基于蚁群算法的重复购买多代创新扩散模型及其应用研究
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摘要
随着全球化进程的加快,企业为了保持其市场优势,不断地在前一代产品的基础上推出新一代产品,新一代产品虽然在性能上有所改进,但进入市场时并不能马上完全替代前代产品,只是开始与之竞争,因而在市场中出现了多代产品共存的现象。同时更新换代的时间间隔逐渐缩短,各代产品之间的依赖关系也越来越强。因此研究多代创新产品扩散这一动态过程,对于企业把握各代产品的扩散趋势,制定相应的市场策略具有重要意义。重复购买是影响多代产品扩散的一个重要方面,新一代产品在进入市场的初期,产品的采用量大多依靠于消费者的尝试性购买即首次购买,随着时间的推移,产品采用量的增加主要来源于消费者对该类产品的重复性购买,尤其在一些多代高科技产品扩散的后期,重复购买对产品扩散量的影响较为明显。因此在多代创新产品扩散模型中考虑重复购买因素能够更加准确的反应市场的现实状况,有利于提高对多代创新产品扩散量的预测精度。由于影响首次购买与重复购买的因素不同,因而区分消费者的首次购买与重复购买对企业来说更有意义。
目前,已有的多代创新产品扩散模型虽然能够基本描述出多代产品在市场中的扩散特征,但模型假设购买者为首次购买者,不考虑重复购买因素。对于考虑重复购买因素的创新扩散研究,如经常性购买模型主要针对日常用品或低值易耗品市场,重复购买生命周期模型主要应用在一些的耐用品的扩散中。这些研究大多是建立在单代产品扩散的基础上,且不适用于多代高科技产品创新扩散。但是对于在多代创新产品扩散模型中考虑重复购买因素的相关研究涉及较少,应用在我国市场中的实证研究更是少之又少。
本文在Norton-Bass基本的多代创新产品扩散模型基础上,进行深入思考,尝试放松模型的假设条件,将购买者划分为首次购买者和重复购买者,并考虑扩散过程中的跳跃现象,给出了考虑重复购买的多代创新产品扩散模型。考虑到模型本身的复杂性,本文采用一种新的用于创新产品扩散模型的参数估计方法即蚁群优化算法,以中国互联网上网方式的扩散为例进行实证检验。得出考虑重复购买的多代创新产品扩散模型相较于Norton-Bass模型的拟合优度较好,预测精度更高。同时对比分析蚁群算法、极大似然估计法以及非线性最小二乘法的估计效果,发现在历史数据较少的情况下采用蚁群算法的预测效果较好。最后本文基于蚁群优化算法采用重复购买多代创新产品扩散模型对中国互联网上网方式扩散的趋势进行预测。
With the rapid develop process of globalization, Companies which in order to maintain their market advantage constantly produce newer generation of products on the basis of the previous generation. Although the performance has improved, the product could not replace the former generation completely when it appeared in the market. They can only compete with the former generation. So the phenomenon of coexistence of multiple generations appeared in the market. Time interval of the replacement is shorter at the same time. The dependence between the generations is growing stronger and stronger. Therefore, we should research more on this dynamic process of multi-generation, which could help companies grasp the trend of diffusion of multi-generation. Enterprises can make the appropriate marketing strategies to guide market operation on the basis of the research. Repeat purchase is one of important factor in multi-generation product diffusion. When the new generation enter the market at the first time, the product sales mainly rely on the consumer's tentative first-time buyers. As time goes on, more and more new product sales depend on consumers repetitive purchases. Especially diffusion in later period of multiple generation high-tech products, repeat purchase factors significantly affected the amount of product proliferation. We consider the factors of the repurchase on the basis of multiple generation innovation product diffusion models. The new model could reflect real market accurately and improve the prediction accuracy of multiple generation innovation products. As the different impact between tentative purchase and repetitive purchase, we should distinguish between two different types of purchase which is more meaningful to company.
At present, the multi-generation innovative products diffusion model can basically describe diffusion characteristics of multiple generations in the market. But the model assumes that buyers for the first time buyers, and does not consider the factors of repeat purchase. There are some researches about innovation diffusion considering repeat buying factors. For example, some studies used frequent-purchased model in everyday items or low-value consumable product. Some other researchers use the life cycle model of repurchased product in some diffusion of durable goods. Most of these researches are on the basis of single generation products diffusion, and not apply to multi-generation high-tech product innovation diffusion. But there is less research on repeatable purchase of multiple generation product innovation diffusion, and the empirical study used in China's market is very little.
