Abstract
Accepted by: Konstantinos Nikolopoulos
This research studies the pricing strategy of a supply chain with a manufacturer and a retailer. We analyze the customers’ purchase behaviour in advance selling with deposit by using utility theory and obtain the pricing decision of the supply chain by using the Stackelberg model. We find that when consumers are not sensitive to the distribution lead time, the retailer’s advance selling strategy could Pareto improve the whole supply chain. Better informed consumers and moderate advance selling distribution lead time information could expand the retailer’s pre-sale possibilities by enlarging the feasible range of advance selling.
1. Introduction
Advance selling is an important means to coordinate production and sales by attracting consumers to buy in advance with certain incentive policies before the official sales period begins (Tang et al., 2006). In recent years, the marketing mode of advance selling with a deposit through e-commerce channels has been more welcomed by most companies and users. In October 2020, Huawei released Mate 40 series cellphones through advance selling with deposit from Tmall, JD.COM and other retail channels. Having observed the pre-sale price, consumers could buy a phone by paying a deposit and pay the final payment at the end of the advance selling period. Then after the merchants deliver the products, the consumers sign to complete the transaction. The Mate 40 series cellphones were all sold up through JD.COM only 28 s after the advance selling opened. According to QuestMobile data, in the Double 11 of 2020, when the first advance selling opened for final payment on November 1, the daily active users reached 681 million, up 39.7% year-on-year. Meanwhile, the percentage of orders placed with prepaid deposits reached 37.3%. Advance selling with a deposit has already become a popular sales mode.
Through collecting the advance selling orders, the retailers can inform manufacturers to effectively arrange production in advance and realize economies of scale to reduce costs (Chintapalli et al., 2017). In addition, the introduction of advance selling has transformed the traditional single-period sales model into a two-period sales model. The prices in the two periods are often different. Comparing the prices, well-informed consumers could strategically choose to buy in the advance selling period or wait until the product to is officially listed to purchase. Consumers who buy in the advance selling period can enjoy the preferential price of the product but be uncertain about the products’ valuation due to a lack of detailed information. Meanwhile, in the advance selling rules formulated by major retail platforms, if consumers who participate in the advance selling give up paying the final payment, the deposit paid in advance will not be refunded. Therefore, consumers make strategic decisions about whether to participate in advance selling because of the potential loss.
Consumers’ strategic behaviour refers to the consumers making decisions based on utility maximization. Usually, consumers make choices by considering available information, their characteristics and reasonable expectations for the future market. Well-informed consumers are more willing to know the product information in advance selling activities released by the retailer and make strategic and favourable purchase decisions (Wong & Lesmono, 2019). Advance selling with deposit requires a final payment to be made before the product could be shipped. Compared to regular online shopping, advance selling will increase consumers’ waiting time from the consumer places an order to the product being shipped, which means longer lead times. Consumers have waiting aversion, so they may reject buying in the advance selling period and consider buying in the spot period, which is called lead time aversion.
Because of the strategic behaviour of consumers in advance selling, retailers need to be flexible to change their pricing strategies in two periods based on consumer utility. The supply chain pricing strategy will also change whilst advance selling due to changes in the downstream consumer side and upstream production side. To sum up, the paper considers the strategic behaviours and consumers’ lead time aversion in advance selling with deposit to study the following issues:
(1) Considering consumers’ strategic behaviour, what are the best pricing strategies for manufacturers and retailers?
(2) Comparing the price, demand and profit of the advance selling mode with the non-advance selling mode, could advance selling mode achieve a Pareto improvement in the supply chain?
(3) What factors and key parameters affect the feasible area for advance selling?
To solve the above problems, we construct a theoretical model to portray and analyze the supply chain. The paper is organized as follows. First, in Section 3, this paper constructs the model of non-advance selling mode (abbreviated as NAS) and advance selling mode (abbreviated as AS), explains the important parameters and analyzes consumers’ strategic choices. In Section 4, we obtain the equilibrium solutions and the prerequisites to do advance selling. In Section 5, we compare the two modes, analyze the advantages of advance selling and discuss the influence of important factors on the models through numerical analysis.
2. Literature review
Two streams of literature are most relevant to this paper: Advance selling pricing strategy of the supply chain with strategic consumers and consumers’ lead time aversion behaviours in advance selling.
At present, the literature analyzing consumer behaviour in advance selling mainly studies how a rational decision-maker sets the optimal pricing and marketing strategy when facing the strategic behaviour of consumers (Nasiry & Popescu, 2012, Yu et al., 2015, Tian & Tian, 2016, Wu et al., 2018). On this basis, some literature considered the problem of advance selling with deposit. Oh and Su (2018) found that with the increase in market scale, enterprises should expand the advance selling capacity in service industries such as restaurants. Yin and Wang et al., (2019) thought that the uncertainty of the value in the advance selling period induced consumers’ strategic delayed purchase behaviour, and the strategy of deposit appreciation could alleviate the negative impact brought by the uncertainty of product value in the advance selling. Pei et al., (2021) took the ‘deposit + final’ payment online promotional pre-sale model based on consumer strategic behaviour as the research goal and established three different models for providing retailers with optimal pre-sale strategies. Zhang and Yang (2021) analyzed the effects of several pre-order strategies for the retailer, namely, free pre-order, deposit pre-order and deposit expansion pre-order. Liu et al., (2023) proposed a combined new retail and pre-sales model and analyzed the impact of bounded consumer rationality on seller’s profitability. They found consumers preferred to bear a higher risk of deposit loss to achieve a higher purchase utility. Zhang et al., (2022a) investigated the effect of deposit expansion on retailer’s advance booking decisions and concluded that the retailer gained further profit under the advance selling strategy with a deposit.
