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Electronic Commerce Research and Applications 21 (2017) 27–37

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Electronic Commerce Research and Applications

journal homepage: www.elsevier.com/locate/ecra

Adding pay-on-delivery to pay-to-order: The value of two payment schemes to online sellers

http://dx.doi.org/10.1016/j.elerap.2016.12.001 1567-4223/� 2016 Elsevier B.V. All rights reserved.

⇑ Corresponding author. E-mail addresses: [email protected] (N. Xu), [email protected] (S.-z.

Bai), [email protected] (X. Wan).

Na Xu a, Shi-zhen Bai b,⇑, Xiang Wan c a School of Business Administration, Shandong Institute of Business and Technology, China b School of Management, Harbin University of Commerce, China c Fisher College of Business, The Ohio State University, OH 43210, USA

a r t i c l e i n f o a b s t r a c t

Article history: Received 6 July 2015 Received in revised form 30 November 2016 Accepted 7 December 2016 Available online 18 December 2016

Keywords: Payment scheme Pay-to-order Pay-on-delivery E-commerce Consumer behavior

In this study, we focus on two main payment options in e-commerce: pay-to-order (consumers pay for products when making an order online) and pay-on-delivery (consumers pay for products after delivery). While pay-to-order is the basic payment option in e-commerce, pay-on-delivery becomes more wel- comed by consumers as an additional option. Using analytical modeling, we characterize the e-tailer’s optimal pricing and inventory decisions under two scenarios: 1) only with pay-to-order, and 2) dual pay- ment scheme (both with pay-to-order and pay-on-delivery). Based on the optimal operation strategy, we compare the e-tailer’s profit under these two scenarios and find the best time for e-tailer to offer each payment scheme. Finally, numerical examples are given to prove the theory results and provide manage- ment suggestions for e-tailers to improve performance.

� 2016 Elsevier B.V. All rights reserved.

1. Introduction

Online shopping has been increasing in recent years especially in China, where the e-commerce market was $1188.36 billion in the first quarter of 2015 (iResearch, 2015). However, in spite of the increase in online shopping, many problems remain that con- tribute to an unsatisfactory shopping experience for customers. The proportion of online customer complaints were 52.38% of all complaints in China in 2013 (CECRC, 2013). Difficulties in making returns and obtaining a refund are the most common customer complaints. These experiences significantly decrease the shopping experience quality of customers. Furthermore, the perceived online risk is higher for customers, due to the physical distance between the online seller and customers, as well as the temporal separation of payment and product delivery (Xiao and Benbasat, 2011). Such perceptions of risk sometimes cause customers to avoid online activities even though they may be safe (Dunn, 2004). This hinders the development of e-commerce. Through 2014, nearly half of all computer users in China have never purchased online. Therefore, it is important for companies to improve customers’ online shop- ping experience, as well as potential customers’ trust in shopping online.

Online sellers have long recognized these problems, and they have attempted to solve them by adjusting the sequence of pay- ment and delivery; that is, offering different payment schemes to online customers. Currently, there are two types of online payment schemes in China which are the most widely used. One is pay-to- order, in which the payment occurs when an order is made. The other is pay-on-delivery, in which customers pay for products after delivery. Although pay-to-order is the most widely used because of its efficiency, pay-on-delivery is also very attractive because it improves the service quality by eliminating the worries regarding returns and refunds, as well as improving payment security. The pay-on-delivery service has been acting like a transition; it helps lead potential customers to shop online. Chiejina and Soremekun (2014) showed that pay-on-delivery will attract more customers, enable the processing of more orders and is more likely to succeed. Currently, in China, dual schemes (both pay-to-order and pay-on- delivery) are provided by many major electronic business plat- forms, such as JD.com, VIP.com, Dangdang.com, Amazon.cn and Paipai.com. Although Alibaba has its own payment scheme, Alipay, many online sellers on Taobao.com also offer dual payment scheme to attract customers, particularly those who distrust online shopping. Selling the product using the pay-on-delivery scheme expands the available market for online seller, but does have some additional costs associated with it. The associated cost of the online seller is higher in pay-on-delivery than in pay-to-order (Mangiaracina and Perego, 2009). Hence, certain critical questions

28 N. Xu et al. / Electronic Commerce Research and Applications 21 (2017) 27–37

emerge. How do different payment schemes affect online cus- tomers’ behavior? Which is the better payment scheme for online seller, pay-to-order or dual scheme? How should the payment scheme be designed to obtain the optimal profit performance? What is the optimal strategy for the online seller in each payment scheme?

To address these questions, we develop a game theoretic model in which one online seller sells the product to online customers under two different payment scheme situations. One is pay-to- order; the other is a dual scheme. Such design is coincident with the practice of e-commerce in China. Different customers perceive differences between the two payment schemes, and they choose the one that maximizes their individual utility. By utilizing the rational equilibrium, we characterize the effect of a customer’s behavior on the online seller’s strategy. The optimal pricing and inventory decisions are obtained to help online sellers obtain the best performance under different payment schemes. We find that the customers want to pay less in a dual scheme than in pay-to- order, which is contrary to common sense. The comparison results of online seller’s profit between pay-to-order and dual scheme mainly depend on the marginal revenue and the potential demand growth, which are also affected by the delivery time at certain sit- uations. The shipping fee negatively affects online seller’s profit in both kinds of payment schemes. In particularly, the negative effect is stronger in pay-to-order than in dual scheme, which helps to expand the application space of dual scheme in practice. For differ- ent types of products, online sellers should also offer different pay- ment schemes. This study contributes to the literature by jointly considering payment scheme design and operation strategy in e- commerce.

The remainder of the paper is organized as follows. Section 2 introduces the background and related work of this study. Section 3 makes notations and the assumptions necessary to this paper. In Section 4, we establish our model under pay-to-order and dual scheme, respectively, and provide an equilibrium analysis. In Sec- tion 5, we conduct sensitivity analysis, and we conclude the paper in Section 6.

2. Literature review

Given its prevalence and importance, the payment scheme has been studied extensively. Research at the firm level has examined the effect of payment options on firms’ inventory decisions (Chen et al., 2013; Song and Tong, 2011). Chen et al. (2013) analyzed three types of payment schemes and demonstrated that payment schemes affect newsvendor’s inventory decisions. Trade credit, which allows buyers to delay payment by offering financing (Chern et al., 2013; Yang et al., 2012), was often utilized to encour- age large orders (Giannetti et al., 2011). Researchers have also studied the effect of payment schemes on customer behavior. Researchers have found that, in reality, there is a preference for both prepayment and post-payment. Prelec and Loewenstein (1998) proposed a ‘‘double-entry” mental accounting approach to describe how the pleasure of consumption and the pain of planning interact to affect customers’ behavior. The temporal distance between payment and consumption under prepayment provides the illusion that consumption is free for customers. Shafir and Thaler (2006) found that the typical wine connoisseur believes her initial purchase of a case of wine is an investment and later believes the wine is free when she drinks it; therefore, she moves through the entire process never experiencing the pain of payment.

