) to consumers with reference quality effect. The market demand is dependent on the retail price and on the consumer reference quality effect that is a dynamic function of past product quality. The problem is modeled as a Stackelberg game with the supplier as the leader and the retailer as the follower. The wholesale price (WP), cost-sharing (CS) and two-part tariff (TP) contracts are used to coordinate the decentralized supply chain. Using the Hamilton-Jacobi-Bellman equation, the dynamic optimal control models are transformed into tractable models to obtain the equilibrium solutions. The results show that the decisions of the supply chain members are dynamic and depend on the consumer initial reference quality, the reference quality effect strength and the memory parameter. The retailer should attract potential consumers with dynamic reference quality effect to purchase the product offline. The TP contract can coordinate the supply chain and can benefit the supplier, the retailer and the consumers. As compared with the WP contract, the CS contract can improve the performance of the supply chain. These results are verified through numerical experiments. The impacts of the major parameters, including the reference quality effect strength, the consumer memory parameter, the cost-sharing rate, the discount rate and the offline consumer rate, on the equilibrium solutions and on the profits of the supply chain members are also examined through numerical experiments.
We study a two‐newsvendor competition problem in which both newsvendors are loss‐averse and have adaptive quantity‐oriented reference points. Each newsvendor faces stochastic demand determined by some demand reallocation rule and aims to choose an optimal inventory level to maximize her expected utility. Since the demand reallocation rule indicates that one newsvendor's demand affects the inventory level of the other newsvendor, this problem can be formulated as a two‐person game. We prove that this competitive newsvendor problem exhibits a unique symmetric Nash equilibrium. We also show that the optimal inventory level decreases in the loss aversion degree and reference level, and increases in the competition intensity. Unlike conventional findings in the integrated risk‐neutral supply chain, we find that a low (high) reference level leads to inventory overstocking (understocking), which is illustrated jointly by the loss aversion degree, reference level, and competition intensity. Finally, we conduct numerical experiments to provide engineering confirmations of our theoretical findings and to generate additional insights.
Overconfidence and optimism are behavioral biases known to impact newsvendor ordering decisions. We develop a model that accounts for both effects by applying a probability weighting function from Prospect Theory (PT). We apply the model to a price-setting newsvendor problem with reference effects. Contrary to previous work claiming that increased optimism leads a newsvendor to adopt a high margin and low volume strategy, we find that greater optimism typically results in lower margins and higher inventory, aligning with the more intuitive interpretation of optimism. In addition, we find that overconfidence and regret have similar impacts on both inventory levels and pricing.
The single-product, single-period newsvendor problem with two decision variables, namely price and stock quantity, is considered. The performance measure, in addition to the expected revenue, includes the variance of the income scaled with a risk parameter. We present conditions for the concavity of this risk-sensitive performance measure and the uniqueness of the optimal solution for both risk-averse and risk-seeking cases under the additive demand model, and compare the results to others previously published. These conditions are introduced in terms of the lost sales rate elasticity. Furthermore, we provide numerical examples that aim to endorse the theoretical results herein explained.
The price-setting newsvendor problem, which models the economic trade-offs associated with uncertain demand of a perishable product, is fundamental to supply chain analysis. However, in settings such as agriculture, there is significant economic risk associated with supply uncertainty. We analyze how risk aversion and the source of uncertainty - demand and/or supply - affect tractability and optimal decisions. We find that concavity of the objective function is preserved under the introduction of risk aversion if the source of uncertainty is demand, but it is not necessarily preserved if the source of uncertainty is supply. We identify a structural difference that explains this result, and show that this difference can lead to opposing directional effects of risk aversion on optimal decisions.
Current understanding in operations management is that prospect theory, as a theory of decision making under uncertainty, cannot systematically explain the ordering behavior observed in experiments on the newsvendor problem. We suggest this is because the newsvendor’s reference point is assumed to be the status quo, i.e., zero payoff. We propose an alternative based on newsvendor’s salient payoffs and show that prospect theory can, in fact, account for experimental results.
This paper was accepted by Serguei Netessine, operations management.
