多维网上拍卖优化机制与决策模型研究
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摘要
近年来,网上拍卖己成为电子商务中一个特别受青睐的交易模式,人们对网上拍卖在理论上和实践上已经展开了广泛研究。作为一种有效的商品定价和资源分配机制,多维网上拍卖的实现与推广是电子商务纵深发展的需要和重要途径,因此近期引起了广大学者高度的关注。但目前多维网上拍卖还缺乏完整的系统的理论支撑和实践指导。一方面,由于多维拍卖自身的复杂性,理论研究相对滞后,运行效率与实践复杂性之间的矛盾成为阻碍其得到广泛应用的瓶颈问题;另一方面,尽管信息技术的飞速发展在技术层面上使得网上拍卖多种物品并考虑多种属性成为可能,但在实际的操作方面还存在很多问题与困难。多维网上拍卖优化机制与决策模型研究正是在这种背景下进行的,通过利用智能计算技术来建立更为复杂的拍卖交易规则,用于拍卖的组织和计划,实现对更为复杂的多物品进行拍卖。
在网上多维拍卖的机理设计中,多维拍卖竞胜标的确定问题是一个十分复杂的问题,事实上它已经被证明是NP(Non-deterministic Polynomial,非确定性多项式)难题。本文是通过应用现代启发式算法来对这一问题展开研究的,现代启发式算法给这一问题的求解带来十分光明的科学前景。本文研究选题的首要动因在于多维拍卖机制的设计要求,这一拍卖机制能够更加准确地反映竞标人的愿望。其次,智能计算技术使得多维网上拍卖机制成为一个十分活跃的研究领域,现有的项目评标、决标模型和采购合同的反向拍卖模型将被拓展。最后,将上述模型和算法在多维网上拍卖系统中的成功实现又为理论应用于实际提供了方法。具体内容如下:
首先,系统地总结和分析传统拍卖理论研究的内容与方法,从而引出网上拍卖这一科学问题。以基准点模型为基础,通过分析网上拍卖最优机制设计的基本原理,指出原有方法的不足,提出了基于智能代理的策略学习方法。
其次,在分析网上拍卖基础理论的基础上,讨论单物品多属性拍卖形式。对单物品多属性网上拍卖的性质进行分析,并构建单物品多属性网上拍卖模型,对竞标人的策略、成本函数以及拍卖的最优评分函数进行详细分析,并放松假设条件,对单物品多属性网上拍卖进行扩展分析。
再次,在对单物品多属性网上拍卖模型进行研究之后,将拍卖物品数量空间进行扩展,研究多物品多属性(多维)网上拍卖模型,将多物品多属性网上拍卖依据拍卖物品性质分成同质多维和异质多维两种情况进行分析,得出具有一般意义的结论。在同质多维模型中,主要对优化机制和团购策略进行分析,在异质多维模型中,主要对激励相容特性和个体理论因素进行描述,同时针对网上拍卖自身的特点,提出了多维网上拍卖的动态优化机制,对动态优化机制的评分函数、投标规则,以及投标策略进行了分析。
第四,在多维拍卖竞胜标问题的优化算法上进行了深入研究。从电子商务中的多维拍卖机理出发,以第一价格密封拍卖方式为背景,通过分析多维拍卖标的集合竞胜标确定的复杂性,给出了组合拍卖竞胜标确定问题的一般模型,并指出了该问题为离散组合优化问题。然后通过引入智能算法思想,在遗传算法中采用自交叉遗传算子和嵌入优先适合启发式规则了设计了求解该模型的优先适合启发式遗传算法。与此同时,利用了混沌吸引子的遍历特性,为该模型设计了优先适合启发式混沌搜索算法。
最后,在上述研究工作的基础之上,本文设计了一个面向电子商务的多维拍卖原型系统,给出了系统分析、系统设计与系统实现的全过程。并在其中的安全协议设计方面进行了创新性研究,通过实际应用系统对本文的研究成果进行了验证。
Recently, because Internet auctions have garnered a great deal of interest, it has become an especially popular trading mode of Electronic Commerce (EC) and a promising field for applying agent and Artificial Intelligence Technologies. Various theoretical and practical studies on Internet auctions have already been conducted. Among these studies, those on multidimensional-auctions have lately attracted considerable attention. However, multidimensional-auctions have also lack of integrity systematic theoretical support and practical guidance. On the one hand, as a result of the complexity of multi-dimensional auction itself, theoretical research has lagged behind, operating efficiency and the complexity of practice have been the bottleneck problem to its extensive usage; On the other hand, despite the rapid development of information technology makes multiple attributes online auctions become possible, there are still many problems and difficulties in operation. Optimize multi-dimensional online auction mechanism and decision-making model are conducted in this context that through the use of intelligent computing technology to set up more complex auction trading rules for the organizations and programs to achieve more complex auctions.