Aversion is the strategic performance of consumers that plays an important role in consumers’ purchase decisions. Such as the consumers’ aversion to risk, there is literature considering risk-averse, and researching the impact of the consumer’s risk-averse attitude on the decision-making of supply chain members (Li et al., 2015, Zhang et al., 2021, Benioudakis et al., 2021). Some literature took loss aversion into account and analyzed the optimal decisions of the advance selling and pricing strategy (Zhao & Stecke, 2010; Wang et al., 2019).
In practice, consumers exhibit lead time aversion when products are not immediately available. Based on this, Hua et al., (2010) examined the impacts of delivery lead time and the customer acceptance in a centralized and decentralized dual-channel supply chain. Li et al., (2017) discussed the effects of retailers’ strategies with different prices and quoted delivery lead time decisions in a dual-channel supply chain. Through the analysis of Tmall sales data, Wang et al., (2020b) found that the remaining time of online pre-sale hurts consumers’ willingness to purchase. Based on the consumers’ time preference, Bai et al., (2017) considered the lead time aversion and analyzed the impact of pre-sale time and the profitability of pre-sale mode. Bai and Jiang (2017) compared the impact of the pre-sale mode and integrated normal sales mode on product market demand and business decisions when consumers have different time sensitivities. Wang et al., (2020a) developed four pre-sale strategies for maximizing the seller’s revenue. They found that with long pre-sale lead times, some consumers are negatively affected by their time preferences. Guo et al., (2020) analyzed the channel configuration strategy of pre-sales and found customer acceptance of the online channel is affected by the delivery lead time.
In summary, there were abundant studies on the advance selling supply chain considering consumers’ strategic behaviours, but most of them studied the influence of consumers’ strategic behaviours on retailers’ advance selling strategies, whilst fewer studies considered the influence of retailers’ advance selling and consumers’ behaviours on upstream manufacturers in the supply chain. Also, research on supply chain pricing strategies of AS mode with deposit is extremely lacking. In addition, there has been a lot of research related to consumer aversion, but there are very few studies focusing on AS supply chains considering consumer lead time aversion, and that is what this research focuses on.
3. Model
In this research, a two-period supply chain system consisting of a manufacturer and a retailer is considered. The first period is the advance selling period, in which the retailer pre-sells products to consumers at price |${p}_1$| before the production is completed, and the second period is spot selling period, in which the retailer sells products in stock at price |${p}_2$| after the production is completed.
The consumers in the market are divided into two categories: well-informed type and information-blocking type, with the proportions of |$\delta$| and |$1-\delta$|, respectively (|$\delta \in \left(0,1\right)$|). Only well-informed consumers are informed about AS (Shi et al., 2018, Zhang et al., 2021). Assumed the consumer’s valuation |$v$| of the product follows a uniform distribution between 0 and 1, and the probability density is 1 (Peng & Tian, 2022). Consumers have strategic behaviours and will make purchase decisions that maximize their utility. The total market size of potential consumers is normalized to 1.
The retailer sets a pre-sale price |${p}_1$| and collects a deposit |$\gamma$| to advance selling. In the first period, well-informed consumers arrive. They observe the AS price |${p}_1$| and decide whether to pay the deposit to get the buying qualification. Due to the lack of detailed evaluation of the products, the consumer’s valuation of the product is expected valuation (Oh & Su, 2018; Shi et al., 2018; Yin & Wang, 2019). At the beginning of the second period, the information-blocking consumers arrive and all consumers will realize their valuations (Zhao et al., 2016; Yin & Wang, 2019; Zhang et al., 2022b). In addition, if consumers who pay the deposit in advance give up the purchase, the deposit will not be refunded (Huang et al., 2017).
There is a time |$t$| from well-informed consumers pay the deposit to actual delivery (that is, distribution lead time). The longer the distribution lead time is, the more dissatisfied the consumers always are. Therefore, it is assumed that the negative impact of distribution lead time on consumer utility in AS period is |$\xi t$|, which |$\xi$| indicates the sensitivity of consumers to distribution lead time. But from the manufacturer’s point of view, AS orders can realize large-scale production. And the longer the distribution lead time is, the more obvious the scale effect is and the lower the unit cost is (Cai & Li, 2023, Imen et al., 2019). Here we suppose the manufacturer’s unit cost is |$c$| under conventional production. Therefore, it is assumed that the unit production cost of AS orders is |$c/t$| (Bai & Jiang, 2019). Furthermore, both the manufacturer and the retailer are rational. The manufacturer produces according to the order and has the sufficient production capacity, regardless of shortage.
