Coupon promotional strategies for buy-online-pick-up-in-store retailing: the role of distribution channel competition Open Access

Omnichannel retailing, a multichannel approach in which retailers provide customers with a consistent and coordinated experience across various distribution channels, has witnessed significant growth in recent years (Gao and Su, 2017). It is reported that 91% of retailers have designed or applied omnichannel strategies (Tanner and O’Carroll, 2018). More recently, a distribution channel widely implemented by omnichannel retailers is the Buy-online-pick-up-in-store (BOPS). Unlike other digital channels, BOPS provides both retailers and shoppers with the opportunity to find a middle ground between online and offline options and bridges the gap between the convenience of e-commerce and the benefits of in-store shopping. During the first half of 2019, nearly 67% of shoppers in the United States used BOPS, and it is predicted that this service will fulfill 10% of all sales by 2025 (Ross, 2019).

Omnichannel retailers optimize their operational strategies by integrating the various shopping channels to expand their online and offline markets. However, omnichannel retailers face intense competition from large e-retailers as well as increased competition from small and local retailers. Existing omnichannel research has focused on monopolistic environments (e.g. De Carvalho et al., 2024; Silva et al., 2024), ignoring the competition generated by different channels. Consequently, we extend this research by focusing on a competitive environment in which omnichannel retailers face channel competition from e-retailers and traditional retailers.

Routinely, coupons have become a marketing mainstay, significantly influencing customers’ channel choices and increasing sales (Zhang et al., 2020). Omnichannel retailers can use targeted coupon promotions to compete with online and offline retailers and provide incentives for customers to use the BOPS channel (Li et al., 2023). This allows them to specifically lower their retail prices in the BOPS channel, without hurting the profit margin of their self-operation online and offline channels. For example, in Australia, major grocery stores such as Woolworths and Coles are attracting customers to their BOPS channels by offering coupons to first-time users. While a considerable number of studies have focused on coupon promotions (e.g. Park and Yoon, 2022), research on the effectiveness of coupons distributed by omnichannel retailers is limited, especially in the BOPS channel. This paper is interested in answering the following questions:

Motivated by these management dilemmas, we develop a game-theoretic model to investigate the coupon strategy of an omnichannel retailer facing competition from an online e-retailer and a traditional retailer. The omnichannel retailer simultaneously operates online, offline, and BOPS channels and conducts coupon promotions in the BOPS channel. We first investigate the omnichannel retailer’s operational strategies without coupon promotion when facing an e-retailer’s channel competition. Second, we explore the omnichannel retailer’s use of coupon promotions in the BOPS channel when facing the channel competition of the e-retailer and the traditional retailer.

Our paper makes the following contributions. First, we introduce coupons as a flexible pricing intervention method in the omnichannel retail BOPS channel to enrich price adjustment and channel integration theories. Second, in contrast to most existing studies, which assumed a monopolistic environment, we propose operational strategies for omnichannel retailers competing with online and offline retailers. Third, our results allow omnichannel retailers to implement channel integration and coupon promotion strategies based on different competitors and channel characteristics, which have seldom been studied.

Previous research on omnichannel retailing has focused on distinct omnichannel models, including BOPS (Li et al., 2024), Showrooming (Arora et al., 2022), ship-to-store (Teixeira et al., 2022), and so forth. Sharma and Dutta (2023) reviewed previous omnichannel-related research and found that it primarily focused on customer behavior, channel integration, technological innovation, and supply chain operations strategy. Meanwhile, Solem et al. (2023) argued that the dynamic capabilities essential for omnichannel retailing include underlying technology, customer experience optimization, internal and external collaboration, and overall omnichannel functionality. BOPS is considered one of the most popular models and this stream of studies focuses on pricing and channel design strategies. For instance, Gao and Su (2017) examined BOPS from the perspective of inventory management revealing that the BOPS strategy enables retailers to reach new customers. Liu et al. (2024a) examined the pricing and omnichannel operational management for online food delivery platforms. Sarkar et al. (2024) discussed the BOPS strategy in relation to advertisement-driven demand. Mahapatra et al. (2025) compared the performance between online-offline modes and BOPS modes. However, existing studies on BOPS strategies focus on monopolistic settings. Our study extends previous research by examining a competitive environment in which omnichannel retailers face competition from both e-retailers and traditional retailers.

