网络外部性对供应链创新技术投资策略的影响
2020-09-09李增禄聂佳佳
郭 强,张 婷,李增禄,聂佳佳
网络外部性对供应链创新技术投资策略的影响
郭 强,张 婷,李增禄,聂佳佳
(西南交通大学 经济管理学院,四川 成都 610031)
考虑由垄断供应商和双寡头制造商组成的二级供应链,在投资成本外生的条件下,研究网络外部性对供应商投资策略和竞争性制造商创新技术选择的影响。研究发现:(1)当网络外部性较小时,若投资成本较低,供应商同时投资两种技术;若投资成本适中,供应商仅投资一种技术;若投资成本较高,供应商不投资任何技术。(2)当网络外部性较大时,若投资成本较低,供应商最优策略为均投资,否则,为均不投资。(3)当网络外部性较小且技术的市场流失率较低或当网络外部性较大时,制造商会选择差异化的均衡策略,否则均会选择市场份额占比更高的技术。(4)供应商仅投资一项技术时,网络外部性使得制造商利润先增加后减少;同时投资两项技术时,网络外部性使得制造商利润均增加。
网络外部性;纳什均衡;创新技术;投资策略
0 引言
随着科技的进步,在汽车和软件等行业内新兴技术得到了蓬勃发展,据统计,我国在2017年的新能源汽车专利为2.1万件,同比增长19.5%。虽然新兴技术得到了广泛认可,但也面临许多问题,以新能源汽车为例,2017年上半年,欧洲市场电动汽车销售涨幅高达56%,而电动汽车的市场份额却不足1%,造成这种现象的原因之一在于高额的生产成本,如特斯拉S型轿车的成本高达两万美元,其远远高于许多燃油车的成本。成本居高不下使得新兴科技产业陷入困境,为了降低生产成本,越来越多的企业选择专利公开,吸引感兴趣的上游供应商为其投资[1]。自2014年美国电动汽车巨头特斯拉宣布将对外公布全部专利后,丰田、宝马、福特等汽车公司纷纷效仿,开放大量专利供竞争对手使用。新兴产业制造商之间拥有不同的专利技术,企业的竞争演变为技术的竞争,例如,特斯拉拥有对8000枚锂电池组的管理技术,而丰田拥有氢燃料电池的专利,作为锂电池和氢燃料电池核心部件原材料的供应商,松下公司的投资策略必须考虑到未来消费者对两项技术的偏好程度与各自的市场前景。供应商在面临此类竞争的技术时,应如何制定自身的投资策略,竞争的制造商又应如何进行生产技术策略的选择?这也成为企业与各学者深思的问题。
企业的投资和技术决策一直是学术界研究的热点话题,国内外学者多集中于投资成本[2-4]、投资动机[5-6]投资策略影响因素[7-10]以及专利技术开放[1]几个角度展开研究。在投资成本方面,Wang等[2]在技术投资成本较高时对比了碳足迹下传统技术与创新技术之间的动态投资;随后,在受到预算约束时,Boyabatlı[3-4]探讨了企业的技术选择与产能水平,并在研究中加入了固定比例技术。从投资动机的角度,Shin与Tunca[5]分析下游企业的竞争对供应链需求预测投资动机的影响,在此基础上,Iyer与Soberman[6]研究了企业对社会责任型创新产品的投资动机,指出投资动机与产品的经济价值有关。部分文献致力于讨论质量溢出效应、技术获取和企业发展战略[7-10]等因素对投资策略产生的影响,牛文举与夏晶[7]分析了质量溢出系数对定价的影响;姜滨滨与匡海波[8]基于技术获取的视角,研究联盟企业的专利策略选择。近些年来,专利技术公开这一话题也逐渐受到重视,基于Wang[2]和Boyabatlı[3-4]等人的研究,Hu等[1]首次探讨了企业专利技术开放策略,发现专利的开放可以吸引供应商投资,而制造商也许会陷入“囚徒困境”,进而导致其不进行技术分享。
以上文献讨论了企业的技术投资与决策问题,消费者作为供应链中的重要一员,其行为偏好是唯一可以检验企业策略有效性的试金石,消费者之间的传播效应是企业决策时不可忽略的重要因素。高新技术产品往往具有较强的网络外部性[11-12],比如,在苹果、三星等品牌主导的手机市场,每款新产品大都会迅速风靡一时。学术界关于网络外部性的研究从未停息,关于网络外部性,其最早可追溯到Katz和Shapiro[13]的研究,他们认为,消费者的效用取决于处于同一网络中的其他用户的数量,会随着购买该产品的总需求的增加而增加。现有文献对网络外部性的研究主要分为两部分,一是对网络外部性本身的研究[14-15],二是在网络外部性背景下的研究[16-26]。