The analysis of consumers purchasing decision is based on rational expectations equilibrium (Zhao et al., 2016; Oh & Su, 2018). In the first period, the retailer decides the deposit |$\gamma$| and the AS price |${p}_1$|, the consumers decide to pre-order or wait. If a consumer decides to pre-order, he will pay the deposit. And then, at the beginning of the second period, information-blocking consumers arrive and all consumers’ valuation is realized. The well-informed consumers who have pre-ordered need to decide to pay the remaining price or give up. If he decides to pay the remaining price, his utility |${U}_1$| is diminished by distribution lead time. Meanwhile, the previously paid deposit and the waiting time cost are regarded as sunk costs, which are no longer considered in subsequent decisions (Oh & Su, 2018; Sun et al., 2018). If he decides to wait and buy in the spot period, his utility is expressed as |${U}_2$|. Information-blocking consumers make purchase decisions according to their utility during the selling period. To clearly express consumers’ purchasing activities, Fig. 1 shows consumers’ purchasing behaviour and its corresponding utility function (Zhao et al., 2016).
Consumers’ purchasing behaviour and utility function in two periods.
In the first period, the products are not launched into the market yet. The consumers lack product details and real experience. Therefore, the product valuation is expected valuation (Bai & Jiang, 2019). Refer to Oh and Su (2018), the consumer’s utility who pre-orders by paying a deposit in the first period can be expressed as:
The consumer’s utility who decides to wait and buy in the second period is as follows:
Game timing is as follows. In the first period, the manufacturer produces a new product which is sold to the retailer at the wholesale price. Observing the wholesale price, the retailer decides whether to make advance selling with a deposit to consumers. If the retailer determines not to pre-sell, the first period ends. Otherwise, if the retailer decides to pre-sell, the AS price and the deposit will be set. The informed consumers arrive. Meanwhile, the informed customers make the purchase decision, and the first period ends. In the second period, the information-blocking consumers arrive, and all consumers, including unordered consumers and new arrivals, will realize their valuations (Yin & Wang, 2019, Zhao et al., 2016). The retailer decides the spot selling price, and all consumers in the market make the purchase decision.
According to the consumer’s utility function, if|$E\left[{U}_1\right]\ge \max \left\{E\left[{U}_2\right],0\right\}$|is met, all informed consumers, which proportion is |$\delta$|, will pre-order (Wang et al., 2020a) and pay the deposit. This group of consumers will realize their product valuation at the beginning of the second period and decide whether to pay the remaining price. Only the consumer whose valuation satisfy |$v-\left({p}_1-\gamma \right)\ge 0$| will buy. Therefore, the demand function of the first period is |${D}_1^{AS}=\left(1-\left({p}_1-\gamma \right)\right)\delta$|, and the demand function of the second period is|${D}_2^{AS}=\left(1-{p}_2\right)\left(1-\delta \right)$|.
When |$E\left[{U}_1\right]<\max \left\{E\left[{U}_2\right],0\right\}$|, even if the retailer carries out advance selling, no consumers will participate. All consumers will make their purchase decision in the second period. In this case, the demand function is |${D}_2^{NAS}=1-{p}_2$|.
The related parameters and notation settings are shown in Table 1.
Parameter definition and explanation of the model
| notation | Explanation |
|---|---|
| |$v$| | Consumers’ valuation of products, and |$v\sim U\left[0,1\right]$| |
| |${U}_i$| | The utility of consumers in the |$i$| period, |$i=1,2$| |
| |$w$| | Wholesale price of unit product given by the manufacturer to the retailer |
| |$\gamma$| | Deposit charged by the retailer from consumers in the first period |
| |${p}_1$| | Advance selling price of unit product decided by the retailer in the first period |
| |${p}_2$| | Spot selling price of unit product decided by the retailer in the second period |
| |$c$| | The manufacturer’s unit cost under conventional production |
| |$t$| | Time from paying a deposit to actual delivery, which is distribution lead time, |$t>1$| |
| |$\xi$| | Sensitivity of consumers to distribution lead time, |$\xi \in \left(0,1\right)$| |
| |$\delta$| | The proportion of well-informed consumers in market demand, |$\delta \in \left(0,1\right)$| |
| |${D}_i$| | Market demand in the |$i$| period, |$i=1,2$| |
| |${\pi}_{R,i}$| | Profit of the retailer in the |$i$| period, |$i=1,2$| |
| |${\pi}_M$| | Profit of the manufacturer |
| AS/NAS | Represents two scenarios: advance selling mode and no advance selling mode |
| notation | Explanation |
|---|---|
| |$v$| | Consumers’ valuation of products, and |$v\sim U\left[0,1\right]$| |
| |${U}_i$| | The utility of consumers in the |$i$| period, |$i=1,2$| |
| |$w$| | Wholesale price of unit product given by the manufacturer to the retailer |