Pioneered by Nobel laureate Harry Markowitz in the 1950s, the mean-variance (MV) formulation is a fundamental theory for risk management in finance. Over the past decades, there is a growing popularity of applying this ground breaking theory in analyzing stochastic supply chain management problems. Nowadays, there is no doubt that the mean-variance (MV) theory is a well-proven approach for conducting risk analysis in stochastic supply chain operational models. In view of the growing importance of MV approach in supply chain management, we review a selection of related papers in the literature that focus on MV analytical models. By classifying the literature into three major areas, namely, single-echelon problems, multi-echelon supply chain problems, and supply chain problems with information updating, we derive insights into the current state of knowledge in each area and identify some associated challenges with a discussion of some specific models. We also suggest future research directions on topics such as information asymmetry, supply networks, and boundedly rational agents, etc. In conclusion, this paper provides up-to-date information which helps both academicians and practitioners to better understand the development of MV models for supply chain risk analysis.
In the classical "newsboy problem", one determines the optimum order quantity to maximize the expected profit. This paper considers the newsboy problem under two new objectives. The relevance of the first objective-"maximizing expected utility"-is well established in decision theory. This paper develops a group of formulas for handling the partial moments arising from adopting this objective, and these formulas are potentially useful to many other management models involving partial moments. The second objective-"maximizing the probability of achieving a budgeted profit"-is commonly adopted by managers but largely ignored in the literature. The analysis reveals some interesting results for determining the optimum order quantity under this objective.
We study the properties of a profit-maximizing monopolist's optimal price distribution when selling to a loss-averse consumer, where (following Kőszegi and Rabin (2006)) we assume that the consumer's reference point is her recent rational expectations about the purchase. If it is close to costless for the consumer to observe the realized price of the product, then – in a pattern consistent with several recently documented facts regarding supermarket pricing – the monopolist chooses low and variable “sale” prices with some probability and a high and sticky “regular” price with the complementary probability. Realizing that she will buy at the sale prices and hence that she will purchase with positive probability, the consumer chooses to avoid the painful uncertainty in whether she will get the product by buying also at the regular price. If it is more costly for the consumer to observe the realized price, then – in a pattern consistent with the pricing behavior of some other retailers (e.g. movie theaters) – the monopolist chooses a sticky price and holds no sales. In this case, a sale is less tempting and hence less effective in generating an expectation to purchase with positive probability. We also show that ex-ante competition for loyal consumers leads to sticky pricing while ex-post competition leads to marginal-cost pricing, and discuss several other extensions of the model.
In the newsvendor problem a decision maker orders inventory before a one period selling season with stochastic demand. If too much is ordered, stock is left over at the end of the period, whereas if too little is ordered, sales are lost. The expected profit-maximizing order quantity is well known, but little is known about how managers actually make these decisions. We describe two experiments that investigate newsvendor decisions across different profit conditions. Results from these studies demonstrate that choices systematically deviate from those that maximize expected profit. Subjects order too few of high-profit products and too many of low-profit products. These results are not consistent with risk-aversion, risk-seeking preferences, Prospect Theory preferences, waste aversion, stockout aversion, or the consequences of underestimating opportunity costs. Two explanations are consistent with the data. One, subjects behave as if their utility function incorporates a preference to reduce ex-post inventory error, the absolute difference between the chosen quantity and realized demand. Two, subjects suffer from the anchoring and insufficient adjustment bias. Feedback and training did not mitigate inventory order errors. We suggest techniques to improve decision making.
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.
The classical risk-neutral newsvendor problem is to decide the order quantity that maximizes the one-period expected profit. In this note, we consider a risk-averse newsvendor with stochastic price-dependent demand. We adopt Conditional Value-at-Risk (CVaR), a risk measure commonly used in finance, as the decision criterion. The aim of our study is to investigate the optimal pricing and ordering decisions in such a setting. For both additive and multiplicative demand models, we provide sufficient conditions for the uniqueness and existence of the optimal policy. Comparative statics show the monotonicity properties and other characteristics of the optimal pricing and ordering decisions. We also compare our results with those of the newsvendor with a risk-neutral attitude and a general utility function.
We consider the dynamic pricing problem of a monopolist firm in a market with repeated interactions, where demand is sensitive to the firm’s pricing history. Consumers have memory and are prone to human decision-making biases and cognitive limitations. As the firm manipulates prices, consumers form a reference price that adjusts as an anchoring standard based on price perceptions. Purchase decisions are made by assessing prices as discounts or surcharges relative to the reference price in the spirit of prospect theory.