In this paper, we try to relax assumption on the basis of Norton-Bass model which is the basic multi-generation innovative products diffusion model. we divide buyers into first-time buyers and repeat buyers, and consider the jump phenomenon of diffusion process. We give a multi-generation innovation product diffusion model when we take into account the repeat purchase. Considering the complexity of the model, the paper adopts a new parameter estimation method that named ant colony optimization for innovative product diffusion model. The model take the modes of connecting with internet in China as an example and conduct empirical test. We get the result that comparing with Norton-Bass model the model have better goodness of fit and more accurate forecasts. We compare estimation results among ant colony optimization, maximum likelihood estimation and nonlinear least squares method at the same time. We found that using ant colony optimization will have better prediction effect with less historical data. Finally, the paper on the basis of repeatable purchase of multiple generation innovation product diffusion model uses ant colony optimization in the modes of connecting with internet in China to predict the tendency of spread.
目前,已有的多代创新产品扩散模型虽然能够基本描述出多代产品在市场中的扩散特征,但模型假设购买者为首次购买者,不考虑重复购买因素。对于考虑重复购买因素的创新扩散研究,如经常性购买模型主要针对日常用品或低值易耗品市场,重复购买生命周期模型主要应用在一些的耐用品的扩散中。这些研究大多是建立在单代产品扩散的基础上,且不适用于多代高科技产品创新扩散。但是对于在多代创新产品扩散模型中考虑重复购买因素的相关研究涉及较少,应用在我国市场中的实证研究更是少之又少。
本文在Norton-Bass基本的多代创新产品扩散模型基础上,进行深入思考,尝试放松模型的假设条件,将购买者划分为首次购买者和重复购买者,并考虑扩散过程中的跳跃现象,给出了考虑重复购买的多代创新产品扩散模型。考虑到模型本身的复杂性,本文采用一种新的用于创新产品扩散模型的参数估计方法即蚁群优化算法,以中国互联网上网方式的扩散为例进行实证检验。得出考虑重复购买的多代创新产品扩散模型相较于Norton-Bass模型的拟合优度较好,预测精度更高。同时对比分析蚁群算法、极大似然估计法以及非线性最小二乘法的估计效果,发现在历史数据较少的情况下采用蚁群算法的预测效果较好。最后本文基于蚁群优化算法采用重复购买多代创新产品扩散模型对中国互联网上网方式扩散的趋势进行预测。
With the rapid develop process of globalization, Companies which in order to maintain their market advantage constantly produce newer generation of products on the basis of the previous generation. Although the performance has improved, the product could not replace the former generation completely when it appeared in the market. They can only compete with the former generation. So the phenomenon of coexistence of multiple generations appeared in the market. Time interval of the replacement is shorter at the same time. The dependence between the generations is growing stronger and stronger. Therefore, we should research more on this dynamic process of multi-generation, which could help companies grasp the trend of diffusion of multi-generation. Enterprises can make the appropriate marketing strategies to guide market operation on the basis of the research. Repeat purchase is one of important factor in multi-generation product diffusion. When the new generation enter the market at the first time, the product sales mainly rely on the consumer's tentative first-time buyers. As time goes on, more and more new product sales depend on consumers repetitive purchases. Especially diffusion in later period of multiple generation high-tech products, repeat purchase factors significantly affected the amount of product proliferation. We consider the factors of the repurchase on the basis of multiple generation innovation product diffusion models. The new model could reflect real market accurately and improve the prediction accuracy of multiple generation innovation products. As the different impact between tentative purchase and repetitive purchase, we should distinguish between two different types of purchase which is more meaningful to company.
At present, the multi-generation innovative products diffusion model can basically describe diffusion characteristics of multiple generations in the market. But the model assumes that buyers for the first time buyers, and does not consider the factors of repeat purchase. There are some researches about innovation diffusion considering repeat buying factors. For example, some studies used frequent-purchased model in everyday items or low-value consumable product. Some other researchers use the life cycle model of repurchased product in some diffusion of durable goods. Most of these researches are on the basis of single generation products diffusion, and not apply to multi-generation high-tech product innovation diffusion. But there is less research on repeatable purchase of multiple generation product innovation diffusion, and the empirical study used in China's market is very little.
In this paper, we try to relax assumption on the basis of Norton-Bass model which is the basic multi-generation innovative products diffusion model. we divide buyers into first-time buyers and repeat buyers, and consider the jump phenomenon of diffusion process. We give a multi-generation innovation product diffusion model when we take into account the repeat purchase. Considering the complexity of the model, the paper adopts a new parameter estimation method that named ant colony optimization for innovative product diffusion model. The model take the modes of connecting with internet in China as an example and conduct empirical test. We get the result that comparing with Norton-Bass model the model have better goodness of fit and more accurate forecasts. We compare estimation results among ant colony optimization, maximum likelihood estimation and nonlinear least squares method at the same time. We found that using ant colony optimization will have better prediction effect with less historical data. Finally, the paper on the basis of repeatable purchase of multiple generation innovation product diffusion model uses ant colony optimization in the modes of connecting with internet in China to predict the tendency of spread.