| |$\gamma$| | Deposit charged by the retailer from consumers in the first period |
| |${p}_1$| | Advance selling price of unit product decided by the retailer in the first period |
| |${p}_2$| | Spot selling price of unit product decided by the retailer in the second period |
| |$c$| | The manufacturer’s unit cost under conventional production |
| |$t$| | Time from paying a deposit to actual delivery, which is distribution lead time, |$t>1$| |
| |$\xi$| | Sensitivity of consumers to distribution lead time, |$\xi \in \left(0,1\right)$| |
| |$\delta$| | The proportion of well-informed consumers in market demand, |$\delta \in \left(0,1\right)$| |
| |${D}_i$| | Market demand in the |$i$| period, |$i=1,2$| |
| |${\pi}_{R,i}$| | Profit of the retailer in the |$i$| period, |$i=1,2$| |
| |${\pi}_M$| | Profit of the manufacturer |
| AS/NAS | Represents two scenarios: advance selling mode and no advance selling mode |
Parameter definition and explanation of the model
| notation | Explanation |
|---|---|
| |$v$| | Consumers’ valuation of products, and |$v\sim U\left[0,1\right]$| |
| |${U}_i$| | The utility of consumers in the |$i$| period, |$i=1,2$| |
| |$w$| | Wholesale price of unit product given by the manufacturer to the retailer |
| |$\gamma$| | Deposit charged by the retailer from consumers in the first period |
| |${p}_1$| | Advance selling price of unit product decided by the retailer in the first period |
| |${p}_2$| | Spot selling price of unit product decided by the retailer in the second period |
| |$c$| | The manufacturer’s unit cost under conventional production |
| |$t$| | Time from paying a deposit to actual delivery, which is distribution lead time, |$t>1$| |
| |$\xi$| | Sensitivity of consumers to distribution lead time, |$\xi \in \left(0,1\right)$| |
| |$\delta$| | The proportion of well-informed consumers in market demand, |$\delta \in \left(0,1\right)$| |
| |${D}_i$| | Market demand in the |$i$| period, |$i=1,2$| |
| |${\pi}_{R,i}$| | Profit of the retailer in the |$i$| period, |$i=1,2$| |
| |${\pi}_M$| | Profit of the manufacturer |
| AS/NAS | Represents two scenarios: advance selling mode and no advance selling mode |
| notation | Explanation |
|---|---|
| |$v$| | Consumers’ valuation of products, and |$v\sim U\left[0,1\right]$| |
| |${U}_i$| | The utility of consumers in the |$i$| period, |$i=1,2$| |
| |$w$| | Wholesale price of unit product given by the manufacturer to the retailer |
| |$\gamma$| | Deposit charged by the retailer from consumers in the first period |
| |${p}_1$| | Advance selling price of unit product decided by the retailer in the first period |
| |${p}_2$| | Spot selling price of unit product decided by the retailer in the second period |
| |$c$| | The manufacturer’s unit cost under conventional production |
| |$t$| | Time from paying a deposit to actual delivery, which is distribution lead time, |$t>1$| |
| |$\xi$| | Sensitivity of consumers to distribution lead time, |$\xi \in \left(0,1\right)$| |
| |$\delta$| | The proportion of well-informed consumers in market demand, |$\delta \in \left(0,1\right)$| |
| |${D}_i$| | Market demand in the |$i$| period, |$i=1,2$| |
| |${\pi}_{R,i}$| | Profit of the retailer in the |$i$| period, |$i=1,2$| |
| |${\pi}_M$| | Profit of the manufacturer |
| AS/NAS | Represents two scenarios: advance selling mode and no advance selling mode |
4. Equilibrium analysis under different selling mode
4.1. Decision of the retailer
The model is solved by backward induction. Firstly, the retailer’s spot selling pricing decision in the second period is analyzed. To express the two-period demand function conveniently, the parameter |$\varepsilon$| is introduced. |$\varepsilon =1$| indicates that the retailer carries out advance selling, and |$\varepsilon =0$| indicates that the retailer does not carry out advance selling. From Section 3, we know that the market demand in the second period is |${D}_2=\left(1-{p}_2\right)\left(1-\varepsilon \delta \right)$|, and then the profit function of the retailer in the second period is:
The optimal spot selling price and profit function of the spot selling period are as follows:
The pricing decision of the retailer in the first period is analyzed. According to Section 3 informed consumers will participate in the advance selling only when the constraint |$E\left[{U}_1\right]\ge \max \left\{\ E\left[{U}_2\right],0\right\}$| is satisfied. Substituting (4) into the constraint|$E\left[{U}_1\right]\ge \max \left\{\mathrm{E}\left[{U}_2\right],0\right\}$|, we get:
Therefore, depending on whether the constraint is satisfied, the following two cases need to be discussed separately: the retailer does not implement advance selling and the retailer does advance selling.
(1) Retailer chooses not to advance selling.
When the retailer chooses not to advance selling, there is no need to consider advance selling price restrictions. All consumers will wait until the second period to purchase products, which is|$\varepsilon =0$|. Formula (5) could be expressed as:
(2) Retailer chooses to do advance selling.
