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A Loss Averse Competitive Newsvendor Problem with Anchoring
Abstract
We study a loss averse competitive newsvendor problem with anchoring under prospect theory. We consider two demand-splitting rules for quantity competition, including proportional demand allocation and demand reallocation. We characterize the optimal order quantity decisions under both demand rules. We find that the newsvendor's order quantity is decreasing with the degree of loss aversion and the value of the anchor. Compared with an integrated risk-neutral supply chain, a positive anchor always leads to inventory understocking, whereas a negative anchor may result in a serious overstocking. Under competition with homogeneous newsvendors, competition always makes newsvendors order more, which does not necessarily lead to a loss of profit. For newsvendors with a high anchor, competition helps to prevent understocking caused by the anchoring effect, which leads to an increase in profit. For newsvendors with a low anchor, competition exacerbates overstocking, which results in a loss of profit. Under competition with heterogeneous newsvendors, a newsvendor with a higher degree of loss aversion or with a higher anchor adopts a more conservative strategy (i.e. choose a lower order quantity), which results in a smaller market share.
... Another line of inquiry has explored anchoring effects on ordering decisions [7] and suboptimal order in the newsvendor game [25]. The presence of anchoring effects has been investigated in real-life managerial settings such as addressing the weight of various dimensions in multidimensional decision-making [26,27], the newsvendor problem [28], and negotiation in a multi-tier supply chain [29]. However, some studies have found minimal impacts or mixed findings [30,31]. ...
... Anchoring effects have been investigated in the business context, such as the performance appraisal of employees [33], promotion decisions in academia [51], order quantity in a newsvendor problem [10,28], and multi-tier supply chain negotiation [52]. ...
... This research provides a crucial theoretical contribution that the effectiveness of the debiasing techniques demonstrated in this research may be applied to various anchoring effects in other business and supply chain decision-making contexts, such as the newsvendor problem [25,28], the supplier evaluation that considers environmental sustainability [79,80] and bargaining in a multi-tier supply chain [52]. Thus, our findings pave the way for future research on debiasing anchoring effects. ...
This research examines how anchoring bias affects managers’ multi-dimensional evaluations of supplier performance, supplier selection, and the effectiveness of two debiasing techniques. We consider the supplier past performance in one performance dimension as the anchor and investigate whether and how this anchor would have a knock-on effects on evaluating a supplier’s performance in other dimensions. We conducted two online experimental studies (Study 1, sample size = 104 and Study 2, sample size = 408). Study 1 adopts a 2 x 1 (high anchor vs. low anchor) between-subjects factorial experimental design, and Study 2 is a 3 (debiasing: no, consider-the-opposite, mental-mapping) x 2 (high anchor vs. low anchor) between-subjects factorial design. The results from Studies 1 and 2 suggest that when a supplier has received a low evaluation score in one dimension in the past, participants assign the same supplier lower scores in the other dimensions compared to a supplier that has obtained a high score in the past. We also find that anchoring has a knock-on effect on how likely participants are to choose the same supplier in the future. Our findings highlight the asymmetric effectiveness of ‘consider-the-opposite’ and ‘mental-mapping’ debiasing techniques. This research is the first study that examines how anchoring bias managers’ evaluations in a multi-dimensional setting and its knock-on effects. It also explores the effectiveness of two low-cost debiasing techniques. A crucial practical implication is that suppliers’ exceptionally good or disappointing past performance affects the judgement of supply managers. Hence, managers should use consider-the-opposite or mental-mapping techniques to debias the effect of high and low anchors, respectively.
... 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). ...
... With the extension to Schweitzer and Cachon (2000) by considering the cost of shortage, Wang and Webster (2009) show that the loss-averse newsboy may carry out either over-ordering or underordering. In the up-to-date research, Wu et al. (2018) study the problem of competitive loss-averse newsvendors and find that the optimal ordering strategies of newsvendors are greatly influenced by each newsvendor's loss aversion and anchoring, and quantity competition between them. Similar studies are conducted by Bai et al. (2019), and the results show that the newsvendors' optimal pricing and ordering strategies are further affected by the types of demand (additive and multiplicative). ...
... Some interesting results are obtained. First, the prior literature showed that the loss-averse decision-maker's order quantity always decreases with the degree of loss aversion (e.g., Wu et al. 2018;Li and Li 2018). However, it is found that the order quantity may become larger for a retailer with a higher loss-averse degree in this study where both uncertain yield and reference profit are considered. ...
... As such, a retailer with a higher loss-averse degree may increase its order quantity to hedge against the risk of low supply. Second, the prior literature (e.g., Wu et al. 2018) that ignored yield uncertainty presented that a loss-averse decisionmaker's order quantity always decreases with the reference profit to avoid the overage cost. Our study shows that a retailer with a higher reference profit should order more in some cases when yield uncertainty is considered. ...
... However, Long and Nasiry (2015) pointed out that Nagarajan and Shechter (2014) ignored a key factor, namely, the reference point, in their model. The reference point is an important feature since it determines how a decision-maker perceives gains and losses under a prospect and thus plays a significant role in explaining the decision-maker's attitude toward that prospect (Uppari and Hasija 2019;Wu et al. 2018). As the zero reference point is a special case in prospect theory, some researchers investigate how a nonzero reference point affects the order quantity of a loss-averse newsvendor. ...
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.
... In the emerging line of research referred to as behavioral newsvendor, the strategic customers are included in the demand analysis-those market-savvy customers who, aware of seasonal trends or marketing schemes, may postpone their purchase until observing a lower price, or may expedite it to exploit the initial low-price demand-boosting distributions. This implies the necessity of including the customers' biases (anchoring) toward past prices in the supply channel's optimization problem [19][20][21]. We argue that including the customers' cognitive biases in the supply channel revenue optimization problem necessitates the inclusion of their memory of the past prices. ...
... We ignore the possibility that the retailer can negotiate this wholesale price. Given w, the retailer (follower) then solves (22) to find ther, which maximizes Π r , and then, substituting thisr into (21) to find out the optimum order quantityq. The manufacturer also knows that the retailer is going to chooseq to maximize the expected profit. ...
... Because a normally distributed variable can take negative values, we must impose restrictions to exclude artificial cases. If q, as given by (21), is negative, we set q = 0. Likewise, if the expected profit in (22) is negative, we assume q = 0. ...
