scholarly journals The Theoretical Relationship between the CCR Model and the Two-Stage DEA Model with an Application in the Efficiency Analysis of the Financial Industry

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 712
Author(s):  
Ming-Chi Tsai ◽  
Ching-Hsue Cheng ◽  
Van Trung Nguyen ◽  
Meei-Ing Tsai
Keyword(s):  
Insurance Companies ◽  
Data Envelopment ◽  
Financial Industry ◽  
Two Stage ◽  
Theoretical Relationship ◽  
Dea Model ◽  
Bank Branches ◽  
Dea Models ◽  
The Relationship ◽  
Ccr Model

Since Charnes, Cooper, and Rhodes introduced data envelopment analysis (DEA) in 1978, later called the DEA-CCR model, many studies applied this technique to different fields. Based on the original CCR model, many modified DEA models were developed by researchers. Since 1999, Seiford and Zhu presented a two-stage DEA model. Later, these models were widely used in many studies. However, the relationship between the efficiency scores that are obtained from the original CCR model and the two-stage DEA model remains unknown. To fill this gap, this study proposed a theoretical relationship between the efficiency scores that are calculated from the two-stage DEA model and those that are obtained from the original CCR model. How the sets of nonsymmetrical weights affected the efficiency scores were also investigated. Theorems regarding the relationship were developed, and then the model was utilized to evaluate the two-stage efficiency scores of the insurance companies (non-life) and bank branches. The results show that using a two-stage DEA model can get more information about operational efficiency than the traditional CCR model does. The findings from this study about the two-stage DEA technique can provide significant reasons for using this model to evaluate performance efficiency.

scholarly journals Efficiency Bounds for Two-Stage Production Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Xiao Shi
Keyword(s):  
Production Systems ◽  
Efficiency Score ◽  
Insurance Companies ◽  
Practical Case ◽  
Data Envelopment ◽  
Production Structure ◽  
Two Stage ◽  
Decision Making Unit ◽  
Real World Applications ◽  
Dea Models

Traditional data envelopment analysis (DEA) models find the most desirable weights for each decision-making unit (DMU) in order to estimate the highest efficiency score as possible. These efficiency scores are then used for ranking the DMUs. The main drawback is that the efficiency scores based on weights obtained from the standard DEA models ignore other feasible weights; this is due to the fact that DEA may have multiple solutions for each DMU. To overcome this problem, Salo and Punkka (2011) deemed each DMU as a “Black Box” and developed models to obtain the efficiency bounds for each DMU over sets of all its feasible weights. In many real world applications, there are DMUs that have a two-stage production system. In this paper, we extend the Salo and Punkka’s (2011) model to a more common and practical case considering the two-stage production structure. The proposed approach calculates each DMU’s efficiency bounds for the overall system as well as efficiency bounds for each subsystem/substage. An application for nonlife insurance companies has been discussed to illustrate the applicability of the proposed approach and show the usefulness of this method.

A slacks-based measure approach for efficiency decomposition in multi-period two-stage systems

2020 ◽  
Vol 54 (6) ◽  
pp. 1657-1671
Author(s):  
Samaneh Esfidani ◽  
Farhad Hosseinzadeh Lotfi ◽  
Shabnam Razavyan ◽  
Ali Ebrahimnejad
Keyword(s):  
Production Systems ◽  
Weighted Average ◽  
Real Data ◽  
Stage Structure ◽  
Data Envelopment ◽  
Two Stage ◽  
Bank Branches ◽  
Proposed Model ◽  
Efficiency Decomposition ◽  
Dea Models

Two-stage production systems are often encountered in many real applications where the production process is divided into two processes. In contrast to the conventional data envelopment analysis (DEA) models, two-stage DEA models take the operations of the internal processes into account. A number of studies have used two-stage DEA models in order to evaluate the performance of decision making units (DMUs) having a network structure. In this paper, we use a non-radial DEA model called the network slacks-based measure (NSBM) model to measure the efficiency of a system with a multi-period two-stage structure. Then we describe the properties of the proposed model in details. Moreover, we shall decompose the overall efficiency of the system over a number of time periods as a weighted average of the efficiency in each period. The efficiency of the stages, in respect to the entire periods shall be decomposed in terms of the weighted average efficiency of the stages in each period. Finally, the real data of Mellat bank branches in Tehran extracted from extant literature is used to illustrate the proposed approach.

scholarly journals Weight restrictions for the DEA model in the presence of dual-role factors: An application to the Iranian banking sector

2021 ◽  
Author(s):  
Amineh Ghazi ◽  
Farhad Hosseinzadeh Lotfi
Keyword(s):  
Banking Sector ◽  
Dual Role ◽  
Data Envelopment ◽  
Weight Restrictions ◽  
New Model ◽  
Dea Model ◽  
Bank Branches ◽  
Additional Information ◽  
New Models ◽  
Dea Models

