Conventional Data Envelopment Analysis Models Research Articles

A joint chance-constrained data envelopment analysis model with random output data

Data envelopment analysis (DEA) is a mathematical programming approach for evaluating the technical efficiency performances of a set of comparable decision-making units that transform multiple inputs into multiple outputs. The conventional DEA models are based on crisp input and output data, but real-world problems often involve random output data. The main purpose of the paper is to propose a joint chance-constrained DEA model for analyzing a real-world situation characterized by random outputs and crisp inputs. After developing the model, we carry out the following: First, we obtain an upper bound of this stochastic non-linear model deterministically by applying a piecewise linear approximation algorithm based on second-order cone programming; Second, we obtain a lower bound with use of a piecewise tangent approximation algorithm, which is also based on second-order cone programming; and then we use a numerical example to demonstrate the applicability of the proposed joint chance-constrained DEA framework.

Corporate diversification, firm productivity and resource allocation decisions: The data envelopment analysis approach

Corporate diversification has been an important research topic in the field of business administration. Although it is regarded as an essential strategy for firms, its relationship with firm performance seems inconclusive in the literature. To fill this gap, our study uses data envelopment analysis (DEA) to develop models that help diversified firms more accurately calculate productivity at both the firm and its business segment levels, and then reallocate resources among business segments in order to achieve better firm overall performance. We empirically test the models using a sample of U.S. public firms for a period of 2012–2016. The results show that in comparison with two conventional DEA models, our model provides more useful productivity expression for diversified firms, and that the model-suggested resource reallocation is linked to better firm performance.

Benchmarking with network dea in a fuzzy environment

Benchmarking is a powerful and thriving tool to enhance the performance and profitabilities of organizations in business engineering. Though performance benchmarking has been practically and theoretically developed in distinct fields such as banking, education, health, and so on, benchmarking of supply chains with multiple echelons that include certain characteristics such as intermediate measure differs from other practices. In spite of incremental benchmarking activities in practice, there is the dearth of a unified and effective guideline for benchmarking in organizations. Amongst the benchmarking tools, data envelopment analysis (DEA) as a non-parametric technique has been widely used to measure the relative efficiency of firms. However, the conventional DEA models that are bearing out precise input and output data turn out to be incapable of dealing with uncertainty, particularly when the gathered data encompasses natural language expressions and human judgements. In this paper, we present an imprecise network benchmarking for the purpose of reflecting the human judgments with the fuzzy values rather than precise numbers. In doing so, we propose the fuzzy network DEA models to compute the overall system scale and technical efficiency of those organizations whose internal structure is known. A classification scheme is presented based upon their fuzzy efficiencies with the aim of classifying the organizations. We finally provide a case study of the airport and travel sector to elucidate the details of the proposed method in this study.

Modelling efficient and anti-efficient frontiers in DEA without explicit inputs

Data envelopment analysis (DEA) is one of the most widely used tools in efficiency analysis of many business and non-profit organisations. Recently, more and more researchers investigated DEA models without explicit input (DEA-WEI). DEA-WEI models can divide DMUs into two categories: efficient DMUs and inefficient DMUs. Usually there is a set of DMUs, which are 'efficient' so that conventional DEA models could not rank them. In this paper, we first develop a performance index based on efficient and anti-efficient frontiers in DEA-WEI models. Further, the corresponding performance index in DEA-WEI models with quadratic utility terms (quadratic DEA-WEI) is proposed also. Finally, we present two case studies on performance assessment of basketball players and the evaluation of research institutes in Chinese Academy of Sciences (CAS) to show the applicability and usefulness of the performance indices developed in this paper.

Modelling efficient and anti-efficient frontiers in DEA without explicit inputs

Data envelopment analysis (DEA) is one of the most widely used tools in efficiency analysis of many business and non-profit organisations. Recently, more and more researchers investigated DEA models without explicit input (DEA-WEI). DEA-WEI models can divide DMUs into two categories: efficient DMUs and inefficient DMUs. Usually there is a set of DMUs, which are ‘efficient’ so that conventional DEA models could not rank them. In this paper, we first develop a performance index based on efficient and anti-efficient frontiers in DEA-WEI models. Further, the corresponding performance index in DEA-WEI models with quadratic utility terms (quadratic DEA-WEI) is proposed also. Finally, we present two case studies on performance assessment of basketball players and the evaluation of research institutes in Chinese Academy of Sciences (CAS) to show the applicability and usefulness of the performance indices developed in this paper.