Almost every supplier faces uncertain and time-varying demand. E-commerce and online
shopping have given suppliers unprecedented access to data on customers’ behavior, which sheds light on demand uncertainty. The main purpose of this research project is to provide an analytic tool for decentralized supply channel members to devise optimal long-term (multi-period) supply, pricing, and timing strategies while catering to stochastic demand in a diverse set of market scenarios. Despite its ubiquity in potential applications, the time-dependent channel optimization problem in its general form has received limited attention in the literature due to its complexity and the highly nested structure of its ensuing equilibrium problems. However, there are many scenarios where a single-period channel optimization solution may turn out to be myopic as it does not consider the
after-effects of current pricing on future demand. To remedy this typical shortcoming, using general memory functions, we include the strategic customers’ cognitive bias toward pricing history in the supply channel equilibrium problem. In the form of two constructive theorems, we provide explicit solution algorithms for the ensuing Nash–Stackelberg equilibrium problems. In particular, we prove that our recursive solution algorithm can find equilibria in the multi-periodic variation of many standard supply channel contracts such as wholesale, buyback, and revenue-sharing contracts.
... In order to address the above problems, this paper investigates a loss-averse newsvendor model with quantity-oriented reference point under CVaR criterion. Here, we introduce a target unit profit as an anchor, and then the reference point is a liner function of the order quantity ( [33]). The loss-averse newsvendor's objective is to maximize the CVaR of utility under the quantity-oriented reference point by selecting the order quantity. ...
... Herweg [11] investigates the expectation-based loss-averse newsvendor problem where both no shortage cost and shortage cost are considered, and obtains the first-order optimality conditions. Wu et al. [33] introduce a target unit profit as an anchor and investigate the loss-averse competitive newsvendor problem, in which proportional demand allocation and demand reallocation rules are considered, respectively. They find that a positive anchor always leads to inventory understocking, whereas a negative anchor may result in inventory overstocking. ...
... 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.
... Long and Nasiry [11] demonstrated that prospect theory can explain the newsvendor's ordering behavior observed in experiments when the reference point is considered. Wu et al. [23] studied the competitive newsvendor problem in the case of proportional demand allocation and demand reallocation. They showed that the total inventory level in the decentralized case may be lower than that in the centralized 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. ...
... However, the decision maker usually has a clear and definite target in practice. In view of this, Wu et al. [23] and Bai et al. [26] suggest that it is easier and more realistic for the newsvendor to choose the target unit profit instead of target gross profit as reference point. Similarly to them, we introduce a target unit profit w 0 ∈ [s − c, p − c] as the reference point, where the minimum s − c < 0 is the loss per unit unsold product and the maximum p − c > 0 is the revenue per unit selling product. ...
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.
... Therefore, in contrast to loss aversion, which always decreases the order quantity, a newsvendor with a reference point could order more or less than a risk-neutral newsvendor (Herweg, 2013;Long and Nasiry, 2015). Wu et al. (2018) study the loss-averse competitive newsvendor problem with anchoring (reference dependence) and show that anchoring (reference dependence) has a significant effect on ordering. In certain situations, the anchoring effect (reference dependence effect) dominates loss aversion and leads to understocking even in a competitive environment. ...
... Wood, 1989;Roels and Su, 2014), and goals (or targets) (e.g. Heath et al., 1999;Hsiaw, 2013;Wu et al., 2018) are three natural candidates. Furthermore, a number of authors extend the formulation of reference points to a more complex environment, e.g. two reference points (survival and aspiration levels, March (1988); internal and external effects, Kirshner and Shao (2018); status quo and minimum profit requirement, Wei et al. (2019)), and three reference points (status quo, goal and survival requirement, Wang and Johnson (2012)). ...
... First, although some studies consider loss aversion with reference dependence (e.g. Wang and Webster, 2009;Long and Nasiry, 2015;Wu et al., 2018;Zhou et al., 2018;Lee et al., 2015), they all assume that the selling price is exogenous, whereas we explore the joint optimization of pricing and ordering decisions. Moreover, we compare the decision differences between two price-dependent demand models (additive and multiplicative). ...
... However, few percent of individuals in the globe may be found risk-neutral. Indeed, most of us tend to be more loss-averse than risk-averse (Wei et al. 2014;Meng et al. 2017;. ...
... To study the newsvendor's risk attitude, many researchers have adopted the utility approach such as (Meng et al. 2017;Hui et al. 2016;Wang and Webster 2009;Guo and Chen 2000;Eeckhoudt et al. 1995). For instance, Meng et al. (2017) employed anchoring as an approach for competitive newsvendors. ...
... To study the newsvendor's risk attitude, many researchers have adopted the utility approach such as (Meng et al. 2017;Hui et al. 2016;Wang and Webster 2009;Guo and Chen 2000;Eeckhoudt et al. 1995). For instance, Meng et al. (2017) employed anchoring as an approach for competitive newsvendors. Loss-averse newsvendor's problem has been solved using a robust optimization in Hui et al. (2016) which has been formerly considered in Wang and Webster (2009). ...
Loss-averse behavior makes the newsvendors avoid the losses more than seeking the probable gains as the losses have more psychological impact on the newsvendor than the gains. In economics and decision theory, the classical newsvendor models treat losses and gains equally likely, by disregarding the expected utility when the newsvendor is loss-averse. Moreover, the use of unbounded utility to model risk attitudes fails to explain some decision-making paradoxes. In contrast, this paper deals with the utility maximization of the newsvendor using a class of bounded utility functions to study the effect of loss aversion on the newsvendor certainty equivalents and risk premiums. New formulas are introduced to find the utility-optimal order quantity of the normal distribution. The results show that when an exponential loss aversion exists, the classical newsvendor optimal quantity serves as a lower bound when the overage costs are high and as an upper bound when the underage costs are high. In addition, we show that high loss aversion entails higher risk premiums. Similar conclusion holds when the overage/underage costs increase. Higher standard deviations, on the other hand, mean lower utility-optimal quantities and higher risk premiums. The presented formulas are advantageous in finding the optimal order quantities and risk premiums of a stochastic short-shelf life inventory when the loss is a key factor in the decision-making process.
... Shalev's version has been received widespread attention in the field of game theory [24][25][26][27]. In particular, the value function and its variants that characterizes the lossaversion preference of decision makers has been applied to supply chain decisions [28][29][30][31][32]. Until recent years, the impacts of loss-aversion preferences on decisions have increasingly received attention from an increasing number of scholars in the SCM [33][34][35][36]. However, the extant works on supply chain involving loss aversion have not adequately taken into account the choice of loss-aversion reference points of supply chain members, but assumed that associated loss-aversion reference points are equal to zero or given exogenously. ...
... Moreover, some scholars considered newsvendor problems with loss aversion. Wang [31], Ma et al. [33] and Wu et al. [35] argued that newsvendors' loss aversion decreases order quantity. Lee et al. [52] considered the supply option problem when a loss-averse newsvendor has multiple options. ...