A production process transforming multiple inputs to different outputs is considered in conventional data envelopment analysis (DEA) models. In various settings, however, there are factors that simultaneously play the roles of both input and output called dual-role factors. In some situations, additional information is available to impose on a DEA model with dual-role factors, or the decision maker is forced to impose some restrictions regarding the importance of dual-role factors on the model. Toward this end, the current research employs two different weighting methods to introduce various weighted DEA models in the presence of dual-role factors. To strengthen the accuracy of the new models, their properties are discussed. Then, each new model is illustrated in details by a numerical example. Moreover, to show that the new models are applicable, they are applied to the Iranian banking sector. To do this, $ 20 $ bank branches which have dual-role factors are assessed. At last, to show the outcome of weight restrictions, the results obtained by each new model are compared with those from Cook and Zhu's model (2007).

scholarly journals Network DEA based on DEA-ratio

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Dariush Akbarian
Keyword(s):  
Insurance Companies ◽  
Data Envelopment ◽  
Validity And Reliability ◽  
Two Stage ◽  
Network Dea ◽  
Black Boxes ◽  
Internal Structures ◽  
Dea Models ◽  
Tchebycheff Norm ◽  
Special Case

AbstractData envelopment analysis (DEA) is a technique to measure the performance of decision-making units (DMUs). Conventional DEA treats DMUs as black boxes and the internal structure of DMUs is ignored. Two-stage DEA models are special case network DEA models that explore the internal structures of DMUs. Most often, one output cannot be produced by certain input data and/or the data may be expressed as ratio output/input. In these cases, traditional two-stage DEA models can no longer be used. To deal with these situations, we applied DEA-Ratio (DEA-R) to evaluate two-stage DMUs instead of traditional DEA. To this end, we developed two novel DEA-R models, namely, range directional DEA-R (RDD-R) and (weighted) Tchebycheff norm DEA-R (TND-R). The validity and reliability of our proposed approaches are shown by some examples. The Taiwanese non-life insurance companies are revisited using these proposed approaches and the results from the proposed methods are compared with those from some other methods.

scholarly journals The Environmental Efficiency Analysis Based on the Three-Step Method for Two-Stage Data Envelopment Analysis

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 7028
Author(s):  
Qingyou Yan ◽  
Fei Zhao ◽  
Xu Wang ◽  
Tomas Balezentis
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Cooperative Game ◽  
Environmental Efficiency ◽  
Data Envelopment ◽  
Step Method ◽  
Two Stage ◽  
Dea Model ◽  
The Status ◽  
Dea Models

This paper suggests that the efficiency of a system (decision-making unit) and its subsystem cannot be properly measured using a two-stage data envelopment analysis (DEA) model either in cooperative or non-cooperative evaluation. Indeed, the existing methods subjectively determine the status of the subsystems in the whole system. The two-stage DEA models, either cooperative game or non-cooperative game, are used to analyze the environmental efficiency. However, when the actual relationship between the two subsystems is inconsistent with the subjective relationship assumptions, the overall efficiency of the system and the efficiency of each subsystem will be biased. The conventional two-stage DEA models require predetermining the relationship between the subsystems within the system based on the subjective judgment of the decision-maker. Based on this, this paper proposes a three-step method to solve the two-stage DEA. First, the position relation among subsystems is determined according to the optimal weights through the model. According to the status relationship among subsystems, the decision units are grouped, and the two-stage DEA model of cooperative game or non-cooperative game is used to analyze the efficiency in each group. This method reduces the subjectivity of decision making and analyzes the efficiency of each decision unit applying the most appropriate two-stage DEA model to find the source of inefficiency. Finally, this paper verifies the rationality and validity of the method by analyzing the water use efficiency of industrial systems in China. It is found that most regions in China value economic development more than environmental protection (as evidenced by the DEA weights). What is more, the method proposed by the paper can be generalized for any two-stage DEA problem.

scholarly journals A Range Adjusted Measure of Super-Efficiency in Integer-Valued Data Envelopment Analysis with Undesirable Outputs

2021 ◽  
Vol 9 (4) ◽  
pp. 378-398
Author(s):  
Chunhua Chen ◽  
Haohua Liu ◽  
Lijun Tang ◽  
Jianwei Ren
Keyword(s):  
Data Envelopment Analysis ◽  
Transportation Systems ◽  
Decision Makers ◽  
Data Envelopment ◽  
Undesirable Outputs ◽  
Super Efficiency ◽  
Dea Model ◽  
Dea Models ◽  
Analysis Models ◽  
Transport Accidents

Abstract DEA (data envelopment analysis) models can be divided into two groups: Radial DEA and non-radial DEA, and the latter has higher discriminatory power than the former. The range adjusted measure (RAM) is an effective and widely used non-radial DEA approach. However, to the best of our knowledge, there is no literature on the integer-valued super-efficiency RAM-DEA model, especially when undesirable outputs are included. We first propose an integer-valued RAM-DEA model with undesirable outputs and then extend this model to an integer-valued super-efficiency RAM-DEA model with undesirable outputs. Compared with other DEA models, the two novel models have many advantages: 1) They are non-oriented and non-radial DEA models, which enable decision makers to simultaneously and non-proportionally improve inputs and outputs; 2) They can handle integer-valued variables and undesirable outputs, so the results obtained are more reliable; 3) The results can be easily obtained as it is based on linear programming; 4) The integer-valued super-efficiency RAM-DEA model with undesirable outputs can be used to accurately rank efficient DMUs. The proposed models are applied to evaluate the efficiency of China’s regional transportation systems (RTSs) considering the number of transport accidents (an undesirable output). The results help decision makers improve the performance of inefficient RTSs and analyze the strengths of efficient RTSs.

