Data Envelopment Analysis Context Research Articles

Theory of binary-valued data envelopment analysis: an application in assessing the sustainability of suppliers

PurposeThe objective of this study is to present a binary-valued data envelopment analysis (DEA) theory. The authors’ proposed approach, for the first time, combines binary-valued and integer-valued theories concurrently in the DEA context. To do so, new production possibility sets (PPSs) with some distinguished features are developed.Design/methodology/approachThe authors address integer inputs and outputs in the proposed approach by introducing a new PPS.FindingsTo take into account the binary data, the authors develop axiomatic DEA principles. The binary production principles guarantee any combination of convexity and feasibility. Furthermore, the authors develop a new DEA model to consider integer and real data. A case study is presented to show the usefulness of the developed models. Using the proposed models, the authors obtained benchmarks to solve the sustainable supplier selection problems.Originality/value(1) For the first time, binary-valued and integer-valued theories are presented in an integrated DEA model. (2) To deal with the pure binary data, a new PPS is proposed. (3) To consider real, integer and binary data, a new PPS is introduced. (4) New technologies are developed to propose feasible solutions. (5) The proposed models can project inefficient decision-making units (DMUs) on efficiency frontier given binary, integer and real data. (6) A case study is given for the performance evaluation of sustainable suppliers.

Scale elasticity in the presence of integer data: An application to electricity distribution companies

Returns to scale and scale elasticity are two important issues in the field of economics and operations research. Recently, estimating returns to scale and scale elasticity using tools such as data envelopment analysis (DEA) has attracted considerable attention among researchers. The existing approaches to calculate scale elasticity in DEA context, assume all inputs and outputs are real-valued and in this sense, the underlying technology is a continuous set. In many real cases, however, we face input/output measures that are restricted to be integer-valued. Scale properties of frontier points in such cases are interesting and important. In this paper, this problem in integer-valued DEA is studied. The Lagrangian dual formulation of a mixed integer linear programming problem is used to calculate the scale elasticity of a frontier point. To illustrate the real applicability of the theoretical framework, a real case on electricity distribution companies is given.

Scale elasticity in the presence of integer data: An application to electricity distribution companies

Returns to scale and scale elasticity are two important issues in the field of economics and operations research. Recently, estimating returns to scale and scale elasticity using tools such as data envelopment analysis (DEA) has attracted considerable attention among researchers. The existing approaches to calculate scale elasticity in DEA context, assume all inputs and outputs are real-valued and in this sense, the underlying technology is a continuous set. In many real cases, however, we face input/output measures that are restricted to be integer-valued. Scale properties of frontier points in such cases are interesting and important. In this paper, this problem in integer-valued DEA is studied. The Lagrangian dual formulation of a mixed integer linear programming problem is used to calculate the scale elasticity of a frontier point. To illustrate the real applicability of the theoretical framework, a real case on electricity distribution companies is given.

Stepwise pricing in evaluating revenue efficiency in Data Envelopment Analysis: A case study in power plants

Data envelopment analysis (DEA) technique is widely applied for performance assessment of decision making units (DMUs). The revenue efficiency (RE) evaluation is one of the controversial subject matters that can be performed through DEA context. The amount of productions and its prices are crucial factors in the RE. The classical DEA models consider the prices to be fixed and known which are not the case in real world. Also, the classical DEA models considers linear pricing in revenue assessment. However, most of real world problems deal with nonlinear prices. This paper evaluates the RE given the piecewise linear theory in non-competitive situations. In doing so, a stepwise pricing function is introduced which lets the prices to be changed in relation to the amount of the production. As an innovative idea, a more accurate mathematical modeling for the RE is proposed. We define a dynamic weights’ function in maximum revenue optimization model which no longer considers fixed prices. A case study validates our proposed model.