基于网络外部性,其研究内容聚焦于产品的定价策略[12,18-21],供应链协调[11,22-23],以及技术兼容决策等方面[24-26]。从产品定价来看,Prasad等[12]比较了网络外部性和产品成本对称性对捆绑策略选择的影响,指出当两个产品的边际成本较低或网络外部性较高时,纯捆绑更有利可图;而易余胤[19]则从演化博弈的视角,在网络外部性背景下分析有限理性的零售商的市场偏好。从供应链协调角度,刘晓婧与艾兴政[11]研究链与链竞争纵向联盟,指出网络外部性对竞争强度影响较大时会导致联盟失效。在技术兼容方面,Toshimitsu[26]分析企业在产品兼容性,产品差异化和网络效应下的均衡行为,认为具有较高兼容性的公司具有更大的竞争优势。还有部分学者讨论网络外部性对新兴平台的影响[27-28],Anderson等[28]从视频游戏行业的出发,研究新兴平台的管理者如何在双边网络外部性的市场中决策每个产品开发周期投资的平台性能水平。正如Katz和Shapiro[13]所述,网络外部性影响了消费者的购买决策。对于本文研究所涉及的供应链各成员,制造商必须考虑选择何种技术进行生产以赢得消费者青睐,获取更大的市场份额,由此影响了制造商的服务水平与最优定价,此外,由于供应链成员之间的信息传递与杠杆效应,供应商势必会在技术投资成本与消费者偏好等因素之间做出权衡以实现自身利益的最大化。可见,网络外部性的存在将会对供应链上下游企业的经营决策造成影响,这也成为本文的研究重点与创新之处。
纵观以往的研究,虽然学者针对企业技术策略与产品网络外部性展开了一系列研究并取得了丰富的成果,然而大部分却忽视了在企业开放专利的情形下,网络外部性对供应商投资策略以及制造商技术选择的影响。鉴于此,本文在Hu等[1]的研究基础上,构建网络外部性背景下由单个供应商与两个竞争制造商组成的二级供应链模型,主要研究以下几个问题:(1)网络外部性对供应商投资策略有何影响?(2)网络外部性对竞争性制造商生产策略的影响?(3)网络外部性是否总对供应链各成员有益?文章的贡献主要有两点,一是扩展了网络外部性与技术型产品的理论研究;二是丰富了供应链上下游各企业的技术创新决策研究。希望所得结论可为相关企业决策提供理论依据和参考。
文章内容主要分为五部分。第一部分对研究问题与模型做出说明;第二部分构建制造商选择各策略时的利润模型;两制造商的均衡策略将在第三部分进行分析;在此基础上,第四部分讨论供应商的最优投资决策;第五部分总结全文并对未来的工作提供一些建议。
1 问题描述及模型假设
图1 生产销售活动决策顺序
Figure 1 Decision-making sequence of production and sales activities
在上述生产销售活动决策顺序的基础之上,我们对模型假设及求解方法做出几点说明:(1)假设供应链信息是对称的,两个制造商同时决策订货量;(2)本文假设制造商是在获取市场偏好之后采取技术投入生产,事实上这种情况在现实中比较常见,例如,惠普在过去是一家生产商业微型电脑的公司,但在IBM公司成功推出个人电脑之后也开始进入个人电脑市场;(3)文中所构建的模型属于多阶段博弈模型,运用逆向归纳法求解子博弈完美纳什均衡,即从最后一个阶段博弈方的行为开始分析,逐步倒推回前一个阶段相应博弈方的行为选择,直到分析至第一个阶段[31]。基于本文的决策顺序,求解过程应是首先根据消费者购买决策与企业的采购博弈得出两个制造商生产策略的纳什均衡,其次根据制造商的均衡策略求出供应商的投资策略。
2 制造商利润模型
2.1 供应商均不投资()
2.2 供应商仅投资一项技术()
根据供应商的最优批发价格,将其代入式(5),得到制造商的最优产量为:
分别将批发价及产量表达式代入(2)、(3)、(4)式,供应商和制造商的最优利润为:
2.3 供应商同时投资()
表1 制造商不同策略下的纳什均衡结果
进而可求得此时制造商与供应商的最优收益,整理结果如表1所示。
情形3与情形4的计算方法分别与情形2和情形1类似,总结制造商四种策略组合下的均衡产量及各自的最优利润如表1所示。
3 制造商均衡策略
图2 制造商与的收益矩阵
3.1 无网络外部性()
命题1:
命题1表明,制造商倾向于选择市场份额较大的技术。而当市场流失率较小时,两项技术的市场份额相差不大时,制造商的策略选择出现差异化。这是因为此时消费者忠诚度较高,相比于选择同一种技术进行产量竞争,制造商垄断自身的消费者市场可以获得更高的利润。
3.2 有网络外部性()
考虑产品网络外部性时,制造商的均衡策略同时受到市场流失率,网络外部性与市场份额的影响。分析图1中双寡头制造商的收益矩阵可得命题2。
命题2:
图3 制造商均衡策略()
图4 制造商均衡策略()
4 供应商投资策略
由逆向归纳法,根据上述第二阶段制造商的策略选择,现求解第一阶段供应商的投资策略,通过比较供应商均不投资、仅投资一项技术、同时投资两项技术三种策略下的期望收益,分析供应商的最优投资策略。
4.1 均不投资()
供应商不投资任何技术时,制造商无法获取原材料生产产品,进而导致供应链各成员的期望收益均为0。
4.2 投资或()
4.3 同时投资()
表2 供应商同时投资两项技术的均衡利润
命题3:网络外部性对制造商期望收益的影响
(1)供应商不投资任何技术时,网络外部性对制造商均衡利润无影响;
(31)
图6 网络外部性较大时供应商投资策略
图6中,随着网络外部性的增大,供应商的投资动机均增大,且该趋势并没有受到市场流失率的影响。这是由于网络外部性较大时,消费者受购买相同产品用户数量的影响也越大,供应商的“仅投资一个”策略将逐渐被“均投资”和“均不投资”所替代,即使技术的外溢效应很大,投资一项技术也不能为供应商带来高收益。对比(a)、(b)两图还可以看出,供应商投资动机随着市场流失率的增大而提高,“均不投资”策略所占面积逐渐减小,而“均投资”和“仅投资一个”策略的范围逐渐增大。这是因为两项技术的可替代性越大,消费者市场潜在需求就会越高,制造商均衡产量也会随之增加,因此,在投资成本一定的情况下,供应商的投资意愿会相应增强。
5 结论与展望
技术竞争与投资在新兴行业中是一种非常普遍的现象,专利技术的开放也逐渐成为制造商吸引供应商对其进行技术投资进而减少生产成本的一种重要手段。基于新兴技术产品具有网络外部性的特征,文章研究网络外部性对供应商投资策略以及竞争性制造商技术选择的影响。首先,讨论供应商不同投资策略下制造商的均衡产量及最优利润,得出制造商均衡策略,然后根据逆向归纳法分析供应商的最优投资策略。研究发现,网络外部性增加了制造商的均衡产量,而对供应商的批发价无影响,这与易余胤[22]和Nan[32]等人的观点一致;我们还发现,制造商的均衡策略主要受到技术市场份额的影响,他们均会选择市场份额占比更高的技术,当网络外部性与市场流失率均较小或网络外部性较大,技术的市场份额大小适中时会促使制造商的策略选择出现差异化,这进一步印证且拓展了Hu[1]的观点;一般而言,企业收益会随着网络外部性的增加单调递增[18,22],部分学者认为网络外部性还可能与企业利润呈负相关[32],但我们的结论表明,当供应商仅投资一项技术时,随着网络外部性的增大,制造商的期望收益先增加后减少,这可能与其竞争强度有关;当网络外部性较小时,若投资成本较低,供应商同时投资两种技术;若投资成本适中,供应商仅投资一种技术;若投资成本较高,供应商不投资任何技术,这与传统认知是相似的,但当网络外部性较大时,无论投资成本如何变化,供应商不会出现仅投资一种策略的情况。本研究丰富了网络外部性的研究范围,文章所得结论可为企业的生产和投资策略提供实践指导。
可以从以下几个方面对文章进行拓展:(1)从供应商角度来看,供应商可能会由于生产规模小等因素造成产能不足[33],因此,在供应商产能约束这一条件下研究供应商的投资策略想必会得出新的结论。(2)从制造商角度来看,竞争性制造商往往会存在公平关切意识[34],考虑制造商的公平关切性对企业技术决策的影响也将会是一个有价值的研究方向。(3)更进一步,从供应链上下游关系来看,在现实中,供应商对制造商技术持股现象较为普遍[35],故而,当供应商与制造商之间存在持股关系时上述结论是否依然成立?也是一个值得关注的问题。
[1] Hu B, Hu M, Yang Y. Open or closed? Technology sharing, supplier investment, and competition[J]. Manufacturing & Service Operations Management, 2017, 19(1): 132-149.
