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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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Ö. S. Alp and E. Büyükbebeci, CMARS and GAM & CQP-modern optimization methods applied to international credit default prediction, J. Comput. Appl. Math., 235 (2011), 4639-4651.  doi: 10.1016/j.cam.2010.04.039.

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T. BaiM. Wu and S. X. Zhu, Pricing and ordering by a loss averse newsvendor with reference dependence, Transportation Research Part E: Logistics and Transportation Review, 131 (2019), 343-365.  doi: 10.1016/j.tre.2019.10.003.

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I. BaltasA. Xepapadeas and A. N. Yannacopoulos, Robust control of parabolic stochastic partial differential equations under model uncertainty, Eur. J. Control, 46 (2019), 1-13.  doi: 10.1016/j.ejcon.2018.04.004.

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N. Beck and D. Rygl, Categorization of multiple channel retailing in Multi-, Cross-, and Omni-Channel Retailing for retailers and retailing, Journal of Retailing and Consumer Services, 27 (2015), 170-178.  doi: 10.1016/j.jretconser.2015.08.001.

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D. R. BellS. Gallino and A. Moreno, Offline showrooms in omnichannel retail: Demand and operational benefits, Management Science, 64 (2018), 1629-1651.  doi: 10.1287/mnsc.2016.2684.

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M. C. ChengT. P. HsiehH. M. Lee and L. Y. Ouyang, Optimal ordering policies for deteriorating items with a return period and price-dependent demand under two-phase advance sales, Operational Research, 20 (2020), 585-604.  doi: 10.1007/s12351-017-0359-9.

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B. CrettezN. Hayek and G. Zaccour, Existence and characterization of optimal dynamic pricing strategies with reference-price effects, CEJOR Cent. Eur. J. Oper. Res., 28 (2020), 441-459.  doi: 10.1007/s10100-019-00645-w.

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B. HeW. Pan and Y. Yang, Joint pricing and overbooking policy in a full payment presale mechanism of new products, Int. Trans. Oper. Res., 26 (2019), 1810-1827.  doi: 10.1111/itor.12436.

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A. ÖzmenE. Kropat and G. W. Weber, Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty, Optimization, 66 (2017), 2135-2155.  doi: 10.1080/02331934.2016.1209672.

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M. M. Pereira and E. M. Frazzon, A data-driven approach to adaptive synchronization of demand and supply in omni-channel retail supply chains, International Journal of Information Management, 57 (2021), 102165.  doi: 10.1016/j.ijinfomgt.2020.102165.

[31]

M. PervinS. K. Roy and G. W. Weber, Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Ann. Oper. Res., 260 (2018), 437-460.  doi: 10.1007/s10479-016-2355-5.

[32]

M. PervinS. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price-and stock-dependent demand: A trade-credit policy, J. Ind. Manag. Optim., 15 (2019), 1345-1373.  doi: 10.3934/jimo.2018098.

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M. M. SerefO. SerefA. Alptekinoglu and S. S. Erengüc, Advance selling to strategic consumers, Comput. Manag. Sci., 13 (2016), 597-626.  doi: 10.1007/s10287-016-0264-3.

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C. S. TangK. RajaramA. Alptekinoglu and J. Ou, The benefits of advance booking discount programs: Model and analysis, Management Science, 50 (2004), 465-478.  doi: 10.1287/mnsc.1030.0188.

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F. von Briel, The future of omnichannel retail: A four-stage Delphi study, Technological Forecasting and Social Change, 132 (2018), 217-229. 

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X. Wang and C. T. Ng, New retail versus traditional retail in e-commerce: Channel establishment, price competition, and consumer recognition, Ann. Oper. Res., 291 (2020), 921-937.  doi: 10.1007/s10479-018-2994-9.

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show all references

References:
[1]

A. AflakiP. Feldman and R. Swinney, Becoming strategic: Endogenous consumer time preferences and multiperiod pricing, Oper. Res., 68 (2020), 1116-1131.  doi: 10.1287/opre.2019.1937.

[2]

Ö. S. Alp and E. Büyükbebeci, CMARS and GAM & CQP-modern optimization methods applied to international credit default prediction, J. Comput. Appl. Math., 235 (2011), 4639-4651.  doi: 10.1016/j.cam.2010.04.039.

[3]

P. Aylan, G. W. Weber and F. Yerlikaya, Continuous optimization applied in MARS for modern applications in finance, science and technology, ISI Proceedings of 20th Mni-EURO Conference Continuous Optimization and Knowledge-Based Technologies, (2008), 317–322.

[4]

T. BaiM. Wu and S. X. Zhu, Pricing and ordering by a loss averse newsvendor with reference dependence, Transportation Research Part E: Logistics and Transportation Review, 131 (2019), 343-365.  doi: 10.1016/j.tre.2019.10.003.

[5]

I. BaltasA. Xepapadeas and A. N. Yannacopoulos, Robust control of parabolic stochastic partial differential equations under model uncertainty, Eur. J. Control, 46 (2019), 1-13.  doi: 10.1016/j.ejcon.2018.04.004.