The selection of winning bids in the first-prices multidimensional-auctions is an extremely complex problem; in fact it has been shown to be NP-complete. Our research problem is to introduce meta-heuristic algorithms to solve the identical problem. The meta-heuristic algorithms put the problem to be solved into a proper science perspective. The primary motivation for studying this problem was an acknowledgement of the need for combinatorial auction mechanism that more accurately reflects the demands of the bidders. Secondly, the ability to harness computational intelligence has made possible more complex combinatorial reverse auction mechanism opening an exciting area of research and the models available has been expanded through this endeavor. Finally, the implementation of the models and algorithms in the combinatorial tendering and bidding software system provides a way to put theory into practice.
The major progresses of this paper are shown as follows:
Firstly, this dissertation summarizes and analyzes the contents and methods of traditional auction theory, which leads to online auctions this scientific problem. To reference point model for the foundation, through the analysis of basic principles to optimal online auction mechanism design, pointing out the inadequacy of the original method, then provide strategy learning method based on intelligent agent.
Based on the analysis to the basic theory of online auctions, the auction space will be extended to multi-dimensional space. The first question is multi-attribute auction to unit item. this dissertation analyze the nature and build a multi-attribute to single-item model for online auctions, and conduct a detailed analysis to bidders strategy, cost function, and the optimal score function; then relax the assumption and take more analysis to multi-attribute to unit item online auctions.
Having fully researched on multi-attributes online auction to unit item, the auction space will be expanded, namely discuss the multi-attributes online auction model to mluti-items, and classify the items to homogeneous and heterogeneous according to the quality, and obtain the generally conclusion. In homogeneous multi-dimensional model, what needs to do is the analysis to optimal mechanism and buy; in the heterogeneous multi-dimensional model, what needs to do is the description to main the incentive compatibility and individual factors theories, and to the characteristics of online auctions. It can provide dynamic optimization mechanism for multi-dimensional online auction, and analyze the score function of dynamic optimization mechanism, bidding rules, as well as the bidding strategy.
Because of the fuzzy character of decision relation, this dissertation presents a fuzzy rough Study on optimization algorithms of winner determination in multi-dimensional auctions. Beginning with combinatorial auctions mechanisms in the electronic commerce, the complexity of the set of target and winner determination is analyzed on the background of the first-rice sealed auction. The general model of winner determination in multi-dimensional auctions is formulated. The model indicated that it is a problem on combinatorial optimization. Adopting self-crossing genetic operators and embedding the Fitting-First heuristic rules presented a genetic algorithm presented on the basis of the ideas of heuristic logarithms. Meanwhile, utilizing the characteristic of attractors in chaos, the fitting-first heuristics embedded chaotic search is also proposed.
Lastly, based on the work outlined above, a prototype system of e-commerce oriented multi-dimensional is analyzed, designed and achieved. The prototype system verifies the conclusion above. This dissertation enriches and fulfills the theory of multi-dimensional online auction, overcomes the shortcomings of existed methods. The further research direction of multi-dimensional online auction is showed clearly in this dissertation. Its results will contribute greatly to future applications.