Lee and Tsai (2014) conducted experiments to examine how price promotions influence postpurchase hedonic consumption experience. Zhao (2012) demonstrated that consumption enjoy- ment is actually reduced if there is a delayed payment after con-

sumption. These researchers indicate that prepayment is much more welcomed by customers if consumption is one-shot, and the utility diminishes relatively quickly after consumption. How- ever, there are certain customers who prefer payment after con- sumption. Prelec and Loewenstein (1998) examined this preference by using the time discounting theory, in which the cost of the product is depreciated during the period of usage. Hence, post-payment is better when the benefits of prepayment are less than the opposing influence of time discounting. Patrick and Park (2006) extended the research by considering the effect of product type on the preference for payment timing and reveal that solely hedonic-nondurable products elicit a preference for prepayment. However, no researchers have examined these issues in the context of e-commerce.

Following the emergence of Internet technologies, e-commerce has provided customers with alternative payment options while shopping online. Some of the literature focuses on the impact of payment schemes on customers’ attitude towards shopping online. In general, payment types based on the Internet (pay-to-order) were more convenient than pay-on-delivery (Chong et al., 2011). However, certain researchers found that individuals were not will- ing to purchase online because they worried about the risk of pay- ment through the Internet (Koyuncu and Bhattacharya, 2004). Although various security measures and mechanisms have been designed for the e-commerce payment systems, many security problems remain (Hsieh, 2001; Chou et al., 2004; Dai and Grundy, 2007; Kousaridas et al., 2008). For example, the transac- tion procedure in e-payment is different from that in the tradi- tional payment solution, which may engender a range of new security issues, including concerns over unauthorized use and transaction status (Hwang et al., 2007; Lim, 2008). Kahneman and Tversky (1979) stated that a person is risk averse if he prefers the certain prospect (x) to any risky prospect with expected value x. Then, customers who perceive risk to online payment want to cease shopping online. Hence, there is a growing need to minimize the risks associated with e-payment transaction processes and develop customers’ trust in payment online.

Kim et al. (2010) divide the influence factors of customers’ per- ception of security and trust in e-payment systems into three levels: security statements, transaction procedures and technical protections. The researchers’ findings show that both technical protections and security statements have a significant influence on improving customers’ perceived security, which is positively related to customers’ perceived trust; additionally, the perceived trust and security have a positive impact on e-payment system use. Certain research on the impact of potential risk on customers’ trust in the mobile payment system (Chandra et al., 2010; Dan and Jing, 2011) indicated that such distrust would reduce the cus- tomers’ intention to utilize a new payment system (Yang et al., 2012). Therefore, a better payment service is necessary for the development of e-commerce. In this paper, we introduce a pay- on-delivery scheme, which is similar to the traditional payment scheme and currently widely used by online customers in China. Pay-on-delivery is helpful to reduce the uncertainty during an online transaction. We believe pay-on-delivery has a transitional effect on the payment scheme shift from pay-on-delivery to pay- to-order with the growing confidence of customers. However, the importance of pay-on-delivery has seldom been examined in the literature.

A few researchers have observed the important meaning of dif- ferent e-commerce payment schemes. Chiejina and Soremekun (2014) established the role of the ‘Pay on Delivery’ payment option in the recent prosperity of the Nigerian e-commerce sector as a major trust builder between customers and the online merchants, with the finding that pay-on-delivery is helpful to increase demand. The most relevant literature to our paper is Zhang and

N. Xu et al. / Electronic Commerce Research and Applications 21 (2017) 27–37 29

Zhang (2014). Both focus on pay-on-delivery/cash-on-delivery, but from different perspectives. Zhang and Zhang (2014) characterized the optimal pricing and inventory decisions for cases with and without a fixed ordering cost by assuming additive demand and linear inventory related costs, and showed the impact of pay-on- delivery on the optimal decisions from the firm’s perspective. In contrast, our research is driven by customer orientation. We study the optimal pricing and inventory decisions for online sellers by considering the customers’ behavior under different payment schemes—pay-to-order and pay-on-delivery—which are widely used by online customers in practice. The method we use is the rational expectations equilibrium, which also differs from Zhang and Zhang (2014). This paper attempts to fill the gap between pay- ment and operation by studying the impact of payment schemes on customer behavior during shopping online, which ultimately affects the online seller’s strategy.

In accordance with the study by Balakrishnan et al. (2014), we believe the return policy in e-commerce serves as a mechanism for the online seller to mitigate the disadvantage of no showroom service. The convenience of online shopping offers potential bene- fits in selling to customer segments; however, the higher likeli- hood of costly product returns because of customers’ incapability to ‘touch and feel’ products also raises new challenges. Ofek et al. (2011) studied competing retailers that operate dual channels (‘‘Bricks & Clicks”) and examined how pricing strategies and phys- ical store assistance levels change as a result of the additional Internet outlet. Considering the costly hidden action for a manufac- turer and hidden information known solely to the retailer, Crocker and Letizia (2014) characterize the class of Pareto optimal returns policies. Hsiao and Chen (2012) investigated the interplay between a returns policy, pricing strategy and quality risk. In the online marketplace, Griffis et al. (2012) examined the relation between a customer’s experience of product returns and subsequent shop- ping behavior. The researchers found that the return management process significantly and positively influences the repurchase behavior. Because return policies and product attributes are known as the two most important factors in product returns, Rao et al. (2014) further demonstrate the aspects of the online retail transac- tion that make such a purchase more return-prone. The research- ers found that inventory scarcity perceptions have an effect on the likelihood of purchases being returned. Moreover, returns depend on the consistency between retailer promises of timeliness in the delivery of orders and the actual delivery performance of the orders. Our paper is similar in spirit because we also study the effect of return policies on online sellers’ strategy. However, we demonstrate them from a different perspective-the payment scheme-where different payment schemes are matched with dif- ferent returns policy.

We turn next to the set-up of our model, followed by results and numerical examples.

Fig. 1. Decision making process of a consumer when shopping online.

3. Notations and assumptions

We begin with the classic newsvendor model. The market demand X is random with distribution F. We interpret market demand as a mass of infinitesimal customers, each with individual valuations v for the product. However, the valuation is uncertain because online customers cannot sense and touch the product physically. To reflect such heterogeneity, let v be identically and independently drawn from the distribution G. We denote �F � 1 � F and �G � 1 � G.