This paper investigates a two-echelon green supply chain (GSC) with a single loss-averse manufacturer and a single loss-averse retailer. Since the Nash bargaining solution exactly characterizes endogenous power and the contribution of the GSC members, it is introduced as the loss-averse reference point for the GSC members. Based on this, a decision model of the two-echelon GSC with loss aversion is formulated. The optimal strategies of price and product green degree are derived in four scenarios: (a) the centralized decision scenario with rational GSC members, namely the CD scenario; (b) the decentralized decision scenario with rational GSC members, namely the DD scenario; (c) the decentralized decision scenario with the GSC members loss-averse, where the manufacturer’s share is below its own loss-averse reference point, namely the DD(∆m ≥ πm) scenario; (d) the decentralized decision scenario with the GSC members loss-averse, where the retailer’s share is below its own loss-averse reference point, namely the DD(∆r ≥ πr) scenario. Then, a comparative analysis of the optimal strategies and profits in these four scenarios is conducted, and the impacts of loss aversion and green efficiency coefficient of products (GECP) on the GSC are also performed. The results show that (i) GECP has a critical influence on the retail price and the wholesale price; (ii) the GSC with loss aversion provide green products with the lowest green degree; (iii) the retail price, the wholesale price and product green degree are decreasing monotonically with the loss aversion level of the GSC member without incurring loss; (iv) furthermore, the effect of the loss aversion level of the GSC member with incurring loss on the optimal strategies is related to GECP and the gap between the GSC members’ loss aversion levels.
... Chan and Xu (2019) used the CVaR method to quantify the potential risks and investigated the loss-averse buyer's optimal order quantity. Other related papers include Wang et al. (2009), Dai and Chao (2013), Lee et al. (2015), Sarkar et al. (2017), and Wu et al. (2018), among others. Most of the literature on risk aversion assumes adequate capital for the supply chain members. ...
The paper aims to provide a theoretical basis for the application of revenue-sharing contract under bounded rationality and capital constraints. We consider an uncooperative ordering model in a supplier-Stackelberg game and coordination strategy with revenue-sharing contract for a loss-averse and capital-constrained retailer. We drive the existence and uniqueness conditions of the optimal solutions under bank financing and revenue-sharing contract. We also develop a series of propositions and corollaries to determine the optimal solutions and offer some managerial insights. The key contribution of the paper is to deepen and expand the revenue-sharing contract under the risk-neutral assumption, and to provide a theoretical basis for the application of revenue-sharing contract under bounded rationality and capital constraints. We find that the revenue-sharing ratio of loss-averse and capital-constrained retailer is larger than that of neutral retailer and the expected utility of loss-averse and capital-constrained retailer is larger than that of neutral retailer under coordination strategy with revenue-sharing contract.
... Hence, the objective is to define the split of demands (among the competing vendors) that maximizes the overall profit and to find possible equilibrium states. It is interesting to note that recently these extensions are jointly considered, as in the work by Wu et al. (2014) and Wu et al. (2018). ...
With Newsvendor Problem (NvP) we refer to a specific class of inventory management problems, valid for a single item with stochastic demand over a single period. In the standard version, the newsvendor is allowed to issue a single order, before he or she can observe the actual demand. Since the newsvendor can face both overage and underage costs, due to lost sales or residual stock, the objective is to define the optimal order size that maximizes the expected profit. In this paper, we consider a specific version of the NvP, in which the buyer has the opportunity to make a last and single order for opportunistic reasons. Specifically, we consider discontinued, collectible items, for which demand will not vanish and whose value might appreciate. Hence, the objective is to define the optimal quantity that should be purchased, just before the item is retired from the market or sold-out, and that should be sold as soon as the price rises over a predefined target level. An optimal solution, maximizing the expected profit, is obtained both in case of negligible and non-negligible stockholding costs. In the latter case, to obtain the optimal solution in implicit form, some simplifying assumptions are needed. Hence, a thorough numerical analysis is finally performed, as a way to empirically demonstrate both the robustness and the accuracy of the model, in several scenarios differentiated in terms of costs and customers’ demand.
... Benzion believes that the order quantity is also affected by the average demand and the optimal order quantity [1]. Camerer, C. F et al. introduced empirical factors into the newsvendor model to improve the accuracy of prediction [4,7,11], and the anchoring effect plays an important role in decisionmaking [22]. ...
... Comparison of orders in the advance period with or without reference price dependence a result of the increase in the advance period order quantity, but instead should appropriately reduce the order quantity in the spot period. This is similar to previous studies where price reference dependence can significantly bias sellers' order quantities [52,4]. Still, in these studies, reference price dependence has only one effect on order quantities in some cases. ...
The purpose of this paper is to study the impact of bounded consumer rationality on the order quantity and profitability of the seller in the advance period and the spot period in the context of the combination of new retail and pre-sale. In this paper, we develop a seller order model in the context of the combination of new retail and pre-sale, with and without reference price dependence. Besides, the model considers the order cancellation and delayed purchase behavior of consumers. We then discuss the optimal profit and optimal order quantity under different conditions and the effect of different reference price dependence and value-added offline service on them. Our research shows that: First, the seller tends to set the deposit too low in pre-sales. Second, reference price dependence has different effects on order quantities in different periods. The seller should pay more attention to the impact of reference price dependence. Third, on the whole, consumer rationality benefits the seller. The seller, or the public policymaker, can benefit new retail businesses by increasing consumer rationality. Last, in the new retail context, an increase in offline service value-added, even if it increases total order quantity, is not always beneficial to the seller and may reduce profits. Therefore, the seller should weigh all factors to determine the optimal value-added offline services.
... A higher value of η means that the buyer has a high expectation for the supply yield. Note that, we formulate the order-dependent reference point as a linear function of order quantity, which is consistent with models from the literature (e.g., [3,20,23,24,29]). ...
A recent experimental study shows that human decision-makers exhibit sourcing diversification due to supply uncertainty. It has been pointed out that loss aversion is unable to explain this ordering bias. In this paper, we show that loss aversion with reference dependency can explain this decision bias, and the type of reference point matters in sourcing decisions.
... Trade credit has some advantages compared to traditional bank financing for enterprises. It could increase order quantities for capital-constrained retailers (Wu, Zhang, and Baron 2019); benefits firms facing with uncertainty (Yin, Li, and Tang 2015;Wu, Bai, and Zhu 2018); reduce financing cost (Melnyk, Narasimhan, and DeCampos 2014); improve buyer's bargaining power (Klapper, Laeven, and Rajan 2011); define default risk quicker (Smith 1987), and lower transaction costs (Emery 1984;Gao et al. 2018) identified optimal Stackelberg strategies for peer-to-peer lending in supply chains. Most works (Kouvelis and Zhao 2011;Chod 2016;Huang, Yang, and Tu 2019) consider original trade credit in supply chains to finance inventory. ...