We prove that optimal pricing policies induce a perception of monotonic prices, whereby consumers always perceive a discount, respectively surcharge, relative to their expectations. The effect is that of a skimming or penetration strategy. The firm’s optimal pricing path is monotonic on the long run, but not necessarily at the introductory stage. If consumers are loss averse, we show that optimal prices converge to a constant steady-state price, characterized by a simple implicit equation; otherwise, the optimal policy cycles. The range of steady states is wider the more loss averse consumers are. Steady-state prices decrease with the strength of the reference effect and with customers’ memory, all else equal. Offering lower prices to frequent customers may be suboptimal, however, if these are less sensitive to price changes than occasional buyers.
If managers ignore such long-term implications of their pricing strategy, the model indicates that they will systematically price too low and lose revenue. Our results hold under very general reference dependent demand models.
We consider a multi-product newsvendor under the law-invariant coherent risk measures. We first establish a few fundamental properties of the model regarding the convexity of the problem, the symmetry of the solution and the impact of risk aversion. Specifically, we show that for identical products with independent demands, increased risk aversion leads to decreased orders. For a large but finite number of heterogenous products with independent demands, we derive closed-form approximations for the optimal order quantities. The approximations are as simple to compute as the classical risk-neutral solutions. We also show that the risk-neutral solution is asymptotically optimal as the number of products tends to infinity, and thus risk aversion has no impact in the limit. For a risk-averse two-product newsvendor with dependent demands, we show that positively (negatively) dependent demands lead to a lower (higher) optimal order quantities than independent demands. Using a numerical study, we examine the convergence rates of the approximations and develop additional insights on the interplay of dependent demands and risk aversion.
Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multi-period inventory models as well as multi-period models that coordinate inventory and pricing strategies. In each case, we characterize the optimal policy for various measures of risk that have been commonly used in the finance literature. In particular, we show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to risk-neutral decision makers with limited information on the demand distribution. Singapore-MIT Alliance (SMA)
We modify the Salop (1979) model of price competition with differentiated products by assuming that consumers are loss averse relative to a reference point given by their recent expectations about the purchase. Consumers' sensitivity to losses in money increases the price responsiveness of demand—and hence the intensity of competition—at higher relative to lower market prices, reducing or eliminating price variation both within and between products. When firms face common stochastic costs, in any symmetric equilibrium the markup is strictly decreasing in cost. Even when firms face different cost distributions, we identify conditions under which a focal-price equilibrium (where firms always charge the same "focal" price) exists, and conditions under which any equilibrium is focal. (JEL D11 , D43, D81, L13)
We analyze the joint inventory and pricing decisions of a firm when demand depends on not only the current selling price but also a memory-based reference price and customers are loss averse. The presence of reference price effect leads to a nonconcave one-period expected revenue in price and reference price. We introduce a transformation technique that allows us to prove under some mild assumptions the optimality of a reference-price-dependent base-stock list-price policy, which is characterized by a base-stock level and a target reference price. In addition, we show that the target reference price is increasing in the reference price, but except in the loss-neutral case, the base-stock level is not monotone in the reference price. We also show that in the steady state of the model with the reference price effect, the optimal price is lower while the optimal base-stock level is higher than their counterparts in the model without the reference price effect.
This study considers a mean-variance (MV) framework for managing disruption risk in a two-echelon supply chain with a risk-averse buyer and multiple unreliable suppliers under newsvendor (NV) setting. An MV objective function is designed to maximize the buyer's expected profit while minimizing its variance. Study of the structural property of the problem proves the existence of a global maxima and a set of efficient portfolios consisting of dominating mean-variance pairs. We demonstrate the effect of model parameters through comparative statics analysis. An algorithm is developed to overcome the computational complexity of the higher dimensional problem. Numerical studies on model behavior show that the proposed algorithm gives the exact optimal solution while being tractable.
We formalize the reference point adaptation process by relating it to a way people perceive prior gains and losses. We then develop a dynamic trading model with reference point adaptation and loss aversion, and derive its semi-analytical solution. The derived optimal stock holding has an asymmetric V-shaped form with respect to prior outcomes, and the related sensitivities are directly determined by the sensitivities of reference point shifts with respect to the outcomes. We also find that the effects of reference point adaptation can be used to shed light on some well documented trading patterns, e.g., house money, break even, and disposition effects.