An innovative super-efficiency data envelopment analysis, semi-variance, and Shannon-entropy-based methodology for player selection: evidence from cricket

The increasing interest in club cricket and online fantasy cricket league games raises the importance of player selection from the perspective of financial and sports performance. Most previous studies focus only on player efficiency and ignore consistency and the player’s importance in a team strategy. This scenario motivates us to design a holistic player selection method based on a player’s efficiency, consistency, and importance in a team strategy. For efficiency measurement, we apply a modified data envelopment analysis (DEA) method, namely, the non-increasing return-to-scale ‘super-efficiency DEA model,’ that provides improved results compared with the conventional Banker, Charnes, and Cooper DEA model in the presence of a higher number of efficient players. We design a modified consistency index based on the semi-variance approach. Unlike the existing methods that apply a player-specific reference frame to capture variability, we use a common reference frame that calculates the consistency in a more effective manner. We aggregate different consistency indices into a single consistency index using Shannon’s entropy concept and introduce a novel ‘value index’ to determine player importance, which can also be used as an indirect measure of the player’s fitness level. Finally, we design a player performance index by aggregating the efficiency and consistency scores using the Shannon-entropy method and incorporating the value index. We perform a rigorous numerical analysis to determine the all-time best one-day international Cricket XI team for the time span of January 5, 1971 to March 29, 2015. Next, we explain the advantages as well as rationale behind the improvement in the proposed measures compared with the existing methods and highlight the key insights. Finally, we perform a comparative analysis of the proposed team, the team announced by the ICC in 2011, and the team announced by the BBC in 2015.

A modified slacks‐based ranking method handling negative data in data envelopment analysis

AbstractPerformance ranking for a set of comparable decision‐making units (DMUs) with multiple inputs and outputs is an important and often‐discussed topic in data envelopment analysis (DEA). Conventional DEA models distinguish efficient units from inefficient ones but cannot further discriminate the efficient units, which all have a 100% efficiency score. Another weakness of these models is that they cannot handle negative inputs and/or outputs. In this paper, a new modified slacks‐based measure is proposed that works in the presence of negative data and provides quantitative data that helps decision makers obtain a full ranking of DMUs in situations where other methods fail. In addition, the new method has the properties of unit invariance and translation invariance, and it can give targets for inefficient DMUs to guide them to achieve full efficiency. Two numerical examples are analysed to demonstrate the usefulness of the new method.

Developing a new chance constrained NDEA model to measure the performance of humanitarian supply chains

Data envelopment analysis (DEA) is a method for measuring performance of decision making units (DMUs). Conventional DEA models view DMUs as black boxes. Network DEA (NDEA) models have been developed to overcome this shortfall. This paper develops a new NDEA model based on modified enhanced Russell measure model. This paper measures performance of humanitarian supply chains (HSCs) by an NDEA model. Capabilities of the proposed model are addressed by theorems. However, in the real world, there might be stochastic data. This paper presents a stochastic version of the proposed NDEA model to measure the performance of HSCs. We analyse main properties of our model. We present a case study to demonstrate the applicability of the proposed model.

How to assess sustainability of suppliers in the presence of volume discount and negative data in data envelopment analysis?

Supplier selection is an important decision-making problem in supply chain management. Selecting appropriate suppliers based on sustainability criteria including economic, environmental, and social criteria can help companies move toward sustainable development. Data envelopment analysis (DEA) is applied to recognize the most sustainable supplier. However, conventional DEA models can be applied only to performance measurement systems characterized by positive input–output data. However, in real world, data can be negative. We propose a new DEA model for evaluating sustainability of suppliers in presence of negative data and volume discounts. Also, we present a super-efficiency model for ranking suppliers. In addition, we prove some main properties of our proposed method. Finally, we present a case study to demonstrate applicability of proposed model.

Shapley value-based multi-objective data envelopment analysis application for assessing academic efficiency of university departments

This paper adopts a modified approach of data envelopment analysis (DEA) to measure the academic efficiency of university departments. In real-world case studies, conventional DEA models often identify too many decision-making units (DMUs) as efficient. This occurs when the number of DMUs under evaluation is not large enough compared to the total number of decision variables. To overcome this limitation and reduce the number of decision variables, multi-objective data envelopment analysis (MODEA) approach previously presented in the literature is applied. The MODEA approach applies Shapley value as a cooperative game to determine the appropriate weights and efficiency score of each category of inputs. To illustrate the performance of the adopted approach, a case study is conducted in a university in the Philippines. The input variables are academic staff, non-academic staff, classrooms, laboratories, research grants, and department expenditures, while the output variables are the number of graduates and publications. The results of the case study revealed that all DMUs are inefficient. DMUs with efficiency scores close to the ideal efficiency score may be emulated by other DMUs with least efficiency scores.

Benchmarking the efficiency of the Chilean water and sewerage companies: a double-bootstrap approach.