This paper investigates the impacts of preferential credit policy, faced by capital constraint retailers, on coordinating the supply chain. Apart from different bank’s and manufacturer’s risk preferences, preferential credit is also affected by the retailers’ exogenous collateral. We establish the preferential credit coordinating model (PCCM) to examine the optimal decisions and coordinate the supply chain with different financing channels, such as the preferential bank loan, preferential trade credit and portfolio credit. In this paper, we conclude some critical findings. Firstly, we find that the retailer’s optimal would improve its optimal order quantity in the coordinated supply chain when he finances from a risk-pursuing bank or the manufacturer. Secondly, the retailer’s financial cost would be shared with the manufacturer whether the retailer utilises preferential trade credit or bank financing channel. Thirdly, the capital constraint retailer would prefer preferential trade credit to the other financing methods for the purpose that the preferential trade credit could improve the coordinated supply chain’s efficiency. Finally, we capture different impacts of collateral and risk preference on the supply chain. This article supplements the existing literature on supply chain finance with a preferential credit insight into the condition of the coordinated supply chain.
... First, the reference point in the loss aversion utility function is set to zero to facilitate the analysis. However, some studies (e.g., [50,55]) have pointed out that the reference point has an important effect on the ordering decisions. The model incorporating reference dependence deserves further study. ...
In this paper, we apply a combined revenue sharing and buyback contract to investigate the channel coordination of a two-echelon supply chain with a loss-averse retailer. Since lossaverse decision makers usually take on more risks, the Conditional Value-at-Risk (CVaR) measure is introduced to hedge against it and the retailer’s objective is to maximize the CVaR of utility. We obtain the retailer’s optimal order quantity under the combined contract. It is shown that there is a unique wholesale price coordinating the supply chain if the retailer’s confidence level is less than a threshold that is independent of contract parameters. Moreover, a complete sensitivity analysis of parameters is carried out. In particular, the retailer’s optimal order quantity and coordinating wholesale price decreases as the loss aversion or confidence level increases, while it increase as the buyback price or sharing coefficient increases. Furthermore, there exists the situation where the combined contract can coordinate the chain even though neither the revenue sharing nor buyback contract can when the contract parameters are constrained.
... Long and Nasiry [29] regarded the existing status as the reference point and developed a prospect theory-based newsvendor model. Wu et al. [30] investigated a loss-averse competitive news supplier problem with the anchor. ey found that the order quantity of newsboys decreased with the degree of loss aversion and anchor value. ...
The optimal inventory control is closely related to an enterprise’s operational efficiency, survival, and development. Market price uncertainty is introduced into the newsvendor model and the uncertainty’s impact on the firm's optimal stocking quantity is discussed. The results show that the impact of stochastic market price on the optimal stocking quantity under a given condition mainly depends on the magnitude of inventory cost. When the inventory cost is low, the market price’s uncertainty leads the firm to increase the stocking quantity. In contrast, when the inventory cost is high, market price uncertainty leads the firm to decrease inventory. Besides, the risk-averse behaviour leads the firm to reduce its stocking quantity.
... However, low percent of individuals can be found risk-neutral. Indeed, most of us tend to be loss-averse more than we do as risk-averse, (Dalalah & Alkhaledi, 2016;Liu, Song, Bing, & Cheng, 2015;Meng, Tian Bai, & Zhu, 2017). ...
The classical newsvendor model in economics and decision theory treats losses and gains equally likely. However, decision makers are usually loss-averse as probable losses have more impact on humans than probable gains. This study presents a new variant of the newsvendor problem of loss-averse decision makers. The optimal order quantity is found by maximizing the expected utility of bounded functions. The implications of loss aversion on the certainty equivalents and risk premiums were also analyzed. Two case studies of exponential utility and normal demand were considered. A new elegant form of the optimal order quantity is established. The results show that when exponential loss aversion exists, the newsvendor optimal quantity serves as a lower(upper) bound on the optimal quantities. Moreover, high loss aversion entails higher RP. Similar findings hold by increasing the over-age/underage costs and the demand standard deviation. Possible future extensions are demonstrated at the end of the paper. ARTICLE HISTORY
... Xu, Chan, and Langevin (2018) considered a loss-averse newsvendor and established the CVaR model with a shortage cost to determine the optimal decisions. In addition, in the loss-averse competitive newsvendor problem with anchoring, Wu, Bai, and Zhu (2018) found that the newsvendor's order quantity decreases as the loss aversion coefficient and the value of anchor increase. Recently, Fan, Feng, and Shou (2020) Initially, Kahneman and Tversky (1979) used the current asset to define gains and losses, but researchers and practitioners in reality commonly perceive revenues as gains or losses in relation to a benchmark, which is known as the reference-dependence behavior. ...
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.
... Trade credit has some advantages compared to traditional bank financing for enterprises. It could increase order quantities for capital-constrained retailers (Wu, Zhang, and Baron 2019); benefits firms facing with uncertainty (Yin, Li, and Tang 2015;Wu, Bai, and Zhu 2018); reduce financing cost (Melnyk, Narasimhan, and DeCampos 2014); improve buyer's bargaining power (Klapper, Laeven, and Rajan 2011); define default risk quicker (Smith 1987), and lower transaction costs (Emery 1984;Gao et al. 2018) identified optimal Stackelberg strategies for peer-to-peer lending in supply chains. Most works (Kouvelis and Zhao 2011;Chod 2016;Huang, Yang, and Tu 2019) consider original trade credit in supply chains to finance inventory. ...
This paper examines how preferential credit based on retailers’ credit line impacts on capital-constraint retailer’s operational decisions. We consider a condition of loan competition when banks and manufacturers offer preferential credit to capital-constraint retailers in the newsvendor model. Different credit lines and discounted rates of preferential credit mainly involve in retailers’ exogenous collateral and risk preference of banks and manufacturers in our model. We investigate impacts of bank financing, trade credit, and portfolio credit (financing from both bank credit and trade credit with different ratios) on retailer’s inventory decision with different cases that the retailer’s financing amounts exceed credit line or not. We derive the equilibrium wholesale price, expected sale price, and order quantity when retailers face with different conditions of collaterals and institutes’ risk preferences facing with market risk. A debt-financed retailer favours items with trade credit compared to bank financing, especially in conditions when its sourcing demand is great and when it finances from high-risk preference institutes. Retailer prefers to using the loan with high trade credit ratio when he opts portfolio credit conditions.
