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.

scholarly journals A full investigation of the directional congestion in data envelopment analysis

2019 ◽  
Author(s):  
somayeh khezri ◽  
Akram Dehnokhalaji ◽  
Farhad Hosseinzadeh Lotfi
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Data Envelopment ◽  
Input Output ◽  
Input And Output ◽  
Dea Models ◽  
Systems Of Inequalities ◽  
Full Investigation ◽  
Decision Making Units ◽  
Inputs And Outputs

One of interesting subjects in Data Envelopment Analysis (DEA) is estimation of congestion of Decision Making Units (DMUs). Congestion is evidenced when decreases (increases) in some inputs re- sult in increases (decreases) in some outputs without worsening (im- proving) any other input/output. Most of the existing methods for measuring the congestion of DMUs utilize the traditional de nition of congestion and assume that inputs and outputs change with the same proportion. Therefore, the important question that arises is whether congestion will occur or not if the decision maker (DM) increases or de- creases the inputs dis-proportionally. This means that, the traditional de nition of congestion in DEA may be unable to measure the con- gestion of units with multiple inputs and outputs. This paper focuses on the directional congestion and proposes methods for recognizing the directional congestion using DEA models. To do this, we consider two di erent scenarios: (i) just the input direction is available. (ii) none of the input and output directions are available. For each scenario, we propose a method consists in systems of inequalities or linear pro- gramming problems for estimation of the directional congestion. The validity of the proposed methods are demonstrated utilizing two nu- merical examples.

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 Designing an Intuitionistic Fuzzy Network Data Envelopment Analysis Model for Efficiency Evaluation of Decision-Making Units with Two-Stage Structures

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Nafiseh Javaherian ◽  
Ali Hamzehee ◽  
Hossein Sayyadi Tooranloo
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Data Envelopment Analysis Model ◽  
Data Envelopment ◽  
Analysis Model ◽  
Two Stage ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Dea Models ◽  
Decision Making Units

Data envelopment analysis (DEA) is a powerful tool for evaluating the efficiency of decision-making units for ranking and comparison purposes and to differentiate efficient and inefficient units. Classic DEA models are ill-suited for the problems where decision-making units consist of multiple stages with intermediate products and those where inputs and outputs are imprecise or nondeterministic, which is not uncommon in the real world. This paper presents a new DEA model for evaluating the efficiency of decision-making units with two-stage structures and triangular intuitionistic fuzzy data. The paper first introduces two-stage DEA models, then explains how these models can be modified with intuitionistic fuzzy coefficients, and finally describes how arithmetic operators for intuitionistic fuzzy numbers can be used for a conversion into crisp two-stage structures. In the end, the proposed method is used to solve an illustrative numerical example.

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 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.

The Assessment of Outsourcing IT Services using DEA Technique

2016 ◽  
Vol 7 (1) ◽  
pp. 45-57
Author(s):  
Mohammad Amin Zare ◽  
Mohammad Taghi Taghavi Fard ◽  
Payam Hanafizadeh
Keyword(s):  
Decision Making ◽  
Information Technology ◽  
Data Envelopment Analysis ◽  
It Outsourcing ◽  
Data Envelopment ◽  
Efficiency Improvement ◽  
Research Centers ◽  
It Services ◽  
Input And Output ◽  
Decision Making Units

This article proposes a model to make an assessment of efficiency in Information Technology (IT) outsourcing in research centers through data envelopment analysis (DEA). In this research input and output variables of DEA model for assessment of IT outsourcing efficiency distinguished. The decision-making units (DMUs) include 36 research centers in Iran. Expenses and capabilities of contractors represent the inputs and the satisfaction of users, risks, and quality constitute the outputs. In order to calculate the input and output values, a questionnaire has been conducted to DMUs. Afterwards, BCC model has facilitated the calculation of the efficiency of the DMUs and classifies efficient and inefficient units. In addition, Anderson Peterson's model is used for ranking efficient DMUs. This research has brought us to the conclusion that the variables of risk and quality account for the biggest shares in efficiency improvement of non-efficient DMUs.