Our work builds on the extensive research investigating channel competition. Traditional channel competition refers to manufacturers establishing their own direct channels, a scenario known as “channel encroachment” (Ha et al., 2016; Lin and Januardi, 2023; Liu et al., 2024b). Unlike traditional channel competition, we explore a competitive context in which incumbent omnichannel retailers face competition from external e-retailers and traditional retailers. Several studies have examined omnichannel competition. Akturk and Ketzenberg (2021) evaluated the competitive effect of an omnichannel competitor launching a BOPS service. Jena and Meena (2022) studied price competition between manufacturers and remanufacturers under different channel structures. More recently, Tang et al. (2023) studied competing firm’s opening strategies across physical channels, online channels, and omnichannel models. A study closely related to our research is Zhang et al. (2023a, b), which studies a framework in which a supplier encroaches on the retailer’s omnichannel retailing through an online channel. Lee and Moon (2024) examined channel competition involving third-party platform channels for omnichannel retailers operating both offline and online channels. Although this stream of research emphasizes the effect of omnichannel competition on pricing strategies, no previous research has considered the role of coupon promotions.

We also contribute to the research stream of coupon promotions. There is a growing body of literature on coupons’ price discrimination and marketing effects. For instance, Reimers and Xie (2019) demonstrated that coupons can be used as a tool for price discrimination, attracting new consumers. Liu et al. (2021) found that coupons positively influence the quantity purchased by customers. Zhang et al. (2023a, b) believed that coupon promotion not only boosts consumers' purchase quantity during the redemption period but also improves the relationship between the customer and firm beyond the redemption period. Other researchers have investigated the effect of coupons on consumers’ buying behaviors (Ha and Im, 2014), brand competition (Park and Yoon, 2022), and coupon redemption (Zhang et al., 2020). Notably, little attention has been paid to channel competition, especially in an omnichannel context. Recently, several studies have examined omnichannel coupon promotion. Li et al. (2023) studied the cross-channel effect of coupons when omnichannel retailers distribute them through both online and offline channels. Zhang et al. (2024) studied coupon promotion and inventory strategies in omnichannel industries. However, these studies focused on coupon promotions within the internal channels of omnichannel retailers. Unlike those works, the present study examines an omnichannel retailer operating through online, BOPS, and offline channels, introducing coupons as a price discrimination tool to counteract channel competition. Table A1 (See the Online Appendix) provides an overview of the key features examined in the literature.

Consider an operational system in which an omnichannel retailer has both an online platform and a brick-and-mortar store (See Figure 1). Likewise, the omnichannel retailer adopts a BOPS channel in which consumers can browse and order products through the online platform and then physically view and pick up their orders in the store. In a competitive market, omnichannel retailers face competition from e-retailers in the online market and traditional retailers in the offline market. In our model, following Gao and Su (2017), the omnichannel retailer charges a uniform price (p_o) across the online, BOPS, and offline channels. The e-retailer sets price p_e, and the traditional retailer charges price p_r to capture the market.

To enhance competitiveness, the omnichannel retailer provides coupons with a face-value f_b in the BOPS channel. This allows the omnichannel retailer to reduce its retail price in the BOPS channel, thereby attracting consumers and maintaining market competitiveness. Consumers enjoy a discounted price of p_o−f_b when redeeming a coupon. To ensure a positive profit margin, we assume that f_b < p_o always holds.

In line with existing literature (e.g. Hu et al., 2022; Zhang et al., 2020; Zhang et al., 2024), we adopt the utility function to characterize consumers’ purchase behavior. Consumers have a basic valuation v (v ∈ [0,1]) for products, which is assumed to be a constant parameter, allowing us to focus on the dimensions of coupon promotions. When consumers make purchases online, they face a risk of product mismatches because they cannot touch or feel the product (Zhuang et al., 2018). Therefore, the product’s perceived value in this channel is worth θ₁v, where 0<θ₁ < 1. In contrast, when shopping in physical stores, consumers can inspect the quality and performance, leading to a higher valuation compared with online purchasing (Li et al., 2023). Thus consumers derive a valuation of θ₂v (θ₂>θ₁) when purchasing through the offline channel, where θ₁ and θ₂ represent the channel preference coefficients for online and offline channels, respectively. In the BOPS channel, consumers gain additional product and pricing information from the website (Cao et al., 2016) while also having the opportunity to physically inspect the product in the store (Gao and Su, 2017). In some instances, consumers do not need to pay immediately when ordering online (Jin et al., 2018). If the product does not match their expectations after in-store inspection, they can then cancel the order (Zhang et al., 2018).

