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.

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.

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.

A generalized fuzzy cost efficiency model

2020 ◽  
Vol 54 (6) ◽  
pp. 1775-1791
Author(s):  
Nazila Aghayi ◽  
Samira Salehpour
Keyword(s):  
Cost Efficiency ◽  
Minimum Cost ◽  
Extensive Literature ◽  
Data Envelopment ◽  
Fuzzy Environment ◽  
Decision Making Unit ◽  
Production Possibility Set ◽  
Fuzzy Cost ◽  
The Cost ◽  
Generalized Cost

The concept of cost efficiency has become tremendously popular in data envelopment analysis (DEA) as it serves to assess a decision-making unit (DMU) in terms of producing minimum-cost outputs. A large variety of precise and imprecise models have been put forward to measure cost efficiency for the DMUs which have a role in constructing the production possibility set; yet, there’s not an extensive literature on the cost efficiency (CE) measurement for sample DMUs (SDMUs). In an effort to remedy the shortcomings of current models, herein is introduced a generalized cost efficiency model that is capable of operating in a fuzzy environment-involving different types of fuzzy numbers-while preserving the Farrell’s decomposition of cost efficiency. Moreover, to the best of our knowledge, the present paper is the first to measure cost efficiency by using vectors. Ultimately, a useful example is provided to confirm the applicability of the proposed methods.

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.

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 Novel models for obtaining the closest weak and strong efficient projections in data envelopment analysis

2021 ◽  
Vol 39 (5) ◽  
pp. 9-24
Author(s):  
Javad Vakili ◽  
Hanieh Amirmoshiri ◽  
Mir Kamal Mirnia
Keyword(s):  
Data Envelopment Analysis ◽  
Relative Efficiency ◽  
Efficient Frontier ◽  
Data Envelopment ◽  
Nonparametric Method ◽  
Target Setting ◽  
Production Possibility ◽  
Production Possibility Set ◽  
And Performance ◽  
Decision Making Units

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the relative efficiency and performance of Decision Making Units (DMUs). Traditionally, there are two issues regarding the DEA simultaneously i.e., the identification of a reference point on the efficient boundary of the production possibility set (PPS) and the use of some measures of distance from the unit under assessment to the efficient frontier. Due to its importance, in this paper, two alternative target setting models were developed to allow for lowefficient DMUs find the easiest way to improve its efficiency and reach to the efficient boundary. One seeks the closest weak efficient projection and the other suggests the most appropriate direction towards the strong efficient frontier surface. Both of these models provides the closest projection in one stage. Finally, a proposed problem is empirically checked by using a recent data related to 30 European airports.

Revenue Efficiency of Fuzzy Sample Decision Making Unit

2015 ◽  
Vol 5 (2) ◽  
pp. 14-27
Author(s):  
Nazila Aghayi ◽  
Samira Salehpour
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Main Role ◽  
Fuzzy Data ◽  
Production Possibility ◽  
Efficiency Assessment ◽  
Decision Making Unit ◽  
Different Types ◽  
Production Possibility Set ◽  
Revenue Efficiency

Revenue efficiency measurement is one of the most important issues in data envelopment analysis (DEA). Most of the proposed models calculate the revenue efficiency of decision making units (DMUs) which play a main role in the formation of the production possibility set by implementing exact or fuzzy data. The revenue efficiency value of a sample decision making unit with exact and fuzzy data has not been investigated by these models yet. There exist different types of fuzzy numbers, however, only a special type of them has been used in revenue efficiency models with fuzzy data. The concept of vector has not been employed to calculate the measure of the revenue efficiency in any of the studies conducted thus far. However, in this article the authors propose a model for evaluating the revenue efficiency measure of a fuzzy sample DMU without the limitations of previous models with regards to the formation of the production possibility set. In the proposed model, data can be selected from different types of fuzzy numbers and there is no limitation on the type of the used fuzzy data. In addition, the current article employs the concept of vector for revenue efficiency assessment for the first time.

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.

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