scholarly journals A Full Ranking for Decision Making Units Using Ideal and Anti-Ideal Points in DEA

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
A. Barzegarinegad ◽  
G. Jahanshahloo ◽  
M. Rostamy-Malkhalifeh
Keyword(s):  
Decision Making ◽  
Real Data ◽  
The Other ◽  
Data Envelopment ◽  
Production Possibility ◽  
Decision Making Unit ◽  
Common Set Of Weights ◽  
Production Possibility Set ◽  
Ideal Points ◽  
Decision Making Units

We propose a procedure for ranking decision making units in data envelopment analysis, based on ideal and anti-ideal points in the production possibility set. Moreover, a model has been introduced to compute the performance of a decision making unit for these two points through using common set of weights. One of the best privileges of this method is that we can make ranking for all decision making units by solving only three programs, and also solving these programs is not related to numbers of decision making units. One of the other advantages of this procedure is to rank all the extreme and nonextreme efficient decision making units. In other words, the suggested ranking method tends to seek a set of common weights for all units to make them fully ranked. Finally, it was applied for different sets holding real data, and then it can be compared with other procedures.

scholarly journals An algorithm for the anchor points of the PPS of the FRH models

2020 ◽  
Author(s):  
Dariush Akbarian
Keyword(s):  
Decision Making ◽  
Sufficient Conditions ◽  
Data Envelopment ◽  
Proposed Model ◽  
Decision Making Unit ◽  
Production Possibility Set ◽  
Anchor Points ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Decision Making Units

In this paper we deal with a variant of non-convex data envelopment analysis, called free replication hull model and try to obtain their anchor points. This paper uses a variant of super-efficiency model to characterize all extreme efficient decision making units and anchor points of the free replication hull models. A necessary and sufficient conditions for a decision making unit to be anchor point of the production possibility set of the free replication hull models are stated and proved. Since the set of anchor points is a subset of the set of extreme units, a definition of extreme units and a new method for obtaining these units in non-convex technologies are given. To illustrate the applicability of the proposed model, some numerical examples are finally provided.

scholarly journals Directional Slack-Based Measure for the Inverse Data Envelopment Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Ali Mirsalehy ◽  
Mohd Rizam Abu Bakar ◽  
Lai Soon Lee ◽  
Azmi B. Jaafar ◽  
Maryam Heydar
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Efficiency Score ◽  
Data Envelopment ◽  
New Production ◽  
Production Possibility ◽  
Novel Technique ◽  
Decision Making Unit ◽  
Measure Model ◽  
Production Possibility Set

A novel technique has been introduced in this research which lends its basis to the Directional Slack-Based Measure for the inverse Data Envelopment Analysis. In practice, the current research endeavors to elucidate the inverse directional slack-based measure model within a new production possibility set. On one occasion, there is a modification imposed on the output (input) quantities of an efficient decision making unit. In detail, the efficient decision making unit in this method was omitted from the present production possibility set but substituted by the considered efficient decision making unit while its input and output quantities were subsequently modified. The efficiency score of the entire DMUs will be retained in this approach. Also, there would be an improvement in the efficiency score. The proposed approach was investigated in this study with reference to a resource allocation problem. It is possible to simultaneously consider any upsurges (declines) of certain outputs associated with the efficient decision making unit. The significance of the represented model is accentuated by presenting numerical examples.

New Models for Computing the Distance of DMUs to the Weak Efficient Boundary of Convex and Nonconvex PPSs in DEA

2017 ◽  
Vol 34 (06) ◽  
pp. 1750035
Author(s):  
J. Vakili
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Data Envelopment ◽  
Production Possibility ◽  
New Models ◽  
Production Possibility Set ◽  
Decision Making Units

In data envelopment analysis (DEA), calculating the distances of decision making units (DMUs) from the weak efficient boundary of a production possibility set (PPS) is a very important subject which has attracted increasing interest of researchers in recent years. The distances of DMUs to the weak efficient boundary of the PPS can be used to evaluate the performance of DMUs, obtain the closest efficient patterns and also assess the sensitivity and stability of efficiency classifications in DEA. The present study proposes some new models which compute the distances of DMUs from the weak efficient boundary of a PPS for both convex and nonconvex PPSs using Hölder norms. In fact, the presented models assist a DMU to improve its performance by an appropriate movement towards the weak efficient boundary.