引文
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[2]马开平,严洪森.重复购买产品的竞争与市场扩散行为分析[J].控制与决策,2007,22:143-146.
[3] Bass,F.M. A new product growth model for consumer durable[J].Management Science, 1969,15:215-227.
[4] Norton, J.A. and Bass, F.M. A Diffusion Theory Model of Adoption and Substitution for Successive Generations of High-Technology Products[J]. Management Science, 1987, 33:1069-1086.
[5] Lilien GL,Ran AG,and Kalish S. Bayesian Estimation and Control of Detailing Effort in a Repeat Purchase Diffusion Environment[J].Management Science,1981,27:493-506.
[6]盛亚.技术创新扩散与新产品营销[M].中国发展出版社.2002.5:195-231 1-10 37-44.
[7] Dodson JA,Muller E.Models of new product diffusion through advertising and word of mouth[J].Management Science,1978,24:1568-1578.
[8] Dolan RJ,Jeuland AP. Experience curves and dynamic demand models:Implications for optimal pricing strategies[J].Journal of Marketing,1981,45:52-73.
[9] Jain D.C,V.Mahajan,and E.Muller. Innovation Diffusion in the Persence of Supply Restrictions[J],Marketing Science,1991,10:83-90.
[10] Islam T.,and Meade N. Modelling and forecasting the diffusion of innovation-A 25 year review[J].International Journal of Forecasting,2006,22:519-545.
[11] Towhidul Islam,and Nigel Meade. The diffusion of successive generations of a technology:a more general model[J].Technological Forecating and Social Change,1997,56:49-60.
[12] Speeee,M.W,and MacIachlan,D.L. Application of a Multi-Generation Diffusion Model to Milk Container Technology[J].Technological Forecasting and Social Change, 1995,49:281-295.
[13] Peter J,Danaher,Bruce G.S.Hardie,and William F. Putsis JR: Marketing-Mix Variables and the Diffusion of Successive Generations of a Technological Innovation [J],Journal of Marketing Research,2001,11:501-514.
[14]官建成,张西武.创新扩散模型的研究进展及展望[J].科学学与科学技术管理,1995, 16(12):14-18.
[15]缪柏其,魏晓芳,王淮学.技术创新的扩散模型[J].预测,1999,2:75-78.
[16]王海云,尚志田.重复购买产品的产品生命周期模型研究[J].中国管理科学,2002,10(2): 24-29.
[17]乔忠,王福华,刘巍.经常购买模型及其参数的极大似然估计[J].系统工程,2004, 22: 25-28.
[18]杨敬辉,武春友.基于Bass模型的两种参数估算算法比较研究[J].数量经济技术经济研究,2005,12:125-132.
[19]张磊,李一军,闫相斌.基于竞争的多代产品扩散模型及其实证研究[J].系统工程理论与实践,2008,12:84-106.
[20] A.Colomi,M.Dorigo,and V.Maniezzo. Distributed optimization by ant colonies[J]. Proceedings of the 1st European Conference on Artificial Life,1991:134-142.
[21]胡宝民.技术创新扩散理论与系统演化模型[M].北京:科学出版社,2002:17-34.
[22]武春友,戴大双,苏敬勤.技术创新扩散[M].北京:化学工业出版社,1997:18-23.
[23] Rogers,E.M. Diffusion of Innovations,Copy-Right,1983 By Free Press.
[24] Robertson,S.Thomas. Innovative Behavior and Communication[J].New York: Holt, Rinehart and Winston,1971:135-156.
[25]盛亚.技术创新扩散的学习论[J].科技进步与对策,2004,1:36-37.
[26] Fisher,J.C.and R.H.Pry .A Simple Substitution Model of Technological Change[J], Technological Forecasting and Social Change,1971,3:75-88.
[27] Kalaitzandonakes N.G.and Boggess W.G. A Dynamic Decision-Theoretic Model of Technology Adoption for the Competitive Firm[J].Technological Forecasting&Social Change,1993,44:17-25.
[28] Reinganum,Jennifer F. On the Diffusion of New Technology:A Game Theoretic Approach[J].Review of Economic Studies,1981,48(153):395-405.
[29]李艾.电子上网商务扩散影响因素实证研究[D].杭州:浙江大学,2005,4:1-173.
[30] Veugelers,Reinhilde. Collaboration in R&D:An Assessment of theoretical and Empirical Findings[J].Quarterly Review of The Royal Netherlands Economic Association,1998,46(3):245-256.
[31]胡知能.创新产品市场扩散模型及其应用[D].四川:四川大学,2005:1-55.
[32]武春友. Bass模型及其两种扩展型的应用研究[D].大连:大连理工大学,2005:1-163.
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