We consider the following two problem settings. An online seller sells goods to online customers with a pay-to-order scheme or a dual scheme (both pay-to-order and pay-on-delivery). In pay- to-order, the customers prepay the price po when placing an order

online. After waiting the delivery period t, customers receive the goods. They retain the products if they are content with them; otherwise, they return the products by paying a return fee m and obtain a refund po. In pay-on-delivery, there is no pay occurred when placing an order online. After the delivery period t, cus- tomers receive the products and they pay the price pd and the addi- tional markup n if the products are ‘‘perfect”. If they are not satisfied with the products, customers can reject the products at the moment they receive them with no charge. Here, online seller charges the additional markup mainly because he provides better service for customers. In practice, the online seller usually charges more to customers who choose pay-on-delivery instead of pay-to- order, which is helpful to induce customers to become accustomed to online payment.

The specific payment process for customers can be observed in Fig. 1.

In this paper, the definitions of main variables can be observed in Table 1.

Timing of the Game. The sequence of events is as follows. In stage 1, the online seller sets the price pi and stocking quantity qiði ¼ o; dÞ. In stage 2, market demand X is realized and minðX; qiÞ units are sold; if X > qi, customers who do not obtain the product leave the market. In stage 3, customers who have bought the prod- ucts evaluate their individual utility and make decisions to retain or return them. Finally, the online seller salvages all leftover units (including the unsold units and the returned units) at the salvage value s. All players are risk neutral.

4. Model

4.1. Model for online customers

A customer’s decision tree involves two sequential decisions under this allocation mechanism: (i) choose one of the payment options when making an order online and (ii) retain or return the product after inspecting it. The expected utility of online cus- tomers can be observed in Table 2.

Table 1 Definitions of variables.

Variables Definition

D Random demand F The distribution of demand, fðxÞ=ð1 � FðxÞÞ is increasing in x,

�F ¼ 1 � F f The density of demand, continuous and has a connected support,

fð0Þ > 0 V Uncertain valuation of the products EðVÞ The consumers’ expected valuation G The distribution of valuation, �G ¼ 1 � G c Unit cost of the product s Unit salvage price of the product, s < c p Unit price of the product, p > c > s q The order quantity of e-tailer m The shipping fee of the product, the same for both retailers and

consumers n The additional markup in pay-on-delivery a The unit disutility of online consumer because of waiting the

delivery of goods in pay-to-order in dual scheme, 0 < a < 1 b The unit disutility of online consumer because of waiting the

delivery of goods in pay-on-delivery, 0 < b < 1 t The delivery time, t > 0 n The influence factor of payment option(pay-to-order) on market

demand, 0 < n < 1 h The hassle cost of e-tailer in pay-on-delivery

Table 2 Net utilities and trade activities for online consumers.

Payment types Order-time utility

Delivery-time utility

Receive-time utility

Make an order Wait Keep Reject

Pay-to-order �p �at v p � m Pay-on-delivery 0 �bt v � p � n 0

30 N. Xu et al. / Electronic Commerce Research and Applications 21 (2017) 27–37

During the transaction, customers seek to maximize individual expected surplus. The customers’ surplus may be one of the follow- ing four cases. If customers purchase and retain the product, the surplus is ex post valuation minus price paid and time cost, v � p � at in pay-to-order and v � p � n � bt in pay-on-delivery; if they purchase but return in pay-to-order, the surplus is the full refund net the return fee, the time cost and the price paid p � m � p � at. If customers reject the product in pay-on- delivery, the surplus is the time cost �bt.

Based on the chronology above, we first describe the customer’s decision problem. We applied the rational expectation hypothesis, which states that economic outcomes do not differ systematically from people’s expectation (Muth, 1961). Consider a particular cus- tomer who wants to pay for the product with pay-to-order. Then, the expected surplus in pay-to-order is

maxfv � p � at; p � m � at � pg: ð1Þ It is clear that the customers in pay-to-order with valuations

v � p � at P p � m � at � p will opt to retain the product, whereas those with valuations v � p � at < p � m � at � p will return it. Hence, in pay-to-order, the customer’s reservation price for the product is

ro ¼ v þ m: ð2Þ Similarly, consider a customer who wants to pay for the product

by cash on delivery; the expected surplus in pay-on-delivery is

maxðv � p � n � bt; �btÞ: ð3Þ Therefore, the customers who use pay-on-delivery with valua-

tions v � p � n � bt P �bt will choose to retain the product, whereas those with valuations v � p � n � bt < �bt will reject it. This finding means that, in pay-on-delivery, the customer’s reser- vation price for the product is

rc ¼ v � n: ð4Þ Next, we consider the online seller’s decision problems. The two

decisions are stocking quantity q and regular online selling price p. Suppose that the online seller expects that all customers have a reservation price f. Given these beliefs, it is clear that he will choose price p ¼ f and quantity qðpÞ ¼ arg max pðq; pÞ.

4.2. Models for online seller under different payment schemes

4.2.1. Performance of online seller in pay-to-order scenario In this scenario, the online seller solely offers pay-to-order for

online customers. According to rational expectations equilibrium (Muth (1961), Su and Zhang (2008)), we can obtain Definition 1 as follows.

Definition 1. A RE equilibrium ðp; qÞ satisfies the following: (i) ro ¼ v þ m, (ii) po ¼ fo, (iii) qo ¼ arg max poðq; pÞ, (iv) fo ¼ ro, where poðq; pÞ ¼ p�Gðp � mÞE minðnX; qÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

sold

þ sGðp � mÞE minðnX; qÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} returned

þ sðq � E minðnX; qÞÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} unsold

� cq � mE minðnX; qÞ ð5Þ

¼ ððp � sÞ�Gðp � mÞ � mÞE minðnX; qÞ � ðc � sÞq: ð6Þ Conditions (i), (ii) and (iii) assert that, under expectation no, the

online seller and all customers will rationally choose the appropri- ate utility-maximizing actions, as discussed above. The last condi- tion requires that expectation must be consistent with outcomes. That is, the online seller must correctly anticipate customers’ reser- vation price.

In Eq. (5), the first term p�Gðp � mÞE minðnX; qÞ corresponds to the realized revenue from selling the products, and the second term sGðp � mÞE minðnX; qÞ results from salvaging units that are bought but returned by customers. The third term sðq � E minðnX; qÞÞ originates from unsold units that are salvaged, and the fourth term cq is the online seller’s procurement or production cost. The last term mE minðnX; qÞ is due to home delivery.

Here, nð0 < n < 1Þ is the influence factor of market demand in pay-to-order; that is, the demand is ðn � XÞ in pay-to-order as well as X in dual scheme. This statement implies that a dual scheme is more able to attract customers. This implication is reasonable because a dual scheme can satisfy both the needs of a pay-to-order liker and a pay-on-delivery liker. Luo et al. (2012), Chiejina and Soremekun (2014) also prove that pay-on-delivery is helpful to increase demand.

