An Interval Efficiency Measurement in DEA When considering Undesirable Outputs

Data envelopment analysis (DEA) is a popular mathematical tool for analyzing the relative efficiency of homogenous decision-making units (DMUs). However, the existing DEA models cannot tackle the newly confronted applications with imprecise and negative data as well as undesirable outputs simultaneously. Thus, we introduce undesirable outputs into modified slack-based measure (MSBM) model and propose an interval-modified slack-based measure (IMSBM) model, which extends the application of interval DEA (IDEA) in fields that concern with less undesirable outputs. The novelties of the model are that it considers the undesirable outputs while dealing with imprecise and negative data, and it is slack-based. Furthermore, the model with undesirable outputs is proven translation-invariant and unit-invariant. Moreover, a numerical example is provided to illustrate the changes of the lower and upper bounds of the efficiency score after considering the undesirable outputs. The empirical results show that, without considering undesirable outputs, most of the lower bounds of the efficiency scores will be overestimated when the DMUs are weakly efficient and inefficient. The upper bound will also change after considering undesirable outputs when the DMU is inefficient. Finally, an improved degree of preference approach is introduced to rank the DMUs.

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Ranking DMUs by Calculating the Interval Efficiency with a Common Set of Weights in DEA

Journal of Applied Mathematics ◽

10.1155/2014/346763 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 4

Author(s):

Vahideh Rezaie ◽

Tahir Ahmad ◽

Siti-Rahmah Awang ◽

Masumeh Khanmohammadi ◽

Normah Maan

Keyword(s):

Decision Maker ◽

Relative Efficiency ◽

Efficiency Score ◽

Upper Bounds ◽

Data Envelopment ◽

Lower And Upper Bounds ◽

Common Set Of Weights ◽

Overall Performance ◽

Interval Efficiency ◽

Decision Making Units

To evaluate the performance of decision making units (DMUs), data envelopment analysis (DEA) was introduced. Basically, the traditional DEA scheme calculates the best relative efficiency score (i.e., the “optimistic” efficiency) of each DMU with the most favorable weights. A decision maker may be unable to compare and fully rank the efficiencies of different DMUs that are calculated using these potentially distinct sets of weights on the same basis. Based on the literature, the assignable worst relative efficiency score (i.e., the “pessimistic” efficiency) for each DMU can also be determined. In this paper, the best and the worst relative efficiencies are considered simultaneously. To measure the overall performance of the DMUs, an integration of both the best and the worst relative efficiencies is considered in the form of an interval. The advantage of this efficiency interval is that it provides all of the possible efficiency values and an expanded overview to the decision maker. The proposed method determines the lower- and upper-bounds of the interval efficiency over a common set of weights. To demonstrate the implementation of the introduced method, a numerical example is provided.

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An Interval Efficiency Measurement without Sign Restrictions in Data

Mathematical Problems in Engineering ◽

10.1155/2020/7258519 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

Liyang Yang ◽

Renbian Mo

Keyword(s):

Real Life ◽

Input Output ◽

Lower And Upper Bounds ◽

Negative Data ◽

Output Data ◽

Translation Invariant ◽

Progressive Development ◽

Dea Models ◽

The Difference ◽

Interval Efficiency

Mostly, all conventional DEA models assume that input-output data are precise and nonnegative, but in real-life application, this condition is mostly not applicable. Through progressive development in the methodology of DEA, some models separately deal with imprecise and negative data. In this study, the IMSBM model is proposed to evaluate the performance of a set of homogenous DMUs with imprecise and negative input-output data. The IMSBM model is far superior to models with similar capability because it considers the inefficiency caused by both radial and nonradial slacks. The lower and upper bounds of interval efficiency calculated by the IMSBM model reflect the performance of observed DMU in most unfavourable and most favourable situations. Further, it is proved that the IMSBM model is units invariant, monotone, and translation invariant. Moreover, we elaborate both bounds of the interval efficiency are in the range of [0,1]. The degree of preference approach is introduced to rank the DMUs. In addition, we compare the interval efficiency scores calculated by the IMSBM model and the interval SORM model and explain the reason for the difference between the scores. By adjusting the weights of inputs and outputs, it is found that only inefficiency scores fluctuate with slack weights.

