Research Article  Open Access
FreshKeeping Effort and Channel Performance in a Fresh Product Supply Chain with LossAverse Consumers’ Returns
Abstract
We consider a fresh product supply chain consisting of one fresh product supplier and one etailer. Supplier sells fresh products through etailer in an online market, and the etailer offers a fullrefund return policy to lossaverse consumers and exerts a freshkeeping effort to keep the product at the optimum freshness level. By developing an analytical model, we derive the optimal price, quantity, and freshkeeping effort jointly and verify that it is unique in the centralized setting. Based on the comparison, we demonstrate that the etailer’s profit is greater with freshkeeping effort than without it; therefore, the etailer has an incentive to engage in freshkeeping effort. We also show that the return rate is independent of the freshkeeping effort and consumers’ loss aversion. In the decentralized setting, we first characterize the optimal wholesale price by the numerical study and then find that although the buyback contract still works, the revenuesharing contract fails to achieve channel coordination under our model formulation. Furthermore, we develop a revenue and costsharing contract that can coordinate the supply chain by designing a new contractual mechanism. Our numerical studies offer the Pareto improvement regions under the buyback and revenue and costsharing contracts in which the supplier and etailer can earn more expected profits compared with being under wholesale price contract.
1. Introduction
With the development of ecommerce, the etailing of fresh (agricultural) products (e.g., live seafoods, fresh meats, fresh fruits, and fresh vegetables) has grown faster in the last ten years in China. The total transaction amounts to ¥139.13 billion in 2017 according to the monitoring data from the China eBusiness Research Center (CeBRC). Although the market is growing fast, fresh product etailing is still in a big trouble, especially for the etailer. According to the CeBRC, in 2014, there are more than 4000 fresh product etailers in Chinese emarket, but only 1% of them yield a positive profit. Among various reasons, the poor coldchain logistics and high return rate for the sales top the list of challenging tasks. For example, according to the monitoring data from the CeBRC, the average loss rate of fresh products is 25%30% because of poor coldchain logistics service, which leads to a loss of $8.9 billion sales annually in fruit and vegetable distribution. Moreover, for poor logistics service and fresh products’ high perishable nature, purchasing fresh products online may seem riskier to the consumer, because they can not examine products physically and must rely only on the website description. Hence, consumers may be more hesitant to make a purchasing decision and more likely to return the product when it does not satisfy their expectation. It indicates that more freshkeeping efforts by the etailer may lead to a lower return rate. Because such efforts can ensure the optimal freshness of fresh products during the total dispatching process and improve consumer satisfaction. Many etailers, such as jd.com, sfbest.com, and yiguo.com, have invested heavily in constructing coldchain logistics to prevent products from spoiling and maintain freshness during the logistics process. In addition to freshkeeping efforts, the refund price is another important factor that influences return rate. Obviously, a higher refund price will lead to a higher return rate.
From the perspective of etailers, decision to put forth more freshkeeping effort is a choice of contradictions. On one side, more freshkeeping effort means greater freshness, leading to low consumer returns, which increases the sales revenue. On the other side, more freshkeeping effort is costly, which decreases the sales revenue. Similarly, decision about price is also contradictory. A higher price means a higher profit margin of fresh products, increasing the sales revenue. However, a higher price will lead to more consumer returns when the etailer exerts a fullrefund return policy, decreasing the sales revenue. Therefore, etailers should trade off the positive and negative effects of their freshkeeping effort and price.
To that end, we develop an analytical model to consider a supply chain in which one supplier sells fresh products through one etailer in online market. We assume the etailer offers a fullrefund return policy to consumers to reduce consumers’ purchasing risk. Consumers are loss averse [1–4], which means they are more averse to losses than to equal gains. Therefore, when consumers who are loss averse receive fresh products, they may return less often than riskneutral consumers; this is also called endowment effect [5, 6]. Given lossaverse consumers and fullrefund return policies, the first goal of this paper is to capture the joint decisions of price, quantity, and freshkeeping effort and also to investigate whether the supply chain has an incentive to exert a freshkeeping effort in the centralized setting; the second goal is to examine supply chain contracts and channel performance in the decentralized setting.
Our main contributions are as follows. First, we construct an analytical model and derive the price, quantity, and freshkeeping effort in the centralized and decentralized settings, offering a useful way to characterize the joint optimal decisions in the fresh product etailing market. Second, based on the comparison, we demonstrate that the etailer’s profit is greater with freshkeeping effort than without it. Therefore, the etailer has an incentive to engage in freshkeeping effort. Third, we find that the return rate is independent of the freshkeeping effort and consumers’ loss aversion. Finally, we develop a new coordination contract by designing a new contractual mechanism and capture the Pareto improvement region for the supplier and etailer under coordinating conditions.
The remainder of this paper is organized as follows. In Section 2, we review the relevant literature. In Section 3, we formulate our model and outline main assumptions. In Section 4, we first characterize the joint optimization in a centralized setting and then make a comparison and sensitive analysis. In Section 5, we first investigate the optimal decisions for the supplier and etailer, respectively, in a decentralized setting and then examine supply chain contracts and channel performance. Finally, concluding remarks and some directions for future work are given in Section 6.
