scholarly journals Allocation of weights using simultaneous optimization of inputs and outputs contribution in cross-efficiency evaluation of DEA

2018 ◽  
Vol 28 (4) ◽  
pp. 521-538
Author(s):  
Seyed Nasseri ◽  
Hamid Kiaei
Keyword(s):  
Decision Making ◽  
Simultaneous Optimization ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Optimal Solutions ◽  
Specific Criterion ◽  
Use Of Resources ◽  
Multiple Weights ◽  
Decision Making Units ◽  
Selection Of

Cross-efficiency evaluation, an extension of the data envelopment analysis (DEA), has found an appropriate function in ranking decision making units (DMU). However, DEA suffers from a potential aw, that is, the existence of multiple optimal solutions. Different methods have been proposed to obtain a unique solution (based on a specific criterion). In this paper, we refer to Wang's method for ranking DMUs but argue that his way of selecting the weights is not the appropriate one. Namely, in the cross-efficiency evaluation of DMUs, we always search for the weights which use minimum resources to increase the production. Therefore, we suggest that the selection of weights among the multiple weights should be determined by decreasing the contribution of inputs in the use of resources, and increasing the contribution of outputs in the production, which should overtly prevent the selection of zero solutions to the extent possible. To this end, some examples are given to illustrate differences and advantages of our method compared to those usually used.

An optimistic-pessimistic DEA model based on game cross efficiency approach

2020 ◽  
Vol 54 (4) ◽  
pp. 1215-1230
Author(s):  
Mediha Örkcü ◽  
Volkan Soner Özsoy ◽  
H. Hasan Örkcü
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Equilibrium Solution ◽  
Data Envelopment ◽  
Optimal Weights ◽  
Discriminating Power ◽  
Proposed Model ◽  
Essential Problem ◽  
Decision Making Units ◽  
Selection Of

The ranking of the decision making units (DMUs) is an essential problem in data envelopment analysis (DEA). Numerous approaches have been proposed for fully ranking of units. Majority of these methods consider DMUs with optimistic approach, whereas their weaknesses are ignored. In this study, for fully ranking of the units, a modified optimistic–pessimistic approach, which is based on game cross efficiency idea is proposed. The proposed game like iterative optimistic-pessimistic DEA procedure calculates the efficiency scores according to weaknesses and strengths of units and is based on non-cooperative game. This study extends the optimistic-pessimistic DEA approach to obtain robust rank values for DMUs. The proposed approach yields Nash equilibrium solution, thus overcomes the problem of non-uniqueness of the DEA optimal weights that can possibly reduce the usefulness of cross efficiency. Finally, in order to verify the validity of the proposed model and to show the practicability of algorithm, we apply a real-world example for selection of industrial R&D projects. The proposed model can increase the discriminating power of DMUs and can fully rank the DMUs.

scholarly journals Choosing weights in optimal solutions for DEA-BCC models by means of a N-dimensional smooth frontier

2009 ◽  
Vol 29 (3) ◽  
pp. 623-642 ◽  
Author(s):  
Flávia Badini Nacif ◽  
João Carlos Correia Baptista Soares de Mello ◽  
Lidia Angulo Meza
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Present Article ◽  
General Model ◽  
Piecewise Linear ◽  
Data Envelopment ◽  
Optimal Solutions ◽  
Single Output ◽  
Single Input ◽  
Decision Making Units

The DEA (Data Envelopment Analysis) smoothed frontier was introduced to solve the problem of multiple optimal solutions in the extreme efficient DMUs (Decision Making Units), which hinders the knowledge of the substitution rates (tradeoffs). It consists of changing the original frontier (piecewise linear) for a smoothed one, being as close as possible to the original one, and having continuous partial derivates at every point. First, a solution was developed only for the BCC (Banker, Charnes and Cooper) model with either a single input or a single output. Then, it was generalized for the N-dimensional BCC model with simultaneous multiplicity of inputs and outputs, but limited by the fact that the polynomial of the output needs to be a linear one. The present article presents a general model, which not only expunges the limitations of the previous models but also includes them.

scholarly journals Global malmquist index for measuring the economic productivity changes

2020 ◽  
Vol 53 (7-8) ◽  
pp. 1278-1285
Author(s):  
Esmaeil Mombini ◽  
Mohsen Rostamy-Malkhalifeh ◽  
Mansor Saraj ◽  
Mohsen Zahraei ◽  
Reza Tayebi Khorami
Keyword(s):  
Decision Making ◽  
Malmquist Index ◽  
Productivity Index ◽  
Programming Models ◽  
Data Envelopment ◽  
Decision Unit ◽  
Economic Productivity ◽  
Use Of Resources ◽  
Decision Making Unit ◽  
Decision Making Units

