考虑贴现因子和供应约束的销售模式选择与定价决策

doi:10.16381/j.cnki.issn1003-207x.2023.1479

Abstract

Abstract:

Based on the time property of revenue， sales model choice and pricing strategy are considered under price regulation. First， three models corresponding to advance-only， spot-only， and advance+spot sales are constructed under no supply constraint， and all possible optimal strategies are obtained. It is shown that advance sale is always beneficial， and spot-only is an inferior strategy. Second， the impact incurred by supply constraints is analyzed. Some significant conclusions are drawn for situations such as：（a） when the previous mode is “advance+spot” sale， it may convert to advance-only or spot-only under the considered supply constraints； and （b） when the previous mode is advance-only， it remains as it is no matter whether supply constraint exists or not. Finally， some numerical examples are designed to analyze the sensitivity of selling strategy with respect to parameters， and examine the impact of supply constraint on sales mode. The presented results provide a well theoretical basis for certain cases in which spot-only sale is the optimal strategy under certain supply constraints.

Key words: discount factor, supply constraint, sales model, pricing strategy

CLC Number:

F274

Zhenkai Lou,Zhiying Wang,Xuming Lou, et al. Sales Model Choice and Pricing Strategy in the Presence of Discount Factor and Supply Constraint[J]. Chinese Journal of Management Science, 2026, 34(8): 246-256.