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.

Inverse DEA in two-stage systems based on allocative efficiency

2021 ◽  
Vol 40 (1) ◽  
pp. 591-603
Author(s):  
Zahra Shiri Daryani ◽  
Ghasem Tohidi ◽  
Behrouz Daneshian ◽  
Shabnam Razavyan ◽  
Farhad Hosseinzadeh Lotfi
Keyword(s):  
Decision Making ◽  
Relative Efficiency ◽  
Allocative Efficiency ◽  
Cost Price ◽  
Data Envelopment ◽  
Price Information ◽  
Two Stage ◽  
Input And Output ◽  
Decision Making Units ◽  
Inputs And Outputs

Inputs and outputs of Decision Making Units (DMUs) are estimated by the Inverse Data Envelopment Analysis (InvDEA) models, while their relative efficiency scores remain unchanged. But, in some cases, cost/price information of the inputs and outputs are available. This paper employs the input and output cost/price information, including the generalized InvDEA concept in two-stage structures. To this end, it proposes a four-stage method to deal with the InvDEA concept, for estimating the inputs and outputs of the DMUs with a two-stage network structure method, while the allocative efficiency scores of all the units remain stable. Eventually, an empirical example is rendered to illustrate the competence of the method which is presented.

Fuzzy integer-valued data envelopment analysis

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1429-1444 ◽  
Author(s):  
Sohrab Kordrostami ◽  
Alireza Amirteimoori ◽  
Monireh Jahani Sayyad Noveiri
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Real World ◽  
Data Envelopment ◽  
First Case ◽  
Dea Models ◽  
Analysis Models ◽  
Fuzzy Dea ◽  
Decision Making Units ◽  
Provided Examples

In conventional data envelopment analysis (DEA) models, the efficiency of decision making units (DMUs) is evaluated while data are precise and continuous. Nevertheless, there are occasions in the real world that the performance of DMUs must be calculated in the presence of vague and integer-valued measures. Therefore, the current paper proposes fuzzy integer-valued data envelopment analysis (FIDEA) models to determine the efficiency of DMUs when fuzzy and integer-valued inputs and/or outputs might exist. To illustrate, fuzzy number ranking and graded mean integration representation methods are used to solve some integer-valued data envelopment analysis models in the presence of fuzzy inputs and outputs. Two examples are utilized to illustrate and clarify the proposed approaches. In the provided examples, two cases are discussed. In the first case, all data are as fuzzy and integer-valued measures while in the second case a subset of data is fuzzy and integer-valued. The results of the proposed models indicate that the efficiency scores are calculated correctly and the projections of fuzzy and integer factors are determined as integer values, while this issue has not been discussed in fuzzy DEA, and projections may be estimated as real-valued data.

scholarly journals New inverse DEA models for budgeting and planning

2021 ◽  
Author(s):  
Tahere Sayar ◽  
Mojtaba Ghiyasi ◽  
Jafar Fathali
Keyword(s):  
Planning Process ◽  
Efficiency Score ◽  
Decision Makers ◽  
Data Envelopment ◽  
Input And Output ◽  
Proposed Model ◽  
Dea Models ◽  
Business Sectors ◽  
Input Level ◽  
Decision Making Units

Data envelopment analysis (DEA) measures the efficiency score of a set of homogeneous decision-making units (DMUs) based on observed input and output. Considering input-oriented, the inverse DEA models find the required input level for producing a given amount of production in the current efficiency level. This article proposes a new form of the inverse DEA model considering income (for planning) and budget (for finance and budgeting) constraints. In contrast with the classical inverse model, both input and output levels are variable in proposed models to meet income (or budget) constraints. Proposed models help decision-makers (DMs) to find the required value of each input and each output's income share to meet the income or budget constraint. We apply the proposed model in the efficiency analysis of 58 supermarkets belonging to the same chain. However, these methods are general and can be used in the budgeting and planning process of any production system, including business sectors and firms that provide services.

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