When the retailer chooses to do advance selling, the constraints need to be met, and all well-informed consumers will participate in advance selling. At this time, the overall profit of the two periods is |${\pi}_R^{AS}={\pi}_{R,1}+{\pi}_{R,2}^{\ast }$|, where |${\pi}_{R,1}=\gamma \delta +\left({p}_1-\gamma -w\right)\left(1-\left({p}_1-\gamma \right)\right)\delta$|. Meanwhile, the retailer’s decision variables are |${p}_1$| and |$\gamma$|, and the profit function (5) of the second period has nothing to do with these two decision variables. Therefore, it is only necessary to maximize the profit function of the advance selling in the first period, and the objective function and the constraint are as follows:
By using the Karush-Kuhn-Tucker (KKT) condition, it is obtained:
Substituting formula (9) into |${\pi}_R^{AS}$|, it is obtained:
Rational retailer will choose the sales strategy to maximize their profits, which is
By comparing the retailer’s profit, here is a threshold of the wholesale price |$\overline{w}=1-2\left(2+\sqrt{3}\right) t\xi$|. The retailer’s profit function is as follows:
When the retailer chooses to advance selling, the AS price needs to be lower than a certain threshold to meet consumers’ expectations, which however reduces the retailer’s marginal profit. Thus, only when the manufacturer also gives out some profits, that is, the wholesale price of the manufacturer is lower than a certain threshold, the rational retailer will be willing to advance selling.
4.2. Decision of the manufacturer
The manufacturer’s optimal decision is related to the retailer’s profit function. Under different wholesale prices given by the manufacturer, the retailer may or may not advance selling.
(1) Retailer chooses not to advance selling (|$w>\overline{w}$|)
When the retailer does not advance selling, the profit function of the manufacturer is |${\pi}_M^{NAS}=\left(w-c\right)\left(1-{p}_2\right)$|, and formula (4) is substituted into the profit function as follows:
So, the optimal wholesale price is |${w}^{NAS\ast }=\left(1+c\right)/2$| and the profit is |${\pi}_M^{NAS\ast }={\left(1-c\right)}^2/8$|. Considering the retailer’s profit function, the optimal equilibrium solution exists only when |${w}^{NAS\ast }>\overline{w}$|. Therefore, there is a critical threshold value |${\xi}_0=\frac{1-c}{\left(8+4\sqrt{3}\right)t}$|, and when |$\xi >{\xi}_0$|, the optimal equilibrium solution exists without advance selling.
(2) Retailer chooses to advance selling (|$w\le \overline{w}$|)
When the retailer chooses to advance selling, the manufacturer has enough time to prepare goods for orders in AS period, which can realize economies of scale in product production. At this time, the unit production cost of the product is assumed to be |$c/t$|(Bai & Jiang, 2019,), and the unit production cost is assumed to be |$c$| for the orders in the spot selling period. The profit function of the manufacturer is as follows:
Substituting the retailer’s pricing decision into the above formula, we have:
|${\pi}_M^{AS}$| is negative definite about |$w$|. According to the first order condition, the optimal solution is obtained as: |${w}_0^{AS}=\frac{t+ ct+2 c\delta +\delta t- c\delta t-2\delta{t}^2\xi }{2t+2\delta t}$|.
Considering the retailer’s participation constraint and the manufacturer is rational, the optimal wholesale price when the retailer does AS is |${w}^{AS\ast }=\min \left\{{w}_0^{AS},\overline{w}\right\}$|, which is obtained by comparing |${w}_0^{AS}$| and |$\overline{w}$|:
Here, |${\xi}_1=\min \left\{\frac{\left( c\delta +\delta -c+1\right)t-2 c\delta}{2\left(2\sqrt{3}\delta +3\delta +2\sqrt{3}+4\right){t}^2},\frac{t- ct+\delta t-3 c\delta t+2 c\delta}{2\delta{t}^2}\right\}$|. The manufacturer will maximize its own profit under the premise of considering the retailer’s profit function. The manufacturer’s objective function is:
Under the advance selling with deposit mode and no advance selling mode, the optimal equilibrium solution has the following three cases, as shown in Table 2.
Threshold |${\xi}_2=\min \left\{\frac{X_1+{X}_2}{4\left(\left(5+3\sqrt{3}\right)\delta +7+4\sqrt{3}\right){t}^2},\frac{1-c}{4t+2\sqrt{3}t}\right\}$|,
The proof is shown in the appendix.
5. Comparative analysis under different selling mode
5.1. Pareto analysis
To analyze whether the retailer should do AS, the NAS and AS equilibrium results are compared. The following conclusions are obtained.
Comparing the pricing strategy and market demand between advance selling and no advance selling, the following requirements are met:
(1) Retailer’s advance selling would create new market demand, which is |$ {D}^{AS}>{D}^{NAS}. $|
(2) The advance selling price and wholesale price respectively are both smaller than the situation when the retailer does not advance selling, that is |${p}_1^{AS\ast }<{p}_2^{NAS\ast }$|, |${w}^{AS\ast }<{w}^{NAS\ast }$|.
The proof is shown in the appendix.