It is important to note that BOPS combines online browsing with offline pickup. In contrast to BOPS, consumers shopping in traditional stores spend more time physically searching for and collecting products. Additionally, they do not have access to product details and pricing information from the retailer’s website. Hu et al. (2022) examined the BOPS omnichannel and suggested that online purchases may be more appealing due to the abundance of customer reviews and easy price comparisons. Business practices also reflect this advantage—when picking up online orders, BOPS customers often receive additional services, such as express checkout lanes. For example, Walmart offers a delivery-to-car service for customers retrieving their online purchases. These conveniences may result in a higher perceived valuation for the BOPS channel compared to the offline channel. Thus, we assume that consumers assign a full valuation (v) to products sold via the BOPS channel.

Consumers incur a shipping cost l_o when purchasing via an online channel (Gao and Su, 2017). Meanwhile, consumers who purchase through the BOPS or offline channels incur a travel cost x, where x is uniformly distributed over [0,1]. BOPS consumers must browse a website to place an order and face both offline transaction costs and potential delays associated with picking up their orders (Cao et al., 2016). We denote these costs as the hassle costs (l_t). Therefore, consumers’ utility is denoted U_o = θ₁v−p_o−l_o, U_b = v−p_o−x−l_t, and U_s = θ₂v−p_o−x in the online, BOPS, and offline channels, respectively. While the BOPS channel offers a higher perceived valuation compared to the offline channel (i.e. v>θ₂v), consumers also incur additional hassle costs that are not present in offline purchases. Similarly, a consumer who purchases from an e-retailer incurs a shipping cost l_o, while one who purchases from a traditional retailer incurs a travel cost x. Thus, consumers’ net utility in the online and offline channels is U_e = θ₁v−p_e−l_o and U_r = θ₂v−p_r−x, respectively. In line with Li et al. (2023), we characterize the contribution of coupons to consumer utility as a linear demand model, whereby a consumer’s utility from purchasing via the BOPS channel with a coupon is U_b = v−p_o−x−l_t + f_b.

Customers are categorized into three types: (1) omnichannel consumers (µ), who consider all available channels; (2) online consumers (η), who search for products via both online and BOPS channels; and (3) offline consumers (1−µ−η), who purchase only through offline channels. The notations used in this study are summarized in Table A2 in the Online Appendix.

First, the e-retailer and traditional retailer decide whether to enter the omnichannel market. Second, the omnichannel retailer chooses whether to conduct coupon promotions. Third, the omnichannel retailer decides on the price p_o and coupon face value f_b (if applicable). Meanwhile, the e-retailer decides on the price p_e, and the traditional retailer decides on the price p_r. Finally, consumers choose a preferred channel. Accordingly, we model the following three strategies:

1. Strategy NE: No coupon offered, and the e-retailer competes.

2. Strategy CE: The omnichannel retailer offers coupons, and the e-retailer competes.

3. Strategy CS: The omnichannel retailer offers coupons, and the traditional retailer competes.

In this scenario, the e-retailer successfully enters the market if $Ue=θ1v−pe−lo>Uo=θ1v−po−lo$ (i.e. $pe<po$⁠). Consumers have three options: the omnichannel retailer’s BOPS channel and offline channel, and the e-retailer’s online channel. Following we specify the channel selection of different types of consumers.

First, we determine whether consumers prefer the BOPS channel or the offline channel. By calculating $Ub=Us$⁠, we have $lt=(1−θ2)v$⁠. We then analyze two scenarios:

Scenario NE-I (⁠$Ub≥Us⇒lt≤(1−θ2)v$⁠): In this case, consumers prefer the BOPS channel over the offline channel since it provides higher utility. Then they have two options: the BOPS channel or the e-retailer’s online channel. They will purchase from the BOPS channel if $Ub≥max{Ue,0}$⁠; that is, $x≤min{(1−θ1)v−po−lt+pe+lo,v−po−lt}$⁠. Since $v−po−lt−[(1−θ1)v−po−lt+pe+lo]=θ1v−pe−lo$⁠, and $Ue=θ1v−pe−lo>0$⁠, consumers will buy from the BOPS channel when the travel cost is low (i.e. $x≤(1−θ1)v−po−lt+pe+lo$⁠); otherwise, when the travel cost is high (i.e. $x>(1−θ1)v−po−lt+pe+lo$⁠) they will buy from the online channel. The market segmentation is shown in Figure 2(a). Then we derive $Db1NE−I=(1−θ1)v−po−lt+pe+lo$ and $De1NE−I=1−[(1−θ1)v−po−lt+pe+lo]$⁠.