Benchmarking the efficiency of water companies is essential to set water tariffs and to promote their sustainability. In doing so, most of the previous studies have applied conventional data envelopment analysis (DEA) models. However, it is a deterministic method that does not allow to identify environmental factors influencing efficiency scores. To overcome this limitation, this paper evaluates the efficiency of a sample of Chilean water and sewerage companies applying a double-bootstrap DEA model. Results evidenced that the ranking of water and sewerage companies changes notably whether efficiency scores are computed applying conventional or double-bootstrap DEA models. Moreover, it was found that the percentage of non-revenue water and customer density are factors influencing the efficiency of Chilean water and sewerage companies. This paper illustrates the importance of using a robust and reliable method to increase the relevance of benchmarking tools.

MEASURING EFFICIENCY OF A UNIVERSITY FACULTY USING A HIERARCHICAL NETWORK DATA ENVELOPMENT ANALYSIS MODEL

An efficiency measurement model of a university faculty is proposed with additional new sub-functions that produce new output variables, based on the network Data Envelopment Analysis (DEA) model for systems with a hierarchical structure.For production systems composed of hierarchical processes, the system efficiency is well represented as the aggregated performance of the components involved in the system. It is identified that the conventional DEA model ignores internal process activities in a university. Therefore, an improved DEA model based on a network structure that accounts for more activities in a university is proposed to measure its overall efficiency. The impact of major functions of a university are taken into account to represent the output variables in assessing the efficiency. Currently, collaboration activities have been given more attention, so, this variable is suggested as a new output for the hierarchical production system. In order to show the practicality of the model, a hypothetical set of data of 14 faculties has been used as a numerical example. The results show that none of the faculties is relatively efficient since its functions were found to be inefficient. The proposed model enables to help the management of university faculties to identify weaknesses of each function and thus to plan for suitable actions on improving the overall performance of the university.

Portfolio optimization by using MeanSharp-βVaR and Multi Objective MeanSharp-βVaR models

The purpose of this study is to develop portfolio optimization and assets allocation using our proposed models. For this, three steps are considered. In the first step, the stock companies screen by their financial data. For second step, we need some inputs and outputs for solving Data Envelopment Analysis (DEA) models. Conventional DEA models assume non-negative data for inputs and outputs. However, many of these data take the negative value, therefore we propose the MeanSharp-?VaR (MSh?V) model and the Multi Objective MeanSharp-?VaR (MOMSh?V) model based on Range Directional Measure (RDM) that can take positive and negative values. Also, we consider one of downside risk measures named Value at Risk (VaR) and try to decrease it. After using our proposed models, the efficient stock companies will be selected for making the portfolio. In the third step, Multi Objective Decision Making (MODM) model was used to specify the capital allocation to the stock companies that was selected for the portfolio. Finally, a numerical example of the purposed method in Iranian stock companies is presented.

Measurement of returns-to-scale using interval data envelopment analysis models

Abstract The economic concept of Returns-to-Scale (RTS) has been intensively studied in the context of Data Envelopment Analysis (DEA). The conventional DEA models that are used for RTS classification require well-defined and accurate data whereas in reality observations gathered from production systems may be characterised by intervals. For instance, the heat losses of the Combined production of Heat and Power (CHP) systems may be within a certain range, hinging on a wide variety of factors such as external temperature and real-time energy demand. Enriching the current literature independently tackling the two problems; interval data and RTS estimation; we develop an overarching evaluation process for estimating RTS of Decision Making Units (DMUs) in Imprecise DEA (IDEA) where the input and output data lie within bounded intervals. In the presence of interval data, we introduce six types of RTS involving increasing, decreasing, constant, non-increasing, non-decreasing and variable RTS. The situation for non-increasing (non-decreasing) RTS is then divided into two partitions; constant or decreasing (constant or increasing) RTS using sensitivity analysis. Additionally, the situation for variable RTS is split into three partitions consisting of constant, decreasing and increasing RTS using sensitivity analysis. Besides, we present the stability region of an observation while preserving its current RTS classification using the optimal values of a set of proposed DEA-based models. The applicability and efficacy of the developed approach is finally studied through two numerical examples and a case study.

On the importance of perspective and flexibility for efficiency measurement: effects on the ranking of decision-making units

The efficiency of a firm can be assessed from several perspectives and using a variety of methodologies. Data envelopment analysis (DEA) is one of the most commonly used methodologies. Conventional DEA analyses or models allow one to classify decision-making units (DMUs) into efficient and inefficient ones based on their efficiency scores, which could also be used for ranking DMUs; however, such rankings generally show many ties. Super-efficiency DEA analyses have been proposed to address the tie issue. On the other hand, conventional DEA analyses only take account of a single perspective in estimating efficiency scores. Cross-efficiency DEA analyses provide an alternative that takes account of the perspectives or perceptions of different DMUs. Conventional DEA analyses designed for handling crisp data have also been extended to deal with fuzzy data. In this paper, we propose a fuzzy version of cross-efficiency DEA analysis along with a method for ranking DMUs. We illustrate our proposal with a real example from the Spanish banking sector. In order to assess the robustness of our proposal, we compared our results with those obtained with three different approaches based on the perspective from which efficiency aims to be evaluated: a fuzzy DEA approach, a cross-efficiency-based approach and a TOPSIS-based approach.