在网上多维拍卖的机理设计中,多维拍卖竞胜标的确定问题是一个十分复杂的问题,事实上它已经被证明是NP(Non-deterministic Polynomial,非确定性多项式)难题。本文是通过应用现代启发式算法来对这一问题展开研究的,现代启发式算法给这一问题的求解带来十分光明的科学前景。本文研究选题的首要动因在于多维拍卖机制的设计要求,这一拍卖机制能够更加准确地反映竞标人的愿望。其次,智能计算技术使得多维网上拍卖机制成为一个十分活跃的研究领域,现有的项目评标、决标模型和采购合同的反向拍卖模型将被拓展。最后,将上述模型和算法在多维网上拍卖系统中的成功实现又为理论应用于实际提供了方法。具体内容如下:
首先,系统地总结和分析传统拍卖理论研究的内容与方法,从而引出网上拍卖这一科学问题。以基准点模型为基础,通过分析网上拍卖最优机制设计的基本原理,指出原有方法的不足,提出了基于智能代理的策略学习方法。
其次,在分析网上拍卖基础理论的基础上,讨论单物品多属性拍卖形式。对单物品多属性网上拍卖的性质进行分析,并构建单物品多属性网上拍卖模型,对竞标人的策略、成本函数以及拍卖的最优评分函数进行详细分析,并放松假设条件,对单物品多属性网上拍卖进行扩展分析。
再次,在对单物品多属性网上拍卖模型进行研究之后,将拍卖物品数量空间进行扩展,研究多物品多属性(多维)网上拍卖模型,将多物品多属性网上拍卖依据拍卖物品性质分成同质多维和异质多维两种情况进行分析,得出具有一般意义的结论。在同质多维模型中,主要对优化机制和团购策略进行分析,在异质多维模型中,主要对激励相容特性和个体理论因素进行描述,同时针对网上拍卖自身的特点,提出了多维网上拍卖的动态优化机制,对动态优化机制的评分函数、投标规则,以及投标策略进行了分析。
第四,在多维拍卖竞胜标问题的优化算法上进行了深入研究。从电子商务中的多维拍卖机理出发,以第一价格密封拍卖方式为背景,通过分析多维拍卖标的集合竞胜标确定的复杂性,给出了组合拍卖竞胜标确定问题的一般模型,并指出了该问题为离散组合优化问题。然后通过引入智能算法思想,在遗传算法中采用自交叉遗传算子和嵌入优先适合启发式规则了设计了求解该模型的优先适合启发式遗传算法。与此同时,利用了混沌吸引子的遍历特性,为该模型设计了优先适合启发式混沌搜索算法。
最后,在上述研究工作的基础之上,本文设计了一个面向电子商务的多维拍卖原型系统,给出了系统分析、系统设计与系统实现的全过程。并在其中的安全协议设计方面进行了创新性研究,通过实际应用系统对本文的研究成果进行了验证。
Recently, because Internet auctions have garnered a great deal of interest, it has become an especially popular trading mode of Electronic Commerce (EC) and a promising field for applying agent and Artificial Intelligence Technologies. Various theoretical and practical studies on Internet auctions have already been conducted. Among these studies, those on multidimensional-auctions have lately attracted considerable attention. However, multidimensional-auctions have also lack of integrity systematic theoretical support and practical guidance. On the one hand, as a result of the complexity of multi-dimensional auction itself, theoretical research has lagged behind, operating efficiency and the complexity of practice have been the bottleneck problem to its extensive usage; On the other hand, despite the rapid development of information technology makes multiple attributes online auctions become possible, there are still many problems and difficulties in operation. Optimize multi-dimensional online auction mechanism and decision-making model are conducted in this context that through the use of intelligent computing technology to set up more complex auction trading rules for the organizations and programs to achieve more complex auctions.
The selection of winning bids in the first-prices multidimensional-auctions is an extremely complex problem; in fact it has been shown to be NP-complete. Our research problem is to introduce meta-heuristic algorithms to solve the identical problem. The meta-heuristic algorithms put the problem to be solved into a proper science perspective. The primary motivation for studying this problem was an acknowledgement of the need for combinatorial auction mechanism that more accurately reflects the demands of the bidders. Secondly, the ability to harness computational intelligence has made possible more complex combinatorial reverse auction mechanism opening an exciting area of research and the models available has been expanded through this endeavor. Finally, the implementation of the models and algorithms in the combinatorial tendering and bidding software system provides a way to put theory into practice.