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An application of data envelopment analysis for Korean banks with negative data

Benchmarking An International Journal ◽

10.1108/bij-02-2016-0023 ◽

2017 ◽

Vol 24 (4) ◽

pp. 1052-1064 ◽

Cited By ~ 9

Author(s):

Yong Joo Lee ◽

Seong-Jong Joo ◽

Hong Gyun Park

Keyword(s):

Data Envelopment Analysis ◽

Data Sets ◽

Data Envelopment ◽

Negative Data ◽

Ownership Type ◽

Data Set ◽

Translation Invariant ◽

Content Type ◽

Dea Models ◽

Regional Banks

Purpose The purpose of this paper is to measure the comparative efficiency of 18 Korean commercial banks under the presence of negative observations and examine performance differences among them by grouping them according to their market conditions. Design/methodology/approach The authors employ two data envelopment analysis (DEA) models such as a Banker, Charnes, and Cooper (BCC) model and a modified slacks-based measure of efficiency (MSBM) model, which can handle negative data. The BCC model is proven to be translation invariant for inputs or outputs depending on output or input orientation. Meanwhile, the MSBM model is unit invariant in addition to translation invariant. The authors compare results from both models and choose one for interpreting results. Findings Most Korean banks recovered from the worst performance in 2011 and showed similar performance in recent years. Among three groups such as national banks, regional banks, and special banks, the most special banks demonstrated superb performance across models and years. Especially, the performance difference between the special banks and the regional banks was statistically significant. The authors concluded that the high performance of the special banks was due to their nationwide market access and ownership type. Practical implications This study demonstrates how to analyze and measure the efficiency of entities when variables contain negative observations using a data set for Korean banks. The authors have tried two major DEA models that are able to handle negative data and proposed a practical direction for future studies. Originality/value Although there are research papers for measuring the performance of banks in Korea, all of the papers in the topic have studied efficiency or productivity using positive data sets. However, variables such as net incomes and growth rates frequently include negative observations in bank data sets. This is the first paper to investigate the efficiency of bank operations in the presence of negative data in Korea.

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New inverse DEA models for budgeting and planning

RAIRO - Operations Research ◽

10.1051/ro/2021069 ◽

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

The Pakistan Development Review ◽

10.30541/v50i4iipp.685-698 ◽

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

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Dealing with Interval DEA Based on Error Propagation and Entropy: A Case Study of Energy Efficiency of Regions in China Considering Environmental Factors

Journal of Systems Science and Information ◽

10.1515/jssi-2015-0538 ◽

2015 ◽

Vol 3 (6) ◽

pp. 538-548 ◽

Cited By ~ 1

Author(s):

Jianping Fan ◽

Weizhen Yue ◽

Meiqin Wu

Keyword(s):

Energy Efficiency ◽

Environmental Factors ◽

Error Propagation ◽

Interval Data ◽

Data Envelopment ◽

Exact Data ◽

Dea Models ◽

Traditional Approaches ◽

Decision Making Units

AbstractThe conventional data envelopment analysis (DEA) measures the relative efficiency of decision making units (DMUs) consuming multiple inputs to produce multiple outputs under the assumption that all the data are exact. In the real world, however, it is possible to obtain interval data rather than exact data because of various limitations, such as statistical errors and incomplete information, et al. To overcome those limitations, researchers have proposed kinds of approaches dealing with interval DEA, which either use traditional DEA models by transforming interval data into exact data or get an efficiency interval by using the bound of interval data. In contrast to the traditional approaches above, the paper deals with interval DEA by combining traditional DEA models with error propagation and entropy, uses idea of the modified cross efficiency to get the ultimate cross efficiency of DMUs in the form of error distribution and ranks DMUs using the calculated ultimate cross efficiency by directional distance index. At last we illustrate the feasibility and effectiveness of the proposed method by applying it to measure energy efficiency of regions in China considering environmental factors.