2. Literature Review
Our study is related to three steams of literature: quality improvement and supply chain coordination, customer return, and lossaverse preference.
The first stream of research related to our paper is quality improvement and supply chain coordination. Assuming the market demand depends on freshkeeping effort, Cai et al. [7] examine optimal decisions of the freshkeeping effort, order quantity, and price in a fresh product supply chain. They demonstrate that a pricediscount sharing mechanism together with a compensation scheme coordinates the distributor’s freshkeeping effort and achieves channel coordination. By investigating a similar problem to Cai et al. [7], Wu et al. [8] investigate the joint decision of price, order quantity, and logistics service level in the three power balance scenarios. They show that revenue and servicecostsharing contract and pricediscount and inventoryrisk sharing contract both can achieve channel coordination. Based on a deterministic demand which depends on the logistics service level and price, Yu and Xiao [9] characterize the pricing and logistics service level decisions of a fresh agriproducts supply chain. Xu [10] considers the joint optimization of price and quality based on a qualitydependent demand function in a distribution channel in which the manufacturer sets the wholesale price and quality simultaneously and retailer sets the price; finding the quality decision is affected by the marginal revenue function. Xie et al. [11] also examine the optimal quality investment and pricing decisions in a maketoorder supply chain based on a qualitydependent demand function; however, they assume the supply chain members are risk averse. Jerath et al. [12] assuming the target demand is a fraction of potential stochastic demand and the fraction is determined by the quality and the retailer price, establish an analytical model to capture optimal price, quality, and order quantity in a centralized setting. The model shows that the buyback, quantity discount, revenuesharing, and twopart contracts all can achieve channel coordination in a decentralized setting based on a responsive price. Leng et al. [13] explore the retailer’s price and quality gatekeeping effort for a manufactureretailer channel based on a price and qualitydependent demand function. By constructing an inverse demand function which depends on product’s emission abatement level, Yang and Chen [14] investigate the impacts of revenuesharing and costsharing on manufacture’s carbon emission abatement efforts. They reveal that costsharing becomes dispensable when both revenuesharing and costsharing are available.
Generally, when in an offline market, consumers examine products physically and make purchasing decisions by trading off the price and quality (freshness). Hence, they assume the demand is dependent on quality or freshkeeping effort but not on a consumer’s return factor. When in an online market, the contrary is true. Consumers cannot be assured of the freshness of products when making a purchasing decision; thus, we assume the demand is independent of freshness and freshkeeping effort but dependent on consumer returns.
Second stream is related to consumer returns. Modeling the return rate by uncertain valuation was previously studied by Che [15] and Davis et al. [16]. Che [15] assumes customers are risk averse and applies the vonNeumann utility function to model customers’ preference; and Davis et al. [16] model customers’ uncertain valuation by using a Bernoulli random variable. Recently, Su [17] examines the full returns and partial returns in a newsvendor model in which the return rate depends on the valuation of product and refund price, and the stochastic demand is independent of price. Assuming refund and price are determined exogenously and are not decision variables, Xiao et al. [18] use a similar method for modeling the return rate and examine the buyback and markdown contracts. Similarly, Chen and Bell [19] also capture the impact of full returns policies on order quantity decisions and buyback contracts. Assuming the stochastic demand is price dependent, Hu et al. [20] reveal the impact of full returns policies on decentralized supply chain under consignment contracts in which the return rate is also dependent on refund price and customer’s uncertain valuation of products. There are still some different methods for modeling customer returns. For example, Chen and Bell [21] and Chen and Bell [22] assume customer returns are a function of quantity sold and refund price; Vlachos and Dekker [23], Mostard and Teunter [24], RuizBenitez and Muriel [25], Chen and Zhou [26], Chen and Chen [27], and Choi and Guo [28] model customer returns are a fixed proportion of quantity sold; Yoo et al. [29] assume consumer returns are an increasing linear function of the refund price. However, the above research all assumes the customer is risk neutral except Che [15].
Third, our article relates to the lossaverse preference. Since Kahneman and Tversky [30] have proposed prospect theory, the lossaverse value function has been used to identify ordering policy [31–33] and supply chain contracts [34]. The value function in these researches is applied to evaluate total outcomes; this means the total outcomes are perceived as gain or loss in relation to a reference point. It is theoretical to formulate the elementary outcomes in single account; but for compound outcomes it can be framed in different ways which is called psychological account (later, Tversky and Kahneman [35] call it mental account) [36]. Thaler [37] and Thaler [38] extend the value function to evaluate compound outcomes and show that mental accounting matters. In operation management, Ho and Zhang [39] first use multiple mental accounts to formulate the twopart tariff contract and provide a behavioral model based on lossaverse value function to investigate the channel efficiency. Later, in stochastic demand scenarios, Beckerpeth et al. [40] explore buyback contracts by formulating newsvendor outcomes as sales revenue and overage cost, confirming that contracts designed using the behavioral model perform better than contracts designed using the standard model. Based on multiple mental accounts, Davis et al. [41] consider the push contract, pull contract, and advance purchase discount contract, showing that behavioral model which combines loss aversion with errors accurately predicts channel efficiency and qualitatively matches decisions. Similarly, Zhang et al. [42] formulate the different sequence and magnitude of costs and revenues into different accounts and examine the contract preferences between buyback and revenuesharing contract for a lossaverse supplier; the results are consistent with the behavioral tendency of loss aversion. Assuming customers are loss aversion, SamatliPac and Shen [43] develop a return rate by using lossaverse value function and uncertain valuation but formulate the value function by a single account. Liao and Li [44] also investigate lossaverse customer’s return. In their research, lossaverse value function is formulated by a single account and is only used to analyze the market demand.