Figures/Tables 6

References 23

[1]	Shugan S M， Xie J. Advance pricing of services and other implications of separating purchase and consumption［J］.Journal of Service Research， 2000，2（3）： 227-239.
[2]	Cachon G P. The allocation of inventory risk in a supply chain： Push， pull， and advance-purchase discount contracts［J］. Management Science， 2004， 50（2）： 222-238.
[3]	Lou Z， Hou F， Lou X. Optimal dual-channel dynamic pricing of perishable items under different attenuation coefficients of demands［J］. Journal of Systems Science and Systems Engineering， 2021， 30（1）： 44-58.
[4]	王道平，周玉. 评论优化策略下考虑退货的网络销售商两阶段定价和订货决策研究［J］. 中国管理科学， 2024， 32（11）： 243-257.
	Wang D P， Zhou Y. Research on two-stage pricing and ordering decision of online sellers considering return under comment improvement strategy［J］. Chinese Journal of Management Science， 2024， 32（11）： 243-257.
[5]	Gale I， Holmes T. Advance-purchase discounts and monopoly allocation of capacity［J］. American Economic Review， 1993， 83（1）：135-146.
[6]	Zhang W， He Y， Gou Q， et al. Optimal advance selling strategy with information provision for omni-channel retailers［J］. Annals of Operations Research， 2023， 329（1-2）： 573-602.
[7]	楼振凯，王治莹，逄金辉. 不确定需求下考虑预售合理性的鲁棒定价决策［J］. 系统科学与数学， 2024， 44（7）： 1945-1958.
	Lou Z K， Wang Z Y， Pang J H. Robust pricing decisions considering the reasonability of advance selling under an uncertain demand［J］. Journal of Systems Science and Mathematical Sciences， 2024， 44（7）： 1945-1958.
[8]	Shi B， Xu Q， Sun Z. Optimal pricing and production decisions of fashion apparel brands in a two-stage sales setting［J］. International Transactions in Operational Research， 2021， 28（2）： 738-763.
[9]	郭春香，房于博，刘羽. 考虑参考价格效应的易逝品预售策略研究［J］. 软科学， 2020， 34（8）： 109-115.
	Guo C X， Fang Y B， Liu Y. Study on the presale strategy of perishable commodities considering the reference price effect［J］. Soft Science， 2020， 34（8）： 109-115.
[10]	Wang X H， Zeng C. A model of advance selling with consumer heterogeneity and limited capacity［J］. Journal of Economics， 2016， 117（2）： 137-165.
[11]	汪旭晖，陈鑫. 基于平台型电商企业声誉和从众效应的预售定价策略［J］.管理工程学报，2021，35（1）： 126-141.
	Wang X H， Chen X. Pre-sale pricing strategies based on the reputation of an e-commerce platform enterprise and herd effect［J］. Journal of Industrial Engineering and Engineering Management， 2021，35（1）： 126-141.
[12]	孙晓杰，高峰，张建雄. 考虑质量不确定的竞争企业预售策略分析［J］.中国管理科学，2023，31（3）： 207-216.
	Sun X J， Gao F， Zhang J X. Advance selling strategies of competing firms with quality uncertainty［J］. Chinese Journal of Management Science，2023，31（3）： 207-216.
[13]	Dye C Y， Hsieh T P. Joint pricing and ordering policy for an advance booking system with partial order cancellations［J］. Applied Mathematical Modelling， 2013， 37（6）： 3645-3659.
[14]	Cho S H， Tang C S. Advance selling in a supply chain under uncertain supply and demand［J］. Manufacturing Service Operations Management， 2013， 15（2）： 305-319.
[15]	徐琪，董琦. 折价与定金膨胀预售下零售商订购量和预售价决策［J］. 系统工程理论与实践， 2021， 41（10）： 2524-2534.
	Xu Q， Dong Q. Order quantity and pre-sale price decision with advance selling under discount and deposit inflation modes［J］. Systems Engineering —Theory Practice， 2021， 41（10）： 2524-2534.
[16]	段永瑞，高一分，喻博峰，等. 预售环境下考虑消费者后悔厌恶的定价问题［J］. 工业工程与管理， 2024， 29（3）： 200-206.
	Duan Y R， Gao Y F， Yu B F， et al. Pricing strategies of advance selling with consumer regret aversion［J］. Industrial Engineering and Management， 2024， 29（3）： 200-206.
[17]	Boyacı T， Özer Ö. Information acquisition for capacity planning via pricing and advance selling： When to stop and act？［J］. Operations Research， 2010， 58（5）： 1328-1349.
[18]	Giampietro M， Guidolin M， Pedio M. Estimating stochastic discount factor models with hidden regimes： Applications to commodity pricing［J］. European Journal of Operational Research， 2018， 265（2）： 685-702.
[19]	王小胜，胡豪，刘欣欣，等. 基于讨价还价模型的分享型合同节水管理利益分配［J］. 系统工程理论与实践， 2020， 40（9）： 2418-2426.
	Wang X S， Hu H， Liu X X， et al. Profit allocation of benefit-sharing water saving management contract based on bargaining model［J］. Systems Engineering —Theory Practice， 2020， 40（9）： 2418-2426.
[20]	Zhang L， Wang J. Coordination of the traditional and the online channels for a short-life-cycle product［J］. European Journal of Operational Research， 2017， 258（2）： 639-651.
[21]	计国君，孙忠锋，杨光勇，等. 基于消费者参照价格效应的限量预售策略研究［J］. 管理工程学报， 2021， 35（4）： 178-189.
	Ji G J， Sun Z F， Yang G Y， et al. Advance selling with consumer reference price effect and limited advance sales［J］. Journal of Industrial Engineering and Engineering Management， 2021， 35（4）： 178-189.
[22]	肖敏，吴健健. 预售模式下考虑产能约束的制造商产量及宣传决策［J］. 工业工程， 2023， 26（4）： 35-43.
	Xiao M， Wu J J. Manufacturer output and publicity decisions considering capacity constraints under pre-sale mode［J］. Industrial Engineering Journal， 2023， 26（4）： 35-43.
[23]	Prasad A， Stecke K E， Zhao X. Advance selling by a newsvendor retailer［J］. Production and Operations Management， 2011， 20（1）： 129-142.

符号	定义
d	市场潜在需求
δ	需求关于价格的敏感系数
θ	不同销售阶段价格对需求的交叉影响系数
k	价格对本阶段需求和对另一阶段需求影响的强度比值，k =δ/θ
p_a	预售期销售价
p_s	现售期销售价格
Q_a	预售阶段的销售量，Q_a = -δp_a + θp_s
Q_s	现售阶段的销售量，Q_s = d - δp_s + θp_a
β	现售阶段相对于预售阶段的贴现因子，0 β 1
c	供应量限制
π_a	预售所获得的利润，π_a = p_a (-δp_a + θp_s )
π_s	现售所获得的利润，π_s = βp_s (d - δp_s + θp_a )
π	同时进行预售和现售所获得的总利润，π = π_a +π_s