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

Journal of Systems Science and Information ◽

10.21078/jssi-2021-378-21 ◽

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.

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

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595918500392 ◽

2018 ◽

Vol 35 (06) ◽

pp. 1850039 ◽

Cited By ~ 2

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.

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A Revised Inverse Data Envelopment Analysis Model Based on Radial Models

Mathematics ◽

10.3390/math8050803 ◽

2020 ◽

Vol 8 (5) ◽

pp. 803

Author(s):

Xiaoyin Hu ◽

Jianshu Li ◽

Xiaoya Li ◽

Jinchuan Cui

Keyword(s):

Data Envelopment Analysis ◽

Efficiency Index ◽

Data Envelopment Analysis Model ◽

Data Envelopment ◽

Analysis Model ◽

Numerical Examples ◽

Wide Range ◽

Dea Models ◽

Overall Efficiency ◽

Decision Making Units

In recent years, there has been an increasing interest in applying inverse data envelopment analysis (DEA) to a wide range of disciplines, and most applications have adopted radial-based inverse DEA models. However, results given by existing radial based inverse DEA models can be unreliable as they neglect slacks while evaluating decision-making units’ (DMUs) overall efficiency level, whereas classic radial DEA models measure the efficiency level through not only radial efficiency index but also slacks. This paper points out these disadvantages with a counterexample, where current inverse DEA models give results that outputs shall increase when inputs decrease. We show that these unreasonable results are the consequence of existing inverse DEA models’ failure in preserving DMU’s efficiency level. To rectify this problem, we propose a revised model for the situation where the investigated DMU has no slacks. Compared to existing radial inverse DEA models, our revised model can preserve radial efficiency index as well as eliminating all slacks, thus fulfilling the requirement of efficiency level invariant. Numerical examples are provided to illustrate the validity and limitations of the revised model.

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Data envelopment analysis in measuring the efficiency of volleyball teams in Primorsko-Goranska County

Zbornik Veleučilišta u Rijeci ◽

10.31784/zvr.8.1.14 ◽

2020 ◽

Vol 8 (1) ◽

pp. 121-134

Author(s):

Jelena Jardas Antonić ◽

Kristina Kregar ◽

Nenad Vretenar

Keyword(s):

Data Envelopment Analysis ◽

Efficiency Analysis ◽

Efficiency Score ◽

Financial Resources ◽

Data Envelopment ◽

Financial Factors ◽

Measuring Efficiency ◽

Dea Models ◽

Sport Organisation ◽

Ccr Model

Every sport organisation strives to evaluate its performance: its weaknesses and strengths. Measuring efficiency and sports are two interrelated concepts and it is not surprising that most of the research on sports is focused on analysing the efficiency of teams according to player techniques, attack and defence efficiency. However, there are very few studies based on the analysis of financial factors such as teams’ revenue and costs. In this paper two Data Envelopment Analysis (DEA) models were used to evaluate 16 young cadet volleyball teams in Primorsko-Goranska County based on two economic inputs. The paper aims to explain the importance of teams’ financial resources in achieving sports efficiency. To analyse the relative efficiency of teams, two frequently used models are employed, the Banker Charnes Cooper (BCC) and the Charnes Cooper Rhodes (CCR) model. In the end, a super efficiency analysis was conducted to make a distinction in efficiency scores between efficient units. Analyses showed that financial factors are not crucial factors for efficiency score and gave possibility to use obtained results and improve the performance of inefficient volleyball teams. The study was conducted on a sample of 16 teams through 4 inputs and 1 output collected during 2017/2018 season.

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