Table 1 provides summary of the related literature. In the aforementioned literature, no model is proposed to consider freshkeeping effort, lossaverse customer return, and mental accounting simultaneously. Therefore, our research difference from the first stream of literature is that we assume the customer demand is related to customer returns, but they assume customer demand is quality dependent. We differ from the second stream of literature as we formulate the customer’s uncertain value by lossaverse value function, but they assume the customer is risk neutral or risk averse. We differ from the third stream of literature as we use multiple mental accounts to formulate the lossaverse customer’s value function and to model return rate, but they use multiple mental accounts to formulate the retailer’s or supplier’s lossaverse value function and focus on retailer’s or supplier’s utility function.

3. Model Formulation and Assumption
We consider a twoechelon fresh product supply chain in which one supplier sells fresh products through one etailer in an online market by retail price . To decrease the consumers’ purchasing risk and increase sales revenue in the online market, etailer offers a fullrefund return policy to consumers. When etailer offers a fullrefund return policy to the consumer, consumer’s online purchasing decision can be divided into two stages. In the first stage, noted as purchasing stage, consumer decides whether to buy the fresh product at retail price based on the product information depicted by the website. In the second stage, named as returning stage, consumer who has purchased the fresh product online decides whether to keep or return the product after receiving it from the express delivery and experiencing it firsthand [17]. This means consumers can return the fresh product they have purchased online and receive the full refund if they are not satisfied with the freshness of the product after receiving it from express delivery. Meanwhile, the etailer exerts a freshkeeping effort to improve freshness of products, which means that is increasing in . The online market demand is stochastic and has CDF and PDF in the region with .
This dyadic supply chain is formulated as Figure 1. Before selling season, the supplier is considered as a dominator who offers supply chain contracts to etailer first; etailer is considered as a follower and sets the price , order quantity , and freshkeeping effort simultaneously based on the contractual arrangement subsequently. Then, the demand is realized and min quantity of fresh products are sold in selling season. If the consumer decides to keep the fresh product, the deal is closed at this stage; but if the consumer returns the fresh product he received because of dissatisfaction, etailer pays the full refund to the consumer. At the end of selling season, the overage order quantity is salvaged by etailer or supplier, depending on the different types of contracts. We assume returned fresh products from consumers have no salvage value and cannot be resold. This is consistent with the practice of the fresh product etailing because fresh products decay easily due to poor reverse logistics. Let be the manufacturing cost for supplier. Let be the salvage value for etailer or suppler. Let be the expected sales.
3.1. Freshness Function with FreshKeeping Effort
More freshkeeping effort could result in fresher products, and the higher the freshness, the more the freshkeeping effort that should be exerted to improve the products’ freshness. Therefore, we use continuously differentiable concave function as the freshness function , where , , and . is interpreted as the initial freshness of fresh products when etailer does not exert any freshkeeping effort. is a scalar parameter [45, 46], and is to ensure the freshness function’s concavity.
3.2. Cost Function with FreshKeeping Effort
More freshkeeping effort will lead to higher costs, and the more the freshkeeping effort, the higher the cost that is needed to increase the freshkeeping effort. Therefore, we use the continuously differentiable convex function as the cost function , where and . is a scalar parameter [45, 46] and is to ensure the freshness function’s convexity. Several studies (e.g., Xie et al. [11], Li et al. [46], and Cachon and Lariviere [47]) use the second differentiable convex function to depict cost structure; hence, our cost function is more common and could cover them.
3.3. Return Rate with a LossAverse Consumer
Because the fresh product was purchased online, the consumer can be assured of the freshness of the fresh product only in returning stage (called postpurchase value). Therefore, the retail price , which the consumer paid during purchasing stage, is a sunk cost to the consumer during returning stage. Whether the consumer will return the fresh product depends on the postpurchase value and full refund but is independent of the retail price . Assume the consumer is heterogeneous and values the freshness by a random variable individually. Therefore, a riskneutral consumer will return the fresh product if postpurchase value is less than full refund ; i.e., [17, 20].
Here, we assume the consumer is loss averse and has a piecewiselinear utility function , where implies the lossaverse coefficient [31]. We also assume the utility function is formulated by multiple mental accounts. This means the utility function will be applied to evaluate each account [38]. Thus, given postpurchase value and full refund , when , the consumer will return the product. Let the return rate equal and assume the random variable y follows uniform distribution and has CDF when ; then .