Proposition 1. In pay-to-order, the online seller’s optimal price ðpoÞ and order quantity ðqoÞ should be characterized by

po ¼ v þ m; �F qo n

� � ¼ c � s

ðv þ m � sÞ�GðvÞ � m : ð7Þ

The conclusion in Proposition 1 indicates that the shipping fee directly affects the final e-tail price. As the shipping fee increases, the e-tail price increases, too. What’s more, the online seller should decrease the order quantity if with a higher shipping fee. Because the lower price is the main reason that customers choose shopping online, so effectively control the logistic cost is very important for online sellers. In China now, both the second (JD.com) and the third (VIP.com) biggest B2C retailers have their own logistics systems, by which they can effectively control the logistic cost. On other plat- forms, such as Taobao.com and Tianmao.com, online sellers usually build a long-time cooperative relationship with certain logistic companies.

N. Xu et al. / Electronic Commerce Research and Applications 21 (2017) 27–37 31

Proposition 1 also demonstrates that the delivery time has no effect on online seller’s price and inventory decisions, which is inconsistent with the reality. In fact, the delivery time negatively affects online customers’ utility when making purchase decisions. However, in our paper, we focus on the customers who have decided to buy the products in pay-to-order; the decision they need to make is to keep or return the products. The effect of delivery time is canceled since the delivery time equally affects the utility of online sellers between keep and return the products in pay-to-order.

Substituting the results in Proposition 1 into Eq. (6), we can get the optimal profit of online seller in pay-to-order, which is shown as

p�o ¼ ððv þ m � sÞ�GðvÞ � mÞðqo � n Z qo=n 0

FðxÞdxÞ � ðc � sÞqo ð8Þ

4.2.2. Performance of online seller in dual payment scenario

Similarly, we can obtain the online seller’s profit function in pay-on-delivery ðpcÞ

pcðq;pÞ ¼ ðpþnÞ�GðpþnÞEminðX;qÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} sold

þsGðpþnÞEminðX;qÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} returned

þsðq�EminðX;qÞÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl} unsold

�cq�ðmEminðX;qÞþmGðpþnÞEminðX;qÞÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} deliverycost

�hEminðX;qÞ|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} hasslecost

¼ ððpþn�sÞ�GðpþnÞ�mGðpþnÞ�m�hÞEminðX;qÞ�ðc �sÞq ð9Þ

In Eq. (9), we observed that each unit that is sold and retained by the customer yields revenue p þ n and each returned by the cus- tomer has the same valuation s with the salvaged unit; in addition, the fourth term cq is the online seller’s procurement or production cost. The fifth term ðmE minðX; qÞ þ mGðp þ nÞE minðX; qÞÞ indicates the delivery cost in pay-on-delivery, which is different from that in pay-to-order because the online seller needs to afford all of the shipping fees in pay-on-delivery. The last term is hassle cost because pay-on-delivery is more time consuming (the delivery person needs to wait for the product inspection, and handle the payment).

We stress that the market demand would be more in a dual scheme than in pay-to-order. Among all customers X who are interested in the product and want to buy it, let Oprob 2 ½0; 1� be the proposition that customers choose pay-to-order in dual scheme, then those remaining 1 � Oprob choose pay-on-delivery. Hence, the online seller’s profit function in a dual scheme ðpdÞ is

pd ¼ ððp�sÞ�Gðp�mÞ�mÞOprobEminðX;qÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} portionbypaymentschemeO

þððpþn�sÞ�GðpþnÞ�mGðpþnÞ�m�hÞð1�OprobÞEminðX;qÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} portionbypaymentschemeD

�ðc �sÞq ð10Þ

Next, we will analyze online seller’s optimal price and inventory decisions to maximize his profit, considering customers with dif- ferent choices on payment schemes in dual scheme.

From Eqs. (2) and (4), we see that the customer’s reservation price for the product is ro ¼ v þ m in pay-to-order and rc ¼ v � n in pay-on-delivery. Obviously, rc < ro. That is, if the e-tail price is higher than rc, then no one would choose pay-on-delivery. Hence, the reservation price in dual scheme is

rd ¼ v � n ð11Þ

Definition 2. A RE equilibrium ðpd; qdÞ satisfies the following: (i) rd ¼ v � n, (ii) pd ¼ fd, (iii)qd ¼ arg maxpdðq; pdÞ, (iv)fd ¼ rd.

Conditions (i), (ii) and (iii) assert that, given the belief fd, the online seller and all customers will rationally choose the appro- priate utility-maximizing actions, as discussed above. Condition (iv) indicates that the online seller must correctly anticipate customers’ reservation price so that his expectation can be consistent with outcomes. The conditions in Definition 2 will be used to explicitly characterize the RE equilibrium below.

Proposition 2. In a dual scheme, the online seller’s equilibrium price ðpdÞ should be given as pd ¼ v � n ð12Þ

From Proposition 2, we can get that, in dual scheme, the customers’ utility after buying the product is Uo ¼ v � pd � at ¼ n � at if choosing pay-to-order and it is Uc ¼ v � n � pd � bt ¼ �bt if choosing pay-on-delivery. Hence, in dual scheme, customers will choose pay-to-order when Uo > Uc; otherwise, they will choose pay-on-delivery. If Uo > Uc, that is

a � b < n t

ð13Þ

Let c ¼ a � b. We assume c � U½�e;e� with distribution C and �C ¼ 1 � C. Then, in dual scheme, the probability that customers choose pay-to-order is

Oprob ¼ C n t

� � ¼ 1

2 þ n 2et

ð14Þ

and the probability that they choose pay-on-delivery is

1 � Oprob ¼ �C n t

� � ¼ 1

2 � n 2et

ð15Þ

By substituting the probability Oprob and the optimal price ðpdÞ into Eq. (10), we can get the optimal profit of online seller in dual scheme with the optimal order quantity qd shown as below.

p�d ¼ A 1 2 þ n 2et

� � þðB�hÞ 1

2 � n 2et

� �� � qd �

Z qd 0

FðxÞdx � �

�ðc �sÞqd

¼ AþB�h 2

þ n 2et

ðA�BþhÞ � �

qd � Z qd 0

FðxÞdx � �

�ðc �sÞqd ð16Þ

where A ¼ ðv � n � sÞ�Gðv � n � mÞ � m and B ¼ ðv þ m � sÞ �GðvÞ � 2m. Note that A and ðB � hÞ are the two parts of marginal revenue for an online seller in dual scheme. The marginal revenue is the number of changes in total revenue caused by the increase or decrease of unit sales. In particularly, A is the part with pay-to- order and ðB � hÞ is the part with pay-on-delivery in dual scheme.

Then, we can get the equilibrium order quantity for online seller in dual scheme, shown in Proposition 3.