Optimal equilibrium whilst advance selling with a deposit
| Advance Selling | No Advance Selling | ||
|---|---|---|---|
| I: |$0<\xi \le{\xi}_1$| | II: |${\xi}_1<\xi \le{\xi}_2$| | III: |${\xi}_2<\xi <1$| | |
| |${w}^{\ast }$| | |${w}_0^{AS}$| | |$\overline{w}$| | |${w}^{NAS^\ast }$| |
| |${p}_1^{\ast }$| | |$\frac{1}{8}\left(3{w}^{\ast 2}+2\left(8 t\xi +1\right){w}^{\ast }+12{t}^2{\xi}^2-8 t\xi +3\right)$| | N/A | |
| |${\gamma}^{\ast }$| | |$\frac{1}{8}\left(3{w}^{\ast 2}+2\left(8 t\xi -3\right){w}^{\ast }+12{t}^2{\xi}^2-16 t\xi +3\right)$| | N/A | |
| |${p}_2^{\ast }$| | |$\frac{1+{w}^{\ast }}{2}$| | |$\frac{1+{w}^{\ast }}{2}$| | |
| Advance Selling | No Advance Selling | ||
|---|---|---|---|
| I: |$0<\xi \le{\xi}_1$| | II: |${\xi}_1<\xi \le{\xi}_2$| | III: |${\xi}_2<\xi <1$| | |
| |${w}^{\ast }$| | |${w}_0^{AS}$| | |$\overline{w}$| | |${w}^{NAS^\ast }$| |
| |${p}_1^{\ast }$| | |$\frac{1}{8}\left(3{w}^{\ast 2}+2\left(8 t\xi +1\right){w}^{\ast }+12{t}^2{\xi}^2-8 t\xi +3\right)$| | N/A | |
| |${\gamma}^{\ast }$| | |$\frac{1}{8}\left(3{w}^{\ast 2}+2\left(8 t\xi -3\right){w}^{\ast }+12{t}^2{\xi}^2-16 t\xi +3\right)$| | N/A | |
| |${p}_2^{\ast }$| | |$\frac{1+{w}^{\ast }}{2}$| | |$\frac{1+{w}^{\ast }}{2}$| | |
Optimal equilibrium whilst advance selling with a deposit
| Advance Selling | No Advance Selling | ||
|---|---|---|---|
| I: |$0<\xi \le{\xi}_1$| | II: |${\xi}_1<\xi \le{\xi}_2$| | III: |${\xi}_2<\xi <1$| | |
| |${w}^{\ast }$| | |${w}_0^{AS}$| | |$\overline{w}$| | |${w}^{NAS^\ast }$| |
| |${p}_1^{\ast }$| | |$\frac{1}{8}\left(3{w}^{\ast 2}+2\left(8 t\xi +1\right){w}^{\ast }+12{t}^2{\xi}^2-8 t\xi +3\right)$| | N/A | |
| |${\gamma}^{\ast }$| | |$\frac{1}{8}\left(3{w}^{\ast 2}+2\left(8 t\xi -3\right){w}^{\ast }+12{t}^2{\xi}^2-16 t\xi +3\right)$| | N/A | |
| |${p}_2^{\ast }$| | |$\frac{1+{w}^{\ast }}{2}$| | |$\frac{1+{w}^{\ast }}{2}$| | |
| Advance Selling | No Advance Selling | ||
|---|---|---|---|
| I: |$0<\xi \le{\xi}_1$| | II: |${\xi}_1<\xi \le{\xi}_2$| | III: |${\xi}_2<\xi <1$| | |
| |${w}^{\ast }$| | |${w}_0^{AS}$| | |$\overline{w}$| | |${w}^{NAS^\ast }$| |
| |${p}_1^{\ast }$| | |$\frac{1}{8}\left(3{w}^{\ast 2}+2\left(8 t\xi +1\right){w}^{\ast }+12{t}^2{\xi}^2-8 t\xi +3\right)$| | N/A | |
| |${\gamma}^{\ast }$| | |$\frac{1}{8}\left(3{w}^{\ast 2}+2\left(8 t\xi -3\right){w}^{\ast }+12{t}^2{\xi}^2-16 t\xi +3\right)$| | N/A | |
| |${p}_2^{\ast }$| | |$\frac{1+{w}^{\ast }}{2}$| | |$\frac{1+{w}^{\ast }}{2}$| | |
Proposition 2 indicates that when the retailer does AS, consumers’ utility constraints need to be met, and the retailer has to offer a lower AS price to attract consumers, so the AS price will be lower than the spot selling price. The manufacturer needs to set a lower wholesale price to ensure the retailer could do AS.
The retailer could implement advance selling with deposit only when |$\xi <{\xi}_2$|. Once the advance selling is implemented, the income of the two members will achieve Pareto improvement, namely |${\pi}_M^{AS}\ge{\pi}_M^{NAS}$|, |${\pi}_R^{AS}\ge{\pi}_R^{NAS}$|.
The proof is shown in the appendix.
Proposition 3 indicates that advance selling can make both manufacturer and retailer get Pareto improvement. Consumers’ sensitivity to distributed lead time should be kept at a small level. If it exceeds the threshold |${\xi}_2$|, no customer will pre-order, and the advance selling could not be realized. Thus, it is vital to increase |${\xi}_2$| for realizing advance selling to gain more income for both sides.