Most of the existing literature about the newsvendor problem mainly focused on choosing an optimal order quantity to maximize the expected profit of a risk-neutral newsvendor. However, some studies pointed out that in practice managers׳ decisions as to order quantities always deviate from the profit-maximization order quantity, which is referred to as decision bias in the newsvendor problem. Then, many studies introduced other preferences rather than risk neutrality of the newsvendor to explain such a decision bias. This paper thus introduces loss aversion to the research of the newsvendor decision bias. We propose a new definition to the loss-averse newsvendor problem–legacy loss, which is defined either as the loss for excess order or the shortage penalty for lost sales when sales time is due. The optimal decisions of a loss-averse newsvendor are obtained through the following three ways: (i) minimizing the expected legacy loss, (ii) minimizing CVaR of legacy loss by combining the CVaR measure in risk management, (iii) minimizing the combination of expected legacy loss and CVaR of legacy loss; and are compared with other existing results. Besides, we present some properties of the optimal decisions as well as relations among them. Some numerical examples are given to illustrate the obtained results.
The newsvendor problem is a fundamental decision problem in operations management. Various independent experimental studies in laboratory settings have shown similar deviations from the theoretical optimal order quantity. We clarify that Prospect Theory, a prevalent framework for decision making under uncertainty, cannot explain the consistent empirical findings.
This paper was accepted by Yossi Aviv, operations management.
We study a newsvendor who sells a perishable asset over repeated periods to consumers with a given consumption valuation for the product. The market size in each period is random, following a stationary distribution. Consumers are loss averse with stochastic reference points that represent their beliefs about possible price and product availability. Given the distribution of reference points, they choose purchase plans to maximize their expected total utility, including gain-loss utility, before visiting the store, and follow the plans in the store. In anticipation of consumers’ purchase plans, in each period, before demand uncertainty resolves, the firm chooses an initial order quantity. After the uncertainty resolves, the firm chooses a contingent price depending on the demand realization, with the option of clearing inventory by charging a sale price, and otherwise, posting a full price. Over repeated periods, the interaction of the firm’s operational decisions about ordering and contingent pricing and the consumers’ purchase actions results in a distribution of reference points, and, in equilibrium, this distribution is consistent with consumers’ beliefs. Under this framework of endogenized reference points, we fully characterize the firm’s optimal inventory and contingent pricing policies. We identify conditions under which the firm’s expected price and profit are increasing in the consumer loss aversion level. We also show that the firm can prefer demand variability over no-demand uncertainty. We obtain a set of insights into how consumers’ loss aversion affects the firm’s optimal operational policies that are in stark contrast to those obtained in classic newsvendor models. As examples, the optimal full price increases in the initial order quantity; and the optimal full price decreases, while the optimal sales frequency increases, in the procurement cost.
In this paper we analyze a single-period inventory model where a risk-averse newsvendor makes a joint decision on ordering, pricing and marketing under the CVaR risk measure criterion. The newsvendor can exert marketing effort to enhance market demand. We assume that the newsvendor’s marketing effort affects the scale of the demand distribution and hence to model the marketing-dependent demand as a multiplicative form. We characterize sufficient conditions that guarantee existence and uniqueness of the optimal solutions under some mild assumptions on demand distribution, expected demand function and marketing effort cost, which are widely used in related literature. We show that the optimal order quantity increases in the newsvendor’s marketing effort, but the optimal price remains unchanged whether the demand is marketing-dependent or not. Additionally, we explore impact of exogenous parameters, such as unit order cost, salvage value and the newsvendor’s risk aversion coefficient, on the optimal decision variables, and find that the optimal marketing effort always keeps the same changing direction with the optimal the marketing-independent order quantity as the exogenous parameters change. This suggests that impact of the parameters on the optimal order quantity gets strengthened in the case of marketing-dependent demand.
We use the portfolio selection model presented in He and Zhou [Manage. Sci., 2011, 57, 315–331] and the NYSE equity and US treasury bond returns for the period 1926–1990 to revisit Benartzi and Thaler’s myopic loss aversion theory. Through an extensive empirical study, we find that in addition to the agent’s loss aversion and evaluation period, his reference point also has a significant effect on optimal asset allocation. We demonstrate that the agent’s optimal allocation to equities is consistent with market observation when he has reasonable values of degree of loss aversion, evaluation period and reference point. We also find that the optimal allocation to equities is sensitive to these parameters. We then examine the implications of money illusion for asset allocation. Finally, we extend the model to a dynamic setting.
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.