Supporting better practice benchmarking: A DEA-ANN approach to bank branch performance assessment

The quest for best practices may lead to an increased risk of poor decision-making, especially when aiming to attain best practice levels reveals that efforts are beyond the organization’s present capabilities. This situation is commonly known as the “best practice trap”. Motivated by such observation, the purpose of the present paper is to develop a practical methodology to support better practice benchmarking, with an application to the banking sector. In this sense, we develop a two-stage hybrid model that employs Artificial Neural Network (ANN) via integration with Data Envelopment Analysis (DEA), which is used as a preprocessor, to investigate the ability of the DEA-ANN approach to classify the sampled branches of a Greek bank into predefined efficiency classes. ANN is integrated with a family of radial and non-radial DEA models. This combined approach effectively captures the information contained in the characteristics of the sampled branches, and subsequently demonstrates a satisfactory classification ability especially for the efficient branches. Our prediction results are presented using four performance measures (hit rates): percent success rate of classifying a bank branch’s performance exactly or within one class of its actual performance, as well as just one class above the actual class and just one class below the actual class. The proposed modeling approach integrates the DEA context with ANN and advances benchmarking practices to enhance the decision-making process for efficiency improvement.

A data envelopment analysis game theory approach for constructing composite indicator: An application to find out development degree of cities in West Azarbaijan province of Iran

Data envelopment analysis (DEA) model has been widely applied for constructing composite indicator and finding development degree of areas. With the increasing number of indicators, the distinguish power of DEA model is decreased. In this paper, in order to increase distinguish power in DEA model and find out the fair weights in cross-efficiency DEA context, the game theory approach is applied. The DEA-Game theory approach is used to rank cities in West Azarbaijan province of Iran. First, 68 suitable indicators are determined and then, the indicators are classified in 10 sectors. Finally, the actual data for year 2013 is gathered and DEA-Game theory model is applied. To verify and validate the DEA-Game theory approach, simple additive weighting (SAW) and TOPSIS methods are used and the results are compared. The Spearman correlation between DEA-Game, SAW and TOPSIS models shows that the DEA-Game theory model is suitable for constructing the composite indicators.

Data envelopment analysis for sustainability evaluation in China: Tackling the economic, environmental, and social dimensions

This study develops a theoretical framework within the data envelopment analysis context to examine the efficiency of sustainable development systems. Such a system is composed of an economic and environmental subsystem and a social subsystem. We first explore the performances of the subsystems and the system under an independently parallel setting and then establish an operational linkage to study the noncooperative and cooperative interactions between the subsystems in a linked parallel setting. A case study of 30 major Chinese cities is presented to illustrate the feasibility of the approach and the results show great discrimination of system performances among the cities. The major cities have distinct geographic characteristics which affect their economic and environmental efficiency as well as the social efficiency. It was found that in some of these sustainable development systems, the subsystems behave inharmoniously, which results in significant inefficiency.

Managerial and program inefficiency for European meat manufacturing firms: A dynamic multidirectional inefficiency analysis approach

This paper proposes a dynamic multidirectional inefficiency analysis approach within the context of Data Envelopment Analysis to measuring input- and investment-specific managerial and program inefficiency for groups of firms characterized by different technologies. Dynamic managerial inefficiency refers to the distance to the firms’ group-specific dynamic frontier of best practices, and dynamic program inefficiency measures the difference between the group-specific dynamic frontier and the pooled dynamic frontier. The empirical application focuses on panel data of large meat processing firms in Eastern, Western and Southern Europe over the period 2005–2012. The results show that Eastern European firms have the highest dynamic managerial inefficiency for all inputs, but have the smallest values for dynamic program inefficiency. Western European firms perform worst in terms of program inefficiency for all inputs, while Southern European firms are the best with regard to dynamic managerial inefficiency. The results also reveal that regardless the dynamic inefficiency dimension considered, investments is the most inefficient input, followed by labor, and materials.