Our definition of return rate is similar to that of Che [15], Su [17], Hu et al. [20], and SamatliPac and Shen [43]; however, they all assume is constant and determined exogenously. If , our return rate reduces to and is equal to that of Su [17] and Hu et al. [20]. If is a vonNeumann utility function, our return rate is also equal to that of Che [15]. When the piecewiselinear utility function is formulated by a single account, our return rate is also equal to that of SamatliPac and Shen [43].
Based on above formulation, we will consider the supply chain in a centralized setting and decentralized setting, respectively. In the centralized setting, we are to examine the optimal price, stocking quantity, and freshkeeping effort simultaneously for a central decision maker and to verify whether the central decision maker has an incentive to exert a freshkeeping effort. In the decentralized setting, we will consider supply chain contracts and design contractual mechanisms to achieve channel coordination. In this paper, the superscript cc represents the supply chain in centralized conditions, and wp, bb, rs, and rc stand for the wholesale price, buyback, revenuesharing, and revenue and costsharing contracts in a decentralized channel, respectively. The subscripts and represent etailer and supplier, respectively; the subscript represents the case without freshkeeping effort.
4. Joint Optimization in a Centralized Setting
In the centralized supply chain, we suppose supplier and etailer form one central decision maker. To focus our research on the online market, we investigate joint optimization in a centralized setting from the perspective of an etailer. This means etailer is the central decision maker and manages both the manufacturing function and etailing function. This model resembles a classic newsvendor model. Given the manufacturing cost c, etailer chooses price p, stocking quantity , and freshkeeping effort simultaneously, and the expected profit of the etailer is as follows:
Assumption 1. .
Assumption 2. Let ; is increasing in , when .
Assumption 1 means the manufacturing cost should not be larger than to ensure etailer yields a positive profit. And Assumption 2 shows the demand distribution should satisfy the increasing failure rate (IFR) condition. IFR is a common and mild assumption. PF2 distributions and the lognormal distribution all satisfy IFR [48, 49].
In order to explore if etailer has an incentive to exert freshkeeping efforts, we provide the comparisons among the cases with and without freshkeeping effort. We denote the case in which etailer does not exert a freshkeeping effort as a benchmark. And, given , the expected profit of etailer is as follows:
Now, we first derive the optimal solution for the etailer under the case without freshkeeping effort, which is given in Proposition 3.
Proposition 3. (i) Letting , given any fixed q, is concave in p; the optimal retail price is unique and given by(ii) Given Assumption 1, is a concave function in the region ; the optimal quantity is unique and given by
Proof. See Appendix.
We denote the optimal solution as , that is, , and the maximized expected profit for etailer is .
And then we investigate the case in which etailer exerts a freshkeeping effort and derive the optimal solution for etailer, which is given in Proposition 4.
Proposition 4. (i) Given any fixed q and t, is concave in p; the optimal retail price is unique and given by(ii) For (5), given any fixed , is concave in ; the optimal freshkeeping effort is unique and given by (iii) For (5) and (6), given Assumptions 1 and 2, is an unimodal function in the region ; the optimal quantity is unique and satisfies
Proof. See Appendix.
Given (5), (6), and (7), we can obtain optimal quantity , optimal freshkeeping effort , and optimal price . We denote optimal solution as , that is, , and the maximized expected profit for etailer is .
Next, we provide the comparison between the maximized expected profits of etailer with and without freshkeeping effort, depicted as Proposition 5.
Proposition 5. Under the centralized setting, , and .
Proof. See Appendix.
Proposition 5 implies that, comparing with no freshkeeping effort, if etailer makes efforts to keep the product fresh, profits of etailer can be improved. Therefore, etailer has an incentive to engage in freshkeeping effort. Because and , the profit margin, especially, the sales revenue, is improved. As long as the increment of sales revenue is larger than the increasing amount of cost of freshkeeping effort, we have ; this may be the intuitive explanation to Proposition 5.
Let be the high profit product and be the lowprofit product. Assumption 1 means that Propositions 3, 4, and 5 only work for high profit products, when the fresh product has low profit, i.e., , leading to . Under this condition, etailers cannot earn a positive profit under our model formulation. This depicts the obstacles encountered in fresh product ecommerce in China currently. To offer highfreshness products, fresh product etailers have to spend quite a bit to improve the coldchain logistics. However, most fresh products have low profit. The limited price margins are not able to offset high dispatch costs, leading to a loss for most fresh product etailers as addressed in the first part of this paper. According to our model formulation, fresh product etailers should focus on high profit products, such as organic produce and highvalue fresh products, to increase price margins and earn a positive profit. According to our knowledge, some fresh product etailers in China, such as MR.FRESH, sfbest.com, womai.com, and www.tootoo.cn, have changed their strategy and switched to high profit fresh products.
In order to offer further insights, we make some sensitivity analysis and a numerical study in the centralized setting, shown as follows.
Corollary 6. Return rate R is independent of t and λ and equals 0.5.