[2] Wang W, Ferguson M E, Hu S, et al. Dynamic capacity investment with two competing technologies[J]. Manufacturing & Service Operations Management, 2013, 15(4): 616-629.
[3] Boyabatlı O, Leng T, Toktay L B. The impact of budget constraints on flexible vs. dedicated technology choice[J]. Management Science, 2015, 62(1): 225-244.
[4] Boyabatlı O. Supply management in multiproduct firms with fixed proportions technology[J]. Management Science, 2015, 61(12): 3013- 3031.
[5] Shin H, Tunca T I. Do firms invest in forecasting efficiently? The effect of competition on demand forecast investments and supply chain coordination[J]. Operations research, 2010, 58(6): 1592-1610.
[6] Iyer G, Soberman D A. Social responsibility and product innovation[J]. Marketing Science, 2016, 35(5): 727-742.
[7] 牛文举, 夏晶, 汤伟,等. 市场竞争中具溢出效应共同供应商质量投资策略[J]. 管理工程学报, 2017, 31(2):222-232.
Niu W J, Xia J, Tang W. Quality investment in a shared supplier with spillover effects in a competitive market[J]. Journal of Industrial Engineering and EngineeringManagement, 2017, 31(2):222-232.
[8] 姜滨滨, 匡海波. 联盟企业专利策略选择及其产出效应研究——技术获取的视角[J]. 科研管理, 2016, 37(8):67-75.
Jing B B, Kuang H B. A research on patent choices and output effect of alliance firms from the perspective of technological acquisition[J]. Science Research Management, 2016, 37(8):67-75.
[9] Chari M D R, Devaraj S, David P. The Impact of Information Technology Investments and Diversification Strategies on Firm Performance. [J]. Management Science, 2008, 54(1):224-234.
[10] Hu S, Souza G C, Ferguson M E, et al. Capacity investment in renewable energy technology with supply intermittency: Data granularity matters![J]. Manufacturing & Service Operations Management, 2015, 17(4): 480-494.
[11] 刘晓婧, 艾兴政, 唐小我. 网络外部性下链与链竞争纵向联盟和收益共享合同[J]. 预测, 2016, 35(4):75-80.
Liu X J, Ai X Z, Tang X W. Vertical alliance and revenue sharing of chain-to-chain competition under network externality[J]. Forecasting, 2016, 35(4):75-80.
[12] Prasad A, Venkatesh R, Mahajan V. Optimal bundling of technological products with network externality[J]. Management Science, 2010, 56(12): 2224-2236.
[13] Katz M L, Shapiro C. Network externalities, competition, and compatibility[J]. The American economic review, 1985, 75(3): 424-440.
[14] Luo X. How Does Shopping With Others Influence Impulsive Purchasing?[J]. Journal of Consumer Psychology, 2005, 15(4):288-294.
[15] Yang J, Mai E. Experiential goods with network externalities effects: An empirical study of online rating system[J]. Journal of Business Research, 2010, 63(9):1050-1057.
[16] Chen Y, Png I. Information goods pricing and copyright enforcement: Welfare analysis[J]. Information Systems Research, 2003, 14(1): 107-123.
[17] Zhang G, Shang J, Yildirim P. Optimal pricing for group buying with network effects ☆[J]. Omega, 2016, 63:69-82.
[18] 郭强, 姚晓玲, 聂佳佳. 网络外部性对电影产品定价策略的影响[J]. 预测, 2016, 35(6):56-62.
