考虑消费者购买后悔的动态闭环供应链微分博弈

doi:10.16381/j.cnki.issn1003-207x.2022.2756

摘要/Abstract

摘要：

考虑消费者存在购买后悔行为，寻找创新产品异质的动态闭环供应链上各个决策变量的最优路径。针对全新品和再制品是异质的，在Bass创新产品扩散模型的基础上，引入消费者后悔系数，构建一个修正的Bass扩散模型，以刻画创新产品进入市场后需求量的变化路径。在此基础上，考虑由一个制造商主导并以固定比率回收废旧产品、零售商跟从的动态闭环供应链系统，并将产品销量作为状态变量构建Stackelberg微分博弈模型。利用微分博弈和最优控制理论，寻找创新产品进入市场后的最优批发价、零售价路径以及供应链各成员的最大利润。并通过算例分析，对比不同状态下供应链成员最优决策的差异。研究表明：制造商的最优批发价不随时间变化，也不会受到消费者后悔系数的影响；零售价随着时间的推移先升后降，且消费者后悔系数越高，零售价越低；随着消费者对全新品或再制品的后悔系数上升，制造商和零售商的利润均下降。因此，无论是制造商还是零售商，都应努力提高消费者对产品的满意度。

关键词: Bass扩散模型, 闭环供应链, 微分博弈, 购买后悔, 产品异质

Abstract:

With the shortening of the product life cycle， the number of discarded electrical and electronic products （such as mobile phones， TV sets， etc.） has grown sharply， which has caused serious energy waste and environmental pollution. Hence， the research of closed-loop supply chain have been paid more attention by the academic circles. However， existed studies have not considered the heterogeneity between new products and reproducts， and the effect of consumer regret. In this paper， the change path of demand is depicted for refurbished innovative products when considering the purchasing regret of consumers based on the closed-loop supply chain differential game system. To deal with homogeneity between new product and remanufactured product， purchasing regret coefficient is introduced to Bass diffusion model， and then a modified Bass diffusion model is built to depict the change path of innovative products’ demand after entering the market. And based on this， a closed-loop supply chain system is considered is considered which is dominated by a manufacturer and followed by a retailer. In this system， the manufacturer recycles used products at a given ratio. Then a differential game model is built under the Stackelberg game taking the sales of product as the state variable. The optimal path of wholesale price， retail price and the maximum profit of supply chain members is obtained by using the differential game theory and the optimal control theory. By numerical examples， the optimal decisions in different market conditions are compared. The results show that：（1） The higher the consumer regret factor， the smaller the sales volume. When new products account for a large proportion of sales， more energy should be devoted to improve the satisfaction of new product users； Conversely， when remanufactured products account for a large proportion of sales， remanufactured sale should be paid more attention. （2） manufacturer’s optimal wholesale price is fixed over time horizon and will not be changed by purchasing regret of consumers. This is because the manufacturer is the leader of the supply chain. Fixed wholesale prices can reduce uncertainty for retailers. Then retailers can adjust the sales volume by adjusting the price；（3） The seller adjusts the price of the product according to the sales volume of each stage. During the whole process， retail price first rises then descends. （4） the higher regret coefficient the lower retail price and the profit of manufacturer and retailer. Hence， both manufacturer and retailer should try best to improve customer satisfaction. our research shows that both manufacturers and retailers should strive to improve consumers' satisfaction with their products.

Key words: bass diffusion model, closed-loop supply chain, differential game, consumers’ purchasing regret, refurbished innovative products

中图分类号:

F270

段梅, 刘振威, 刘浪. 考虑消费者购买后悔的动态闭环供应链微分博弈[J]. 中国管理科学, 2025, 33(8): 321-330.

Mei Duan, Zhenwei Liu, Lang Liu. Differential Game of Dynamic Closed-Loop Supply Chain Considering Consumers' Purchasing Regret[J]. Chinese Journal of Management Science, 2025, 33(8): 321-330.

