Finding an Initial Basic Feasible Solution for DEA Models with an Application on Bank Industry

Toloo, Mehdi; Masoumzadeh, Atefeh; Barat, Mona

doi:10.1007/s10614-014-9423-1

Cited by 14 publications

(12 citation statements)

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“…More precisely, to solve the SORM model (3) by the simplex method, we must firstly put it to the standard form which needs imposing |I | + |R| + 2(|I c | + |R c |) more slack and surplus variables. Empirically, the simplex method to solve the SORM model requires roughly on the order of |I | + |R| + 2(|I c | + |R c |) + 1 to 3(|I | + |R| + 2(|I c | + |R c |) + 1) iterations and in each iteration it needs (n + 1) (|I | + |R| + 2(|I c | + |R c |)) + n + 1 multiplications and (n + 1)(|I | + |R| + 2(|I c | + |R c |)) additions (for deeper discussion about the number of elementary computations in DEA models, see Toloo et al [29]). Furthermore, the model must be solved n times to obtain the efficiency score of all DMUs.…”

Section: Semi-oriented Radial Measure (Sorm)mentioning

confidence: 99%

Evaluation efficiency of large-scale data set with negative data: an artificial neural network approach

2015

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Data envelopment analysis (DEA) is the most widely used methods for measuring the efficiency and productivity of decision-making units (DMUs). The need for huge computer resources in terms of memory and CPU time in DEA is inevitable for a large-scale data set, especially with negative measures. In recent years, wide ranges of studies have been conducted in the area of artificial neural network and DEA combined methods. In this study, a supervised feed-forward neural network is proposed to evaluate the efficiency and productivity of large-scale data sets with negative values in contrast to the corresponding DEA method. Results indicate that the proposed network has some computational advantages over the corresponding DEA models; therefore, it can be considered as a useful tool for measuring the efficiency of DMUs with (large-scale) negative data.Keywords Artificial neural network · Data envelopment analysis (DEA) · SORM-DEA · Negative data · Levenberg-Marquardt (LM) · LM-DEA

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Section: Semi-oriented Radial Measure (Sorm)mentioning

confidence: 99%

Evaluation efficiency of large-scale data set with negative data: an artificial neural network approach

2015

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“…This significant algorithm is more useful, especially when we focus on computational issues and complexity analysis. Toloo et al (2015) considered the following standard form of CCR model to obtain an IBFS:…”

Section: Epsilon Algorithm;mentioning

confidence: 99%

“…On the other hand, A contains an identity matrix of order n and in conclusion, m + s + 1 artificial variables are necessary to find a starting basis matrix. Toloo et al (2015) considered the following phase I of CCR model to eliminate artificial variables:…”

Section: Epsilon Algorithm;mentioning

confidence: 99%

“…The constraint matrix for model (4) appears as follows: Toloo et al (2015) acquired the following closed form of optimal BFS of phase I:…”

Section: Epsilon Algorithm;mentioning

confidence: 99%

“…This paper is organized as follows: Sect. 2 reviews the approach of Toloo et al (2015) to obtain an initial basic feasible solution (IBFS) for the CCR model. In Sect.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

LU Decomposition in DEA with an Application to Hospitals

Toloo

Jalili

2015

Comput Econ

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A fundamental problem that usually appears in linear systems is to find a vector x satisfying Bx = b. This linear system is encountered in many research applications and more importantly, it is required to be solved in many contexts in applied mathematics. LU decomposition method, based on the Gaussian elimination, is particularly well suited for spars and large-scale problems. Linear programming (LP) is a mathematical method to obtain optimal solutions for a linear system that is more being considered in various fields of study in recent decades. The simplex algorithm is one of the mostly used mathematical techniques for solving LP problems. Data envelopment analysis (DEA) is a non-parametric approach based on linear programming to evaluate relative efficiency of decision making units (DMUs). The number of LP models that has to be solved in DEA is at least the same as the number of DMUs. Toloo et al. (Comput Econ 45(2):323-326, 2015) proposed an initial basic feasible solution for DEA models which practically reduces at least 50 % of the whole computations. The main contribution of this paper is in utlizing this solution to implement LU decomposition technique on the basic DEA models which is more accurate and numerically stable. It is shown that the number of computations in applying the Gaussian elimination method will be fairly reduced due to the special structure of basic DEA models. Potential uses are illustrated with applications to hospital data set. B Mehdi Toloo

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Selecting most efficient information system projects in presence of user subjective opinions: a DEA approach

Toloo

Nalchigar

Sohrabi

2018

Cent Eur J Oper Res

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Finding an Initial Basic Feasible Solution for DEA Models with an Application on Bank Industry

Cited by 14 publications

References 4 publications

Evaluation efficiency of large-scale data set with negative data: an artificial neural network approach

Evaluation efficiency of large-scale data set with negative data: an artificial neural network approach

LU Decomposition in DEA with an Application to Hospitals

Selecting most efficient information system projects in presence of user subjective opinions: a DEA approach

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