Scenario NE-II (⁠$Ub<Us⇒lt>(1−θ2)v$⁠): In this case, consumers prefer the offline channel over the BOPS channel due to its higher utility. Following, they have two options: the offline channel or the e-retailer’s online channel. They purchase from the offline channel if $Us≥max{Ue,0}$⁠; that is, $x≤min{(θ2−θ1)v−po+pe+lo,θ2v−po}$⁠. Since $θ2v−po−[(θ2−θ1)v−po+pe+lo]=θ1v−pe−lo=Ue≥0$⁠, consumers will buy from the offline channel when the travel cost is low (i.e. $x≤(θ2−θ1)v−po+pe+lo$⁠); however, when the travel cost is high (i.e. $x>(θ2−θ1)v−po+pe+lo$⁠), they will buy from the online channel. The market segmentation is shown in Figure 2(b). Then we derive $Ds1NE−II=(θ2−θ1)v−po+pe+lo$ and $De1NE−II=1−[(θ2−θ1)v−po+pe+lo]$⁠.

Online consumers will choose between the BOPS channel or the e-retailer’s online channel. Consumers compare the utility they receive from each channel to determine their purchase decision. They choose the BOPS channel if $Ub≥max{Ue,0}$⁠, meaning, they opt for BOPS when the travel cost is low $x≤(1−θ1)v−po−lt+pe+lo$⁠. Conversely, they will buy from the online channel when the travel cost is high $x>(1−θ1)v−po−lt+pe+lo$⁠. The market segmentation is shown in Figure 2(c). Then we derive $Db2NE−I/Db1NE−II=(1−θ1)v−po−lt+pe+lo$ and $De2NE−I/De2NE−II=1−[(1−θ1)v−po−lt+pe+lo]$⁠.

Offline consumers only purchase from the offline channel and they will buy products if $Us≥0$ (i.e. the travel cost is low; $x≤θ2v−po$⁠). However, if the travel cost is high (i.e. $x>θ2v−po$⁠), they choose to exit the market. The market segmentation is shown in Figure 2(d). Then we derive $DsNE−I/Ds2NE−II=θ2v−po$⁠.

Accordingly, we summarize the demand as follows (the calculation process is presented in the Appendix. Note: o-retailer = omnichannel retailer):

The omnichannel retailer’s and e-retailer’s decision problems are given as:

The first, second, and third terms of $ΠORNE$ represent the revenue earned from omnichannel, online, and offline consumers, respectively. The profit of the e-retailer includes the revenue earned from omnichannel and online consumers. We present the equilibrium solutions in Table A3 in the Appendix. Next, we discuss the impact of key parameters on the equilibrium prices and profits.

• (i).

  Price: The larger the l_o, the higher the price p_o set by the omnichannel retailer, while the lower the price p_e set by the e-retailer (i.e. $dpoNE−κ*dlo>0$; $dpeNE−κ*dlo<0$). The larger the l_t, the lower the price p_o set by the omnichannel retailer, while the higher the price p_e set by the e-retailer (i.e. $dpoNE−κ*dlt<0$; $dpeNE−κ*dlt>0$).

• (ii).

  Revenue: The revenue of the omnichannel retailer and the e-retailer first decreases and then increases with l_o and l_t (i.e. $d2ΠORNE−κ*dlo2>0$; $d2ΠORNE−κ*dlt2>0$; $d2ΠERNE−κ*dlo2>0$; $d2ΠERNE−κ*dlt2>0$).

In Corollary 1(i), a high l_o indicates the online purchase is less attractive and thus the e-retailer reduces price p_e. Conversely, this gives the omnichannel retailer a competitive advantage, allowing it to raise price p_o. Similarly, a high l_t implies the BOPS channel is at a disadvantage and the e-retailer’s online channel is more competitive. Thus the omnichannel retailer will reduce p_o, whereas the e-retailer will raise p_e. Regarding Corollary 1(ii), since the e-retailer raises price p_e when l_o is low, if the price becomes too high, it may reduce consumer utility, leading to market loss and lower revenue. Notably, the omnichannel retailer suffers fierce channel competition from the e-retailer, which reduces profit margins and reduces revenue. Interestingly, the e-retailer’s revenue increases with l_o when l_o is high. This is because the e-retailer reduces the price to enter the market. Although this reduces margin profit, if the captured market is large enough, the total revenue increases. The same logic applies to the impact of l_t. This highlights the importance of balancing price strategy and market share to maximize revenue.