图/表 6

图1

表1

符号及含义"

符号	含义
$c m$	制造商生产全新品的单位生产成本
$c 0$	制造商回收旧产品的单位成本
$c τ$	制造商利用旧产品进行再制造的生产成本
$w (t)$	全新品批发价格，为制造商的控制变量
$w (t) - a$	制造商对再制品的批发价格， $a > 0$
$τ$	废旧产品回收率
$N$	全部潜在消费者的数量
$p (t)$	全新品零售价格，为零售商的控制变量
$p (t) - b$	再制品零售价格， $b > 0$
$ρ$	价格对创新者向模仿者转换的影响系数
$ς 1$	消费者购买全新品的后悔系数
$ς 2$	消费者购买再制品的后悔系数
$π M (t)$	制造商的利润函数
$π R (t)$	零售商的利润函数

表1

图2

图3

图4

图5

参考文献 29

[1]	Guide V D R， Van Wassenhove L N. The evolution of closed-loop supply chain research［J］.Operations Research， 2009， 57（1）： 10-18.
[2]	Bulmus S C， Zhu S X， Teunter R. Competition for cores in remanufacturing［J］. European Journal of Operational Research， 2014， 233（1）： 105-113.
[3]	Savaskan R C， Bhattacharya S， Van Wassenhove L N. Closed-loop supply chain models with product remanufacturing［J］. Management Science， 2004， 50（2）： 239-252.
[4]	Savaskan R C， Van Wassenhove L N. Reverse channel design： The case of competing retailers［J］. Management Science， 2006， 52（1）： 1-14.
[5]	Hong X， Xu L， Du P， et al. Joint advertising， pricing and collection decisions in a closed-loop supply chain［J］. International Journal of Production Economics， 2015， 167： 12-22.
[6]	孙朝苑，田思源. 碳交易政策和广告宣传对供应链回收渠道选择的影响［J］. 管理评论， 2020， 32（12）： 242-252.
	Sun C Y， Tian S Y. The impact of carbon trading policy and advertising on the choice of supply chain recycling channels［J］. Management Review， 2020， 32（12）： 242-252.
[7]	林贵华，单仁邦，陈拼博. 政府补贴下闭环供应链回收渠道的选择策略［J］.运筹与管理， 2020，29（4）： 43-53.
	Lin G H， Shan R B， Chen P B. Selection strategies of recycling channels in closed-loop supply chain under government subsidy［J］. Operations Research and Management Science， 2020， 29（4）： 43-53.
[8]	Ma W M， Zhao Z， Ke H. Dual-channel closed-loop supply chain with government consumption-subsidy［J］. European Journal of Operational Research， 2013， 226（2）： 221-227.
[9]	Yang L， Hu Y， Huang L. Collecting mode selection in a remanufacturing supply chain under cap-and-trade regulation［J］. European Journal of Operational Research， 2020， 287（2）： 480-496.
[10]	Souza G C. Closed-loop supply chains： A critical review， and future research［J］. Decision Sciences， 2013， 44（1）： 7-38.
[11]	Minner S， Kiesmüller G P. Dynamic product acquisition in closed loop supply chains［J］. International Journal of Production Research， 2012， 50（11）： 2836-2851.
[12]	De Giovanni P， Reddy P V， Zaccour G. Incentive strategies for an optimal recovery program in a closed-loop supply chain［J］. European Journal of Operational Research， 2016， 249（2）： 605-617.
[13]	王道平，张可，周玉. 政府奖惩下考虑回收率动态随机的闭环供应链微分博弈［J］. 中国管理科学， 2024， 32（5）： 158-170.
	Wang D P， Zhang K， Zhou Y. Differential game of closed-loop supply chain with dynamic stochastic recovery rate under reward-penalty mechanism of government［J］. Chinese Journal of Management Science， 2024， 32（5）： 158-170.
[14]	王一雷，夏西强，张言. 碳交易政策下供应链碳减排与低碳宣传的微分对策研究［J］. 中国管理科学， 2022， 30（4）： 155-166.
	Wang Y L， Xia X Q， Zhang Y. Differential strategies of carbon emission reduction and low-carbon promotion of the supply chain under cap-and-trade policy［J］. Chinese Journal of Management Science， 2022， 30（4）： 155-166.