The major progresses of this paper are shown as follows:
Firstly, this dissertation summarizes and analyzes the contents and methods of traditional auction theory, which leads to online auctions this scientific problem. To reference point model for the foundation, through the analysis of basic principles to optimal online auction mechanism design, pointing out the inadequacy of the original method, then provide strategy learning method based on intelligent agent.
Based on the analysis to the basic theory of online auctions, the auction space will be extended to multi-dimensional space. The first question is multi-attribute auction to unit item. this dissertation analyze the nature and build a multi-attribute to single-item model for online auctions, and conduct a detailed analysis to bidders strategy, cost function, and the optimal score function; then relax the assumption and take more analysis to multi-attribute to unit item online auctions.
Having fully researched on multi-attributes online auction to unit item, the auction space will be expanded, namely discuss the multi-attributes online auction model to mluti-items, and classify the items to homogeneous and heterogeneous according to the quality, and obtain the generally conclusion. In homogeneous multi-dimensional model, what needs to do is the analysis to optimal mechanism and buy; in the heterogeneous multi-dimensional model, what needs to do is the description to main the incentive compatibility and individual factors theories, and to the characteristics of online auctions. It can provide dynamic optimization mechanism for multi-dimensional online auction, and analyze the score function of dynamic optimization mechanism, bidding rules, as well as the bidding strategy.
Because of the fuzzy character of decision relation, this dissertation presents a fuzzy rough Study on optimization algorithms of winner determination in multi-dimensional auctions. Beginning with combinatorial auctions mechanisms in the electronic commerce, the complexity of the set of target and winner determination is analyzed on the background of the first-rice sealed auction. The general model of winner determination in multi-dimensional auctions is formulated. The model indicated that it is a problem on combinatorial optimization. Adopting self-crossing genetic operators and embedding the Fitting-First heuristic rules presented a genetic algorithm presented on the basis of the ideas of heuristic logarithms. Meanwhile, utilizing the characteristic of attractors in chaos, the fitting-first heuristics embedded chaotic search is also proposed.
Lastly, based on the work outlined above, a prototype system of e-commerce oriented multi-dimensional is analyzed, designed and achieved. The prototype system verifies the conclusion above. This dissertation enriches and fulfills the theory of multi-dimensional online auction, overcomes the shortcomings of existed methods. The further research direction of multi-dimensional online auction is showed clearly in this dissertation. Its results will contribute greatly to future applications.
引文
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65 Maskin and Reily. Efficient Auctions. Quarterly Journal of Economics. 2000, 95(2): 341~88
66 M. L.Emiliani. Squaring Online Reverse Auctions with the Caux Round Table Principles for Business. Supply Chain Management. 2002, 7(2): 92~100
67 Bergemann, Disk and Juuso Valimaki. Information Acquisition and Efficient Mechanism Design Jj, Econometrica. 2002, 70(3): 1007~1033
68 C.M. Campbell, D. Levin, Can the Seller Benefit from an Insider in Common-value Auctions. J. Econ. Theory. 2006, (91): 106~120
69 Rica Gonen, Daniel Lehmam. Optimal Solutions for Multi-unit combinatorial Auctions: Branch and Bound Heuristics. The Second ACM Conference on Electronic Commerce, Proceedings. 2000: 13~21
70 C.Dellarocas, M. Fan. Reciprocity and Participation in Online Reputation Systems Working Paper.University of Notre Dame, Notre. 2003: 24~56
