By Joe Zhu
This guide represents a milestone within the development of knowledge Envelopment research (DEA). Written through specialists who're usually significant individuals to DEA concept, it encompasses a number of chapters that characterize the present cutting-edge in DEA examine. themes contain distance services and their price duals, cross-efficiency measures in DEA, integer DEA, weight regulations and creation trade-offs, part research in DEA, scale elasticity, benchmarking and context-dependent DEA, fuzzy DEA, non-homogenous devices, partial input-output family members, tremendous potency, therapy of bad measures, translation invariance, stochastic nonparametric envelopment of information, and worldwide frontier index.
Focusing merely on new models/approaches of DEA, the publication contains contributions from Juan Aparicio, Mette Asmild, Yao Chen, Wade D. cook dinner, Juan Du, Rolf Färe, Julie Harrison, Raha Imanirad, Andrew Johnson, Chiang Kao, Abolfazl Keshvari, Timo Kuosmanen, Sungmook Lim, Wenbin Liu, Dimitri Margaritis, Reza Kazemi Matin, Ole B. Olesen, Jesus T. Pastor, Niels Chr. Petersen, Victor V. Podinovski, Paul Rouse, Antti Saastamoinen, Biresh okay. Sahoo, Kaoru Tone, and Zhongbao Zhou.
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Extra resources for Data Envelopment Analysis: A Handbook of Models and Methods
Ur yrj + ξ ≥ 0, j = 1, . . 1) r=1 i=1 m vi xi0 = 1 i=1 vi , ur ≥ ε ∀i, r, ξ free in sign. where ε is a positive non-Archimedean infinitesimal. When the above model is solved, an input-oriented efficiency score of DMU0 and input-oriented crossefficiencies of the other DMUs (evaluated by DMU0 ) are obtained together. 2) where * denotes an optimal solution to the model. 2) may be negative when ξ > 0, which results in problematic situation. Averaging eijI over i, we get a (conventional input-oriented) I cross-efficiency score of DMUj .
15) The VRS multiplicative cross efficiency score can be defined in a similar manner. 16) 32 W. D. Cook and J. 12). 12). 6 Maximum Log Cross Efficiency We now present the approach developed in Cook and Zhu (2014). 15)) subject to the condition that Ekk = θk∗ for all k = 1, . . , n. Specifically, for DMUjo we have 1/n μ s rk r=1 yrjo ν m ik k=1 i=1 xijo μ s rk r=1 yrj ≤ 1, j = 1, . . , n, k = 1, . . n ν m ik x i=1 ij μ s rk r=1 yrk Ekk = m ν = θk∗ , k = 1, . . t. 18) k = 1, . . n; i − 1, . .
Now let us illustrate how the problem of negative cross-efficiency arises in the input-oriented VRS model using a simple one-input and one-output example. 1 is given, which consists of seven DMUs with a single input and a single output. 1. 3) as well as RTS classifications. 1). Hyperplane HF represents an optimal bundle of weights (v∗ , u∗ , ξ ∗ ) = 41 , 38 , 45 for DMU F, with which DMU F attains an efficiency score of unity. Using an input-oriented radial distance measure, (conventional input-oriented) cross-efficiencies of DMUs D, E, and G evaluated by DMU F can be determined with reference to the hyperplane HF .
Data Envelopment Analysis: A Handbook of Models and Methods by Joe Zhu