Proposition 3. In a dual scheme, the online seller’s equilibrium order quantity ðqdÞ should be given as

�FðqdÞ ¼ 2ðc � sÞ

A þ B � h þ net ðA � B þ hÞ ð17Þ

32 N. Xu et al. / Electronic Commerce Research and Applications 21 (2017) 27–37

where A ¼ ðv � n � sÞ�Gðv � n � mÞ � m and B ¼ ðv þ m � sÞ �GðvÞ � 2m.

From Proposition 3, it is obvious that the order quantity increases along with the more marginal revenues A and ðB � hÞ. By this way, online seller can obtain more total revenue. It is one valuable way to increase marginal revenue by decreasing the shipping fee m. As illustrated below Proposition 1, online sellers must effectively control the logistic cost. What’s more, when A > B � h, that is, the marginal revenue with pay-to-order is higher in dual scheme, the delivery time has a direct and negative effect on the optimal order quantity in dual scheme. It is because that longer delivery time means bigger difference of delivery time sensitivity ðetÞ between pay-to-order and pay-on-delivery, then the probability that cus- tomers choose pay-to-order gets lower. The average marginal revenue of online seller goes to decrease in dual scheme. Hence, online seller lowers the order quantity if with longer delivery time. Furthermore, when A < B � h, the delivery time positively affects the order quantity of online seller in dual scheme. It is because more customers would choose pay-on-delivery if with longer delivery time, which increases the average marginal revenue of online seller in dual scheme. As a result, online seller increases the order quantity to increase his profit. The conclusions remind online sellers that deliver time may play absolutely opposite role in the decision making of order quantity, with different value of marginal revenue of pay-to-order and pay-on-delivery in dual scheme.

4.2.3. The comparison on online seller’s performance

Proposition 4. The price satisfies po > pd. This result stems from the finding that the price in pay-to-order

is higher than that in pay-on-delivery. In fact, it is easy to understand this phenomenon, which is apparently unreasonable. Customers who prefer pay-on-delivery usually worry more regard- ing the trade uncertainty. Such uncertainty regarding the purchase process causes anxiety and the perceived loss of power and anxiety increase with the increased uncertainty (Luo et al., 2012). Accord- ing to prospect theory, individuals experience loss with respect to a reference wealth (Kahneman and Tversky, 1979); therefore, cus- tomers with more uncertainty want to pay less to reduce less. That is, customers who choose pay-on-delivery want to pay less.

Next, we compare both the optimal order quantity and profit of online sellers between in pay-to-order and in dual scheme. From

Proposition 1 and 3, we can get that �F qon � �

=�FðqdÞ > 1 when

ðA � B þ hÞ 1 þ n et

� � > 2ðm þ hÞ ð18Þ

Therefore, if A � B þ h 6 0, then there is no positive t to satisfy the relation in Eq. (18), that is, �F qo

n

� � < �FðqdÞ; if A � B þ h > 0, Eq.

(18) also can be expressed by

t < n e

ðA � B þ hÞ ½2ðm þ hÞ � ðA � B þ hÞ� ð19Þ

Note t� ¼ ne ðA�BþhÞ

½2ðmþhÞ�ðA�BþhÞ�. From Eq. (19), we see that

ðA þ B � hÞ=2 P B þ m when 2ðm þ hÞ 6 ðA � B þ hÞ, further, we can get AþB�h2 þ n2et ðA � B þ hÞ > B þ m. Coupled with the Eqs. (7) and (17), we find that �F qo

n

� � > �FðqdÞ in this situation. If

2ðm þ hÞ > ðA � B þ hÞ, then t� > 0, and

�F qo n

� � > �FðqdÞ; t < t�

�F qo n

� � ¼ �FðqdÞ; t ¼ t�

�F qo n

� � < �FðqdÞ; t > t�

8>>>>< >>>>:

ð20Þ

Name Q ¼ qo=n. From Eq. (8), the optimal profit of online seller in pay-to-order also can be shown as

p�o ¼ n ððv þ m � sÞ�GðvÞ � mÞðQ � Z Q 0

FðxÞdxÞ � ðc � sÞQ � �

¼ n ðB þ mÞðQ � Z Q 0

FðxÞdxÞ � ðc � sÞQ � � ð21Þ

Based on the above analyses, we can get the comparison results between two different payment schemes, which can be seen in Proposition 5.

Proposition 5. There exist a threshold t� ¼ ne ðA�BþhÞ

½2ðmþhÞ�ðA�BþhÞ� and a

threshold nodð0 < nod < 1Þ such thatwhen A 6 B � h, then

qd < qo=n p�d > p

� o; n 2 ð0; nodÞ

p�d ¼ nodp�o; n ¼ nod p�d < p

� o; n 2 ðnod; 1Þ

8>< >:

8>>>< >>>:

ð22Þ

when A > B � h, then

qd < qo=n p�d > p

� o; n 2 ½0; nodÞ

p�d ¼ nodp�o; n ¼ nod p�d < p

� o; n 2 ðnod; 1�

8>< >: ;

8>>>< >>>:

t > t� > 0

qd ¼ qo=n p�d ¼ p�o=n

;

t ¼ t� > 0

qd > qo=n > qo p�d > p

� o

;

0 < t < t�

8>>>>>>>>>>>>>< >>>>>>>>>>>>>:

ð23Þ

Proposition 5 shows the comparison results regarding inven- tory and profit performance between pay-to-order scheme and dual scheme, are related with the two parts of marginal revenue of online seller in dual scheme, A and ðB � hÞ, which are also affected by the delivery time t in certain conditions. In particularly, when the marginal revenue with pay-to-order is no more than that with pay-on-delivery in dual scheme (that is A 6 B � h), the com- parison result is only related with the demand change from pay- to-order to dual scheme (which is decided by n). Only when dual scheme has a strong and positive effect in enlarging market demand, which means n is certain small and 1 � n is certain big, that dual scheme is absolutely more profitable than pay-to- order; otherwise, pay-to-order is better. It is because the marginal revenue is smaller in dual scheme than in pay-to-order (which can be obtained by A 6 B � h < B þ m, furthermore ðA þ B � hÞ=2 < B þ m, where ðB þ mÞ is the marginal revenue in pay-to-order), then only when there is certain more increase in market sales in dual scheme, that online sellers can get more profit in dual scheme. Therefore, Online sellers should offer dual scheme if more cus- tomers shop online because of pay-on-delivery. In China, the risk perceptions of online customers are mainly origin from product risk, the security of personal information and online transactions (Michael et al., 2014). Liu et al. (2008) indicated that a safe pay- ment method should be provided by B2C online retailers to protect customers’ privacy and guarantee their financial security. Pay-on- delivery can effectively protect customers’ bank information and mitigate the product risk. Hence, dual scheme is definitely helpful for increasing market demand in e-business. Dual scheme is also helpful for the development of mobile e-commerce. Among the factors that make customers hesitate to use mobile e-commerce, the top two are the percentage of worrying about the payment security (40.5%) and the real information on products (38.5%)

Fig. 3. The effect of t and n on q when A < B � h.