The decoy effect in relative performance evaluation and the debiasing role of DEA

There is overwhelming evidence that performance ratings and evaluations are context dependent. A special case of such context effects is the decoy effect, which implies that the inclusion of a dominated alternative can influence the preference for non-dominated alternatives. Adapting the well-known experimental setting from the area of consumer behavior to the performance evaluation context of Data Envelopment Analysis (DEA), an experiment was conducted. The results show that adding a dominated decision making unit (DMU) to the set of DMUs augments the attractiveness of certain dominating DMUs and that DEA efficiency scores discriminating between efficient and inefficient DMUs serve as an appropriate debiasing procedure. The mention of the existence of slacks for distinguishing between strong and weak efficient DMUs also contributes to reducing the decoy effect, but it is also associated to other unexpected effects.

A NEW RANKING APPROACH WITH A MODIFIED CROSS EVALUATION MATRIX

Cross evaluation matrix was suggested to resolve a ranking problem in the data envelopment analysis (DEA) context. The cross evaluation matrix is composed of simple efficiency and cross-efficiency (CE) values of decision making units (DMUs). However, simple efficiency cannot discriminate efficient DMUs because of the nature of basic DEA models. To make complete use of the efficiency information of DMUs, a modified cross evaluation matrix is proposed. The modified matrix consists of super-efficiency (SE) values for diagonal elements and CE values for nondiagonal elements. As the efficiency values are not limited to "1" in SE approach, the proposed matrix can explain the difference of efficiency of efficient DMUs. The proposed matrix can be more accurate than the original cross evaluation matrix. Consequently, the rank order of DMUs generated by the suggested matrix reflects differences in relative efficiency of DMUs. A numerical example is given to show the superiority of the proposed approach. This is done by comparing with other available ranking methods in the DEA context. Several distance measures are utilized to compare rank consistency of the ranking methods. Finally, a case study is presented to explain how our approach is applied to real ranking problems.

A decision-making support system module for project manager selection according to past performance

This paper proposes a decision-making support system (DMSS) module for selecting project managers and demonstrates its implementation. The selection of a new project manager is based mainly on the past performance of potential managers, for example, on the relative performance evaluations they have received on projects managed by them in the past. Past projects are ranked in accordance with a ranking method. Project managers are ordered according to past project rank. The difference in quality between the past performance of the candidates is statistically examined using the Mann–Whitney–Wilcoxon U test. This enables the establishment of a subgroup of one or more preferred candidates, where the significance level of the statistical test has an impact on the subgroup size. The final candidate may be selected from this subgroup according to personal qualifications and suitability for the specific project. We demonstrated the use of such a DMSS module by an Israeli information technology company as part of their process to select a project manager. A ranking method within the Data Envelopment Analysis context (the Cross-Efficient method) was implemented with three inputs and four outputs selected for the project ranking.

Network-based method for ranking of efficient units in two-stage DEA models

This study presents a methodology that is able to further discriminate the efficient decision-making units (DMUs) in a two-stage data envelopment analysis (DEA) context. The methodology is an extension of the single-stage network-based ranking method, which utilizes the eigenvector centrality concept in social network analysis to determine the rank of efficient DMUs. The mathematical formulation for the method to work under the two-stage DEA context is laid out and then applied to a real-world problem. In addition to its basic ranking function, the exercise highlights two particular features of the method that are not available in standard DEA: suggesting a benchmark unit for each input/intermediate/output factor, and identifying the strengths of each efficient unit. With the methodology, the value of DEA greatly increases.

An extended aggregated ratio analysis in DEA

Data Envelopment Analysis (DEA) and Ratio Analysis (RA) are two widely used methods for measuring units’ productivity and any other criteria that could be assessed based on the available input and output variables. A number of researchers have studied DEA and RA and noted the positive and negative differences between them. Aggregated ratio analysis (ARA) model, which provide an important linkage between DEA and RA theory, is equivalent to the CCR DEA model, and this equivalence property offers a great deal of opportunities for DEA to be interpreted and applied in different ways. This paper extends the results of ARA model and proposes an extended aggregated ratio analysis (EARA) model, similar as the development from CCR model to BCC model in DEA context. The proposed model can offer an insight into the characteristic of returns to scale, playing the corresponding role as BCC model does. The numerical example is revisited in the paper and the results are compared.