DEA Efficiency Region for Variations of Inputs and Outputs

2021 ◽  
pp. 1-26
Author(s):  
Mohammad Khoveyni ◽  
Robabeh Eslami
Keyword(s):  
Decision Making ◽  
Czech Republic ◽  
Data Envelopment Analysis ◽  
Banking Industry ◽  
Data Envelopment ◽  
The Czech Republic ◽  
Production Possibility ◽  
Dea Efficiency ◽  
Production Possibility Set ◽  
Decision Making Units

Finding efficiency regions (ERs) for extremely efficient decision-making units (DMUs) is one of the important issues from the managerial and economic viewpoints. An extremely efficient DMU will remain efficient if and only if after changing its inputs and/or its outputs this DMU stays within its ER. Thus, by applying the ER information, decision maker(s) of the evaluated extremely efficient DMU can precisely understand the values of input(s) increment and output(s) decrement of this DMU so that it remains efficient. Hence, in this study, we propose a data envelopment analysis (DEA) approach based on the defining hyperplanes of the production possibility set (PPS), which is capable of finding the ERs of the DMUs when their inputs increase and/or their outputs decrease. To demonstrate the applicability of the proposed approach, in the real world, a numerical example and an empirical application to the banking industry in the Czech Republic are provided.

A DATA ENVELOPMENT ANALYSIS (DEA) EVALUATION METHOD BASED ON SAMPLE DECISION MAKING UNITS

2010 ◽  
Vol 09 (04) ◽  
pp. 601-624 ◽  
Author(s):  
QUANLING WEI ◽  
HONG YAN
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Evaluation Method ◽  
Evaluation Procedure ◽  
Data Envelopment ◽  
Training Set ◽  
Production Possibility ◽  
Original Definition ◽  
Production Possibility Set ◽  
Decision Making Units

Most of evaluation methods on large number of candidates are based a single criterion. To bring the multiple attribute evaluation method Data Envelopment Analysis (DEA) into evaluating large number of elements, it needs to set up the performance standards and an evaluation procedure by the DEA model. In this paper, we first determine a set of "standard" candidates, called in decision making units (DMUs) in the DEA terminology. This standard set is called "training set". We then establish the evaluation procedure based on this "training set" for measuring a large number of DMUs. We first investigate the efficiency evaluation of a new DMU along with the original definition based on the sum formed production possibility set which is formed by the n DMUs in the training set and the new DMU. We then identify the intersection form of the production possibility set formed only by the n DMUs from the training set. And show that the new DMU evaluation is simply to check if the DMU satisfies a set of linear inequalities. The intersection formed production possibility set formed by the n DMUs from the training set is fixed for evaluating any new DMU. Therefore, it provides an efficient and effective method for dealing with a large amount of data. The method can be regarded as a complementary approach for data mining.

Development of a new cost PPS and decomposition of observed actual cost for DMU in a non-competitive space in DEA

2019 ◽  
Vol 53 (5) ◽  
pp. 1563-1580
Author(s):  
Elham Rezaei Hezaveh ◽  
Reza Fallahnejad ◽  
Masoud Sanei ◽  
Mohammad Izadikhah
Keyword(s):  
Decision Making ◽  
Cost Efficiency ◽  
Allocative Efficiency ◽  
Data Envelopment ◽  
Actual Cost ◽  
Production Possibility ◽  
Production Possibility Set ◽  
The Cost ◽  
Revenue Efficiency ◽  
Decision Making Units

Data Envelopment Analysis (DEA) is an appropriate tool for estimating various types of efficiency such as cost efficiency. There are two different sates in cost spaces; in the first space prices are equal for all Decision Making Units (DMUs) which is competitive space, and in the second space prices are different form one DMU to another; this is known as non-competitive space. The present paper introduces a new method to assess Cost Efficiency (CE), Revenue Efficiency (RE) and Profit Efficiency (PE) in a non-competitive space. The present paper also proposes a Production Possibility Set (PPS) in which DMUs are evaluated based on both their own prices and the prices of other DMUs in non-competitive space. Moreover, a new decomposition is provided for observed actual cost DMUs based on the cost efficiency model and the proposed PPS, thus the observed actual cost can be shown by summation of several technical, price and allocative efficiency (AE) losses. The biggest advantage of this method comparing to the previous methods is that passive the developed cost efficiency and the cost Production Possibility Set has been developed and the performed decomposition is more accurate; this is because the new inefficiency sources are defined and added to this new decomposition. Therefore, it includes more inefficient sources.

Relative Efficiency of Decision Making Units Producing Both Desirable and Undesirable Outputs: A Case of Textile Processing Units in Pakistan.

