DEA Models for Extended Two-Stage Network Structures
01 Oct 2012-Omega-international Journal of Management Science (Springer, Boston, MA)-Vol. 40, Iss: 5, pp 611-618
TL;DR: Two models are proposed to evaluate the performance of this type general two-stage network structures where all outputs of the first stage are the only inputs to the second stage, and a non-cooperative model, in which one of the stages is regarded as the leader and the other is the follower.
Abstract: This chapter discusses DEA modeling technique for a two-stage network process where the inputs of the second stage include both the outputs from the first stage and additional inputs to the second stage. Two models are proposed to evaluate the performance of this type two-stage network structures. One is a non-linear centralized model whose global optimal solutions can be estimated using a heuristic search procedure. The other is a non-cooperative model, in which one of the stages is regarded as the leader and the other is the follower. The newly developed models are illustrated with a case of regional R&D of China.
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TL;DR: This study is the first literature survey that focuses on DEA applications, covering DEA papers published in journals indexed by the Web of Science database from 1978 through August 2010, and suggests that the two-step contextual analysis and network DEA are the recent trends across applications.
Abstract: The literature of data envelopment analysis (DEA) encompasses many surveys, yet all either emphasize methodologies or do not make a distinction between methodological and application papers. This study is the first literature survey that focuses on DEA applications, covering DEA papers published in journals indexed by the Web of Science database from 1978 through August 2010. The results show that on the whole around two-thirds (63.6%) of DEA papers embed empirical data, while the remaining one-third are purely-methodological. Purely-methodological articles dominated the first 20 years of DEA development, but the accumulated number of application-embedded papers caught up to purely-methodological papers in 1999. Among the multifaceted applications, the top-five industries addressed are: banking, health care, agriculture and farm, transportation, and education. The applications that have the highest growth momentum recently are energy and environment as well as finance. In addition to the basic statistics, we uncover the development trajectory in each application area through the main path analysis. An observation from these works suggests that the two-step contextual analysis and network DEA are the recent trends across applications and that the two-step contextual analysis is the prevailing approach.
622 citations
TL;DR: In this paper, the authors proposed a dynamic DEA model involving network structure in each period within the framework of a slacks-based measure approach, and applied this model to a dataset of US electric utilities and compared the result with that of DSBM.
Abstract: We propose a dynamic DEA model involving network structure in each period within the framework of a slacks-based measure approach. We have previously published the network SBM (NSBM) and the dynamic SBM (DSBM) models separately. Hence, this article is a composite of these two models. Vertically, we deal with multiple divisions connected by links of network structure within each period and, horizontally, we combine the network structure by means of carry-over activities between two succeeding periods. This model can evaluate (1) the overall efficiency over the entire observed period, (2) dynamic change of period efficiency and (3) dynamic change of divisional efficiency. The model can be implemented in input-, output- or non-(both) oriented forms under the CRS or VRS assumptions on the production possibility set. Finally, we applied this model to a dataset of US electric utilities and compared the result with that of DSBM.
480 citations
TL;DR: This paper reviews studies on network DEA by examining the models used and the structures of the network system of the problem being studied, and highlights some directions for future studies from the methodological point of view.
446 citations
TL;DR: This study reviews the literature on data envelopment analysis (DEA) applications in sustainability using citation-based approaches and constructs a directional network based on citation relationships among DEA papers published in journals indexed by the Web of Science database from 1996 to March 2016.
235 citations
TL;DR: This study applies a network clustering method to group the literature through a citation network established from the DEA literature over the period 2000 to 2014, and presents the research fronts, a coherent topic or issue addressed by a group of research articles in recent years.
Abstract: Research activities relating to data envelopment analysis (DEA) have grown at a fast rate recently. Exactly what activities have been carrying the research momentum forward is a question of particular interest to the research community. The purpose of this study is to find these research activities, or research fronts, in DEA. A research front refers to a coherent topic or issue addressed by a group of research articles in recent years. The large amount of DEA literature makes it difficult to use any traditional qualitative methodology to sort out the matter. Thus, this study applies a network clustering method to group the literature through a citation network established from the DEA literature over the period 2000 to 2014. The keywords of the articles in each discovered group help pinpoint its research focus. The four research fronts identified are “bootstrapping and two-stage analysis”, “undesirable factors”, “cross-efficiency and ranking”, and “network DEA, dynamic DEA, and SBM”. Each research front is then examined with key-route main path analysis to uncover the elements in its core. In addition to presenting the research fronts, this study also updates the main paths and author statistics of DEA development since its inception and compares them with those reported in a previous study.
217 citations
References
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TL;DR: A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs and methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs.
25,433 citations
"DEA Models for Extended Two-Stage N..." refers background or methods in this paper
...[2], is a mathematical programming approach for analyzing the relative efficiency of peer decision making units (DMUs), which have multiple inputs and multiple outputs....
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...[2]), we can establish the following model for Fig....
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...[2] lopment Analysis, edited by [12] develop a network DEA model that evaluate both divisional and overall efficiencies of DMUs....
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TL;DR: In this article, the authors present DEA Software Tools and Technology: A State-of-the-Art Survey with DEA Estimators and their Applications in Data Envelopment Analysis.