DEA Models for Parallel Systems: Game-Theoretic Approaches

2015 ◽  
Vol 32 (02) ◽  
pp. 1550008 ◽  
Author(s):  
Juan Du ◽  
Joe Zhu ◽  
Wade D. Cook ◽  
Jiazhen Huo
Keyword(s):  
Black Box ◽  
Data Envelopment ◽  
System Efficiency ◽  
Data Set ◽  
Dea Models ◽  
Game Theoretic ◽  
Work Shifts ◽  
The Relationship ◽  
Relevant Component ◽  
Plant Efficiency

In many settings, systems are composed of a group of independent sub-units. Each sub-unit produces the same set of outputs by consuming the same set of inputs. Conventional data envelopment analysis (DEA) views such a system as a "black-box", and uses the sum of the respective inputs and outputs of all relevant component units to calculate the system efficiency. Various DEA-based models have been developed for decomposing the overall efficiency. This paper further investigates this kind of structure by using the cooperative (or centralized) and non-cooperative (Stackelberg or leader–follower) game theory concepts. We show that the existing DEA approaches can be viewed as a centralized model that optimizes the efficiency scores of all sub-units jointly. The proposed leader–follower model will be useful when the priority sequence is available for sub-units. Consider, for example, the evaluation of relative efficiencies of a set of manufacturing facilities where multiple work shifts are operating. Management may wish to determine not only the overall plant efficiency, but as well, the performance of each shift in some priority sequence. The relationship between the system efficiency and component efficiencies is also explored. Our approaches are demonstrated with an example whose data set involves the national forests of Taiwan.

scholarly journals Two-stage DEA for Bank Efficiency Evaluation Considering Shared Input and Unexpected Output Factors

2020 ◽  
Vol 214 ◽  
pp. 01036
Author(s):  
Song Aifeng ◽  
Zhang XiaoYang ◽  
Huang Weilai ◽  
Yang xue ◽  
Yang Juan
Keyword(s):  
Market Competition ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Uncertain Information ◽  
Two Stage ◽  
Bank Efficiency ◽  
Dea Model ◽  
Stochastic Dea ◽  
Output Factors ◽  
Fierce Competition

With the increasingly fierce market competition, only by relying on high-quality products and high customer satisfaction can enterprises survive in the fierce competition. Among many evaluation methods, Data Envelopment Analysis (DEA), as a non-parametric statistical method to effectively deal with multi-input and multi-output problems, has received more and more attention in evaluating the relative efficiency of decision-making units. In the process of bank efficiency evaluation based on DEA method, there will be a situation that banks have both dual role factors and unexpected output factors. The Two-stage DEA model provides an effective analysis method to solve the problem of bank efficiency evaluation of complex organizational structure. In order to evaluate the efficiency of unexpected output with uncertain information, a stochastic DEA model of unexpected output is established.

scholarly journals Quantifying Electricity Supply Resilience of Countries with Robust Efficiency Analysis

Energies ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1535 ◽  
Author(s):  
Patrick Gasser ◽  
Marco Cinelli ◽  
Anna Labijak ◽  
Matteo Spada ◽  
Peter Burgherr ◽  
...  
Keyword(s):  
Robustness Analysis ◽  
Energy Systems ◽  
Efficiency Analysis ◽  
Electricity Supply ◽  
Data Envelopment ◽  
Hybrid Framework ◽  
Dea Models ◽  
Overall Performance ◽  
Electricity Systems ◽  
Ccr Model

The interest in studying energy systems’ resilience is increasing due to a rising awareness of the importance of having a secure energy supply. This growing trend is a result of a series of recent disruptions, among others also affecting electricity systems. Therefore, it is of crucial importance for policymakers to determine whether their country has a resilient electricity supply. Starting from a set of 12 indicators, this paper uses data envelopment analysis (DEA) to comprehensively evaluate the electricity supply resilience of 140 countries worldwide. Two DEA models are applied: (1) the original ratio-based Charnes, Cooper, and Rhodes (CCR) model and (2) a novel hybrid framework for robust efficiency analysis incorporating linear programming and Monte Carlo simulations. Results show that the CCR model deems 31 countries as efficient and hence lacks the capability to differentiate them. Furthermore, the CCR model considers only the best weight vectors for each country, which are not necessarily representative of the overall performance of the countries. The robustness analysis explores these limitations and identifies South Korea, Singapore and Canada as the most resilient countries. Finally, country analyses are conducted, where Singapore’s and Japan’s performances and improvement potentials are discussed.

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