... Recently, there has been an increase in interest in including the supplier's cognitive bias toward previous demand information -referred to as anchoring effect by Tversky and Kahneman [30] in the study of the newsvendor problem. Wu et al. [33] analyze the effect of the newsvendor's anchoring with demand information. That is, in their paper, the loss-averse newsvendor, biased with previous demand, may change her order quantity (inventory level). ...
We extend the single-period decentralized channel optimization problem with stochastic demand into a multi-period, non-autonomous one and propose an efficient general solution algorithm for it. A supply channel composed of two price-setting agents in a bi-level (Stackelberg) framework has to address an uncertain dynamic demand for a perishable good at different times. The stochastic demand model is general (additive-multiplicative). A class of price-dependent memory functions is embedded in the proposed representation of uncertain demand such that they carry the effect of demand level at present over to the demand in the future. Due to this dependence of the current demand to the pricing history, the state space of the ensuing games becomes highly nested. The proposed iterative algorithm decouples the nested equilibria into separate yet interdependent sub-problems and provides explicit solutions. All the model variables and parameters are considered explicitly time-dependent enabling the model to cover cases with finite and infinite time-horizons. Flexibility and generality of our solution scheme make it applicable to a wide variety of economic contexts. In a series of examples we demonstrate how, fed by different market specifications and memory functions, the solution algorithm can find equilibrium results for a diverse set of scenarios at different times.
... Note that, if λ = 0, then the loss-averse utility reduces to the riskneutral utility. This piecewise-linear form of the loss-averse utility function is a special case of a prospect theory function, which has been widely used in the literature on economics and operations management (e.g., Long & Nasiry, 2015;Wu, Bai & Zhu, 2018). Furthermore, to make the problem nontrivial, we assume that the reference target valuation V 0 is greater than the spot selling price p, that is, V 0 ≥ p; otherwise, any loss-averse utility reduces to risk neutral utility. ...
Many firms offer consumers the opportunity to place advance orders at a discount when introducing a new product to the market. Doing so has two main advantages. First, it can increase total expected sales by exploiting valuation uncertainty of the consumers at the advance ordering stage. Second, total sales can be estimated more accurately based on the observed advance orders, reducing the need for safety stock and thereby obsolescence cost. In this research, we derive new insights into trading off these benefits against the loss in revenue from selling at a discount at the advance stage. In particular, we are the first to explore whether firms should advertise the advance ordering opportunity. We obtain several structural insights into the optimal policy, which we show is driven by two dimensions: the fraction of consumers who potentially buy in advance (i.e., strategic consumers) and the size of the discount needed to make them buy in advance. If the discount is below some threshold, then firms should sell in advance and they should advertise that option if the fraction of strategic consumers is sufficiently large. If the discount is above the threshold, then firms should not advertise and only sell in advance if the fraction of strategic consumers is sufficiently small. Graphical displays based on the two dimensions provide further insights.
... However, they do not assume that any decision-maker is financially constrained. Wu et al. [23] consider a loss-averse competitive newsvendor problem with an anchoring effect, however, they do not assume that any decision-maker is financially constrained. Yan et al. [24] consider a Stackelberg model of a financially constrained supply-chain system including a supplier, a financially constrained retailer, and a bank that provides loans on the basis of the supplier's credit guarantee. ...
Traditionally, in the area of production and operations management, the financial states and decision-makers’ behaviour regarding loss have been ignored in the supply chain, which may lead to infeasible or unrealistic practices or even catastrophic losses in practical supply chain operations. Therefore, this study aims to provide a model for operational efficiency in a financially constrained supply-chain system consisting of a financially deficient retailer, a supplier, and a bank, and to analyse the impact of the behaviour of the bank and the supplier on the operational decision. It is assumed that the bank provides a loan to the retailer considering the supplier’s credit guarantee for the retailer. The supplier’s credit guarantee implies that, if the retailer goes bankrupt after the sales season, then a pre-guaranteed proportion of the retailer’s loan is repaid by the supplier. Moreover, to capture the decision-makers’ behaviour regarding loss, it is assumed that the supplier and the bank are loss-averse in their risk preference on the final profit. Under this circumstance, it is intended to draw the theoretical implications by analysing a loss-averse behaviour model for a supplier and a bank, in which a kinked piecewise linear and concave utility function is considered. The optimal decision is analytically derived for the retailer (the optimal order quantity), the supplier (the optimal wholesale price), and the bank (the optimal interest rate). In addition, a sensitivity analysis is conducted to investigate how the model parameters affect the optimal decision for the retailer, the supplier, and the bank under different degrees of loss-aversion. The optimal decisions are shown to be highly affected by the degree of the loss-aversion coefficient of the bank and the supplier and to be more conservative than the result in the traditional case which optimises the risk-neutral expected profit (the unit degree of loss-aversion). The analytical results can be summarised as follows. First, as the wholesale price and the interest rate increase, the optimal order quantity decreases. Second, the more loss-averse the supplier is, the higher the optimal wholesale price that is offered to the retailer by the supplier. Third, the larger the credit guarantee that is provided to the retailer by the supplier, the higher the optimal wholesale price that is provided to the retailer. Fourth, the more loss-averse the bank is, the higher the interest rate that is offered to the retailer; and the larger the credit guarantee that is provided by the supplier, the lower the interest rate that is offered to the retailer.
... However, low percent of individuals can be found risk-neutral. Indeed, most of us tend to be loss-averse more than we do as risk-averse, (Dalalah & Alkhaledi, 2016;Liu, Song, Bing, & Cheng, 2015;Meng, Tian Bai, & Zhu, 2017). ...
The classical newsvendor model in economics and decision theory treats losses and gains equally likely. However, decision makers are usually loss-averse as probable losses have more impact on humans than probable gains. This study presents a new variant of the newsvendor problem of loss-averse decision makers. The optimal order quantity is found by maximizing the expected utility of bounded functions. The implications of loss aversion on the certainty equivalents and risk premiums were also analyzed. Two case studies of exponential utility and normal demand were considered. A new elegant form of the optimal order quantity is established. The results show that when exponential loss aversion exists, the newsvendor optimal quantity serves as a lower(upper) bound on the optimal quantities. Moreover, high loss aversion entails higher RP. Similar findings hold by increasing the overage/underage costs and the demand standard deviation. Possible future extensions are demonstrated at the end of the paper.