In the newsvendor problem, a decision maker facing random demand for a perishable product decides how much of it to stock for a single selling period. This simple problem with its intuitively appealing solution is a crucial building block of stochastic inventory theory, which comprises a vast literature focusing on operational efficiency. Typically in this literature, market parameters such as demand and selling price are exogenous. However, incorporating these factors into the mode l can provide an excellent vehicle for examining how operational problems interact with marketing issues to influence decision making at the firm level. In this paper we examine an extension of the newsvendor problem in which stocking quantity and selling price are set simultaneously. We provide a comprehensive review that synthesizes existing results for the single period problem and develop additional results to enrich the existing knowledge base. We also review and develop insight into a dynamic inventory extension of this problem, and motivate the applicability of such models.
This paper addresses the simultaneous determination of pricing and inventory replenishment strategies in the face of demand uncertainty. More specifically, we analyze the following single item, periodic review model. Demands in consecutive periods are independent, but their distributions depend on the item's price in accordance with general stochastic demand functions. The price charged in any given period can be specified dynamically as a function of the state of the system. A replenishment order may be placed at the beginning of some or all of the periods. Stockouts are fully backlogged. We address both finite and infinite horizon models, with the objective of maximizing total expected discounted profit or its time average value, assuming that prices can either be adjusted arbitrarily (upward or downward) or that they can only be decreased. We characterize the structure of an optimal combined pricing and inventory strategy for all of the above types of models. We also develop an efficient value iteration method to compute these optimal strategies. Finally, we report on an extensive numerical study that characterizes various qualitative properties of the optimal strategies and corresponding optimal profit values.
In spite of the high level of interest in inventory control that has sprung up recently among statisticians, economists, and businessmen, very little has been written that indicates the fundamental connection between price theory and inventory control. Most of the inventory control systems now in operation assume a given price structure. The analysis is frequently restricted to cost minimization. Economic theorists, on the other hand,~have concerned themselves with profit maximization but have not ordinarily concerned themselves with the realistic details underlying the construction of their curves. Only in the event that other variables external to the cost minimization problem are assigned optimal values will the cost minimization problem be equivalent to profit maximization.
In this paper, we review the contributions to date for analyzing the newsvendor problem. Our focus is on examining the specific extensions for analyzing this problem in the context of modeling customer demand, supplier costs, and the buyer risk profile. More specifically, we analyze the impact of market price, marketing effort, and stocking quantity on customer demand; how supplier prices can serve as a coordination mechanism in a supply chain setting; integrating alternative supplier pricing policies within the newsvendor framework; and how the buyer's risk profile moderates the newsvendor order quantity decision. For each of these areas, we summarize the current literature and develop extensions. Finally, we also propose directions for future research.
The effects of risk and risk aversion in the single-period inventory ("newsboy") problem are examined. Comparative-static effects of changes in the various price and cost parameters are determined and related to the newsboy's risk aversion. The addition of a random background wealth and of an increase in the riskiness of newspaper demand are also examined. Although many of the comparative effects generally are ambiguous, some fairly simple restrictions on preferences and/or risk increases are shown to lead to qualitatively deterministic results.
Newsvendor models are widely used in the literature, and usually based upon the assumption of risk neutrality. This paper uses loss aversion to model manager's decision-making behavior in the single-period newsvendor problem. We find that if shortage cost is not negligible, then a loss-averse newsvendor may order more than a risk-neutral newsvendor. We also find that the loss-averse newsvendor's optimal order quantity may increase in wholesale price and decrease in retail price, which can never occur in the risk-neutral newsvendor model.
In this paper, we consider the minimization of the conditional value-at-risk (CVaR), a most preferable risk measure in financial risk management, in the context of the well-known single-period newsvendor problem, which is originally formulated as the maximization of the expected profit or the minimization of the expected cost. We show that downside risk measures including the CVaR are tractable in the problem due to their convexity, and consequently, under mild assumptions on the probability distribution of products’ demand, we provide analytical solutions or linear programming (LP) formulation of the minimization of the CVaR measures defined with two different loss functions. Numerical examples are also exhibited, clarifying the difference among the models analyzed in this paper, and demonstrating the efficiency of the LP solutions.
According to prospect theory [Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk, Econometrica, 47, 263–292], gains and losses are measured from a reference point. We attempted to ascertain to what extent the reference point shifts following gains or losses. In questionnaire studies, we asked subjects what stock price today will generate the same utility as a previous change in a stock price. From participants’ responses, we calculated the magnitude of reference point adaptation, which was significantly greater following a gain than following a loss of equivalent size. We also found the asymmetric adaptation of gains and losses persisted when a stock was included within a portfolio rather than being considered individually. In studies using financial incentives within the BDM procedure [Becker, G. M., DeGroot, M. H., & Marschak, J. (1964). Measuring utility by a single-response sequential method. Behavioral Science, 9(3), 226–232], we again noted faster adaptation of the reference point to gains than losses. We related our findings to several aspects of asset pricing and investor behavior.