71 Ledyard, J. The first use of a combined value auction for transportation services. 2002, 32 (5): 4~12.
72 G. Hohner, An. Combinatorial and Quality Discount Procurement Auctions with Mutual Benefit s at Mars Incorporated. 2003, 33 (1): 23~35
73 E. Wolfstetter. Auctions: An Introduction. Journal of Economic Surveys.1996, 10(4): 257~420
74 E. Maskin, J. Riley. Optimal Auctions with Risk-averse Buyers. Ecometrica.1984, 52(6): 1473~1518
75 R. Gunther Raidi, Jens Gottlieb. EmpiricaL Analyses of Locality, Heritability and Heuristic l3ia.s, Technical Report of Technische Univfrsitat. 2004: 18~37
76 H. Kim, B. S. Ahn. Interactive Group Decision Making Procedure under Incomplete Information. European Journal of Operational Research. 1999, 116(3): 498~507
77 P. C. Fishburn. Analysis of Decisions with Incomplete Knowledge of Probabilities. Operations Research. 1965, 13(2): 217~237
78 K. J. Arrow. Social Choice and Individual Value. New York: John Wiley &Sons. 1951.钱晓敏,孟岳良译.首都经济贸易大学出版社. 2000: 81
79 I. Watson. Case-based Reasoning is a Methodology not a Technology. Knowledge-Based Systems. 1999, 12(5~6): 303~308
80 J. L. Kolodner. Improving Human Decision Making through Cased-BasedReasoning Techniques. AI Magazine. 1991, 12(3): 52~59
81 A. Aamodt and E. Plaza. Case-Based Reasoning: Foundational Issues Methodological Variations, and System Approaches. AI Communications IOS Press. 1994, 17(1): 39~59
82 R. Greiner. Efficient Reasoning. ACM Computing Surveys. 2001, 33(1): 1~30.
83 Z. Pawlak. Rough Set Theory and Its Applications to Data Analysis. Cybernetics and Systems. 1998, 29(7): 661~688
84 S. H. Kim, B. S. Ahn. Group Decision-Making Procedure Considering Preference Strength under Incomplete Information. Computers and Operations Research. 1997, 24(12):1101~1112
85 Chen Xiang, Hu Shan. Vickery type protocol and strategy for automated multi-attribute auctions. ICMLC 2005 , Guangzhou , 2005: 231- 236
86 M Bichler, BidTaker An application of multi-attribute auction markets in tourism. Wirtschafts informatik 2001 , Augsburg , Germany , 2001:39
87 G. D. Holt, P. O. Olomolaiye, and F.C. Harris. Applying Multi-Attribute Analysis to Contractor Selection Decisions. European Journal of Purchasing & Supply Management. 1994, 1(3): 139~148
88 A. Blum, V. Kumar, A. Rudra, and F. Wu. Online Learning in Online Auctions. Theoretical Computer Science. 2004, 324(2): 137~146
89 S. C. Carlos, F. C. Yolanda, and M. M. Cecilio. Measuring DEA Efficiency in Internet Companies. Decision Support Systems. 2005, 38(4): 557~573
90 V. Dequiedt. Efficient Collusion in Optimal Auctions. Journal of Economic Theory. 2006: 302~323
91 R. Engelbrecht-Wiggans. Optimal Reservation Price in Auctions. Management Science. 1987 (33): 763~770
92 Z. Pawlak, R. Slowinski. Rough Set Approach to Multi-Attribute Decision Analysis. European Journal of Operational Research. 1994, 72(3): 443~459.
