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doi: 10.3934/jimo.2021217
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## Pre-sale ordering strategy based on the new retail context considering bounded consumer rationality

 Business School, SiChuan University, Chengdu 610065, China

*Corresponding author: Chun-xiang Guo

Received  January 2021 Revised  July 2021 Early access December 2021

Fund Project: The study is supported by the National Natural Science Foundation of China (Project No.71871150)

The purpose of this paper is to study the impact of bounded consumer rationality on the order quantity and profitability of the seller in the advance period and the spot period in the context of the combination of new retail and pre-sale. In this paper, we develop a seller order model in the context of the combination of new retail and pre-sale, with and without reference price dependence. Besides, the model considers the order cancellation and delayed purchase behavior of consumers. We then discuss the optimal profit and optimal order quantity under different conditions and the effect of different reference price dependence and value-added offline service on them. Our research shows that: First, the seller tends to set the deposit too low in pre-sales. Second, reference price dependence has different effects on order quantities in different periods. The seller should pay more attention to the impact of reference price dependence. Third, on the whole, consumer rationality benefits the seller. The seller, or the public policymaker, can benefit new retail businesses by increasing consumer rationality. Last, in the new retail context, an increase in offline service value-added, even if it increases total order quantity, is not always beneficial to the seller and may reduce profits. Therefore, the seller should weigh all factors to determine the optimal value-added offline services.

Citation: Yu Liu, Chun-xiang Guo, Hong Zhou, Xin-yi Chen. Pre-sale ordering strategy based on the new retail context considering bounded consumer rationality. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021217
##### References:

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##### References:
The pre-sale model based on the new retail context
Consumer market segmentation based on different wait time sensitivities
Comparison of orders in the advance period with or without reference price dependence
Comparison of orders in the advance period with or without reference price dependence
Changes in the seller's profit over the advance period with acquisition and loss coefficients
Changes in the seller's profit over the spot period with acquisition and loss coefficients
The impact of value-added offline service on dual-channel order quantities
The impact of value-added offline services on dual-channel profits
Market segmentation of consumers in the spot period
The meaning of the symbols
 $\xi$ Probability of consumers not canceling their orders during the advance period. It's the consumer's prediction of their behavior.$(1-\xi)$ is the probability that the consumer will cancel the order.$\xi \in [0, 1]$ $\beta$ Consumer preference for online channels, $(1-\beta)$is consumers' preference for offline channels. $c$, $c_0$, $c_1$ Cost of storage per unit of product per unit of time/Cost of value-added services per unit of product in the offline channel/Order costs for the seller. $p$, $w$, $S$ Price of the unit of product in the spot period/Wholesale cost per unit of product./Residual value of unit of product $\lambda$, $v$ The discount rate of a product's advance price compared to its spot price/Consumer valuation of products. $\alpha$, $g$ Advance deposits for unit products/Out-of-stock losses per unit of product. $\eta$ Consumer sensitivity to waiting time for the seller shipments. $t_0$ Point in time when the seller sends an order request. $T_1$, $T_2$ The end of the advance period/The end of the spot period. $L$ The lead time, i.e. from the time an order is placed by the seller to the time the goods are delivered to the warehouse. $r_0$, $r_1$, $r_2$ Consumer aversion coefficient for "deposit loss"/Consumer's reference dependence coefficient on "acquisition"/The end of the advance period.$0 < r_1 < {r_2} \le 1.$ $X$ Consumers who are concerned about pre-sales and they will enter the market during the pre-sales period.$X\sim N({\mu _x}, \delta _x^2).$ $Y$ Consumers who are concerned about pre-sales and they will enter the market during the pre-sales period$Y\sim N({\mu _y}, \delta _y^2)$ $\tau$ $\tau \in (1, + \infty )$, $\tau Y$represents the number of consumers reaching the market in the new retail model in the spot period. $S_{off}$ Value-added services for consumers in offline channels, $S_{off}\in (l, + \infty )$ $\rho$ Indicates the correlation coefficient between market size in period $t_0\sim T_1$and in period. $\rho_x, \rho_y$ $\rho_x$ represents the correlation coefficient between the market size in the advance period and in period $0\sim t_0$.$\rho_y$represents the correlation coefficient between the market size in the spot period and in period $0\sim t_0$. $U_a^{(i)}$ In case $(i)$, the utility of the consumer's purchase during the advance period, $i={1, 2},$1 and 2 denote the new retail marketing model when reference price dependence is not considered and considered, respectively. $U_s^{(i)}$ In case $(i)$, the utility of the consumer's purchase in the spot period, $s={on, off}$, on and off denote online and offline channels respectively. $\Pi_j^{(i)}$ In case $(i)$, the seller's profit during stage j, $j={1, 2, 3}$, 1, 2, 3 denote the period $0\sim t_0$, $t_0\sim T_1$, $T_1\sim T_2$, respectively. $D_j^{(i)}$, $D_j^{(i)'}$ In case $(i)$, the market demand in period $j$, $D_j^i\sim N(\mu _j^i, {(\delta _j^i)^2})$/In case $(i)$, the updated market demand in period $j$, $D_j^{i'}\sim N(\mu_j^{i'}, {(\delta_j^{i'})^2})$. $C^{(i)}$ In case $(i)$, the seller's total inventory cost. $Q_j^{(i)}$, $x_j^{(i)}$ In case $(i)$, the order quantity of the seller to meet the demand in period$j$/In case $(i)$, the actual quantity of orders within period $j$. $\eta_i$ In case $(i)$, the time-sensitive thresholds for when a consumer's purchase utility in the advance period equals the purchase utility in the spot period. $\theta_i$ In case $(i)$, the threshold at which a consumer's purchase utility equals zero during the presale period.
 $\xi$ Probability of consumers not canceling their orders during the advance period. It's the consumer's prediction of their behavior.$(1-\xi)$ is the probability that the consumer will cancel the order.$\xi \in [0, 1]$ $\beta$ Consumer preference for online channels, $(1-\beta)$is consumers' preference for offline channels. $c$, $c_0$, $c_1$ Cost of storage per unit of product per unit of time/Cost of value-added services per unit of product in the offline channel/Order costs for the seller. $p$, $w$, $S$ Price of the unit of product in the spot period/Wholesale cost per unit of product./Residual value of unit of product $\lambda$, $v$ The discount rate of a product's advance price compared to its spot price/Consumer valuation of products. $\alpha$, $g$ Advance deposits for unit products/Out-of-stock losses per unit of product. $\eta$ Consumer sensitivity to waiting time for the seller shipments. $t_0$ Point in time when the seller sends an order request. $T_1$, $T_2$ The end of the advance period/The end of the spot period. $L$ The lead time, i.e. from the time an order is placed by the seller to the time the goods are delivered to the warehouse. $r_0$, $r_1$, $r_2$ Consumer aversion coefficient for "deposit loss"/Consumer's reference dependence coefficient on "acquisition"/The end of the advance period.$0 < r_1 < {r_2} \le 1.$ $X$ Consumers who are concerned about pre-sales and they will enter the market during the pre-sales period.$X\sim N({\mu _x}, \delta _x^2).$ $Y$ Consumers who are concerned about pre-sales and they will enter the market during the pre-sales period$Y\sim N({\mu _y}, \delta _y^2)$ $\tau$ $\tau \in (1, + \infty )$, $\tau Y$represents the number of consumers reaching the market in the new retail model in the spot period. $S_{off}$ Value-added services for consumers in offline channels, $S_{off}\in (l, + \infty )$ $\rho$ Indicates the correlation coefficient between market size in period $t_0\sim T_1$and in period. $\rho_x, \rho_y$ $\rho_x$ represents the correlation coefficient between the market size in the advance period and in period $0\sim t_0$.$\rho_y$represents the correlation coefficient between the market size in the spot period and in period $0\sim t_0$. $U_a^{(i)}$ In case $(i)$, the utility of the consumer's purchase during the advance period, $i={1, 2},$1 and 2 denote the new retail marketing model when reference price dependence is not considered and considered, respectively. $U_s^{(i)}$ In case $(i)$, the utility of the consumer's purchase in the spot period, $s={on, off}$, on and off denote online and offline channels respectively. $\Pi_j^{(i)}$ In case $(i)$, the seller's profit during stage j, $j={1, 2, 3}$, 1, 2, 3 denote the period $0\sim t_0$, $t_0\sim T_1$, $T_1\sim T_2$, respectively. $D_j^{(i)}$, $D_j^{(i)'}$ In case $(i)$, the market demand in period $j$, $D_j^i\sim N(\mu _j^i, {(\delta _j^i)^2})$/In case $(i)$, the updated market demand in period $j$, $D_j^{i'}\sim N(\mu_j^{i'}, {(\delta_j^{i'})^2})$. $C^{(i)}$ In case $(i)$, the seller's total inventory cost. $Q_j^{(i)}$, $x_j^{(i)}$ In case $(i)$, the order quantity of the seller to meet the demand in period$j$/In case $(i)$, the actual quantity of orders within period $j$. $\eta_i$ In case $(i)$, the time-sensitive thresholds for when a consumer's purchase utility in the advance period equals the purchase utility in the spot period. $\theta_i$ In case $(i)$, the threshold at which a consumer's purchase utility equals zero during the presale period.
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