• (i).

  Price: The larger the θ₁, the lower the price p_o set by the omnichannel retailer, while the higher the price p_e set by the e-retailer (i.e. $dpoNE−κ*dθ1<0$; $dpeNE−κ*dθ1>0$). The larger the θ₂, the higher the price p_o and p_e set by the omnichannel retailer and e-retailer, respectively (i.e. $dpoNE−κ*dθ2>0$; $dpeNE−κ*dθ2>0$).

• (ii).

  Revenue: The revenue of the omnichannel retailer and e-retailer first decreases and then increases with l_o and l_t (i.e. $d2ΠORNE−κ*dθ12>0$, $d2ΠORNE−κ*dθ22>0$⁠. $d2ΠERNE−κ*dθ12>0$, $d2ΠERNE−κ*dθ22>0$).

In Corollary 2(i), a high θ₁ indicates consumers are willing to purchase online, which enables the e-retailer to enjoy a channel advantage. Thus the omnichannel retailer has to reduce price p_o. In contrast, a high θ₂ indicates the offline channel is attractive, enabling the omnichannel retailer to enjoy a channel advantage and thus raise prices. Note that, a high θ₁ leads to a high online price p_e since the online channel is attractive. Regarding the impact of θ₂, since only a fraction of offline consumers will purchase from the offline channel, the competitiveness of the offline channel is not that strong. This allows the e-retailer to follow the omnichannel retailer’s high-price strategy to maximize revenue. In Corollary 2(ii), the changing rule is primarily driven by the trade-off between profit margin and market share, which is akin to the mechanism observed for l_o and l_t in Corollary 1.

This section explores a scenario in which the omnichannel retailer offers a coupon f_b in the BOPS channel to combat the e-retailer. Thus, the consumer utility for the BOPS channel is $Ub=v−po−x−lt+fb$⁠. We identify the channel selection of different consumers. For parsimony, we present the market demand and provide the proof process in the Appendix.

The omnichannel retailer’s and e-retailer’s decision problems are given as:

The first, second, and third terms of $ΠORCE$ is the revenue earned from omnichannel, online, and offline consumers, respectively. The first and second terms of $ΠERCE$ is the revenue earned from omnichannel and online consumers, respectively. Analogously, we derive the equilibrium solutions and provide them in Table A4 in the Appendix.

This section explores the effectiveness of coupon promotion through the following propositions.

Proposition 1 implies that the omnichannel retailer will raise price when offering coupons, compared to not offering coupons, if l_t is high. When l_t is high, the omnichannel retailer has a stronger incentive to use coupons to attract consumers. To maintain positive marginal revenue, it may raise prices even in a competitive market with an e-retailer. In summary, there is a positive relationship between coupon promotion intensity and price—as the hassle cost increases, the omnichannel retailer compensates by raising prices while offering coupons to sustain profitability.

Surprisingly, the e-retailer may raise the price even if the BOPS channel is at an advantage (i.e. l_t is low). Recall that the omnichannel retailer will not provide coupons when l_t is low (see Proposition 1). If a low-value coupon is offered, the e-retailer will raise the price. However, if the omnichannel retailer offers coupons with a larger value, the e-retailer should reduce the price to capture market share. This dynamic underscores the need for the e-retailer to adjust its pricing strategy based on the omnichannel retailer’s coupon policy, ensuring it remains competitive in the market.

In Proposition 3(i), when l_t is high, the omnichannel retailer will increase coupon promotions in the BOPS channel (see Proposition 1), thereby deriving a higher market share. Nonetheless, Proposition 3(ii) shows that the offline channel will capture a larger market share if l_t is low. Unlike the impact of coupon promotions in the BOPS channel, the retailer is less likely to offer coupons when l_t is low, which strengthens consumer preference for the offline channel.

In Proposition 4, when l_t is low, the promotional effect of coupons is weak, providing the online channel an opportunity to capture a greater market share. The findings of Propositions 2 and 4 indicate that e-retailers will not be disadvantaged when omnichannel retailers offer coupons in the BOPS channel. In some cases, the e-retailer may even experience higher prices and increased market share, especially when l_t is low or when the omnichannel retailer provides only a low-value coupon.

This section examines the effect of coupon promotions on profit. Given the complexity of the analytical results, we employ numerical simulation to demonstrate our findings (see Figure A1 in the Online Appendix).