A General Input Distance Function Based on Opportunity Costs

There are several distance function definitions in a general production framework, including Data Envelopment Analysis, which can be used to describe the production technology and to define corresponding measures of technical efficiency (notably the Shephard and the directional distance functions). This paper introduces a generalisation of the distance function concept based on the idea of minimizing firm's opportunity cost. We further state a general dual correspondence between the cost function and this new general distance function, which encompasses all previously published duality results. All our results also hold under the assumption that we work in a Data Envelopment Analysis context.

Efficiency measurement using independent component analysis and data envelopment analysis

Efficiency measurement is an important issue for any firm or organization. Efficiency measurement allows organizations to compare their performance with their competitors’ and then develop corresponding plans to improve performance. Various efficiency measurement tools, such as conventional statistical methods and non-parametric methods, have been successfully developed in the literature. Among these tools, the data envelopment analysis (DEA) approach is one of the most widely discussed. However, problems of discrimination between efficient and inefficient decision-making units also exist in the DEA context ( Adler and Yazhemsky, 2010). In this paper, a two-stage approach of integrating independent component analysis (ICA) and data envelopment analysis (DEA) is proposed to overcome this issue. We suggest using ICA first to extract the input variables for generating independent components, then selecting the ICs representing the independent sources of input variables, and finally, inputting the selected ICs as new variables in the DEA model. A simulated dataset and a hospital dataset provided by the Office of Statistics in Taiwan’s Department of Health are used to demonstrate the validity of the proposed two-stage approach. The results show that the proposed method can not only separate performance differences between the DMUs but also improve the discriminatory capability of the DEA’s efficiency measurement.

Improving discrimination in data envelopment analysis: PCA–DEA or variable reduction

Within the data envelopment analysis context, problems of discrimination between efficient and inefficient decision-making units often arise, particularly if there are a relatively large number of variables with respect to observations. This paper applies Monte Carlo simulation to generalize and compare two discrimination improving methods; principal component analysis applied to data envelopment analysis (PCA–DEA) and variable reduction based on partial covariance (VR). Performance criteria are based on the percentage of observations incorrectly classified; efficient decision-making units mistakenly defined as inefficient and inefficient units defined as efficient. A trade-off was observed with both methods improving discrimination by reducing the probability of the latter error at the expense of a small increase in the probability of the former error. A comparison of the methodologies demonstrates that PCA–DEA provides a more powerful tool than VR with consistently more accurate results. PCA–DEA is applied to all basic DEA models and guidelines for its application are presented in order to minimize misclassification and prove particularly useful when analyzing relatively small datasets, removing the need for additional preference information.

Discriminating efficient units using MAJ FDH

Free Disposal Hull (FDH) is one of the tools in the theoretical and empirical work on the measurement of productive efficiency. Excluding linear combinations of extremal observations to construct this reference technology entails that many of the observations belonging to an evaluated dataset are labeled efficient by this method. Few researchers have sought to improve the discrimination power of FDH. Van Puyenbroeck [H. Tulkens, On FDH efficiency analysis: some methodological issues and applications to retail, banking, courts and urban transit, Journal of Productivity Analysis 4 (1993) 183–210] modified standard FDH method by using Andersen and Petersen [N. Adler, L. Friedman, Z. Siunuany-Stern, Review of ranking methods in the data envelopment analysis context, European Journal of Operational Research, 140 (2002) 249–265], referred to A&P FDH. Jahanshahloo et al. [J. Doyle, R. Green, Efficiency and cross-efficiency in DEA: derivation, meanings and uses, Journal of Operational Research Society 45 (5) (1994) 567–578] used 0-1 linear programming (LP), referred to 0-1 LP FDH to find FDH-efficient units. The purpose of this paper is two-folds: to propose MAJ FDH, similar to in spirit as the ranking method in data envelopment analysis by Mehrabian et al. [S. Mehrabian, M.R. Alirezaee, G.R. Jahanshahloo, A complete efficiency ranking of decision making units in data envelopment analysis, Communicational Optimization and Applications 14 (1999) 261–266] that may thus be used to discriminate between FDH-efficient units and to examine the tie-breaking ability of A&P FDH, 0-1 LP FDH, and MAJ FDH by using three numerical examples. Results of the comparisons show: (i) as the number of DMU, input and output is small where all of input and output levels are positive, the A&P FDH can provide a full ranking; (ii) as the number of DMU, input and output is small where some of input and output levels are equal to zero, none of three extended FDH methods can provide a full ranking; and (iii) as the number of DMU, input and output are increased where all of input and output levels are positive, it seems that ranking by MAJ FDH is more precise than other FDH methods.