Sales Model Choice and Pricing Strategy in the Presence of Discount Factor and Supply Constraint

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 6

References 23

Related Articles 15

Metrics

Comments

Recommended 0

[1]	Xinyue Tan, Jiafu Tang, Tingting Li. Analysis of O2O Food Delivery Platform Commission Model Selection and Pricing Strategy Considering Bounded Rationality [J]. Chinese Journal of Management Science, 2026, 34(8): 127-138.
[2]	Xinxin Liu, Zilai Sun, Jiliang Han, Xiangpei Hu, Junhu Ruan. Research on Pricing Strategy of Agricultural Service Platform Considering Farmers’ Mental Cost and Cooperative Loss [J]. Chinese Journal of Management Science, 2026, 34(7): 323-335.
[3]	Xiaoqing Zhang, Xigang Yuan, Jiajia Chen, Qiang Wei, Baofeng Huo. Research on Trade-in Pricing Strategies for Consumer Goods Considering Customer Privacy Concerns [J]. Chinese Journal of Management Science, 2026, 34(6): 291-302.
[4]	Jie Xu, Wen Hu, Chunlin Luo, Dongdong Yu. Pricing Strategies for the Echelon Utilization of New Energy Vehicle Power Batteries Enabled by Blockchain Technology [J]. Chinese Journal of Management Science, 2026, 34(5): 285-294.
[5]	Tao Li, Jun Zhao, Yang Liu, Bin Liu. Pricing Strategy in a Competitive Supply Chain under Retailers’“Virtual Bargaining” [J]. Chinese Journal of Management Science, 2026, 34(3): 275-285.
[6]	Fei Yan, Hongzhuan Chen. Research on Dynamic Licensing Pricing Strategy of Dual-use Defense Patent Considering the Social Efficiency [J]. Chinese Journal of Management Science, 2025, 33(9): 148-160.
[7]	Rui Wang, Xiuli Xu. Customer Behavior and Pricing Analysis Based on “Service Intelligence Queueing System” [J]. Chinese Journal of Management Science, 2025, 33(8): 260-270.
[8]	Zhenkai Lou, Zhiying Wang, Huimin Zhang, Jinhui Pang. Selling Strategy Choices in the Presence of a Discount Factor and Sales Promotion at the Advance Period [J]. Chinese Journal of Management Science, 2025, 33(12): 318-327.
[9]	Xiaogang Lin, Hailing Huang, Wenzhuo Li, Qiang Lin. Blockchain Provision Strategy in Agricultural Products E-commerce under Hybrid Sales Model [J]. Chinese Journal of Management Science, 2025, 33(10): 259-268.
[10]	Siming Pan,Shaokai Lu,Pan Liu. Research on Additional Investment and Pricing Strategy of Network Platform Considering Heterogeneous Bilateral Effect [J]. Chinese Journal of Management Science, 2024, 32(9): 193-200.
[11]	Jizhou Zhan,Yaqi Jin. Research on Pricing Strategy of Competitive E-commerce Platforms Considering Return Freight Insurance [J]. Chinese Journal of Management Science, 2024, 32(5): 325-334.
[12]	Junfei Ding,Weida Chen,Shuaishuai Fu. Pricing and Coordination in a Supply Chain with Emission Option Contract under a Remanufacturing Environment [J]. Chinese Journal of Management Science, 2024, 32(3): 95-104.
[13]	Le Wang,Yang Song,Tijun Fan. Strategies of Manufacturers Introducing Live Streaming [J]. Chinese Journal of Management Science, 2024, 32(2): 276-284.
[14]	Qifa Xu, Zezhou Wang, Cuixia Jiang. Research on Mixed Frequency Asset Pricing Based on Generative Adversarial Network [J]. Chinese Journal of Management Science, 2024, 32(11): 53-64.
[15]	Zhiyuan Zhang,Taofeng Ye. Pricing Strategies of SaaS Service Providers Considering Different Billing Methods [J]. Chinese Journal of Management Science, 2024, 32(10): 214-223.