The standard newsvendor problem has attempted to determine the ideal ordering quantity considering the trade-off between over-stocking and under-stocking. Behavioral operations management have started to analyse the social and behavioural dynamics involved in the newsvendor problem from the year 2000. Later many researchers have conducted experiments to understand the ordering biases and pricing decisions involved in the area of inventory management. The concept of loss-aversion plays a significant part in the inventory related decisions. This paper presents a detailed examination to understand the influence of loss aversion, prospect theory and reference points on supply chain and related decisions. The systematic review of the existing literature is carried out using the keywords such as newsvendor, loss aversion in inventory management, loss-aversion of newsvendor, experimental studies of inventory management. This review analyses the research progress related to loss aversion and its associated biases on the inventory management problem. This evaluation helps in contributing new insights that will support the researchers and practitioners working in the areas of behavioural economics, experimentation, behavioral operations management, boundedly rational, modelling of newsvendor problem, supply chain practices and contracts. It will also act as a key reference paper to understand the behavioural issues related to the loss-aversion of newsvendor. This paper finds the research gap to highlight on the upcoming research potentials and primacies. This examination confirms the presence of an extensive room for research potential and highlights the specific areas for further research.
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 how individuals choose prices for two substitutes under stochastic demand in an airline setting. We design two treatments: “symmetrical” and “asymmetrical,” meaning the demand distribution of the two flights having the same size of support or not. Several insights are obtained. First, the decision makers' price choices are closer to the theoretical benchmarks in the symmetrical setting. Next, the subjects do not want to overprice and fly with empty seats, exhibiting “loss aversion with reference point.” Finally, the subjects often treat the flights as independent rather than interrelated and price them separately, using an anchoring-and-adjusting heuristic.
Traditional modeling in supply chain contract analysis shows that a wholesale price contract cannot coordinate a supply chain, whereas a buyback contract can coordinate. In this study, we consider a supply chain involving a risk-neutral supplier and a behavioral retailer under wholesale price and buyback contracts. We characterize the structural properties of the wholesale price contract in a supply chain with a behavioral retailer. Our study reveals that a wholesale price contract can coordinate a supply chain with a behavioral retailer under certain conditions. Under the same conditions, our analysis shows that a buyback contract coordinates the supply chain. Furthermore, we derive the conditions under which a buyback contract will not coordinate a supply chain involving a behavioral retailer. We validate our model with the existing experimental results on supply chain contracts. Finally, we show that a wholesale price contract can outperform a buyback contract in a supply chain having a behavioral retailer.
Platelets, one of the most significant materials in treating leukemia, have a limited shelf life of approximately five days. Because platelets cannot be manufactured and can only be centrifuged from whole or donated blood directly, an accurate ordering policy is necessary for the efficient use of this limited blood resource. Given this motivation, the present study examines an ordering policy for platelets to minimize the expected shortage and overage. Rather than using the two-step model-driven method that first fits a demand distribution and then optimizes the order quantity, we solve the issue using an integrated data-driven method. Specifically, the data-driven method works directly with demand data and does not rely on the assumption of demand distribution. Consequently, we derive theoretical insights into the optimal solutions. Through a comparative analysis, we find that the data-driven method has a mean anchoring effect, and the amounts of shortage and overage reduced by this method are greater than those reduced by the model-driven method. Finally, we present an extended model with the service level requirement and conclude that the order decided by the data-driven method can precisely satisfy the service level requirement; however, the order decided by the model-driven method may be either higher or lower than the service level requirement and can lead to a higher cost.
Experimental results support that overconfident newsvendors deviate from the optimal inventory levels to place orders closer to the mean of demand distributions, thereby lowering profits. To improve performance, we investigate whether nonstandard preferences based on prospect theory can manage overconfident newsvendors. We develop a framework where a manager determines a profit‐based target, which serves as a reference point in the newsvendor's utility function. We show that target‐setting can induce optimal orders for low‐margin products. We extend our model to a duopoly and show that the type of competition determines whether target‐setting improves performance beyond the monopolist setting. Decentralized competition, where competing newsvendors have differet managers, reduces the effectiveness of target‐setting. However, centralized competition, where competing newsvendors share the same manager, increases the range of profit margins within which target‐setting can achieve the system‐optimal order quantities. We compare profit‐margin targets with gross‐profit targets throughout our analysis. Although the targets offer similar performance, we find that profit‐margin [gross‐profit] targets dominate for extremely [moderately] low‐margin products when the manager is uncertain about the newsvendor's overconfidence level. However, when managing a newsvendor with an uncertain degree of loss aversion, we find that profit‐margin targets offer greater benefits regardless of the product's profitability.
At present, the research on relevant decision-making considering the loss risk/ default risk in trade credit is on the rise This paper presents a supply chain model with a risk-averse retailer and a supplier offering loss sharing and trade credit in a supplier-Stackelberg game where the decision variables are the optimal order quantity and loss sharing ratio. The model is analyzed and compared to a newsvendor model without loss sharing and trade credit. Meanwhile, we provide a numerical example and sensitivity analysis to obtain managerial insights. We determine the trend and sensitivity hierarchies between the parameters and the optimal results. The main novelty and contribution of the paper can be demonstrated in two aspects. First, the risk tolerance largely affects the profit of supply chain members, therefore, we incorporate risk-averse parameter into trade credit policy. Second, we incorporate loss sharing into the supplier-Stackelberg game with trade credit for a loss-averse retailer. The findings highlight that for a risk-averse retailer, the supplier can improve the retailer’s utility and its own profits through trade credit and loss sharing.
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.
Vaccination is an effective intervention against epidemics. Previous work has demonstrated that psychological cognition affects individual behavior. However, perceptual differences between individuals, as well as the dynamics of perceptual evolution, are not taken into account. In order to explore how these realistic characteristics of psychological cognition influence collective vaccination behavior, we propose a prospect theory based evolutionary vaccination game model, where the evolution of reference points is used to characterize changes in perception. We compare the fractions of vaccinated individuals and infected individuals under variable reference points with those under the expected utility theory and the fixed reference point, and highlight the role of evolving perception in promoting vaccination and contributing to epidemic control. We find that the epidemic size under variable reference point is always less than that under the expected utility theory. Finding that there exists a vaccination cost threshold for the cognitive effect, we develop a novel mixed-reference-point mechanism by combining individual psychological characteristics with network topological feature. The effectiveness of this mechanism in controlling the network epidemics is verified with numerical simulations. Compared with pure reference points, the mixed-reference-point mechanism can effectively reduce the final epidemic size, especially at a large vaccination cost.