[6]

N. Beck and D. Rygl, Categorization of multiple channel retailing in Multi-, Cross-, and Omni-Channel Retailing for retailers and retailing, Journal of Retailing and Consumer Services, 27 (2015), 170-178.  doi: 10.1016/j.jretconser.2015.08.001.

[7]

D. R. BellS. Gallino and A. Moreno, Offline showrooms in omnichannel retail: Demand and operational benefits, Management Science, 64 (2018), 1629-1651.  doi: 10.1287/mnsc.2016.2684.

[8]

T. Boyaci and Ö. Özer, Information acquisition for capacity planning via pricing and advance selling: When to stop and act?, Oper. Res., 58 (2010), 1328-1349.  doi: 10.1287/opre.1100.0798.

[9]

M. C. ChengT. P. HsiehH. M. Lee and L. Y. Ouyang, Optimal ordering policies for deteriorating items with a return period and price-dependent demand under two-phase advance sales, Operational Research, 20 (2020), 585-604.  doi: 10.1007/s12351-017-0359-9.

[10]

B. CrettezN. Hayek and G. Zaccour, Existence and characterization of optimal dynamic pricing strategies with reference-price effects, CEJOR Cent. Eur. J. Oper. Res., 28 (2020), 441-459.  doi: 10.1007/s10100-019-00645-w.

[11]

M. Graczyk-Kucharska, M. Szafrański and S. Gütmen, Modeling for human resources management by data mining, analytics and artificial intelligence in the logistics departments, Smart and Sustainable Supply Chain and Logistics-Trends, Challenges, Methods and Best Practices. Springer, Cham, (2011), 291–303. doi: 10.1007/978-3-030-61947-3_20.

[12]

V. Gupta and A. Chutani, Supply chain financing with advance selling under disruption, Int. Trans. Oper. Res., 27 (2020), 2449-2468.  doi: 10.1111/itor.12663.

[13]

B. HeX. Gan and K. Yuan, Entry of online presale of fresh produce: A competitive analysis, European J. Oper. Res., 272 (2019), 339-351.  doi: 10.1016/j.ejor.2018.06.006.

[14]

B. HeW. Pan and Y. Yang, Joint pricing and overbooking policy in a full payment presale mechanism of new products, Int. Trans. Oper. Res., 26 (2019), 1810-1827.  doi: 10.1111/itor.12436.

[15]

S. HelmS. H. Kim and S. Van Riper, Navigating the 'retail apocalypse': A framework of consumer evaluations of the new retail landscape, Journal of Retailing and Consumer Services, 54 (2020), 101683.  doi: 10.1016/j.jretconser.2018.09.015.

[16]

T. P. Hsieh and C. Y. Dye, Optimal dynamic pricing for deteriorating items with reference price effects when inventories stimulate demand, European J. Oper. Res., 262 (2017), 136-150.  doi: 10.1016/j.ejor.2017.03.038.

[17]

P. HuS. Shum and M. Yu, Joint inventory and markdown management for perishable goods with strategic consumer behavior, Oper. Res., 64 (2016), 118-134.  doi: 10.1287/opre.2015.1439.

[18]

X. P. HuM. Z. WangZ. Z. WangY. J. Sun and S. X. Ye, The overviews on operation management for the new retail mode of online and offline integration, Systems Engineering Theory & Practice, 40 (2020), 2023-2036. 

[19]

K. L. HuangC. W. Kuo and H. J. Shih, Advance selling with freebies and limited production capacity, Omega, 73 (2017), 18-28.  doi: 10.1016/j.omega.2016.12.002.

[20]

E. C. M. HuiC. LiangZ. Wang and Y. Wang, The roles of developer's status and competitive intensity in presale pricing in a residential market: A study of the spatio-temporal model in Hangzhou, China, Urban Studies, 53 (2016), 1203-1224.  doi: 10.1177/0042098015572317.

[21]

D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, In Handbook of the Fundamentals of Financial Decision Making: Part Ⅰ, 99–127.

[22]

T. J. KullM. BarrattA. C. Sodero and E. Rabinovich, Investigating the effects of daily inventory record inaccuracy in multichannel retailing, Journal of Business Logistics, 34 (2013), 189-208.  doi: 10.1111/jbl.12019.

[23]

T. S. KuthambalayanP. Mehta and K. Shanker, Managing product variety with advance selling and capacity restrictions, International Journal of Production Economics, 170 (2020), 287-296.  doi: 10.1016/j.ijpe.2015.10.006.

[24] M. LevyB. A. Weitz and D. Grewal, Retailing Management, Irwin/McGraw-Hill, New York, NY, 1998. 
[25]

L. LiuL. FengB. Xu and W. Deng, Operation strategies for an omni-channel supply chain: Who is better off taking on the online channel and offline service?, Electronic Commerce Research and Applications, 39 (2020), 100918.  doi: 10.1016/j.elerap.2019.100918.

[26]

N. Mishra and S. V. Venkataraman, Optimal order quantity in the presence of strategic customers, Annals of Operations Research, 11 (2020), 1-24.  doi: 10.1007/s10479-020-03731-4.

[27]

L. Nageswaran LS. H. Cho and A Scheller-Wolf, Consumer return policies in omnichannel operations, Management Science, 66 (2020), 5558-5575. 