93 Z. Pawlak. Rough Set Approach to Knowledge-Based Decision Support. European Journal of Operational Research. 1997, 99(1): 48~57
94 J. Fjermestad. An Analysis of Communication Mode in Group Support Systems Research. Decision Support Systems. 2004, 37(2): 239~263
95 G. Mentzas, C. Halaris, and S. Kavadias. Modeling Business Process with Workflow Systems: An Evaluation of Alternative Approaches. International Journal of Information Management. 2001,21(2): 123~135
96 D. Georgakopoulos, M. Hornick, and A. Sheth. An Overview of Workflow Management: From Process Modelling to Workflow Automation Infrastructure.Distributed and Parallel Databases. 1995, 3(2): 119~153
97 K. Salimifard, M. Wright. Petri Net-Based Modeling of Workflow Systems: An Overview. European Journal of Operational Research. 2001,134(3): 664~676
98 S. Y. Li, B. H. Song. Normalized Workflow Net (NWF-net): Its Definition and Properties. Future Generation Computer Systems. 2005, 21(7): 1004~1014
99 W. M. P. Van der Aalst. Structural Characterizations of Sound Workflow Nets. Technical Reprots, 96/23, Eindhoven: Eindhoven University of Technology. 1996
100 W. M. P. Van der Aalst. Verification of Workflownets Application and Theory of Petri Nets. LNCS 1248. Springer-Verlag, Berlin. 1997: 407~426
101陈国良.遗传算法及其应用.人民邮电出版社. 1996:1~37
102潘正君.演化计算.清华大学出版社. 1998:23~41
103戴晓晖.遗传算法理论研究综述.控制与决策. 2000, 5: 263~268
104张晓缋.遗传算法的编码机制研究.信息与控制. 1997, 26(2):134~139
105陈明.基于进化遗传算法的优化计算.软件学报. 1998, 9 (11):876~879
106 W. M. P. Van der Aalst. Workflow Verification: Finding Controlflow Errors Using Petri-Net Based Techniques, Business Process Management—Models Techniques and Empirical Studies, LNCS 1806. 2000: 161~183
107李亚东,李少远.一种新的遗传混沌优化组合方法.控制理论与应用. 2002, 19(1): 143~145
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63 Milgrom and Weber. Decision-Making with Incomplete Information. European Journal of Operational Research. 1987, 28(1): 44~57
64 R. B. Myerson, M. A. Satterthwaite. Efficient Mechanisms for Bilateral Trading. Journal of Economic Theory. 1983, 29(3): 265~281
65 Maskin and Reily. Efficient Auctions. Quarterly Journal of Economics. 2000, 95(2): 341~88
66 M. L.Emiliani. Squaring Online Reverse Auctions with the Caux Round Table Principles for Business. Supply Chain Management. 2002, 7(2): 92~100
67 Bergemann, Disk and Juuso Valimaki. Information Acquisition and Efficient Mechanism Design Jj, Econometrica. 2002, 70(3): 1007~1033
68 C.M. Campbell, D. Levin, Can the Seller Benefit from an Insider in Common-value Auctions. J. Econ. Theory. 2006, (91): 106~120
69 Rica Gonen, Daniel Lehmam. Optimal Solutions for Multi-unit combinatorial Auctions: Branch and Bound Heuristics. The Second ACM Conference on Electronic Commerce, Proceedings. 2000: 13~21
70 C.Dellarocas, M. Fan. Reciprocity and Participation in Online Reputation Systems Working Paper.University of Notre Dame, Notre. 2003: 24~56
71 Ledyard, J. The first use of a combined value auction for transportation services. 2002, 32 (5): 4~12.
72 G. Hohner, An. Combinatorial and Quality Discount Procurement Auctions with Mutual Benefit s at Mars Incorporated. 2003, 33 (1): 23~35
73 E. Wolfstetter. Auctions: An Introduction. Journal of Economic Surveys.1996, 10(4): 257~420
74 E. Maskin, J. Riley. Optimal Auctions with Risk-averse Buyers. Ecometrica.1984, 52(6): 1473~1518
75 R. Gunther Raidi, Jens Gottlieb. EmpiricaL Analyses of Locality, Heritability and Heuristic l3ia.s, Technical Report of Technische Univfrsitat. 2004: 18~37
76 H. Kim, B. S. Ahn. Interactive Group Decision Making Procedure under Incomplete Information. European Journal of Operational Research. 1999, 116(3): 498~507
77 P. C. Fishburn. Analysis of Decisions with Incomplete Knowledge of Probabilities. Operations Research. 1965, 13(2): 217~237
78 K. J. Arrow. Social Choice and Individual Value. New York: John Wiley &Sons. 1951.钱晓敏,孟岳良译.首都经济贸易大学出版社. 2000: 81
79 I. Watson. Case-based Reasoning is a Methodology not a Technology. Knowledge-Based Systems. 1999, 12(5~6): 303~308
80 J. L. Kolodner. Improving Human Decision Making through Cased-BasedReasoning Techniques. AI Magazine. 1991, 12(3): 52~59
81 A. Aamodt and E. Plaza. Case-Based Reasoning: Foundational Issues Methodological Variations, and System Approaches. AI Communications IOS Press. 1994, 17(1): 39~59