ANOTHER VIEW OF EFFICIENCY IMPROVEMENT IN DATA ENVELOPMENT ANALYSIS

ABSTRACT Data envelopment analysis (DEA) is a mathematical programming approach for measuring the relative efficiencies within a group of decision making units. An important outcome of such an analysis is a set of values for dual variables which indicate how the associated factors should be adjusted so that input wastages and/or output shortfalls can be eliminated. The traditional DEA model gives a dual variable to associate with the normalizing equation. This setting implies that the adjustment proportions of all input or output factors are the same for efficiency improvement. This study modifies the original DEA model by decomposing the normalizing equation in order to for it to be associated with different dual variables. As a consequence, to improve efficiency the adjustment proportion of each input or output factor can be different. In essence, the proposed approach can not only set targets of factors for inefficient decision making units to eliminate inefficiency, but can also deal with the exogenous variables in a DEA context.

Review of ranking methods in the data envelopment analysis context

Within data envelopment analysis (DEA) is a sub-group of papers in which many researchers have sought to improve the differential capabilities of DEA and to fully rank both efficient, as well as inefficient, decision-making units. The ranking methods have been divided in this paper into six, somewhat overlapping, areas. The first area involves the evaluation of a cross-efficiency matrix, in which the units are self and peer evaluated. The second idea, generally known as the super-efficiency method, ranks through the exclusion of the unit being scored from the dual linear program and an analysis of the change in the Pareto Frontier. The third grouping is based on benchmarking, in which a unit is highly ranked if it is chosen as a useful target for many other units. The fourth group utilizes multivariate statistical techniques, which are generally applied after the DEA dichotomic classification. The fifth research area ranks inefficient units through proportional measures of inefficiency. The last approach requires the collection of additional, preferential information from relevant decision-makers and combines multiple-criteria decision methodologies with the DEA approach. However, whilst each technique is useful in a specialist area, no one methodology can be prescribed here as the complete solution to the question of ranking.

An AHP/DEA methodology for ranking decision making units

This paper presents a two-stage model for fully ranking organizational units where each unit has multiple inputs and outputs. In the first stage, the Data Envelopment Analysis (DEA) is run for each pair of units separately. In the second stage, the pairwise evaluation matrix generated in the first stage is utilized to rank scale the units via the Analytical Hierarchical Process (AHP). The consistency of this AHP/DEA evaluation can be tested statistically. Its goodness of fit with the DEA classification (to efficient/inefficient) can also be tested using non-parametric tests. Both DEA and AHP are commonly used in practice. Both have limitations. The hybrid model AHP/DEA takes the best of both models, by avoiding the pitfalls of each. The nonaxiomatic utility theory limitations of AHP are irrelevant here: since we are working with given inputs and outputs of units, no subjective assessment of a decision maker evaluation is involved. AHP/DEA ranking does not replace the DEA classification model, rather it furthers the analysis by providing full ranking in the DEA context for all units, efficient and inefficient.