We find that in Scenarios CE-I and CE-II, the omnichannel retailer will be better off by implementing coupon promotion when l_o is high and l_t is low (See Figures A1(ai) and (aii)). At a high l_o and a low l_t, the omnichannel retailer’s BOPS and offline channels have an advantage over the online channel, which may derive larger revenues. Note in Figure A1(aii) that Scenario CE-II may perform worse than Scenario NE-I when l_t is high. This is because consumers obtain a low utility from the BOPS channel, and coupon promotion is weak (i.e. f_b ≤ l_t-(1-θ₂)v in Scenario CE-II). Thus, in Scenario CE-II, the omnichannel retailer will withdraw its coupons when l_t is high. Conversely, Scenario CE-III outperforms Scenario NE-II when l_o is sufficiently low and l_t is sufficiently high (See Figure A1(aiii)). When the omnichannel consumer purchases from either the omnichannel retailer’s offline channel or the e-retailer’s online channel (i.e. Scenario CE-III), the omnichannel retailer should offer a coupon to capture online consumers. In this way, the omnichannel retailer can benefit from coupon promotions.

In most cases, see Figure A1(b), the e-retailer suffers losses when competing with the omnichannel retailer in Scenarios CE-I and CE-II, where the omnichannel retailer has an absolute advantage owing to its coupon promotion. However, the e-retailer can derive higher profits in Scenario CE-III than in Scenario NE-II when l_o is low. This is because a low l_o indicates that the online channel is attractive, benefiting the e-retailer. Obviously, it is best for e-retailers to avoid competition in the BOPS channel.

This section investigates the scenario in which the omnichannel retailer suffers from the traditional retailer and implements a coupon promotion in the BOPS channel. The traditional retailer enters the market if $Ur=θ2v−pr−x>Us=θ2v−po−x$ (i.e. $pr<po$⁠). We specify the demand functions as follows (t-retailer = traditional retailer) (see the calculation in the Online Appendix):

The omnichannel retailer’s and traditional retailer’s decision problems are given as:

The terms in Eqs. (11) and (12) are akin to Strategy CE and thus we will not explain them here. Analogously, we derive the equilibrium solutions and provide them in Table A5 in the Appendix.

This section compares the omnichannel retailer’s strategy when competing with the e-retailer (Strategy CE) and the traditional retailer (Strategy CS).

Regarding Proposition 5(i), if l_t is low, the BOPS channel will enjoy an advantage over other channels. Thus, the omnichannel retailer still has the opportunity to increase its prices. Proposition 5(ii) shows that the omnichannel retailer is more likely to conduct coupon promotions when competing with a traditional retailer. First, in Strategy CS, the omnichannel retailer can capture all omnichannel and online consumers in Scenario CS-I and all online consumers in Scenarios CS-II and CS-III. Therefore, offering coupons is beneficial for the omnichannel retailer. Second, generally, the offline channel may have a higher price. Thus, the price set by the omnichannel retailer may be higher when competing with traditional retailers. In this case, the omnichannel retailer will increase coupon promotion in Strategy CS.

Recall from Proposition 5 that when l_t is low, the omnichannel retailer will charge a higher price in Strategy CS than in Strategy CE. Hence, the traditional retailer will follow the omnichannel retailer’s price policy, resulting in higher prices. According to conventional wisdom, offline prices will always be higher than online prices (Li et al., 2023). Unlike previous works, we reveal this result under strict conditions.

Next, we illustrate the profit discrepancies between Strategy CS and Strategy CE via Figure A2 (see in the Online Appendix). We find that the omnichannel retailer derives a higher profit in Strategy CS than in Strategy CE when l_o and l_t are low. In a low l_o and l_t, the online and BOPS channels are more profitable than the offline channel. Therefore, the omnichannel retailer has a competitive advantage, resulting in a higher profit. Meanwhile, the profits of the traditional retailer will be less than the e-retailer in Scenario CS-I. It follows that omnichannel and online consumers will purchase from the online and BOPS channels. Therefore, the offline channel will obtain less market and derive less profit. However, in Scenario CS-II and Scenario CS-III, compared with the e-retailer, the traditional retailer may earn a higher revenue when l_o is high. A high l_o means that the online channel will be less attractive, and consumers will shift to offline channels. Thus, traditional retailers are more likely than e-retailers to earn a higher profit.