N. Xu et al. / Electronic Commerce Research and Applications 21 (2017) 27–37 33

(CNIT, 2014). Pay-on-delivery allows customers to pay for products after delivery, which helps to eliminate their worries and increase sales. Similarly, dual scheme is also attractive for new online cus- tomers especially during the introduction period of new products.

Proposition 5 also indicates that the comparison result is not only related with the market demand change, but also with the delivery time, when the marginal revenue with pay-to-order is more than that with pay-on-delivery in dual scheme (that is A > B � h). For online sellers, dual scheme tends to be more profitable than pay-to-order if with a shorter delivery time. At the same time, the order quantity gradually gets more in dual scheme. The conclusion reminds online sellers who offer dual scheme to try best to improve delivery efficiency. In fact, it is consistent with the reality. For example, dual scheme service is the hallmark of JD.com. And the service quality especially delivery efficiency becomes better and better since JD.com has built its own logistics system. This helps it to get the highest revenue growth in the world, and become the second largest B2C e-commerce company in China now. With the development of e-commerce, the requirement on delivery efficiency will be strengthened. Hence, online sellers should try out to shorter delivery time, including building their owned logistics systems, developing deep corporation relationship with the-third-logistics, and storing inventory in main cities around country. When the delivery efficiency improves, dual scheme becomes more welcomed. It indicates that dual scheme has a vast application prospect in future.

Fig. 4. The effect of t and n on p when A > B � h.

5. Numerical examples and managerial insights

To illustrate the theoretical results, we provide certain numeri- cal examples in this section. In particular, we are interested in the effect of key model parameters on online seller’s inventory and profit performance. The sensitivity analyses are performed by varying different parameters and are shown in Fig. 2–9.

Let c ¼ 10, s ¼ 8, n ¼ 0:1 and e ¼ 0:2. Market demand follows a normal distribution Nð3000; 500Þ. These data remain the same in the following examples. The other parameters can be observed in Table 3.

Example 1. The sensitivity analysis of delivery time ðtÞ and market demand influence factor ðnÞ on online seller’s performance

We select the delivery time t varying from 0 to 4 with a step increase of 1, and the influence factor of pay-to-order on market demand n varying from 0 to 1. The valuation V is normal, followed

Fig. 2. The effect of t and n on q when A > B � h. Fig. 5. The effect of t and n on p when A < B � h.

Fig. 6. The effect of m on p.

Fig. 7. The effect of h on p.

Fig. 8. The effect of l1 on p.

Fig. 9. The effect of r1 on p.

34 N. Xu et al. / Electronic Commerce Research and Applications 21 (2017) 27–37

with Nðl1;r1Þ, where l1 ¼ 50 and r1 ¼ 30. By Proposition 2 and 3, we can obtain certain thresholds given in Table 4. The sensitivity analysis is shown in Figs. 2–5.

The results in Figs. 2–5 are consistent with Proposition 5. When n ¼ 0:1, we can get A > B � h. Under this situation, the perfor- mances are shown in Figs. 2 and 4. We observe that both the inventory ðqÞ and the profit ðpÞ are higher in dual scheme than in pay-to-order if t < t�; the performances are the same between dual scheme and pay-to-order when t ¼ t�; and the comparison results of online seller’s performances are also affected by the market demand influence factor ðnÞ when t > t�. When n ¼ 7, we can get A < B � h. Under this situation, we find that the comparison results of two payment schemes are influenced by both the delivery time and the market demand influence factor.

When A > B � h, online seller’s profit is less in dual payment scenario than in pay-to-order if n is sufficiently large but t is not very small (observed from Fig. 4). This statement indicates that it is not necessary to offer a dual payment scheme if the improvement of market demand is limited. Particularly for items with significant digital attributes, the valuation of product can be well known by customers from the online introduction. Hence, pay-to-order is appropriate for such kinds of goods. Furthermore, customers shift to choose pay-on-delivery in dual scheme if with higher delivery period, which decreases online seller’s revenue because the margin revenue of pay-to-order is higher than pay-on-delivery under this situation. Therefore, it is not a great idea for online sellers who cannot efficiently control delivery time to offer dual scheme.

When A < B � h, the comparison results of online seller’s performance between the two payment schemes mainly depend on the market demand influence factor n (observed from Fig. 5). This finding tells us that the key for online sellers to offer dual payment scheme is the increase of market demand. Hence, dual scheme maybe a better choice if the potential market is certain large, especially for the markets that customers are more uncertain about the safety of online transaction. In practice, pay-on-delivery can be used as a market tool to develop some certain markets, such as the rural ecommerce, and to launch new products, experienced products or high–valued products. In contrary, pay-to-order is enough for online sellers if they have steady markets, like the star- sellers in Taobao.com.

Example 2. The sensitivity analysis of other important parameters on online seller’s profit ðpÞ.

Table 3 The value of parameters in different figures.

Fig n m h t n l1 r1

Fig. 2 0:1 4 1 0 : 4 0 : 1 50 30 Fig. 3 7 4 1 0 : 4 0 : 1 50 30 Fig. 4 0:1 4 1 0 : 4 0 : 1 50 30 Fig. 5 7 4 1 0 : 4 0 : 1 50 30 Fig. 6 0:1 1 : 6 1 1:06 0:8; 0:9; 1 50 30 Fig. 7 0:1 3 0 : 6 1:06 0:6; 1 50 30 Fig. 8 0:1 3 1 1:06 0:7; 1 45 : 85 30 Fig. 9 0:1 3 1 1:06 0:6; 1 50 25 : 70

Note. The combination of numbers i : j means the number varying from i to j, and i; j means i and j.

Table 4 Thresholds with different parameters.

n A B A � ðB � hÞ t�

0:1 7:65 1:86 6:79 1:06 7 12:14 13:44 �0:30 n

Note. t� ¼ ne ðA�BþhÞ

½2ðmþhÞ�ðA�BþhÞ�.

N. Xu et al. / Electronic Commerce Research and Applications 21 (2017) 27–37 35

From Figs. 6–9, we can obtain the conclusions as follows.

(1) From Fig. 6, we can observe that the shipping fee m has abso- lutely negative effect on online seller’s profit both in pay-to- order and dual scheme. The finding reminds online sellers the importance of effectively controlling logistics cost in e- commerce. What’s more, a surprise result is that this nega- tive effect is much stronger in pay-to-order than in dual pay- ment scenario when the shipping fee is certain large. It is mainly because of the direct influence of shipping fee on price in pay-to-order. Hence, online sellers may consider offer dual scheme if they cannot obtain relative low shipping cost. This finding helps to expand the application space of dual scheme in practice.