Guo Q, Yao X L, Nie J J. Impact of the network externality on pricing strategy of movie products[J]. Forecasting, 2016, 35(6):56-62.
[19] 易余胤, 杨海深, 张显玲. 网络外部性下双零售商竞争的演化博弈分析[J]. 管理科学学报, 2016, 19(9):34-48.
Yi Y Y, Yang H S, Zhang X L. Evolutionary game analysis of duopoly retailers' competition under network externality[J]. Journal of Management Sciences in China, 2016, 19(9):34-48.
[20] 刘维奇, 张苏. 双边平台兼并策略下的定价问题分析[J]. 中国管理科学, 2017, 25(5):17-24.
Liu W Q, Zhang S. Pricing analysis of merger strategy in two-sided markets[J]. Chinese Journal of Management Science, 2017, 25(5):17-24.
[21] Luo X, Li M, Feng H, et al. Intertemporal mixed bundling strategy of information products with network externality[J]. Computers & Industrial Engineering, 2017, 113: 369-381.
[22] 易余胤, 姚俊江. 基于网络外部性的延保服务供应链模型研究[J]. 管理工程学报, 2016, 30(3):141-150.
Yi Y Y, Yao J J. Supply chain coordination with extended warranty under network externality[J]. Journal of Industrial Engineering and Engineering Management, 2016, 30(3):141-150.
[23] 孟卫东, 邱冬阳, 赵世海. 网络外部性下基于溢出效应的供应链合作研发模型[J]. 系统管理学报, 2011, 20(6):670-676.
Meng W D, Qiu D Y, Zhao S H.Research on cooperative R&D policy in supply chain with network externality[J]. Journal of Systems & Management, 2011, 20(6):670-676.
[24] Mak V, Zwick R. Investment decisions and coordination problems in a market with network externalities: An experimental study [J]. Journal of Economic Behavior & Organization, 2010, 76(3):759-773.
[25] Chen H C, Chen C C. Compatibility under differentiated duopoly with network externalities[J]. Journal of Industry, Competition and Trade, 2011, 11(1): 43-55.
[26] Toshimitsu T. Compatibility under differentiated duopoly with network externalities: A comment[J]. Journal of Industry, Competition and Trade, 2014, 14(3): 331-335.
[27] Chu J, Manchanda P. Quantifying cross and direct network effects in online consumer-to-consumer platforms[J]. Marketing Science, 2016, 35(6): 870-893.
[28] Anderson Jr E G, Parker G G, Tan B. Platform performance investment in the presence of network externalities[J]. Information Systems Research, 2013, 25(1): 152-172.
[29] 聂佳佳. 预测信息分享对制造商开通直销渠道的影响[J]. 管理工程学报, 2012, 26(2):106-112.
Nie J J. The Effect of forecast information sharing on manufacturer's launching direct channels[J]. Journal of Industrial Engineering and Engineering Management, 2012, 26(2):106-112.
[30] 潘小军, 陈宏民, 胥莉. 基于网络外部性的固定与比例抽成技术许可[J]. 管理科学学报, 2008, 11(6):11-17.
Pan X J, Chen H M, Xu L.Fee versus royalty technology licensing with network externality[J]. Journal of Management Sciences in China, 2008, 11(6):11-17.
[31] 谢识予. 经济博弈论[M]. 复旦大学出版社, 2002.
Xie S Y. Economic game theory[M]. Fudan University Press, 2002.
[32] Nan G, Shi F, Dou R, et al. Duopoly Pricing of Software Products under Free Strategy: Limited-feature vs. Seeding[J]. Computers & Industrial Engineering, 2016, 100:13-23.
[33] Tomlin B. On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks[J]. Management Science, 2006, 52(5):639-657.
[34] 姚锋敏, 滕春贤. 公平关切下第三方回收闭环供应链决策模型[J]. 中国管理科学, 2016, 24:577-583.
Yao F M, Teng C X. Decision models of closed-loop supply chain with third party recycler considering fairness concern[J]. Chinese Journal of Management Science, 2016, 24:577-583.
[35] 张楠, 周宗放. 供应商持股制造商的供应链协调[J]. 系统工程, 2016,34(4):89-93.
Zhang N, Zhou Z F. Coordinating a supply chain when supplier holds equity in manufacturer[J]. Systems Engineering, 2016,34(4):89-93.