Graphical abstract:
In the decision-making of perishable product, newsvendors may be overconfident as they have a more precise estimate about future outcomes, and they may be ambiguity-averse as only partial knowledge of the demand distribution is available. This paper investigates the overconfident behavior bias of a newsvendor when he is ambiguity-averse. By reducing the variance of demand distribution but preserving the mean with a linear function, we formulate a theoretical max–min optimization model that accounts for the influence of overconfidence and ambiguity aversion on the newsvendor’s decision. The closed-form solution for optimal order quantity is achieved by maximizing the expected profit against the worst distribution. Some conclusions are accordingly included. Firstly, the optimal order quantity is a linear function of the overconfident level, and it is decreasing in the overconfident level in the high-profit case, and increasing in the low-profit case. Secondly, overconfident newsvendors believe they are more precise, and thus gain more profits than the unbiased ones. However, overconfidence may actually raise order bias, and the expected costs increase in the overconfident level. Thirdly, overconfidence helps to alleviate the conservatism of ambiguity-averse optimization and the robust strategy performs reasonably better even if the demand distribution exists some misspecifications. In addition, we provide experiments supporting the theoretical relations. The closed-form solutions are tractable, and thus of great significance to the practical applications.
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.
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.
This paper examines the importance of aspirations as reference points in a multi-period decision-making context. After stating their personal aspiration level, 172 individuals made six sequential decisions among risky prospects as part of a choice experiment. The results show that individuals make different risky-choices in a multi-period compared to a single-period setting. In particular, individuals’ aspiration level is their main reference point during the early stages of decision-making, while their starting status (wealth level at the start of the experiment) becomes the central reference point during the later stages of their multi-period decision-making.
Previous experimental work has shown that individuals make suboptimal decisions in newsvendor problems (e.g. Schweitzer and Cachon 2000). We present a theoretical (behavioral) model of overconfident newsvendors that is consistent with these observed results. We show that overconfident newsvendors place suboptimal orders (which can be either higher or lower than optimal quantities) and earn lower profits than well-calibrated newsvendors. We also derive incentive contracts using salvage costs and price adjustments which a well-calibrated manager might offer to an overconfident newsvendor in order to induce optimal orders.
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.
Previous experimental work has shown that individuals make suboptimal decisions in newsvendor problems. We argue that these decisions may be caused by overconfidence, and explore a theoretical (behavioral) model of overconfident newsvendors first presented in Ren and Croson (2013) that is consistent with these observed results. Using classical analysis techniques, we show that overconfident newsvendors will over-order in low-profit situations and under-order in high-profit situations, exhibiting the ordering pattern observed in the field and in the lab. In this paper, we further demonstrate that order bias is linear in the level of overconfidence, and is increasing with the variance of the demand distribution. Order bias also has a U-shaped relationship with market profitability, and the costs of overconfidence are convex. We use the theory to develop new predictions which can be themselves tested in future work.
Modeling the manufacturer as a newsvendor, in this paper we study the ordering decisions of a loss-averse newsvendor with supply and demand uncertainties. Using the stylized newsvendor models, we analyse several key issues, including the effect of the newsvendor's loss aversion, the effect of demand uncertainty, and the effect of supply uncertainty on the decision maker's optimal decision under the procurement model, in which the decision maker only pays for the actual quantity received. Through our analysis, we find the following facts: the optimal order quantity decreases with respect to the degree of loss-aversion; the supply uncertainty induces the decision maker to order more than that in a deterministic environment; a stochastically larger demand always results in a larger order quantity and a larger expected utility; the optimal expected utility decreases in the demand volatility while the optimal order quantity may increase or decrease. Moreover, with numerical experiments, we demonstrate that the supply risk negatively affects the utility more than the demand risk does.
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.
Previous studies have shown that individuals make suboptimal decisions in a variety of supply chain and inventory settings. We hypothesize that one cause is that individuals are overconfident (in particular, overprecise) in their estimation of order variation. Previous work has shown theoretically that underestimating the variance of demand causes orders to deviate from optimal in predictable ways. We provide two experiments supporting this theoretical link. In the first, we elicit the precision of each individual's beliefs and demonstrate that overprecision significantly correlates with order bias. We find that overprecision explains almost one-third of the observed ordering mistakes and that the effect of overprecision is robust to learning and other dynamic considerations. In the second, we introduce a new technique to exogenously reduce overprecision. We find that participants randomly assigned to this treatment demonstrate less overprecision and less biased orders than do those in a control group.
This paper was accepted by Peter Wakker, decision analysis.
Optimal inventory policy is first derived for a simple model in which the future (and constant) demand flow and other relevant quantities are known in advance. This is followed by the study of uncertainty models — a static and a dynamic one — in which the demand flow is a random variable with a known probability distribution. The best maximum stock and the best reordering point are determined as functions of the demand distribution, the cost of making an order, and the penalty of stock depletion.
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.
This paper studies a newsvendor game in which two substitutable products are sold by two different retailers (newsvendors) with loss-averse preferences. Each loss-averse retailer facing stochastic customer demand and deterministic substitution rate will make an order quantity decision to maximize his expected utility. Since product substitution causes two retailers to make decisions in a competitive environment, game theory is used to find the retailers' optimal order quantities. It is shown that under certain conditions, there exists a unique Nash equilibrium in the newsvendor game. Under a symmetry assumption, each retailer's equilibrium order quantity is decreasing in the loss aversion coefficient and increasing in the substitution rate. Further, if the effect of loss aversion on the order quantity is strong enough to dominate the effect of competition, the total inventory level of a decentralized supply chain will be lower than that of a centralized supply chain. Numerical experiments are conducted to illustrate our results.
We modify the classic single-period inventory management problem by assuming that the newsvendor is expectation-based loss averse according to B. Köszegi and M. Rabin [Q. J. Econ. 121, No. 4, 1133–1165 (2006; Zbl 1179.91059); “Reference-dependent risk attitudes”, Am. Econ. Rev. 97, No. 4, 1047–1073 (2007; doi:10.1257/aer.97.4.1047)]. We show that the expectation-based loss-averse newsvendor orders less than the profit-maximizing quantity. Moreover, the order placed by the expectation-based loss-averse newsvendor features plausible comparative statics of cost and price changes.