With the increase in the number of well-informed consumers, the feasible domain of advance selling expands. When |$t\le{t}_1$|, as the distribution lead time increases, the feasible domain of advance selling expands. And when |$t>{t}_1$|, as the delivery lead time increases, the feasible domain of advance selling narrows. Here, |${t}_1=\frac{\left(6+4\sqrt{3}\right) c\delta}{\left(1+\sqrt{3}\right)\delta +\left(2+\sqrt{3}\right)\left( c\delta -c+1\right)}$|.
The proof is shown in the appendix.
Proposition 4 shows that, with the increase of well-informed consumers, the feasible domain of advance selling will also expand. The distribution lead time of advance selling is a double-edged sword for the members of the supply chain. Its increase, on the one hand, helps the manufacturer to achieve economies of scale in product production. On the other hand, it will reduce consumers’ willingness to purchase products during the advance selling period. Therefore, moderate distribution lead time can maximize the feasible range of advance selling.
5.2. Numerical analysis
Consumers strategically make purchase choices when the retailer does AS. To explore whether pre-sale is beneficial to consumers, the consumer surplus is calculated: |$ C{S}^{AS} $|
By comparison, the following conclusions can be drawn.
Compared with no advance selling, the overall consumer surplus of advance selling mode is significantly improved, that is, |$C{S}^{AS}\ge C{S}^{NAS}$|. Only consumers who pay the deposit but do not pay the final payment get a negative consumer surplus.
For a more intuitive expression, depict the figure of consumer surplus through numerical experiments. Let |$c=0.05$|, |$\delta =0.8$|, |$t=1.2$|, and draw the consumer surplus in advance selling mode and no advance selling mode as shown in Fig. 2.
Comparison of consumer surplus between advance selling and no advance selling.
As shown in Fig. 2, the blue and black lines represent the consumer surplus in the AS and NAS mode. In the public feasible range |$0<\xi \le{\xi}_2$|, advance selling could improve consumer surplus. Furthermore, when |${\xi}_1<\xi \le{\xi}_2$|, the consumer surplus is significantly higher than it in other ranges.
Further, consumer surplus is shown in Fig. 3. In the AS mode, consumer surplus, who pay a deposit only is shown by the blue line, who pay a deposit and the final payment is shown by the green line, and who buy in spot period is shown by the red line. In the NAS mode, consumer surplus is shown by the black line. If the deposit is paid, the well-informed consumer will get the highest consumer surplus by paying the final payment and will get the lowest consumer surplus by giving up the purchase. However, if the informed consumers wait until the spot period to buy, the consumer surplus is less than the situation in the retailer does not sell in advance.
Comparison of all types of consumer surplus in advance selling mode and no advance selling mode.
Proposition 5 indicates the consumer surplus is the largest when the consumer pre-orders and pays the final payment. That is, the strategic behaviour of consumers brings better benefits for them. As a result, the AS mode can achieve a win–win situation for all parties in the supply chain under certain conditions. From the consumer’s view, it is beneficial to actively acquire product information and improve strategic decision-making. From the perspective of the manufacturer and the retailer, they should increase the publicity of advance selling, and help consumers to become professional strategic consumers.
6. Conclusions
This research studies the pricing strategy of a supply chain with a manufacturer and a retailer. We analyze the customers’ purchase behaviour in advance selling with deposit by using utility theory and obtain the pricing decision of the supply chain by using Stackelberg model. Compared with no advance selling, we find that the wholesale price and the spot selling price will decrease in the case of advance selling. The retailer’s advance selling with a deposit could Pareto improve the profits of the whole supply chain members when the lead time has little impact on the consumers. More well-informed consumers and moderate advance selling distribution lead time could expand the retailer’s pre-sale possibilities by enlarging the feasible range of advance selling.
According to the research of this paper, we get the following management implications. To achieve a win–win profit of supply chain members, the retailer should actively implement advance selling strategy under a certain condition. He should make efforts to spread advance selling information and the manufacturer should help the retailer to promote the advance selling. In addition, the retailer should control the pre-sale lead time, not blindly control the cost to extend the pre-sale lead time, so as not to reduce the purchase intention of consumers. This research on consumer lead-time aversion is still quite superficial, and more in-depth research is needed in the future.
Funding
Hainan Provincial Natural Science Foundation of China (719QN202); University Scientific research project of Hainan Science and Technology Department (Hnsk2018-18).
Data Availability Statement
Data sharing is not applicable to this article as no new data were created or analyzed in this study.