Given follows uniform distribution in the support and the return rate and is independent of and because and . The proof is simple; hence, we omit it. The main reason is that when etailers exert a freshkeeping effort to improve the freshness of products, they will increase retail price to increase price margins. Since the return rate is increasing in the full refund and decreasing in freshness of products, the negative effect equals the positive effect, because of the linear probability density function of the uniform distribution.
Corollary 7. (i)The optimal order quantity is increasing in t, i.e., .(ii)The optimal price is increasing in t, i.e., .
Proof. See Appendix.
When etailer exerts a freshkeeping effort, more freshkeeping effort implies fresher products, inducing etailer to set a higher price and a higher order quantity. Therefore, efforts to keep products fresher can increase profit margins and can also increase expected sales revenue. Let be the expected net sales revenue given any fixed . Since the return rate is independent of and λ, the expected net sales revenue is also increasing in freshkeeping effort. Thus, it also supports etailer to exert a freshkeeping effort, which is consistent with Proposition 5.
Corollary 8. (i); ; ; .(ii); ; ; .(iii); ; ; .(iv); ; ; .
Proof. See Appendix.
Comparing with consumers who are risk neutral, when consumers are loss averse, etailer will engage in more freshkeeping efforts and will also set a higher price and order more. When the consumer receives fresh product, he or she considers the return as a loss and refund as a gain in returning stage. Because of loss aversion, the consumer will value the fresh product more than riskneutral consumer if he or she returns it. Therefore, etailer will set higher price when dealing with lossaverse consumers. Although this may be counterintuitive, it is consistent with the findings in the literature [5]. Further, because of the loss aversion of consumers, the expected net sales revenue is higher compared with selling to riskneutral consumers. Thaler [5] also states that given a twoweek trial period with a money back guarantee, the sale is more likely for endowment effect. Therefore, a fullrefund return policy benefits etailer more when the consumer is loss averse compared with selling to riskneutral consumer in the online market. Moreover, , , , and are all increasing in and but decreasing in . An intuitive explanation is that, as and increases, etailer benefits more by decreasing overordering cost and increasing profit margin, which results in a larger order quantity, more freshkeeping effort and a higher price, and also a larger expected net sales revenue subsequently. However, a larger may shrink the profit margin, leading to opposite side. Thus, it offers a guideline for etailer about how to change the optimal decision according to the key model inputs.
Next, we will use numerical experiments to provide the impact of loss aversion λ, salvage value , initial freshness , and purchasing cost on the expected profit . Set c = 5, s = 1, = 20, a = 2, β = 2, γ = 2, = 3, and λ = 2. Let follow truncated norm distribution in the region ; therefore, , where is a norm distribution with mean μ = 200 and standard deviation σ = 50. Table 2 lists the expected profit changing with , , , and , respectively.

Table 2 shows that the expected profit of etailer is increasing in , , and , respectively, but decreasing in . Therefore, our numerical results are directly consistent with Corollary 8, in which the sensitivity of optimal decision to λ, , , and is the same as the expected profit to λ, , , and . The etailer can increase profits by choosing more lossaverse consumers and increasing the salvage value and initial freshness of the fresh products and also can increase profits by decreasing the purchasing cost of fresh products.
5. Joint Optimization in a Decentralized Setting and Channel Performance
Here, we consider the supply chain in a decentralized setting and examine wholesale price, buyback, and revenuesharing and revenue and costsharing contracts, respectively. By treating as the first best solution, our purpose is to design a contractual mechanism and to achieve supply chain coordination. We also examine whether the Pareto improvement is possible in the coordinated setting with contracts, even when the supply chain is affected by consumer returns, consumers’ loss aversion, and freshkeeping efforts.
5.1. Wholesale Price Contracts
Under the wholesale price contract, supplier first sets the wholesale price , and then etailer in response sets the price , order quantity , and freshkeeping effort jointly. Therefore, etailer’s expected profit is
Based on Proposition 4 and (8), we can obtain the joint optimal decision for etailer straightforwardly just substituting as , denoted as . That is,
Corollary 8 states that optimal order quantity , optimal price , and optimal freshkeeping effort are all decreasing in ; therefore, when the supplier offers a single wholesale price to etailer in the decentralized supply chain, etailer will order less, set lower price, and exert fewer freshkeeping efforts for , rendering the entire supply chain suboptimal.
Then, we will turn to the supplier’s decision. Knowing etailer’s selfinterested order quantity , the supplier’s expected profit is
Unfortunately, it is impossible to obtain the optimal wholesale price analytically for (12) even when the stochastic demand follows a uniform distribution. Therefore, we analyze it using a numerical method and show our findings as follows.
From Proposition 4, the value of should satisfy in the decentralized channel given any and ; therefore, . Obviously, is the lower bound of . Similar to the numerical studies in Section 4, we compute supplier’s and retailer’s expected profit as well as the channel’s total expected profit in the decentralized setting when varies from to by step 0.1, shown in Figure 2.