[15]	Jørgensen S， Taboubi S， Zaccour G. Cooperative advertising in a marketing channel［J］. Journal of Optimization Theory and Applications， 2001， 110（1）： 145-158.
[16]	卓四清，韩雪. 碳补贴与零售商竞争下供应链合作方式的微分博弈研究［J］. 管理工程学报， 2023， 37（2）： 80-89.
	Zhuo S Q， Han X. Research on the differential game of supply chain cooperation under carbon subsidy and retailer competition［J］. Journal of Industrial Engineering and Engineering Management， 2023， 37（2）： 80-89.
[17]	Skelton A C H， Allwood J M. Questioning demand： A study of regretted purchases in Great Britain［J］. Ecological Economics， 2017， 131： 499-509.
[18]	Jiang B， Narasimhan C， Turut Ö. Anticipated regret and product innovation［J］.Management Science， 2016， 63（12）： 4308-4323.
[19]	Nasiry J， Popescu I. Advance selling when consumers regret［J］. Management Science， 2012， 58（6）： 1160-1177.
[20]	高鹏，杜建国，聂佳佳，等. 消费者后悔预期对再制造供应链质量决策的影响［J］. 管理评论， 2018， 30（11）： 234-246.
	Gao P， Du J G， Nie J J， et al. Impact of consumer’s anticipated regret on quality decision of remanufacturing supply chain［J］. Management Review， 2018， 30（11）： 234-246.
[21]	叶燚，郭强，聂佳佳. 消费者预期后悔对企业低碳策略选择的影响［J］. 中国管理科学， 2025， 33（2）： 242-247.
	Ye Y， Guo Q， Nie J J. The impact of consumer expected regret on the low-carbon strategy choices of enterprises［J］. Chinese Journal of Management Science， 2025， 33（2）： 242-247.
[22]	段永瑞，徐超，刘晶晶. 考虑预期后悔的创新产品定价和质量决策研究［J］.工业工程与管理， 2021， 26（3）： 185-194.
	Duan Y R， Xu C， Liu J J. Pricing and quality policies for innovated products with consumers' anticipated regret［J］. Industrial Engineering and Management， 2021， 26（3）： 185-194.
[23]	Mukhopadhyay S K， Setaputra R. Return policy in product reuse under uncertainty［J］. International Journal of Production Research， 2011， 49（17）： 5317-5332.
[24]	Bass F M. A new product growth for model consumer durables［J］. Management Science， 1969， 15（5）： 215-227.
[25]	De Cesare L， Di Liddo A. A Stackelberg game of innovation diffusion： Pricing， advertising and subsidy strategies［J］. International Game Theory Review， 2001， 3（4）： 325-339.
[26]	全雄文，涂菶生，魏杰. 新产品销售定价的制造商与销售商斯坦克尔伯格博弈［J］. 系统工程理论与实践， 2007， 27（8）： 111-117+145.
	Quan X W， Tu B S， Wei J. A manufacturer-retailer Stackelberg game of innovation pricing［J］. Systems Engineering-Theory & Practice， 2007， 27（8）： 111-117+145.
[27]	Guo Z. Optimal decision making for online referral marketing［J］. Decision Support Systems， 2012， 52（2）： 373-383.
[28]	段永瑞，尹佳. 基于巴斯模型的消费者推荐奖励和广告投入动态定价决策［J］. 中国管理科学， 2020， 28（8）： 65-75.
	Duan Y R， Yin J. Optimal dynamic pricing of consumer referral reward and advertising investment based on bass model［J］. Chinese Journal of Management Science， 2020， 28（8）： 65-75.
[29]	刘浪，刘振威，陈烁. 制造商分担创新产品回收成本的闭环供应链微分博弈［J］. 电子科技大学学报（社科版）， 2023， 25（6）： 67-76.
	Liu L， Liu Z W， Chen S. Differential game of closed-loop supply chain with manufacturer sharing the cost recovery of innovative products［J］. Journal of University of Electronic Science and Technology of China （Social Sciences Edition）， 2023， 25（6）： 67-76.