In this paper, we study how social planners should exploit social comparisons to pursue their objectives. We consider two modes of social comparison, referred to as behind-averse and ahead-seeking behaviors, depending on whether individuals experience a utility loss from underperforming or a utility gain from overperforming relative to their peers. Modeling social comparison as a game between players, we find that ahead-seeking behavior leads to output polarization, whereas behind-averse behavior leads to output clustering. A social planner can mitigate these effects in two ways: (i) by providing the full reference distribution of outputs instead of an aggregate reference point based on the average output and (ii) by assigning players into uniform rather than diverse reference groups. Social planners may thus need to tailor the reference structure to the predominant mode of social comparison and their objective. A performance-focused social planner may set the reference structure so as to maximize the output of either the top or the bottom player depending on whether she puts greater marginal weight to larger or smaller outputs. When the social planner also cares about utility, she faces a dilemma because performance optimization may not be aligned with utility maximization. Inevitably, the social planner will have to confront equity issues because better performance may not reflect greater effort or greater ability.
This paper was accepted by Serguei Netessine, operations management.
In this paper we investigate the impact of a target on newsvendor decisions. Different to the existing approach that maximizes the probability of the profit reaching the target, in this paper we model the effect of a target by maximizing the satisficing measure of a newsvendor's profit with respect to that target. We study two satisficing measures: CVaR satisficing measure that evaluates the highest confidence level of CVaR achieving the target; and Entropic satisficing measure that assesses the smallest risk tolerance level under which the certainty equivalent for exponential utility function achieves the target. For both satisficing measures, we find that the optimal ordering quantity increases with the target level. Further, the newsvendor orders more than the risk-neutral solution (over-order) sometimes and less than that (under-order) other times, depending on the target level. The more interesting finding is that if the target is proportional to the unit marginal profit and is also determined by only one other demand-related factor, then the newsvendor over-orders low-profit product and under-orders high-profit product. This is consistent with the existing findings in newsvendor experiments, and suggests that our modelling framework may provide a potential explanation for the behavioral findings.
Thirty-two college students rated the “risk” inherent in playing each of 27 gambles. The results indicated that perceived risk was determined primarily by a gamble’s probability of losing. The variance of a gamble had little influence upon its riskiness. The results were contrasted with those of a previous experiment in which Ss rated the attractiveness, rather than the riskiness, of these same bets.
We consider a competitive version of the classical newsboy problem – in which a firm must choose an inventory or production level for a perishable good with random demand, and the optimal solution is a fractile of the demand distribution – and investigate the impact of competition upon industry inventory. A splitting rule specifies how initial industry demand is allocated among competing firms and how any excess demand is allocated among firms with remaining inventory. We examine the relation between equilibrium inventory levels and the splitting rule and provide conditions under which there is a unique equilibrium. Our most general result is that if all excess demand is reallocated, i.e., there is perfect substitutability, then competition never leads to a decrease in industry inventory.
This chapter reviews the supply chain coordination with contracts. Numerous supply chain models are discussed. In each model, the supply chain optimal actions are identified. The chapter extends the newsvendor model by allowing the retailer to choose the retail price in addition to the stocking quantity. Coordination is more complex in this setting because the incentives provided to align one action might cause distortions with the other action. The newsvendor model is also extended by allowing the retailer to exert costly effort to increase demand. Coordination is challenging because the retailer's effort is noncontractible—that is, the firms cannot write contracts based on the effort chosen. The chapter also discusses an infinite horizon stochastic demand model in which the retailer receives replenishments from a supplier after a constant lead time. Coordination requires that the retailer chooses a large basestock level.
This article uses game theoretic concepts to analyze the inventory problem with two substitutable products having random demands. It is assumed that the two decision makers (players) who make ordering decisions know the substitution rates and the demand densities for both products. Since each player's decision affects the other's single-period expected profit, game theory is used to find the order quantities when the players use a Nash strategy (i.e., they act rationally). We prove the existence and uniqueness of the Nash solution. It is also shown that when one of the players acts irrationally for the sole purpose of inflicting maximum damage on the other, the maximin strategy for the latter reduces to using the solution for the classical single-period inventory problem. We also discuss the cooperative game and prove that the players always gain if they cooperate and maximize a joint objective function.
The anchoring effect is one of the most robust cognitive heuristics. This paper reviews the literature in this area including various different models, explanations and underlying mechanisms used to explain anchoring effects. The anchoring effect is both robust and has many implications in all decision making processes. This review paper documents the many different domains and tasks in which the effect has been shown. It also considers mood and individual difference (ability, personality, information styles) correlates of anchoring as well as the effect of motivation and knowledge on decisions affected by anchoring. Finally the review looks at the applicants of the anchoring effects in everyday life.
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.
This paper extends the standard newsvendor problem based upon risk neutrality to a game setting where multiple newsvendors with loss aversion preferences are competing for inventory from a risk-neutral supplier. We show that if the supplier allocates the total demand among the newsvendors proportional to their order quantities, then there exists a unique Nash equilibrium order quantity in this newsvendor game. We also find that while the demand-stealing effect increases the total order quantity of the newsvendors, the loss aversion effect decreases the newsvendors’ total order quantity and if strong enough, may lead to a lower total inventory level of the decentralized supply chain than that of an integrated supply chain.
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.
This article described three heuristics that are employed in making judgements under uncertainty: (i) representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; (ii) availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and (iii) adjustment from an anchor, which is usually employed in numerical prediction when a relevant value is available. These heuristics are highly economical and usually effective, but they lead to systematic and predictable errors. A better understanding of these heuristics and of the biases to which they lead could improve judgements and decisions in situations of uncertainty.
We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability. Copyright 1992 by Kluwer Academic Publishers
Analysis of decision making under risk has been dominated by expected utility theory, which generally accounts for people's actions. Presents a critique of expected utility theory as a descriptive model of decision making under risk, and argues that common forms of utility theory are not adequate, and proposes an alternative theory of choice under risk called prospect theory. In expected utility theory, utilities of outcomes are weighted by their probabilities. Considers results of responses to various hypothetical decision situations under risk and shows results that violate the tenets of expected utility theory. People overweight outcomes considered certain, relative to outcomes that are merely probable, a situation called the "certainty effect." This effect contributes to risk aversion in choices involving sure gains, and to risk seeking in choices involving sure losses. In choices where gains are replaced by losses, the pattern is called the "reflection effect." People discard components shared by all prospects under consideration, a tendency called the "isolation effect." Also shows that in choice situations, preferences may be altered by different representations of probabilities. Develops an alternative theory of individual decision making under risk, called prospect theory, developed for simple prospects with monetary outcomes and stated probabilities, in which value is given to gains and losses (i.e., changes in wealth or welfare) rather than to final assets, and probabilities are replaced by decision weights. The theory has two phases. The editing phase organizes and reformulates the options to simplify later evaluation and choice. The edited prospects are evaluated and the highest value prospect chosen. Discusses and models this theory, and offers directions for extending prospect theory are offered. (TNM)
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