(2) The hassle cost h also plays an important role in dual pay- ment scenario. It negatively affects online seller’s profit (observed from Fig. 7). The pay-on-delivery scheme loses its temptation if with high hassle cost. To solve this problem, online sellers can set many experience stores (also called ‘‘showroom”) to let customers know the products before delivery. In China, there are many showrooms, including MIUI phone, Heike of SF Express and cloth art store of Tmall.com.

(3) The customers’ evaluation of product l1, matters much. From Fig. 8, we observe that the profit increases as the mean of the valuation of product increases. It implies that online seller should attempt to improve the evaluation of product, such as improving the quality and service. Albert et al. (2014) found that perceived value is important because it can potentially be managed toward positive purchasing intention effect.

(4) As shown in Fig. 9, the online seller’s profit p becomes higher if the customers’ evaluation on product r1 is more different. Because the more different the customers’ evalua- tion is, the less likely the customers return back the product. The products with clear value are not as beneficial as those valued differently by customers. Hence, compared with search goods, online sellers prefer the experienced goods, such as cloths.

6. Conclusion

This study makes a number of contributions which are relevant to both academics and practitioners. Driven by customer orienta-

tion, this paper fills the gap between customer behavior and oper- ations management through the perspective of payment scheme. It develops a model for exploring the customers’ behavior under dif- ferent payment schemes and the combined impact of customers’ behavior and payment scheme on online seller’s profit perfor- mance. Since online seller offers one more kinds of payment ser- vice in dual scheme, we usually think that he would charge a higher price in dual scheme than in pay-to-order. Yet, seemingly opposite to the common sense, we find that the online seller should make a lower price in dual scheme than in pay-to-order. This is because the customers who decide shopping online because of the existence of pay-on-delivery in dual scheme are usually loss averse and uncertain about the online transaction. They further avoid the loss by paying less. Conversely, the customers can reject the product without any fee; hence, return rate increases if the price is higher than the expectation.

In this paper, we also find that the comparison result of profit between pay-to-order and dual scheme mainly depends on the marginal revenue and the potential demand growth, which are also affected by the delivery time at certain situations. When designing the payment scheme, online seller should consider the characteris- tics of products and the types of market. Nevertheless, dual scheme is absolutely preferred if it can effectively increase customers’ trust and enlarges demand. That is, online sellers should offer dual scheme when there are potential customers who hesitate to shop online because of worry about it. This finding provides the practical application space of dual scheme.

In practice, dual scheme is very necessary to improve the relia- bility of product and the whole transaction. It can be used in mobile e-commerce, where mobile shopping customers hesitate to pay online because of distrust of the safety of payment online and the value of products, with a percentage of 40.5% and 38.5%, respectively (CNIT, 2014). If there is pay-on-delivery, mobile cus- tomers could check the products and finish payment after delivery offline. Hence, pay-on-delivery can be used as a catalyst for the development of the mobile e-commerce market.

The application space of dual scheme is also very large in rural e-commerce. With the strong purchasing power in rural areas, rural electronic has been observed as the next ‘‘blue sea” and has gained much support from the national policy in China. Among the online customers in rural areas, 56% of them have the ability to make online payment. However, there are 89% of all users mak- ing pay-on-deliver as the first choice (Cyzone, 2015). Therefore, e- commerce managers should consider the comparison results between pay-to-order and dual scheme, to make a better design on payment scheme. The results in this paper provide a reference for decision makers in e-commerce firms.

In fact, although e-commerce has been developing very quickly in China, many problems remain. For example, certain sellers on Taobao.com employ people to make false purchases and support- ive comments (also named ‘‘Brush auger”) to increase sales and credit. According to a report from CECRC (2015), the defective rate

36 N. Xu et al. / Electronic Commerce Research and Applications 21 (2017) 27–37

is three times more in pay-to-order than in pay-on-delivery; the processing time due to quality problem is one to two days in pay-on-delivery, but five to six days in pay-to-order. These data indicate that sellers are more faithful with pay-on-delivery. Hence, we believe online firms should set pay-on-delivery during business hours; this acts as a type of supervision mechanism.

This work also has limitations. First, we did not empirically val- idate the difference in online customers’ behavior between pay-to- order and pay-on-delivery. However, substantial empirical support exists regarding the stimulation effect of pay-on-delivery on demand (Chiejina and Soremekun, 2014). Second, customers’ shop- ping experience with one payment scheme may be different between different countries. For example, the delivery period is much longer in many other countries, and there may be a change in price during the delivery period, which certainly affects cus- tomers’ willingness to retain the product. Chinese sellers have real- ized this question. Therefore, they usually tell customers the promotion price when customers purchase prior to large sales. For example, the price is much lower during the ‘‘Double-11” fes- tival in China. Customers who purchase products during the Nov. 1–10 periods can observe the actual price on Nov. 1 from online sellers. In general, the price may decrease without notice. If this decrease occurs during the delivery period, customers can consult with the sellers to request a return of the price difference or directly reject the shipped products and buy a new one at the lower price. If the price decrease occurs after delivery, customers can also request a return of the price difference in the same man- ner because they have the right of ‘‘No reason to return in seven days”. Usually, sellers return the price difference in time. To further protect customers from price discrimination, online sellers propose a price protection policy. For example, JD.com allows customers to request a return of the price difference for household applications within 30 days after the sale. However, it is worth noting that this situation is the current one in China, where the distribution is very fast and ‘‘next day delivery” is very common. The situations may be different in other countries. Therefore, we will further research the effect of payment scheme on customers’ behavior in different countries. Finally, operations management in an e-commerce sup- ply chain with different payment schemes may be further elabo- rated; the coordination strategy of the e-commerce supply chain from the payment scheme perspective will be studied in the future. Despite the above-mentioned limitations, we believe that this paper furthers our understanding of the intention to use different payment schemes, and will provide a useful set of guidelines for the provisions of different payment services.

Acknowledgements

This work was supported by the grants from the NSFC – China 71371061 and NSFC – China 71671054.