82 R. Greiner. Efficient Reasoning. ACM Computing Surveys. 2001, 33(1): 1~30.
83 Z. Pawlak. Rough Set Theory and Its Applications to Data Analysis. Cybernetics and Systems. 1998, 29(7): 661~688
84 S. H. Kim, B. S. Ahn. Group Decision-Making Procedure Considering Preference Strength under Incomplete Information. Computers and Operations Research. 1997, 24(12):1101~1112
85 Chen Xiang, Hu Shan. Vickery type protocol and strategy for automated multi-attribute auctions. ICMLC 2005 , Guangzhou , 2005: 231- 236
86 M Bichler, BidTaker An application of multi-attribute auction markets in tourism. Wirtschafts informatik 2001 , Augsburg , Germany , 2001:39
87 G. D. Holt, P. O. Olomolaiye, and F.C. Harris. Applying Multi-Attribute Analysis to Contractor Selection Decisions. European Journal of Purchasing & Supply Management. 1994, 1(3): 139~148
88 A. Blum, V. Kumar, A. Rudra, and F. Wu. Online Learning in Online Auctions. Theoretical Computer Science. 2004, 324(2): 137~146
89 S. C. Carlos, F. C. Yolanda, and M. M. Cecilio. Measuring DEA Efficiency in Internet Companies. Decision Support Systems. 2005, 38(4): 557~573
90 V. Dequiedt. Efficient Collusion in Optimal Auctions. Journal of Economic Theory. 2006: 302~323
91 R. Engelbrecht-Wiggans. Optimal Reservation Price in Auctions. Management Science. 1987 (33): 763~770
92 Z. Pawlak, R. Slowinski. Rough Set Approach to Multi-Attribute Decision Analysis. European Journal of Operational Research. 1994, 72(3): 443~459.
93 Z. Pawlak. Rough Set Approach to Knowledge-Based Decision Support. European Journal of Operational Research. 1997, 99(1): 48~57
94 J. Fjermestad. An Analysis of Communication Mode in Group Support Systems Research. Decision Support Systems. 2004, 37(2): 239~263
95 G. Mentzas, C. Halaris, and S. Kavadias. Modeling Business Process with Workflow Systems: An Evaluation of Alternative Approaches. International Journal of Information Management. 2001,21(2): 123~135
96 D. Georgakopoulos, M. Hornick, and A. Sheth. An Overview of Workflow Management: From Process Modelling to Workflow Automation Infrastructure.Distributed and Parallel Databases. 1995, 3(2): 119~153
97 K. Salimifard, M. Wright. Petri Net-Based Modeling of Workflow Systems: An Overview. European Journal of Operational Research. 2001,134(3): 664~676
98 S. Y. Li, B. H. Song. Normalized Workflow Net (NWF-net): Its Definition and Properties. Future Generation Computer Systems. 2005, 21(7): 1004~1014
99 W. M. P. Van der Aalst. Structural Characterizations of Sound Workflow Nets. Technical Reprots, 96/23, Eindhoven: Eindhoven University of Technology. 1996
100 W. M. P. Van der Aalst. Verification of Workflownets Application and Theory of Petri Nets. LNCS 1248. Springer-Verlag, Berlin. 1997: 407~426
101陈国良.遗传算法及其应用.人民邮电出版社. 1996:1~37
102潘正君.演化计算.清华大学出版社. 1998:23~41
103戴晓晖.遗传算法理论研究综述.控制与决策. 2000, 5: 263~268
104张晓缋.遗传算法的编码机制研究.信息与控制. 1997, 26(2):134~139
105陈明.基于进化遗传算法的优化计算.软件学报. 1998, 9 (11):876~879
106 W. M. P. Van der Aalst. Workflow Verification: Finding Controlflow Errors Using Petri-Net Based Techniques, Business Process Management—Models Techniques and Empirical Studies, LNCS 1806. 2000: 161~183
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