This section identifies the differences in consumer surplus by comparing Strategy CE and Strategy CS. We provide the mathematical analysis in the Online Appendix B. We find that Scenario CS-I outperforms Scenario CE-I and Scenario CE-II in terms of consumer surplus. This is because (1) the omnichannel retailer has a greater incentive to provide coupons in Scenario CS-I (see Proposition 5), and (2) all omnichannel and online consumers purchase from the omnichannel retailer in Scenario CS-I, while a certain proportion of them will shift to the e-retailer in Scenario CE-I and Scenario CE-II. Note that consumer surplus may be lower in Scenario CS-II than in Scenario CE-III when l_o is high and l_t is low. This is because the omnichannel retailer sets a higher price under a low l_t (see Proposition 5(i)). Moreover, omnichannel consumers will shift to offline channels in a high l_o, while the omnichannel retailer can capture offline consumers in Scenario CE-III, resulting in a lower consumer surplus. Additionally, the consumer surplus in Scenario CS-III is lower than that in Scenario CE-III. It follows that l_t is sufficiently high in Scenario CS-III, indicating that consumers may obtain low utility from the BOPS channel. Despite the omnichannel retailer implementing a stronger coupon promotion in Scenario CS-III, it may also charge higher prices, thereby deriving a lower consumer surplus. It should be noted that Strategy CS will not always outperform Strategy CE because it depends on consumer preferences and the omnichannel retailer’s promotion policy.

This section considers a situation where not all customers are accustomed to using the BOPS channel. We discuss a market with omnichannel consumers (ξ), who consider all available channels, and traditional consumers (1−ξ), who rely on either online or offline channels. The mathematical derivation is detailed in Online Appendix C. Several key insights emerge from this analysis.

First, as highlighted in Remark 1 (See Appendix C), when l_t is either very low or very high, the omnichannel retailer is more likely to offer coupon promotions when competing with an e-retailer. When l_t is low enough, the omnichannel retailer has an advantage when competing with the e-retailer. Since not all consumers will purchase from the BOPS channel, the omnichannel retailer intensifies its promotional efforts to attract omnichannel consumers. Conversely, when competing with a traditional retailer, the omnichannel retailer already captures all omnichannel consumers, reducing the need for aggressive promotions. When l_t is large enough, the BOPS channel is less attractive. This disadvantage is more pronounced in competition with an e-retailer, as omnichannel consumers are more inclined to buy online. Consequently, the omnichannel retailer increases promotional intensity when facing an e-retailer. In contrast, for intermediate l_t, the optimal strategy is to focus coupon promotions on competition with a traditional retailer.

Second, the omnichannel retailer can effectively compete with the e-retailer through coupon promotion when l_t is not that high (see Figure C1). However, when l_t is sufficiently large, coupon promotion becomes less effective. Intuitively, a high l_t discourages omnichannel consumers to purchase from the BOPS channel regardless of its availability. In this case, offering coupon promotion may lead to a higher price, which weakens the competitiveness of the omnichannel retailer’s online and offline channels. Third, the omnichannel retailer derives a higher profit when competing with the traditional retailer than when competing with the e-retailer if l_o is low (see Figure C2). This aligns with our theoretical prediction that it may be hard to compete with the e-retailer when l_o is low since the online channel is at an advantage.

To incorporate the results of our theoretical model into practical retail strategies, we conduct a numerical study (see Appendix D) and offer the following recommendations for omnichannel retailers to optimize coupon promotions with BOPS.

First, retailers should offer coupons and promotional discounts to encourage BOPS shopping, thereby boosting customer engagement across both online and physical channels. For instance, Walmart provides $10 off coupons for BOPS orders, while Nordstrom integrates BOPS offers into its loyalty program. Similarly, Macy’s incentivizes customers with an “Extra 10% off” for choosing in-store pickup, aligning the promotion with their loyalty benefits. Retailers can also use higher-value BOPS coupons to encourage larger or bulkier purchases, particularly when competing with traditional brick-and-mortar stores. For example, Best Buy in the U.S. offers “Save $25 on your BOPS order of $250 or more”, and Woolworths in Australia promotes “Get $20 off when spending $150 with direct-to-boot or pickup orders”. These incentives not only encourage BOPS adoption over home delivery—reducing delivery expenses—but also increase in-store foot traffic.

Second, BOPS promotions can be used to drive sales of specific products. For instance, Walmart pairs discounts with curated product bundles to attract shoppers, Home Depot offers “$10 off $50” on BOPS purchases of DIY tools and supplies, and Sephora frequently provides 10% off BOPS coupons for select beauty products. By targeting specific categories, retailers can strategically boost sales of high-margin or priority inventory.