From Figure 2, the expected profit of supplier is increasing in in the region ; hence, the optimal wholesale price is . When , the supplier’s expected profit and etailer’s expected profit are 795.0651 and 216.4, respectively, and the channel’s total expected profit is 1011.5. Similar to the analytical results addressed above, numerical studies also show that the channel’s total expected profit in decentralized setting is less than it is in centralized setting, where the channel’s total expected profit is 1170.4. This means the channel’s efficiency under wholesale price contract in decentralized setting is only 86.42%. The result shows that the channel cannot be totally coordinated by pure wholesale price contract.
5.2. Buyback Contracts
Under buyback contract , supplier first sets and , and then etailer in response sets the price , order quantity , and freshkeeping effort to maximize expected profits. For the buyback contract, etailer can return the overage order to supplier and receive a buyback price per unit; but, for consumer’s return, assume etailer cannot return it to supplier. Based on the above formulation, the etailer’s expected profit is
Given buyback contract, we first derive the optimal price, order quantity, and freshkeeping effort similar to Proposition 4, denoting the joint optimal decision as , and then letting we have Proposition 9.
Proposition 9. Given and , for , buyback contracts can coordinate the supply chain and allocate the profit between etailer and supplier arbitrarily.
Proof. See Appendix.
Pasternack [50] shows that buyback contracts can coordinate a common dyadic supply chain when retail price is exogenously determined. When retail price is endogenously determined, Bernstein and Federgruen [51] reveal that buyback contracts cannot coordinate the supply chain. Su [17] also examines the coordinating mechanism of the buyback contract, but he illustrates that it fails to achieve channel coordination when etailer offers return policies to consumer. However, when etailer offers a fullrefund return policy to consumers, the supplier can still use buyback contracts to induce the etailer to choose the first best solution and achieve channel coordination if etailer exerts a freshkeeping effort. Proposition 9 also demonstrates that the supplier can adjust the profit between etailer and himself by choosing different wholesale price. Thus, buyback contract in our model which coordinates three decision variables, i.e., price, order quantity, and freshkeeping effort, is still simple and easy to be implemented as it is designed by Pasternack [50] which coordinates only one decision variable, i.e., order quantity.
Based on Proposition 9, taking the derivative of with respect to λ, Corollary 10 can be obtained.
Corollary 10. Buyback price b is decreasing in λ.
Proof. See Appendix.
Corollary 10 shows that the buyback price is lower when dealing with lossaverse consumers than when dealing with riskneutral consumers. In other words, it is easy to coordinate etailer for suppliers by using buyback contracts when etailers face lossaverse consumers.
Setting wholesale price contract as a benchmark, we now examine whether the buyback contract can achieve the Pareto improvement, which means supplier and etailer both can obtain more expected profits under better coordination.
Let , and .
We adopt the same values of parameters as in Section 4 and depict and as changing with as shown in Figure 3 by using numerical studies.
Let and . We compute when in the point A1 and when in the point B1. Figure 3 shows that and when in the region . The supplier and etailer both can earn more expected profits, leading to a Pareto improvement. Therefore, we have Observation 1 as follows.
Observation 1. When and , given buyback contracts , supplier and etailer both can earn more expected profits than those under the wholesale price contract.
This result indicates that, comparing with wholesale price contract, buyback contract is more efficient for this fresh product supply chain. Given certain range of wholesale price, suppliers and etailers both can be better off under this buyback contract. Thus, we provide a requirement for this buyback contract to be implemented. Under this condition, suppliers have an incentive to offer and etailers would like to join in.
5.3. RevenueSharing Contracts
In this part, we try to investigate whether the revenuesharing contract can coordinate the supply chain. Revenuesharing contract is another common coordination contract which is applied massively in supply chain management. Under revenuesharing contract , supplier first sets the wholesale price and etailer’s share of revenue , and then etailer in response sets the price , order quantity , and freshkeeping effort to maximize expected profits. Based on whether the salvage value is shared or not, it can be divided into two types. When only sales revenue is shared, given etailer’s revenue share , the expected profit of etailer is as follows:
And when sales revenue and salvage values are both shared, given sales revenue and salvage values share , the expected profit of etailer is as follows:
Similar to Proposition 9, given revenuesharing contracts and , we first derive the joint optimal decisions, denoted as and , respectively, and then let and . However, only when = 1, ; and only when = 1, . Thus, we have Proposition 11.
Proposition 11. Whether salvage values are shared, revenuesharing contracts could not coordinate etailer when exerting a freshkeeping effort.
Proof. See Appendix.
For a pricesetting retailer, Cachon and Lariviere [47] illustrate that revenuesharing contracts could achieve channel coordination when the sales revenue and salvage values are both shared. Proof of Proposition 11 shows that () only when = 1 ( = 1). And when = 1 ( = 1), () in our model formulation. This is a trivial case and the supplier can earn zero profit under the revenuesharing contract. This means that when the etailer offers a fullrefund return policy to consumers and sets the price, order quantity, and freshkeeping effort jointly, the supplier cannot coordinate etailer by revenuesharing contracts, even if the salvage value is shared. It is mainly because of lacking of costsharing between supplier and etailer. If without costsharing, the total cost of the freshkeeping effort is internalized by etailer. Therefore, under pure revenuesharing contracts, etailer has no incentive to choose the first best solution and instead chooses the suboptimal solution, in line with their selfinterests, which leads to the failure of revenuesharing contracts to achieve channel coordination.