Impact of network externalities on supply chain innovation technology investment strategy
GUO Qiang, ZHANG Ting, LI Zenglu, NIE Jiajia
(School of Economics and Management, Southwest Jiao tong University, Chengdu 610031, China)
With the advancement of technology, emerging technologies in the automotive and software industries have flourished. Although emerging technologies are widely recognized, they also face many problems. High costs keep the emerging technology industry in a difficult position. In order to reduce production costs, more and more companies choose to open patents to attract interested upstream suppliers to invest in them. The investment strategy of suppliers must take into account future consumers’ degree of preference for each technology and their respective market prospects. High-tech products often have strong network externalities, which may affect consumers' purchasing decisions. For example, in the mobile phone market, dominated by brands such as Apple and Samsung, most new products will immediately become popular, and stay popular for a while. Therefore, this paper will focus on the impact of network externalities on suppliers’ investment strategies and competitive manufacturers’ technology production decisions.
Consider a secondary supply chain consisting of a single supplier and a duopoly of manufacturers. The two manufacturers each have a patented technology, and the supplier supplies each manufacturer with the raw materials needed for production. In order to keep the production cost of the technologies at a reasonable level, the supplier faces three investment choices; that is, invest in both technologies at the same time, in only one, or in neither. Subsequently, the two manufacturers simultaneously select the technology for production according to market preferences. If the supplier does not invest in either technology, the manufacturer is unable to obtain raw materials, which then hinders production activities. The first step is to establish a supplier investment model under the condition of technology investment cost being exogenous; the next step is to consider the network externalities and preferences of the market, using the Cournot model to build a competitive manufacturer production model, solving the model for the equilibrium production and income of the manufacturer by means of game theory related methods, and from there deriving the expected profit of the supplier; finally, the last step is to determine the optimal decision by comparing and analyzing the expected return of the supplier with corresponding quantitative analysis.
Through the above research, it is found that network externalities increase the equilibrium output of the manufacturer while having no effect on the wholesale price of the supplier. The manufacturer's equilibrium strategy is mainly affected by the technology’s market share. Manufacturers always choose technologies with a higher market share. When both network externalities and the market loss rate are small, or network externalities are large and the market share is moderate, manufacturers will be prompted to differentiate their strategic choices. When a supplier invests only in one technology, as network externalities increase, the expected return of the manufacturer increases first and then decreases, possibly in relation to the strength of its competition. When network externalities are small, if the investment cost is low, the supplier will invest in two technologies at the same time; if the investment cost is moderate, the supplier will only invest in one technology; if the investment cost is high, the supplier will not invest in any technology, similarly to traditional cognition. But when network externalities are large, regardless of how the investment cost changes, the supplier will not choose to invest in only one technology. This study enriches the scope of research on network externalities, and the conclusions of this article are intended to provide practical guidance for corporate production and investment strategies. This article can be expanded from the following aspects: 1) From the suppliers’ point of view, a supplier may have insufficient capacity due to factors such as a small production scale. Therefore, studying the supplier's investment strategy under the condition of capacity constraints may lead to new conclusions; 2) From the manufacturers’ point of view, competitive manufacturers often have a desire for fairness. Considering the influence of manufacturers' fairness on corporate technology decisions will also be valuable, in terms of decision outcomes and the future direction of this research; 3) Further, from the perspective of the upstream and downstream relationships of the supply chain, in reality, it is more common for the supplier to have a shareholding in the technology of the manufacturer. Therefore, when a shareholding relationship exists between the supplier and the manufacturer, is the above conclusion maintained? It is also worth paying attention to this issue.
Network externality; Nash equilibrium; Production strategy; Investment incentive
2017-09-29
2018-08-20
Supported by the Natural Science Foundation of China (71440016, 71672153); the Soft Science Research Program of Sichuan Province (2018ZR0362) and the Sichuan Science and Technology Program (2015gz0083-1)
F270.5
A
1004-6062(2020)04-0079-010
10.13587/j.cnki.jieem.2020.04.009
2017-09-29
2018-08-20
国家自然科学基金资助项目(71440016、71672153);四川省软科学研究计划项目(2018ZR0362);四川省科技计划项目(2015GZ0083-1)
郭强(1970—),男,河南偃师人;博士、教授;研究方向为运营管理与决策优化分析。
中文编辑:杜 健;英文编辑:Boping Yan