References
Appendix
A. Appendix 1: Prove of the proposition 1
From the analysis of (1), when |$\xi >{\xi}_0$|, the equilibrium solution of no advance selling exists. By comparing the sizes of |${\xi}_0$| and |${\xi}_1$|, it is found that |${\xi}_0<{\xi}_1$| holds, so the profit of the manufacturer needs to be discussed in three sections. When |$0<\xi \le{\xi}_0$|, the equilibrium solution of no advance selling does not exist, and the manufacturer will set the wholesale price of advance selling. Meanwhile, because of |${\xi}_0<{\xi}_1$|, in this interval |${w}_0^{AS}<\overline{w}$| holds and the max value could be obtained, and manufacturer choose the optimal wholesale price |${w}_0^{AS}$|. When |${\xi}_0<\xi \le{\xi}_1$|, the manufacturer will compare the profits of |${\pi}_M^{AS}\left({w}_0^{AS}\right)$| and |${\pi}_M^{NAS}\left({w}^{NAS\ast}\right)$|, and find that |${\pi}_M^{AS}\left({w}_0^{AS}\right)>{\pi}_M^{NAS}\left({w}^{NAS\ast}\right)$| holds, so the optimal wholesale price of the manufacturer is |${w}_0^{AS}$|. When |${\xi}_1<\xi <1$|, manufacturers will compare the profits of |${\pi}_M^{AS}\left(\overline{w}\right)$| and |${\pi}_M^{NAS}\left({w}^{NAS\ast}\right)$|, and it is found that exists a parameter |${\xi}_2$| that when |${\xi}_1<\xi \le{\xi}_2$|, |${\pi}_M^{AS}\left(\overline{w}\right)\ge{\pi}_M^{NAS}\left({w}^{NAS\ast}\right)$|, and when |${\xi}_2<\xi <1$|, |${\pi}_M^{AS}\left(\overline{w}\right)<{\pi}_M^{NAS}\left({w}^{NAS\ast}\right)$|. Thus, the optimal wholesale price of manufacturer is selected as follows:
Bring the equilibrium result of wholesale price into the retailer’s pricing response function could get Table 2, and the proposition is proved.
B. Appendix 2: Prove of proposition 3
Firstly, analyze the profit of the manufacturer. From the analysis in expression (17), it could be seen that the manufacturer, as the leader of the game, will compare its own profit when the retailer advance selling and its own profit when the retailer does not advance selling, and make the decision with the maximum profit. Therefore, when advance selling, the profit of the manufacturer will definitely improve compared with that of no advance selling.
Secondly, to analyze the profit of the retailer, substitute the equilibrium solution in Table 2 into the profit function of the retailer. It is found that when |$0<\xi \le{\xi}_1$|,
When |${\xi}_1<\xi \le{\xi}_2$|, |${\pi}_R^{AS}={\pi}_R^{AS}\left(\overline{w}\right)=\left(7+4\sqrt{3}\right){t}^2{\xi}^2$|. When retailer does not advance selling,|${\pi}_R^{NAS}=\frac{1}{16}{\left(1-c\right)}^2$|, it is found that when the wholesale price takes the extreme value solution |${w}_0^{AS}$|, that is, |$0<\xi \le{\xi}_1$|, exists a threshold |${\xi}_3$|, |${\xi}_3=\frac{-t\left(3\left(c+1\right){\delta}^2+\left(5-c\right)\delta -2c+2\right)+6c{\delta}^2+4 c\delta +2\sqrt{X_3}}{2\left(3{\delta}^2-2\delta -4\right){t}^2}$|, |${X}_3={\left(1+\delta \right)}^2\left(\left(6{\delta}^2-7\delta +8\right){t}^2-4\left(3{\delta}^2-5\delta +2\right)t+4{c}^2\left(3{\delta}^2-2\delta \right)\right)+c\left(6{\delta}^2-\delta -8\right){t}^2-4c\left(3{\delta}^2+\delta -2\right)t.$|
When |$0<\xi \le{\xi}_3$|, |${\pi}_R^{AS}\left({w}_0^{AS}\right)\ge{\pi}_R^{NAS}$|, comparing the size of |${\xi}_1$| and |${\xi}_3$|, it is found that |${\xi}_3\ge{\xi}_1$| holds. Thus, in the feasible region of extreme value solution, |${\pi}_R^{AS}\left({w}_0^{AS}\right)\ge{\pi}_R^{NAS}$| holds. When the wholesale price takes boundary value solution |$\overline{w}$|, that is, |${\xi}_1<\xi \le{\xi}_2$|, exists a threshold |${\xi}_4$|, and |${\xi}_4=\sqrt{\frac{1-2c+{c}^2}{112{t}^2+64\sqrt{3}{t}^2}}$|. When |$\xi \ge{\xi}_4$|, |${\pi}_R^{AS}\left(\overline{w}\right)\ge{\pi}_R^{NAS}$|, comparing the size of |${\xi}_1$| and |${\xi}_4$| could find that |${\xi}_4<{\xi}_1$| holds. Thus, in the feasible region of boundary value solution, |${\pi}_R^{AS}\left(\overline{w}\right)\ge{\pi}_R^{NAS}$| holds. In conclusion, |${\pi}_R^{AS}\ge{\pi}_R^{NAS}$| holds all the time.
C. Appendix 3: Prove of proposition 4
As it is seen from Table 2, when |$0<\xi \le{\xi}_2$|, the advance selling with deposit is the equilibrium result of the supply chain. Derivation shows that within the feasible range, |$\frac{\partial{\xi}_2}{\partial \delta }>0$| holds, which proves that with the increase of the number of well-informed consumers, the feasible range of advance selling expands. Let |$\frac{\partial{\xi}_2}{\partial t}>0$|, we have:
Therefore, it could be proved that the feasible region of advance selling will expand at first and then shrink with the increase of advance selling distribution lead time.