5.4. Revenue and costsharing contracts
In Section 5.3, Proposition 11 shows that a pure revenuesharing contract could not coordinate the fresh product supply chain. Therefore, we examine a new contract in this part, called revenue and costsharing contracts . Under this contract, supplier shares revenue and cost of the freshkeeping effort with etailer. We assume etailer’s share is ϕ and supplier’s share is 1 ϕ. Similar to Section 5.3, the analysis can also be divided into two scenarios, depending on whether the salvage value is shared. If the salvage value is not shared and given revenue and costsharing contract 1 , the etailer’s expected profit is as follows:
If the salvage value is also shared and given revenue and costsharing contract 2 , the etailer’s expected profit is as follows:
Similar to Propositions 9 and 11, we first derive the joint optimal decisions under revenue and costsharing contracts and , respectively, denoted as and , and then let and . Thus, we have Proposition 12.
Proposition 12. (i) When the salvage value is not shared, givenand , for , revenue and costsharing contract 1 can coordinate supply chain and allocate the profit between etailer and supplier arbitrarily.
(ii) When the salvage value is also shared, given , for , revenue and costsharing contract 2 can coordinate supply chain and divide profit between etailer and supplier arbitrarily.
Proof. See Appendix.
Proposition 12 demonstrates that when etailer exerts a freshkeeping effort, it is necessary to share the cost of the freshkeeping effort between the supply chain members to achieve channel coordination. This is consistent with Zhang et al. [52] that investigate the dyadic supply chain for deteriorating items and show that a revenuesharing and cooperative investment contract can achieve coordination. Wu et al. [8] also demonstrate that revenue and servicecostsharing contracts can coordinate the logistics service level and achieve full channel coordination in a fresh product supply chain consisting of a distributor and a thirdparty logistics service provider. In industries, for collaborative new product development, Bhaskaran and Krishnan [53] address the fact that investment and innovation sharing complementary with revenuesharing can help firms coordinate investments and improve products’ quality and firms’ profits. For example, two companies, i.e., Alpha Labs and Mega Pharmaceuticals, share the development investment and revenues both when developing a new innovative class of diabetes drugs [53]. Actually, revenue and costsharing scheme has attracted more and more attention in the business world and is superior to pure revenuesharing contracts when coordinating quality improvement efforts. However, our result is in sharp contrast to Yang and Chen [14] that address the fact that when the revenuesharing and costsharing are both available, costsharing becomes dispensable. This contrast first may arise from the different model formulation between ours and Yang and Chen’s [14]. Yang and Chen [14] formulate the model by deterministic demand and assume the retailer is Stackelberg leader. And our model is based on stochastic demand and assumes the supplier is Stackelberg leader. Second, the decision sequence is also different between ours and Yang and Chen’s [14]. In Yang and Chen [14], the strategic interaction is modeled as a fourstage game; that is, the retailer moves first and offers the incentive scheme to the manufacturer; then, the manufacturer decides abatement level and wholesale price in the second and third stage, respectively; lastly, the retailer chooses his order quantity. And the strategic interaction in our model is much simpler; the supplier first offers an incentive scheme to etailer; then, the etailer chooses the price, order quantity, and freshkeeping effort. Moreover, the channel efficiency when adding costsharing is also different. In Yang and Chen [14], costsharing is dispensable because revenuesharing contract and revenue and costsharing contract can achieve the same channel efficiency; however, the channel efficiency is only 3/4 under the twoincentive scheme. In our view, costsharing is necessary based on channel coordination and 100% channel efficiency. For these differences, the contract mechanism between ours and Yang and Chen’s [14] also may be different.
Based on Proposition 12, taking the derivative of () with respect to , Corollary 13 can be obtained.
Corollary 13. Revenue and costsharing ratio is increasing in λ, i.e., ; and is independent of λ.
Proof. See Appendix.
Corollary 13 further shows that when the salvage value is not shared, etailer shares more revenue and cost when facing lossaverse consumers, compared with facing riskneutral consumers. This means etailer’s power will be increasing in λ in a coordinated setting. When the salvage value is also shared, etailer’s share is independent of the lossaverse preference.
Similar to Section 5.2, we now examine whether the revenue and costsharing contract can achieve Pareto improvement by using numerical studies. Letting , , , and , numerical results are depicted in Figures 4 and 5.
Let and . We compute when in the point A2 and when in the point B2. Figure 4 shows that and when in the region supplier and etailer both can earn more expected profits, leading to Pareto improvement. Let and . We compute when in the point A3 and when in the point B3. Figure 5 shows that and when in the region supplier and etailer both can earn more expected profits, leading to Pareto improvement. Therefore, we have Observations 2 and 3 as follows.
Observation 2. When and , given revenue and costsharing contract 1 , supplier and etailer both can earn more expected profits than those under the wholesale price contract.
Observation 3. When and , given revenue and costsharing contract 2 , supplier and etailer both can earn more expected profits than those under the wholesale price contract.