Abstract: -Preface W.W. Cooper, L.M. Seiford, J. Zhu. -1. Data Envelopment Analysis: History, Models and Interpretations W.W. Cooper, L.M. Seiford, J. Zhu. -2. Returns to Scale in DEA: R.D. Banker, W.W. Cooper, L.M. Seiford, J. Zhu. -3. Sensitivity Analysis in DEA: W.W. Cooper, Shanling Li, L.M. Seiford, J. Zhu. -4. Incorporating Value Judgments in DEA: E. Thanassoulis, M.C. Portela, R. Allen. -5. Distance Functions with Applications to DEA R. Fare, S. Grosskopf, G. Whittaker. -6. Qualitative Data in DEA W.D. Cook. -7. Congestion: Its Identification and Management with DEA W.W. Cooper, Honghui Deng, L.M. Seiford, J. Zhu. -8. Malmquist Productivity Index: Efficiency Change Over Time K. Tone. -9. Chance Constrained DEA: W.W. Cooper, Zhimin Huang, S.X. Li. -10. Performance of the Bootstrap for DEA Estimators and Iterating the Principle: L. Simar, P.W.Wilson. -11. Statistical Tests Based on DEA Efficiency Scores R.D. Banker, R. Natarajan. -12. Performance Evaluation in Education: Modeling Educational Production J. Ruggiero. -13. Assessing Bank and Bank Branch Performance: Modeling Considerations and Approaches J.C. Paradi, S. Vela, Zijiang Yang. -14. Engineering Applications of Data Envelopment Analysis: Issues and Opportunities: K.P. Triantis. -15. Benchmarking in Sports: Bonds or Ruth: Determining the Most Dominant Baseball Batter Using DEA T.R. Anderson. -16. Assessing the Selling Function in Retailing: Insights from Banking, Sales forces, Restaurants & Betting shops A.D. Athanassopoulos. -17. Health Care Applications: From Hospitals to Physicians, From Productive Efficiency to Quality Frontiers: J.A. Chilingerian, H.D. Sherman. -18. DEA Software Tools and Technology: A State-of-the-Art Survey R. Barr. -Notes about Authors. Author Index. Subject Index.
1,462 citations
"DEA Models for Extended Two-Stage N..." refers background in this paper
...Previous works have shown that DEA can be applied in various of settings, such as bank performance [3,4], production planning [5], bankruptcy assessment [6], R&D performance [7], agricultural economics [8], airport performance [9] and other applications [10]....
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TL;DR: A neglected aspect of Data Envelopment Analysis: cross-efficiency is examined, and an intuitive understanding of cross- efficiency is ground in the concept of peer-appraisal, as opposed to self-appRAisal implied by simple efficiency.
Abstract: In this paper we examine a neglected aspect of Data Envelopment Analysis: cross-efficiency. We develop the concept of cross-efficiency in a number of new directions. We ground an intuitive understanding of cross-efficiency in the concept of peer-appraisal, as opposed to self-appraisal implied by simple efficiency, and discuss the relative merits of each. We also present mathematical formulations of, and intuitive meanings for three possible implementations of aggressive and benevolent cross-efficiency. We have implemented two of these formulations in computer programs; their performance is compared empirically on a real data set. Finally, we suggest practical uses for cross-efficiency, illustrated with reference to the same data set.
1,127 citations
Additional excerpts
...Doyle and Green [22] develop second goal models to solve a similar problem in DEA cross-efficiency....
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...[22] Doyle J, Green R. Efficiency and cross-efficiency in DEA: derivations, meanings and uses....
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TL;DR: The relational model developed in this paper is more reliable in measuring the efficiencies and consequently is capable of identifying the causes of inefficiency more accurately.
1,112 citations
"DEA Models for Extended Two-Stage N..." refers background or methods in this paper
...For example, consider the approach of Kao and Hwang [16] where a set of insurance companies are assumed to have a two-stage operations of premium acquisition and profit generation....
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...[1] or Kao and Hwang [16] is developed under the assumption that the outputs from the first stage all become the only inputs to the second stage....
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...[1] or Kao and Hwang [16] assumes that the outputs from the first stage all become the...
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...[1] or Kao and Hwang [16] will result a non-linear program that cannot be converted into linear programming problems if we assume that the overall efficiency is a geometric mean of two stages’ efficiency....
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...[1] or Kao and Hwang [16], the centralized model cannot be transformed to a linear program due to the existence of additional inputs to the second stage....
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TL;DR: A slacks-based network DEA model is proposed, called Network SBM, that can deal with intermediate products formally and evaluate divisional efficiencies along with the overall efficiency of decision making units (DMUs).
954 citations
"DEA Models for Extended Two-Stage N..." refers background or methods in this paper
...[2] lopment Analysis, edited by [12] develop a network DEA model that evaluate both divisional and overall efficiencies of DMUs....
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...In recent years, a number of studies have looked at DMUs with network structures (see, e.g., Färe and Grosskopf [11], Tone and Tsutsui [12], Fukuyama and Weber [13], Castelli et al. [14], Kao [15], Kao and Hwang [16] and Liang et al. [1])....
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...[12] Tone K, Tsutsui M. Network DEA: a slacks-based measure approach....
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..., Färe and Grosskopf [11], Tone and Tsutsui [12], Fukuyama and Weber [13], Castelli et al....
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...Using slacks-based models, Tone and Tsutsui ll rights reserved. ao_Chen@uml.edu (Y. Chen), ....
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