The single-period problem (SPP), also known as the newsboy or news-vendor problem, is to find the order quantity which maximizes the expected profit in a single period probabilistic demand framework. Interest in the SPP remains unabated and many extensions to it have been proposed in the last decade. These extensions include dealing with different objectives and utility functions, different supplier pricing policies, different news-vendor pricing policies and discounting structures, different states of information about demand, constrained multi-products, multiple-products with substitution, random yields, and multi-location models. This paper builds a taxonomy of the SPP literature and delineates the contribution of the different SPP extensions. This paper also suggests some future directions for research.
We formulate and carry out an analytical treatment of a single-period portfolio choice model featuring a reference point in wealth, S-shaped utility (value) functions with loss aversion, and probability weighting under Kahneman and Tversky's cumulative prospect theory (CPT). We introduce a new measure of loss aversion for large payoffs, called the large-loss aversion degree (LLAD), and show that it is a critical determinant of the well-posedness of the model. The sensitivity of the CPT value function with respect to the stock allocation is then investigated, which, as a by-product, demonstrates that this function is neither concave nor convex. We finally derive optimal solutions explicitly for the cases in which the reference point is the risk-free return and those in which it is not (while the utility function is piecewise linear), and we employ these results to investigate comparative statics of optimal risky exposures with respect to the reference point, the LLAD, and the curvature of the probability weighting.
This paper was accepted by Wei Xiong, finance.
We examined reference point adaptation following gains or losses in security trading using participants from China, Korea, and the US. In both questionnaire studies and trading experiments with real money incentives, reference point adaptation was larger for Asians than for Americans. Subjects in all countries adapted their reference points more after a gain than after an equal-sized loss. When we introduced a forced sale intervention that is designed to close the mental account for a prior outcome, Americans showed greater adaptation toward the new price than their Asian counterparts. We offer possible explanations both for the cross-cultural similarities and the cross-cultural differences.
We consider the single period stochastic inventory (newsvendor) problem with downside risk constraints. The aim in the classical newsvendor problem is maximizing the expected profit. This formulation does not take into account the risk of earning less than a desired target profit or losing more than an acceptable level due to the randomness of demand. We utilize Value at Risk (VaR) as the risk measure in a newsvendor framework and investigate the multi-product newsvendor problem under a VaR constraint. To this end, we first derive the exact distribution function for the two-product newsvendor problem and develop an approximation method for the profit distribution of the N-product case (N>2). A mathematical programming approach is used to determine the solution of the newsvendor problem with a VaR constraint. This approach allows us to handle a wide range of cases including the correlated demand case that yields new results and insights. The accuracy of the approximation method and the effects of the system parameters on the solution are investigated numerically.
We model a risk-averse newsvendor's decision-making behavior with some commonly used classes of utility functions within the expected utility theory (EUT) framework. Under fairly general conditions of EUT, we show that a risk-averse newsvendor will order less than an arbitrarily small quantity as selling price gets larger if price is higher than a threshold value, i.e., the optimal order quantity decreases as the selling price increases.
We study the risk-averse newsvendor model with a mean-variance objective function. We show that stockout cost has a significant impact on the newsvendor's optimal ordering decisions. In particular, with stockout cost, the risk-averse newsvendor does not necessarily order less than the risk-neutral newsvendor. We illustrate this finding analytically for the case where the demand follows the power distribution.
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.
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.
We develop a model of reference-dependent preferences and loss aversion where “gain-loss utility” is derived from standard
“consumption utility” and the reference point is determined endogenously by the economic environment. We assume that a person's
reference point is her rational expectations held in the recent past about outcomes, which are determined in a personal equilibrium by the requirement that they must be consistent with optimal behavior given expectations. In deterministic environments,
choices maximize consumption utility, but gain-loss utility influences behavior when there is uncertainty. Applying the model
to consumer behavior, we show that willingness to pay for a good is increasing in the expected probability of purchase and
in the expected prices conditional on purchase. In within-day labor-supply decisions, a worker is less likely to continue
work if income earned thus far is unexpectedly high, but more likely to show up as well as continue work if expected income
is high.
Newsvendor selling to loss-averse consumers with stochastic reference points
- Baron
The newsvendor problem: review and directions for future research
- Qin