[28]

A. ÖzmenE. Kropat and G. W. Weber, Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty, Optimization, 66 (2017), 2135-2155.  doi: 10.1080/02331934.2016.1209672.

[29]

A. ÖzmenG. W. WeberI. Batmaz and E. Kropat, RCMARS: robustification of CMARS with different scenarios under polyhedral uncertainty set, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 4780-4787.  doi: 10.1016/j.cnsns.2011.04.001.

[30]

M. M. Pereira and E. M. Frazzon, A data-driven approach to adaptive synchronization of demand and supply in omni-channel retail supply chains, International Journal of Information Management, 57 (2021), 102165.  doi: 10.1016/j.ijinfomgt.2020.102165.

[31]

M. PervinS. K. Roy and G. W. Weber, Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Ann. Oper. Res., 260 (2018), 437-460.  doi: 10.1007/s10479-016-2355-5.

[32]

M. PervinS. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price-and stock-dependent demand: A trade-credit policy, J. Ind. Manag. Optim., 15 (2019), 1345-1373.  doi: 10.3934/jimo.2018098.

[33]

A. PrasadK. E. Stecke and X. Zhao, Advance selling by a newsvendor retailer, Production and Operations Management, 20 (2011), 129-142. 

[34]

H. Ren and T. Huang, Modeling customer bounded rationality in operations management: A review and research opportunities, Comput. Oper. Res., 91 (2018), 48-58.  doi: 10.1016/j.cor.2017.11.002.

[35]

E. Savku and G. W. Weber, A stochastic maximum principle for a Markov regime-switching jump-diffusion model with delay and an application to finance, J. Optim. Theory Appl., 179 (2018), 696-721.  doi: 10.1007/s10957-017-1159-3.

[36]

E. Savku and G. W. Weber, Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market, Annals of Operations Research, (2020), 1-26.  doi: 10.1007/s10479-020-03768-5.

[37]

D. D. Schoenbachler and G. L. Gordon, Multi-channel shopping: Understanding what drives channel choice, Journal of consumer marketing, 19 (2002), 42-53.  doi: 10.1108/07363760210414943.

[38]

M. M. SerefO. SerefA. Alptekinoglu and S. S. Erengüc, Advance selling to strategic consumers, Comput. Manag. Sci., 13 (2016), 597-626.  doi: 10.1007/s10287-016-0264-3.

[39]

S. M. Shugan and J. Xie, Advance selling for services, California Management Review, 46 (2004), 7-54.  doi: 10.2307/41166220.

[40]

X. Su, A model of consumer inertia with applications to dynamic pricing, Production and Operations Management, 18 (2009), 365-380. 

[41]

L. SuoaR. C. Lub and G. D. Linb, Analysis of factors influencing consumers' purchase intention based on perceived value in e-commerce clothing pre-sale model, Journal of Fiber Bioengineering and Informatics, 13 (2020), 23-36. 

[42]

C. S. TangK. RajaramA. Alptekinoglu and J. Ou, The benefits of advance booking discount programs: Model and analysis, Management Science, 50 (2004), 465-478.  doi: 10.1287/mnsc.1030.0188.

[43]

W. Tang and K. Girotra, Using advance purchase discount contracts under uncertain information acquisition cost, Production and Operations Management, 26 (2017), 1553-1567.  doi: 10.1111/poms.12703.

[44]

F. von Briel, The future of omnichannel retail: A four-stage Delphi study, Technological Forecasting and Social Change, 132 (2018), 217-229. 

[45]

L. WangH. Song and Y. Wang, Pricing and service decisions of complementary products in a dual-channel supply chain, Computers & Industrial Engineering, 105 (2017), 223-233. 

[46]

Q. WangN. ZhaoJ. Wu and Q. Zhu, Optimal pricing and inventory policies with reference price effect and loss-Averse customers, Omega, 99 (2019), 102174.  doi: 10.1016/j.omega.2019.102174.

[47]

X. Wang and C. T. Ng, New retail versus traditional retail in e-commerce: Channel establishment, price competition, and consumer recognition, Ann. Oper. Res., 291 (2020), 921-937.  doi: 10.1007/s10479-018-2994-9.

[48]

G. W. WeberI. BatmazG. Köksal and Ye rlikaya-Özkurt, CMARS: A new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization, Inverse Probl. Sci. Eng., 20 (2012), 371-400.  doi: 10.1080/17415977.2011.624770.

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Figure 1.  The pre-sale model based on the new retail context
Figure 2.  Consumer market segmentation based on different wait time sensitivities
Figure 3.  Comparison of orders in the advance period with or without reference price dependence
Figure 4.  Comparison of orders in the advance period with or without reference price dependence
Figure 5.  Changes in the seller's profit over the advance period with acquisition and loss coefficients
Figure 6.  Changes in the seller's profit over the spot period with acquisition and loss coefficients
Figure 7.  The impact of value-added offline service on dual-channel order quantities
Figure 8.  The impact of value-added offline services on dual-channel profits
Figure 9.  Market segmentation of consumers in the spot period
Table 1.  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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