Observations 2 and 3 both demonstrate that, comparing with wholesale price contract, revenue and costsharing contract is more efficient for this fresh product supply chain. Given certain range of wholesale price, suppliers and etailers both can be better off under these revenue and costsharing contracts. Thus, we provide a requirement for these revenue and costsharing contracts to be implemented. Under this condition, suppliers have an incentive to offer and etailers would like to join in.
6. Conclusion
By considering consumer returns and lossaverse preference, we develop an analytical model to capture the price, inventory, and freshkeeping effort decisions and coordination contracts for a fresh product supply chain. Our main results of this work can be summarized as follows:
(1) Given that the fresh product is high profit and demand distribution satisfies IFR, there exists a unique joint optimal solution of price, order quantity, and freshkeeping effort. Based on the comparison, we find that profits are more with than without freshkeeping effort. Therefore, the etailer has an incentive to engage in freshkeeping effort.
(2) When the random variable y follows a uniform distribution, we further show that the return rate is independent of the freshkeeping effort and consumers’ loss aversion; but the optimal price and order quantity are both increasing in the freshkeeping effort. Hence, exerting a freshkeeping effort can increase the price and order quantity as well as expected net sales revenue.
(3) By making a sensitivity analysis, we also reveal that the optimal price, order quantity, freshkeeping effort, and expected net sales revenue are all increasing in consumers’ loss aversion, salvage value, and initial freshness but decreasing in purchasing cost. Hence, it is necessary to give higher price, order more, and exert more freshkeeping effort for the company when facing lossaverse customers.
(4) In a decentralized setting, we first characterize the unique optimal joint decisions for etailer and then deliver the optimal wholesale price for supplier using a numerical study. A single wholesale price contract will induce etailer to set lower price and lower order quantity and also to exert fewer freshkeeping efforts, which leads to a suboptimal supply chain.
(5) In a decentralized setting, we further examine the buyback and revenuesharing contracts when etailer offers a fullrefund return policy to the lossaverse consumer, demonstrating that the buyback contract still works, but the revenuesharing contract fails to coordinate the supply chain. By designing new contractual mechanisms, we develop a new coordination contract: a revenue and costsharing contract, which can coordinate the supply chain whether the salvage value is shared or not.
(6) Using numerical studies, we capture the Pareto improvement regions under the buyback and revenue and costsharing contracts, under which the supplier and etailer both can earn more expected profits than those under the wholesale price contract.
Therefore, the insight from our model and analysis can be distilled into some rules for the managers in real business world. First, our research provides a principle for managers of when and how to exert a freshkeeping effort. When the fresh product is in high profit scenarios, etailer can give higher price, order more, and earn more profit if exerting a freshkeeping effort. Second, we ensure that the supplier can coordinate etailer’s freshkeeping effort and provide a guideline for managers on how to choose the supply chain contract among wholesale price, buyback, and revenue and costsharing contracts. Finally, consumers also will be benefited by receiving fresher products, and more of them will purchase online because the expected sales are increasing in freshkeeping effort.
Our research can be extended in several directions. First, the elegance of our results is based on a uniform distribution of the random variable y; therefore, in future work, it will be interesting to derive the closedform solutions by alternative distributions. Second, similar to Su [15], we assume the stochastic demand is independent of the price; however, although incorporating a pricedependent demand function into our model is necessary, it will be difficult to derive analytical results. This will be our future endeavor. Third, our research is based on the fullrefund return policy, though the partialrefund return policy may be more common, under which joint decisionmaking presents ample opportunities for future research.
Appendix
Proof of Proposition 3. (i) Given (2), take the first and second partial derivative of with respect to p as follows:Therefore, is concave in .
For and , hence, in the region , there exists unique optimal retail price maximizing when , which brings out (3).
(ii) For (3), we have the following: Take the first and second partial derivative of with respect to are as follows:Given Assumption 1, follows and then .
Therefore, is concave in q.
For (Assumption 1) and , hence, in the region , there exists unique optimal quantity maximizing when , which brings out (4).
Proof of Proposition 4. (i) Given (1), take the first and second partial derivative of with respect to p, as follows:Therefore, is concave in p.
For and , hence, in the region , there exists unique optimal retail price maximizing when , which brings out (5).
(ii) For (5), , and , we have the following: Take the first and second partial derivative of with respect to , as follows:Therefore, is concave in .
For and , hence, in the region , there exists unique optimal freshkeeping effort maximizing when , which brings out (6).
(iii) For (6), , and , we have the following:Take the first derivative of with respect to q, as follows:Let and ; we have the following:Then, we haveFor · and given , and based on Assumption 2, then, we have the following:Therefore, is a unimodal function.
For and , therefore, in the region , has only one root .
For when and when , therefore, in the region , is a unimodal function and reaches its maximum at the firstorder condition , which is satisfied with (7).
Proof of Proposition 5. For (7), + + follows; therefore, and .
For (3), (5), and (6), we also can obtain and .
Denote the solution space for as ; that is,Therefore, and .
For (1) and (2), we have .
From the proof of Proposition 4,