2011 ◽  
Vol 50 (4II) ◽  
pp. 685-698
Author(s):  
Samina Khalil
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Relative Efficiency ◽  
Value Added ◽  
Data Envelopment ◽  
Undesirable Outputs ◽  
Textile Processing ◽  
Decision Making Unit ◽  
Desirable And Undesirable Outputs ◽  
Decision Making Units

This paper aims at measuring the relative efficiency of the most polluting industry in terms of water pollution in Pakistan. The textile processing is country‘s leading sub sector in textile manufacturing with regard to value added production, export, employment, and foreign exchange earnings. The data envelopment analysis technique is employed to estimate the relative efficiency of decision making units that uses several inputs to produce desirable and undesirable outputs. The efficiency scores of all manufacturing units exhibit the environmental consciousness of few producers is which may be due to state regulations to control pollution but overall the situation is far from satisfactory. Effective measures and instruments are still needed to check the rising pollution levels in water resources discharged by textile processing industry of the country. JEL classification: L67, Q53 Keywords: Data Envelopment Analysis (DEA), Decision Making Unit (DMU), Relative Efficiency, Undesirable Output

A Common Set of Weights for Ranking Decision-Making Units with Undesirable Outputs: A Double Frontiers Data Envelopment Analysis Approach

2018 ◽  
Vol 35 (06) ◽  
pp. 1850039 ◽  
Author(s):  
Lei Chen ◽  
Fei-Mei Wu ◽  
Feng Feng ◽  
Fujun Lai ◽  
Ying-Ming Wang
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Optimal Solution ◽  
Data Envelopment ◽  
Undesirable Outputs ◽  
Discrimination Power ◽  
Efficiency Optimization ◽  
Common Set Of Weights ◽  
Desirable And Undesirable Outputs ◽  
Decision Making Units

Major drawbacks of the traditional data envelopment analysis (DEA) method include selecting optimal weights in a flexible manner, lacking adequate discrimination power for efficient decision-making units, and considering only desirable outputs. By introducing the concept of global efficiency optimization, this study proposed a double frontiers DEA approach with undesirable outputs to generate a common set of weights for evaluating all decision-making units from both the optimistic and pessimistic perspectives. For a unique optimal solution, compromise models for individual efficiency optimization were developed as a secondary goal. Finally, as an illustration, the models were applied to evaluate the energy efficiency of the Chinese regional economy. The results showed that the proposed approach could improve discrimination power and obtain a fair result in a case where both desirable and undesirable outputs exist.

scholarly journals Finding the Most Preferred Decision-Making Unit in Data Envelopment Analysis

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Shirin Mohammadi ◽  
S. Morteza Mirdehghan ◽  
Gholamreza Jahanshahloo
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Data Envelopment Analysis ◽  
Utility Function ◽  
Decision Maker ◽  
Programming Models ◽  
Data Envelopment ◽  
Production Possibility ◽  
Decision Making Unit ◽  
Inputs And Outputs

Data envelopment analysis (DEA) evaluates the efficiency of the transformation of a decision-making unit’s (DMU’s) inputs into its outputs. Finding the benchmarks of a DMU is one of the important purposes of DEA. The benchmarks of a DMU in DEA are obtained by solving some linear programming models. Currently, the obtained benchmarks are just found by using the information of the data of inputs and outputs without considering the decision-maker’s preferences. If the preferences of the decision-maker are available, it is very important to obtain the most preferred DMU as a benchmark of the under-assessment DMU. In this regard, we present an algorithm to find the most preferred DMU based on the utility function of decision-maker’s preferences by exploring some properties on that. The proposed method is constructed based on the projection of the gradient of the utility function on the production possibility set’s frontier.

USING THE MINIMUM DISTANCE OF DMUs FROM THE FRONTIER OF THE PPS FOR EVALUATING GROUP PERFORMANCE OF DMUs IN DEA

2012 ◽  
Vol 29 (02) ◽  
pp. 1250010 ◽  
Author(s):  
G. R. JAHANSHAHLOO ◽  
J. VAKILI ◽  
S. M. MIRDEHGHAN
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Minimum Distance ◽  
Group Performance ◽  
Returns To Scale ◽  
Data Envelopment ◽  
Production Possibility ◽  
Variable Returns To Scale ◽  
Decision Making Units

Evaluating group performance of decision-making units (DMUs) is an application of data envelopment analysis (DEA) and usually provides a measure to compare the frontiers of the production possibility sets (PPSs) corresponding to different groups and the internal inefficiencies of DMUs associated with their group. In this paper, first, a method is presented for obtaining the minimum distance of DMUs from the frontier of the PPS by ‖⋅‖1, which itself can be a very important subject in DEA, and then, for stating an application of these distances, an approach is provided for evaluating group performance of DMUs based on the production ability of the PPSs such that both constant and variable returns to scale assumptions can be used in this method in contrast with some other methods. Therefore, providing the methods for both obtaining the minimum distance of DMUs from the frontier of the PPS and evaluating group performance of DMUs is the most important contribution of this paper.

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