Appendix

Proof of Proposition 1. Suppose that the seller expects that all customers have a reservation price in pay-to-order, it is clear that the online seller will choose the price as much as the customer’s reservation price (Muth, 1961; Su and Zhang, 2008). According to Definition 1, the reservation price is ro ¼ v þ m in pay-to-order. Then, the price in pay-to-order is po ¼ v þ m, where v is the valuation of the products, and m is the shipping fee. Because the order quantity is q ¼ arg max poðq; poÞ, so

qo ¼ argmax½ððpo �sÞ�Gðpo �mÞ�mÞEminðnX;qÞ�ðc �sÞq� ¼ argmaxfððpo �sÞ�Gðpo �mÞ�mÞ½q�n

R q=n 0 FðxÞdx��ðc �sÞqg:

Because the second-order-condition on order quantity satisfies the relationship that @p2oðq; poÞ=@q2 ¼ �ððv þ m � sÞ�GðvÞ � mÞ < 0, and the first-order-condition is @poðq; poÞ=@q ¼ ððv þ m � sÞ �GðvÞ � mÞð1 � Fðqo=nÞÞ � ðc � sÞ, hence, we can get �Fðqo=nÞ ¼ ðc � sÞ=ððv þ m � sÞ�GðvÞ � mÞ. h

Proof of Proposition 2. As shown in Eqs. (4) and (11), the highest price the customer would like to pay for is rc ¼ v � n under pay- on-delivery. According to Definition 2, we can get that online seller makes a decision on price as pc ¼ v � n in dual scheme. h

Proof of Proposition 3. We can get the online seller’s profit from Eq. (16), which is

pd ¼ Að12 þ n2etÞ þ ðB � hÞð12 � n2etÞ �

½q � R q 0 FðxÞdx� � ðc � sÞq

¼ AþB�h2 þ n2et ðA � B þ hÞ�½q � R q 0 FðxÞdx

� � ðc � sÞq

Note @2pd=@q2 ¼ � AþB�h2 þ n2et ðA � B þ hÞ �

fðqÞ < 0, that pd is concave with respect to q. Hence, there exists a unique qd > 0. pd increases as q 2 ð0; qdÞ, and decreases as q 2 ðqd; þ1Þ. @pd=@qjq¼qd ¼

AþB�h 2 þ n2et ðA � B þ hÞ

� ½1 � FðqÞ� � ðc � sÞ ¼ 0, then

we can get the optimal order quantity in dual scheme is �FðqdÞ ¼ 2ðc�sÞAþB�hþnetðA�BþhÞ. h

Proof of Proposition 4. Since po ¼ v þ m and pd ¼ v � n, it is obvi- ous to get po > pd. h

Proof of Proposition 5. Since p�d ¼ pdðpd; qdÞ, p�o ¼ poðpo; qoÞ, then the optimal profit of online seller in pay-to-order and dual scheme are given as

p�o ¼ n ððv þ m � sÞ�GðvÞ � mÞðQ � Z Q 0

FðxÞdxÞ � ðc � sÞQ � �

¼ n ðB þ mÞðQ � Z Q 0

FðxÞdxÞ � ðc � sÞQ � �

and p�d ¼ AþB�h2 þ n2et ðA � B þ hÞ �

qd � R qd 0 FðxÞdx

� � ðc � sÞqd,

respectively, where Q ¼ qo=n. Hence, the comparison of online seller’s profits between pay-to-

order and dual scheme is shown as

p�o � p�d ¼ p�o

¼ n ðB þ mÞðQ � Z Q 0

FðxÞdxÞ � ðc � sÞQ � �

� K qd � Z qd 0

FðxÞdx � �

þ ðc � sÞqd

,where Q ¼ qo=n. From the analysis above Proposition 4, we see that if

�F qon � �

< �FðqdÞ; otherwise, there is

�F qo n

� � > �FðqdÞ; t < t�

�F qo n

� � ¼ �FðqdÞ; t ¼ t�

�F qo n

� � < �FðqdÞ; t > t�

8>>>>< >>>>:

:

Case (i): A � B þ h 6 0 Since A � B þ h 6 0, we can get that A 6 B � h < B þ m, which

indicates that AþB�h2 < B þ m, furthermore, AþB�h2 þ n2et ðA � B þ hÞ < B þ m. That is, the marginal revenue is smaller in dual scheme than in pay-to-order under this situation.

N. Xu et al. / Electronic Commerce Research and Applications 21 (2017) 27–37 37

In this situation, we also can get that �FðQÞ < �FðqdÞ, furthermore, we see that Q > qd.

When n ¼ 1, the profit of online seller in pay-to-order is p�o ¼ ðB þ mÞðQ �

R Q 0 FðxÞdxÞ � ðc � sÞQ, and p�o > ðB þ mÞ

qd � R qd 0 FðxÞdx

� � ðc � sÞqd > AþB�h2 þ n2et ðA � B þ hÞ

� qd �

R qd 0 FðxÞdx

� �ðc � sÞqd, that is p�o > p�d.

When n ¼ 0, p�o ¼ 0 < p�d. Define a function UðnÞ ¼ p�o � p�d, then, there exists a threshold nod 2 ð0; 1Þ such that UðnÞ ¼ p�o � p�d < 0 for n 2 ½0; nodÞ, UðnÞ ¼ p�o � p�d ¼ 0 for n ¼ nod, and UðnÞ ¼ p�o � p�d > 0 for n 2 ðnod; 1�.

Case (ii): A � B þ h > 0 In this case, t� > 0 when A � B þ h < 2ðm þ hÞ. That is,

AþB�h 2 < B þ m. Based on the analysis above Proposition 5,

we see that �F qon � �

> �FðqdÞ when t < t�, which means AþB�h2 þ n 2et ðA � B þ hÞ > B þ m and Q < qd.

Therefore, we can get that

p�d ¼ AþB�h2 þ n2et ðA � B þ hÞ �

qd � R qd 0 FðxÞdx�

� ðc � sÞqd

> AþB�h2 þ n2et ðA � B þ hÞ �

Q � R Q 0 FðxÞdx

h i � ðc � sÞQ

> ðB þ mÞðQ � R Q 0 FðxÞdxÞ � ðc � sÞQ ¼ p�o=n

:

Because 0 < n < 1, then it is obvious to see qd > qo and p�d > p � o

under this situation. Similarly with the proof process when t < t�, we can easily get

that qd ¼ qo=n and p�d ¼ p�o=n if t ¼ t�. When t > t�, from the analysis above this proposition, we see

that �Fðqo=nÞ < �FðqdÞ. Then the proof process in this situation is similar with that in case (i). Here we neglect it. h

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Na Xu is a PhD at the School of Business Administration, Shandong Institute of Business and Technology (Yantai 264026, PR China). Her research interests include supply chain coordination and customer behavior and management in e-commerce supply chain. She has published research in European Journal of Industrial Engi- neering.

Shi-zhen Bai is a professor at the School of Management, Harbin University of Commerce (Harbin 150028, PR China). His research interests include supply chain management, logistics management, logistics finance, and service management in e-commerce. He has published research in European Journal of Industrial Engi- neering.

Xiang Wan is an Assistant Professor at the Fisher College of Business, The Ohio State University (OH 43210, USA). His research interests include supply chain coordina- tion and product and service variety management in supply chains. He has pub- lished research in Strategic Management Journal, Production and Operations Management Journal, Journal of Operations Management, Journal of Business Logistics, Decision Sciences Journal, Transportation Research (E): Logistics and Transportation Review, Business Research, and China Market Modern Business.