Data envelopment analysis is a nonparametric method for measuring of the performance of decision-making units—which do not need to have or compute a firm’s production function, which is often difficult to calculate. For any manager, the progress or setback of the thing they manage is important because it makes planning and adoption of future policies for the organization or decision-making unit more rational and scientific. Different methods have been used to calculate the improvements and regressions using Malmquist Index. In this article, we evaluate the units under review in terms of economic efficiency, and the units in terms of spending, production, revenue and profit over several periods, and the rate of improvement or regression of each of these units. Considering the minimal use of resources and consuming less money, generating more revenue, and maximizing profits, the improvement or retreat of the recipient’s decision unit in terms of cost, revenue, and profit was examined by presenting a method based on solving linear programming models using the productivity index is Malmquist and Malmquist Global. Finally, by designing and solving a numerical example, we emphasize and test the applicability of the material presented in this article.

scholarly journals Cross-Efficiency Evaluation Method with Compete-Cooperate Matrix

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Qiang Hou ◽  
Xue Zhou
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Evaluation Method ◽  
Peer Assessment ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Self Assessment ◽  
Dea Method ◽  
Decision Making Units

Cross-efficiency evaluation method is an effective and widespread adopted data envelopment analysis (DEA) method with self-assessment and peer-assessment to evaluate and rank decision making units (DMUs). Extant aggressive, benevolent, and neutral cross-efficiency methods are used to evaluate DMUs with competitive, cooperative, and nontendentious relationships, respectively. In this paper, a symmetric (nonsymmetric) compete-cooperate matrix is introduced into aggressive and benevolent cross-efficiency methods and compete-cooperate cross-efficiency method is proposed to evaluate DMUs with diverse (relative) relationships. Deviation maximization method is applied to determine the final weights of cross-evaluation to enhance the differentiation ability of cross-efficiency evaluation method. Numerical demonstration is provided to illustrate the reasonability and practicability of the proposed method.

scholarly journals Gap Minimization for Peer-Evaluation in DEA Cross-Efficiency

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Anrong Yang ◽  
Zigang Zhang ◽  
Yishi Zhang ◽  
Dunliang Chen
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Peer Evaluation ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Self Evaluation ◽  
Criterion A ◽  
The Cross ◽  
Similarity Distance ◽  
Decision Making Units

Cross-efficiency evaluation is an effective and widely used method for ranking decision making units (DMUs) in data envelopment analysis (DEA). Gap minimization criterion is introduced in aggressive and benevolent cross-efficiency methods to avoid possible extreme efficiency from peer-evaluation and to get equitable results. On the basis of this criterion, a weighted cross-efficiency method with similarity distance that, respectively, considers the aggressive and the benevolent formulations is proposed to determine cross-efficiency. The weights of the cross-evaluation determined by this method are positively influenced by self-evaluation and thus are propitious to resolving conflict. Numerical demonstration reveals the feasibility of the proposed method.

scholarly journals THE PROPORTION OF SPORTS PUBLIC SERVICE FACILITIES BASED ON THE DEA MODEL IN COLLEGES AND UNIVERSITIES

2021 ◽  
Vol 27 (spe) ◽  
pp. 97-100
Author(s):  
Haonan Niu ◽  
Yu Zhang
Keyword(s):  
Decision Making ◽  
Public Service ◽  
Colleges And Universities ◽  
Scale Efficiency ◽  
Data Envelopment ◽  
Sports Facilities ◽  
Dea Model ◽  
Matching Efficiency ◽  
Decision Making Units ◽  
Selection Of

ABSTRACT In order to strengthen the physical education of college students, it is necessary to reasonably allocate university sports public service resources. In order to improve the allocation of university sports resources, this study constructs the Data Envelopment Analysis (DEA) model by analyzing the proportion of public sports service facilities in colleges and universities. Through the selection of input index and output index of sports public service facilities in colleges and universities, as well as selecting 20 colleges and universities as decision-making units, this paper constructs a DEA model, and studies the use of the DEA Tobit two-stage method to evaluate the matching efficiency of public sports service facilities in colleges and universities. The results show that the pure technical efficiency of sports public service facilities in colleges and universities is effective, and the scale efficiency of most colleges and universities is relatively high, and the proportion of sports facilities is relatively reasonable. However, there are still large problems in the proportion of public sports service facilities in colleges and universities, so it is necessary to adjust the proportion and scale of sports facilities allocation reasonably. This study verified the effectiveness of the DEA model in evaluating the proportion of public sports service facilities in colleges and universities, hoping to provide certain reference for improving the proportion of public sports service facilities in colleges and universities.

