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Game Perspectives of DEA Models and Their Duals  [PDF]
Fang Xu,DaQun Zhang,GuoLiang Yang,WenBin Liu
Journal of Applied Mathematics , 2013, DOI: 10.1155/2013/879325
Abstract: We present a series of two-person games, which lead to various DEA models. The relationship between the DEA models and the games is explicit in our setting, although the Nash equilibrium solutions do not generally exist. Besides the classic DEA models, we also establish an explicit relationship between the games and some extended DEA models, such as free disposable hull DEA models and “negative” or “inverted” DEA models. 1. Introduction DEA has widely been used in performance evaluation or productivity evaluation. The DEA models have been derived from different perspectives like econometrics and operations research; see for example, Charnes et al. [1], Banker et al. [2], and Liu et al. [3] for the details. Also, several researchers found that there are close connections between DEA and the game theory [4]. As a pioneer, Banker et al. [5, 6] explored the connections between DEA and the game theory. In their work, they first built the following payoff matrix: In their formulation, the DMU0 being evaluated acts as player 1, who wishes to maximize its payoff and has pure strategies defined by the selection of some inputs . On the other hand, player 2 acts as a “central evaluator,” who wishes to minimize the payoff of player 1 and has pure strategies defined by the selection of a competitive DMU . Then, the authors used a mixed strategy formed from the pure strategies and computed an expected payoff function constructed from the finite payoff matrix above. They formulated the game model as the pair of linear programming problems shown in Table 1. Table 1 After several transformations of the problem (*), the authors obtained the “CCR ratio form,” which is also the maximal expected gains that DMU0 can obtain from the corresponding payoff matrix. However, the game model developed by Banker [5] requires that the output in the model is a number. Banker et al. [6] extended their initial work to include multiple outputs, but they had to replace the original CCR model with the BCC model, which makes it possible to write the linear programming problem for player 2 directly. To establish a rigorous connection between the CCR model and the game theory, Rousseau and Semple [7] developed a class of two-person ratio efficiency games, which have ratio payoff functions solved by two equivalent primal and dual linear programming problems. The authors argued that “the richest information is available from the primal-dual linear programs: one side emphasizes “envelopment” multipliers, the other emphasizes input-output multipliers.” And the most general form of the games is
Review of the utilization of HEEPF – competitive projects for educational enhancement in the Egyptian medical sector
Galal Abdellah, Salah Taher, Somaya Hosny
Human Resources for Health , 2008, DOI: 10.1186/1478-4491-6-7
Abstract: In Egypt, the medical sector of higher education includes five major specialties; medicine, pharmacy, dentistry, nursing, and physical medicine. It represents about 8% and 36% of the total force of higher education in terms of students enrolled and working staff, respectively. Thus, this sector has an average student teacher ratio of 9.5:1, which is a relatively better ratio as compared to the average total ratio in all sectors (39.8:1) [1].Enrolment into higher education in Egypt depends solely on the total score of the secondary school graduation certificate. Applicants for medical sector colleges always have the highest marks among high school graduates, as these colleges admit relatively limited numbers of students in comparison to other sectors. Medical sector colleges have still a highly prestigious outlook and corroborate certified opportunities at national and regional job markets; this renders them a target for the highest achieving students [2].Education in the medical sector is offered via three relatively independent bodies; public secular, public religious, and private. The public secular body contains 49 colleges in which 116 326 (79.7%) students are enrolled. The private body includes 13 colleges in which 19 942 (13.7%) students are registered, while the religious body (Al-Azhar University) has 10 colleges which have a total of 9601 (6.6%) students, according to data of academic year 2004–2005 [1].Because the public secular body of the medical sector has the largest share in terms of students' enrolment (see Figure 1), it became the main target of the educational enhancement projects funded by the World Bank and the Egyptian government.The system of higher education in Egypt has been facing a number of problems and challenges during the last decades. This situation that led to a state of low system efficiency was previously addressed and analyzed [3,4].Besides the typical problems of overcrowding, limited financial resources, lack of a sustainable fin
Method of allocating the fixed cost based on data envelopment analysis and cooperative game
基于DEA与联盟博弈的固定成本分摊方法

LI Yong-jun,LIANG Liang,
李勇军
,梁樑

系统工程理论与实践 , 2008,
Abstract: 结合DEA(Data Envelopment Analysis)和联盟博弈方法研究固定成本分摊问题.首先证明了如果将分摊成本作为新的投入,则所有的决策单元将是DEA有效.在此基础上,结合联盟博弈理论,定义了联盟博弈的特征函数,提出了Shapley值的成本分摊方案,最后通过算例说明了该方法的有效,以及与已有的用DEA进行固定成本分摊的方法相比在可实施方面具有一定的优势.
Study on the Allocating and Planning of Brands and Goods  [cached]
Xiaoyun Wang,Jing Wu
International Journal of Business and Management , 2009, DOI: 10.5539/ijbm.v4n6p38
Abstract: By the field survey, we obtained corresponding data, and established the mathematical model by the analytical hierarchy process (AHP). The mathematical model was used to analyze the rationality of the brand introduction and goods allocating and planning in the marketplace in order to enhance the competitive level of the business area, offer more shopping choices when promoting citizens’ purchasing power, exert the advantage of the business area to the largest extent, generate the maximum benefit and ensure the win-win in the same types of operation.
DEA cross efficiency evaluation method for competitive and cooperative decision making units
同时考虑决策单元竞争与合作关系的DEA交叉效率评价方法