Third, retailers should implement personalized e-coupons based on competitive product analysis and consumer preferences. Since shipping costs vary by location, offering customers the flexibility to select coupons that align with their preferred shopping method enhances both convenience and value. For example, Kroger’s website allows shoppers to choose digital coupons tailored to their preferred fulfillment method—whether in-store, pickup, delivery, or shipping. This level of personalization not only improves the customer experience but also strengthens loyalty and increases conversion rates.

In this study, we examined coupon strategies for omnichannel retailers competing with e-retailers and traditional retailers. We investigate omnichannel retailers’ optimal coupon promotional strategies and identify the strategy differences when competing with e-retailers and traditional retailers. This study presents important managerial insights.

Pricing strategy for omnichannel retail managers. We suggest that when competing with e-retailers, omnichannel retailers can charge higher prices if the BOPS channel’s hassle cost is low. Meanwhile, when offering coupons through the BOPS channel, omnichannel retailers have a chance to increase prices despite the BOPS channel’s hassle cost being high. For instance, before providing $10 off coupons for BOPS orders, Walmart may first increase the retail price of certain products. Although consumers receive promotional discounts, their actual payment may still be higher than before the promotion. Furthermore, omnichannel retailers should set a lower (higher) price when competing with traditional retailers than when competing with e-retailers if the hassle cost is high (low). Retailers, such as Best Buy in the U.S., often set lower prices to encourage larger or bulkier purchases, particularly in competition with traditional brick-and-mortar stores. However, since pricing strategy is closely tied to hassle cost, many omnichannel retailers are exploring ways to minimize these costs. Walmart, for example, provides a delivery-to-car service for customers retrieving online orders, effectively reducing hassle and improving the BOPS experience.

Coupon strategy facing e-retailers and traditional retailers. Omnichannel retailers may provide coupons with larger value when competing with traditional retailers than when competing with e-retailers. Likewise, omnichannel retailers will benefit more from providing coupons when competing with traditional retailers than when competing with e-retailers if the hassle and shipping costs are low. Consequently, we recommend that retailers such as Best Buy in the U.S. and Woolworths in Australia use higher-value BOPS coupons to encourage larger or bulkier purchases, especially when competing with brick-and-mortar stores. When competing with e-retailers, omnichannel retailers should leverage coupon promotions when shipping costs are high. Conversely, when competing with traditional retailers, coupon promotions should be implemented when shipping costs are low. Since hassle costs and shipping costs vary by geographic location, omnichannel retailers should design e-coupon strategies based on competitive product analysis and consumer preferences. For example, Kroger’s approach—allowing customers to choose digital coupons tailored to their shopping preferences—demonstrates how personalized promotions can enhance the customer experience, drive loyalty, and increase conversion rates.

The e-retailer’s and traditional retailer’s competitive strategies. It is beneficial for e-retailers to enter the omnichannel system when shipping costs are low or when consumers place a high value on online shopping. In contrast, traditional retailers should enter the omnichannel system when shipping costs are high, as consumers are more likely to shift towards offline purchases. However, when omnichannel consumers strongly prefer the BOPS channel, both e-retailers and traditional retailers should reconsider entering the omnichannel system, especially if the omnichannel retailer is conducting coupon promotions. Instead of engaging in direct competition, both e-retailers and traditional retailers should focus on segmenting the market and targeting specific consumer groups. Today, companies such as Alibaba Cloud and Temu in China increasingly use AI-driven precision marketing to optimize promotional strategies. By analyzing consumer profiles from sales data, these companies design personalized promotions, demonstrating the growing importance of data-driven marketing in the competitive omnichannel landscape.

Several directions can be extended. First, we assumed that only the omnichannel retailer conducts coupon promotions, and these are only offered through the BOPS channel. One can expand to the cases where coupons are offered by e-retailers/traditional retailers or offered through online and offline channels. Second, some coupons can only be redeemed after purchase. This generates a multicycle problem, which deserves in-depth investigation. Third, future researchers could investigate a scenario under which the omnichannel retailer simultaneously competes with e-retailers and traditional retailers or even other omnichannel retailers.

Funding: This work was supported by the National Natural Science Foundation of China [Grant 72232002; 72402157], the Social Science Foundation of Jiangsu Province [Grant 23HQB021], the Natural Science Foundation of Jiangsu Province [Grant BK20230467].

Conflict of interest: All authors declare that they have no conflict of interest.

Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.