scholarly journals Efficiency evaluation of a small number of DMUs: an approach based on Li and Reeves's model

2009 ◽  
Vol 29 (1) ◽  
pp. 97-110 ◽  
Author(s):  
João Carlos Correia Baptista Soares de Mello ◽  
João Carlos Namorado Clímaco ◽  
Lidia Angulo Meza
Keyword(s):  
Decision Making ◽  
Numerical Data ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Objective Functions ◽  
Dea Models ◽  
Evaluation Measure ◽  
Decision Making Units ◽  
Joint Evaluation ◽  
Do So

This paper deals with the evaluation of Decision Making Units (DMU) when their number is not large enough to allow the use of classic Data Envelopment Analysis (DEA) models. To do so, we take advantage of the TRIMAP software when used to study the Li and Reeves MultiCriteria DEA (MCDEA) model. We introduce an evaluation measure obtained with the integration of one of the objective functions along the weight space. This measure allows the DMUs joint evaluation. This approach is exemplified with numerical data from some Brazilian electrical companies.

scholarly journals The basic solution ellipsoid method approach for the efficiency measurement problems

2016 ◽  
Vol 57 ◽  
Author(s):  
Eligijus Laurinavičius ◽  
Daiva Rimkuvienė ◽  
Aurelija Sakalauskaitė
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Data Envelopment Analysis ◽  
Basic Solution ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Parametric Approach ◽  
Ellipsoid Method ◽  
Method Approach ◽  
Decision Making Units

The efficiency is a measure of a performance of a decision making units (DMUs can be a firm, a person, an organization). The data envelopment analysis (DEA) is a datadriven non-parametric approach for measuring the efficiency of a set of DMUs. The DEA is a linear programming (LP) based technique which deals with the basic models (CCR, BCC, SBM, additive) of the efficiency evaluation. This paper presents basic solution ellipsoid method approach associated with some problems of initial basic solution and the steps of it.

scholarly journals A multiobjective approach for non-discretionary variables in data envelopment analysis

DYNA ◽  
2016 ◽  
Vol 83 (195) ◽  
pp. 9-15 ◽  
Author(s):  
Lidia Angulo Meza ◽  
João Carlos Soares de Mello ◽  
Silvio Gomes Junior
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Decision Maker ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Data Set ◽  
Numerical Example ◽  
Multiobjective Approach ◽  
Ratio Optimization ◽  
Decision Making Units

Data Envelopment Analysis is a non-parametrical approach for efficiency evaluation of so-called DMUs (Decision Making Units) and takes into account multiple inputs and outputs. For each inefficient DMU, a target is provided which is constituted by the inputs or outputs levels that are to be attained for the inefficient DMU to become efficient. However, multiobjective models, known as MORO (Multiobjective Model for Ratio Optimization) provide a set of targets for inefficient DMU, which provides alternatives among which the decision-maker can choose. In this paper, we proposed an extension of the MORO models to take into account non-discretionary variables, i.e., variables that cannot be controlled. We present a numerical example to illustrate the proposed multiobjective model. We also discuss the characteristics of this model, as well as the advantages of offering a set of targets for the inefficient DMUs when there are non-discretionary variables in the data set.

scholarly journals An Extension of Cross Redundancy of Interval Scale Outputs and Inputs in DEA

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Farhad Hosseinzadeh-Lotfi ◽  
Gholam-Reza Jahanshahloo ◽  
Mansour Mohammadpour
Keyword(s):  
Decision Making ◽  
Linear Combination ◽  
Data Envelopment ◽  
Ratio Scale ◽  
Interval Scale ◽  
Output Variable ◽  
Input And Output ◽  
Dea Models ◽  
Decision Making Units ◽  
Selection Of

It is well known that data envelopment analysis (DEA) models are sensitive to selection of input and output variables. As the number of variables increases, the ability to discriminate between the decision making units (DMUs) decreases. Thus, to preserve the discriminatory power of a DEA model, the number of inputs and outputs should be kept at a reasonable level. There are many cases in which an interval scale output in the sample is derived from the subtraction of nonnegative linear combination of ratio scale outputs and nonnegative linear combination of ratio scale inputs. There are also cases in which an interval scale input is derived from the subtraction of nonnegative linear combination of ratio scale inputs and nonnegative linear combination of ratio scale outputs. Lee and Choi (2010) called such interval scale output and input a cross redundancy. They proved that the addition or deletion of a cross-redundant output variable does not affect the efficiency estimates yielded by the CCR or BCC models. In this paper, we present an extension of cross redundancy of interval scale outputs and inputs in DEA models. We prove that the addition or deletion of a cross-redundant output and input variable does not affect the efficiency estimates yielded by the CCR or BCC models.

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