YANG Feng,XIA Qiong,LIANG Liang,
杨锋
,夏琼,梁樑

系统工程理论与实践 , 2011,
Abstract: To eliminate the possible multiple solutions in the cross efficiency method,researchers proposed two approaches including the aggressive strategy and the benevolent strategy in which all of the other decision-making units are simultaneously treated as adversaries(allies) to the unit under evaluation. However,none of the strategy may accord completely with the individual preference of a specific DMU. Therefore this paper proposed a DEA cross-efficiency method considering both competition and cooperation amon...
Sharing the Carbon Emission Reduction Responsibility across Chinese Provinces: A Zero Sum Gains DEA Model
中国各省区碳减排责任分摊——基于零和收益DEA模型的研究

ZHENG Liqun,
郑立群

资源科学 , 2012,
Abstract: 研究如何基于国家整体的碳减排目标,进行中国各省区碳减排责任的分摊,以明确区域间"共同但有差别的责任"。从共摊成本分配问题的公平与效率角度出发,对碳减排责任分摊进行了经济学分析。基于分配效率视角,探讨了在分配总量固定的条件下,利用投入导向的零和收益DEA(ZSG-DEA)模型进行碳减排责任分摊的可行性。在实证分析部分,采取非期望产出作为投入法,将碳排放量作为模型的投入,将人口、能源耗费和GDP作为模型产出变量。依照我国2015年碳减排整体目标和各省区经济社会发展特征,进行了投入产出数据的预测。为了与ZSG-DEA模型进行对比,首先建立了碳减排责任分摊的DEABCC模型,计算结果表明:仅有9个省区达到DEA有效,需要对碳排放配额进行再分配。应用ZSG-DEA模型,对我国30个省区的碳减排责任进行了再分配。通过两次迭代计算,得出了达到统一DEA有效边界的分配方案。
Cogenerational sources of energies and their allocating problem
Hrádocky Ladislav,Majerník Milan,Badida Miroslav
Acta Montanistica Slovaca , 1997,
Abstract: Energy production in industrial communities consume a main part of primary raw materials and it is one of the sources of ecologicall impact. Electric power plants and warm produce plants are mostly important investment consuming establishments with a long time of return, what stress along with the economical, predictional, logistical and environmental decision making aspect of their allocating. Already input of the mentioned aspects along with the price movement after the energy depression motivate a formation of new conception of combinated so-called items, which are able to use the energetic potential of fuels with a higher concurrent efficiency and, on the other hand, can reduce ecologic impacts of fossil combustion.
Computations in DEA
Dulá, José H.;
Pesquisa Operacional , 2002, DOI: 10.1590/S0101-74382002000200005
Abstract: dea is a well-established, widely used, and powerful analytical resource in the toolbox of the or/ms analyst. it is used to assess relative efficiency of many, functionally similar, entities. it has applications in diverse areas including finance and banking, education, and healthcare. dea is computationally intensive and, as the scale of applications grows, this intensity rapidly becomes one of the limiting factors in its utility. in this paper, we explore computations in dea. we investigate the theory behind schemes, procedures and algorithms used in performing a dea study and we report on current practices ranging from the basic and standard to the advanced and sophisticated. our objective is to give researchers and practitioners an appreciation for the computational aspects of dea that will permit them to understand the performance, problems, complications, limitations, as well as the potential of this technique.
Computations in DEA  [cached]
Dulá José H.
Pesquisa Operacional , 2002,
Abstract: DEA is a well-established, widely used, and powerful analytical resource in the toolbox of the OR/MS analyst. It is used to assess relative efficiency of many, functionally similar, entities. It has applications in diverse areas including finance and banking, education, and healthcare. DEA is computationally intensive and, as the scale of applications grows, this intensity rapidly becomes one of the limiting factors in its utility. In this paper, we explore computations in DEA. We investigate the theory behind schemes, procedures and algorithms used in performing a DEA study and we report on current practices ranging from the basic and standard to the advanced and sophisticated. Our objective is to give researchers and practitioners an appreciation for the computational aspects of DEA that will permit them to understand the performance, problems, complications, limitations, as well as the potential of this technique.
Application of DEA in Investment Effects Evaluation of Non coal Industry
DEA 在非煤产业投资效果评价中的应用

Mu Dong,Li Guan,
穆 东
,李 冠

系统工程理论与实践 , 1998,
Abstract: Whether or not success of an investment project depends to a large extent on running process after investment. In this paper, using a method of date envelopment analysis(DEA) we evaluate the running process of the investment projects of non coal industries in mining enterprises group, and provide theory basis for following management of the projects.
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