A directional distance based super-efficiency DEA model handling negative data

This paper develops a new radial super-efficiency data envelopment analysis (DEA) model, which allows input–output variables to take both negative and positive values. Compared with existing DEA models capable of dealing with negative data, the proposed model can rank the efficient DMUs and is feasible no matter whether the input–output data are non-negative or not. It successfully addresses the infeasibility issue of both the conventional radial super-efficiency DEA model and the Nerlove–Luenberger super-efficiency DEA model under the assumption of variable returns to scale. Moreover, it can project each DMU onto the super-efficiency frontier along a suitable direction and never leads to worse target inputs or outputs than the original ones for inefficient DMUs. Additional advantages of the proposed model include monotonicity, units invariance and output translation invariance. Two numerical examples demonstrate the practicality and superiority of the new model.

A robust data envelopment analysis model with different scenarios

Input and output data, under uncertainty, must be taken into account as an essential part of data envelopment analysis (DEA) models in practice. Many researchers have dealt with this kind of problem using fuzzy approaches, DEA models with interval data or probabilistic models. This paper presents an approach to scenario-based robust optimization for conventional DEA models. To consider the uncertainty in DEA models, different scenarios are formulated with a specified probability for input and output data instead of using point estimates. The robust DEA model proposed is aimed at ranking decision-making units (DMUs) based on their sensitivity analysis within the given set of scenarios, considering both feasibility and optimality factors in the objective function. The model is based on the technique proposed by Mulvey et al. (1995) for solving stochastic optimization problems. The effect of DMUs on the product possibility set is calculated using the Monte Carlo method in order to extract weights for feasibility and optimality factors in the goal programming model. The approach proposed is illustrated and verified by a case study of an engineering company.

MEASURING THE EFFICIENCY OF INDUSTRIES BY FUZZY DATA ENVELOPMENT ANALYSIS

Manufacturing is a part of the income of any country, helping to grow the economy by generating productivity, stimulating research and development, and investing in the future. Therefore, this paper seeks to explain the productivity growth performance of Ethiopian's manufacturing sector using a dataset of 14 types of industries for the year of 2008; utilizing data envelopment analysis (DEA) techniques either traditional or fuzzy DEA models. Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. Conventional DEA models assume that input and output values should be certain (crisp data). However, the observed values of the input and output data in real-world situations are sometimes vague or imprecise. In this paper, three approaches that transform the original data (crisp data) into interval data, in the form of upper and lower frontier data, are suggested. Then, by using these upper and lower frontier data; the intervalDEA efficiency scores can be achieved. These approaches are applied on the real-life data and the results show that data envelopment analysis (DEA) techniques are suitable to evaluate and compare the performances of industries that enable the decision makers to analyze the situation better.

Dual-role factors for imprecise data envelopment analysis

Efficiency analyses are crucial to managerial competency for evaluating the degree to which resources are consumed in the production process of gaining desired services or products. Among the vast available literature on performance analysis, Data Envelopment Analysis (DEA) has become a popular and practical approach for assessing the relative efficiency of Decision-Making Units (DMUs) which employ multiple inputs to produce multiple outputs. However, in addition to inputs and outputs, some situations might include certain factors to simultaneously play the role of both inputs and outputs. Contrary to conventional DEA models which account for precise values for inputs, outputs and dual-role factors, we develop a methodology for quantitatively handling imprecision and uncertainty where a degree of imprecision is not trivial to be ignored in efficiency analysis. In this regard, we first construct a pair of interval DEA models based on the pessimistic and optimistic standpoints to measure the interval efficiencies where some or all observed inputs, outputs and dual-role factors are assumed to be characterized by interval measures. The optimal multipliers associated with the dual-role factors are then used to determine whether a factor is designated as an output, an input, or is in equilibrium even though the status of the dual-role factors may not be unique based upon the pessimistic and optimistic standpoints. To deal with the problem, we present a new model which integrates both pessimistic and optimistic models. The integrated model enables us to identify a unique status of each imprecise dual-role factor as well as to develop a structure for calculating an optimal reallocation model of each dual-role factor among the DMUs. As another method to investigate the role for dual-role factors, we introduce a fuzzy decision-making model which evaluates all DMUs simultaneously. We finally present an application to a data set of 20 banks to showcase the applicability and efficacy of the proposed procedures and algorithm.

Fuzzy efficiency measures in data envelopment analysis using lexicographic multiobjective approach

There is an extensive literature in data envelopment analysis (DEA) aimed at evaluating the relative efficiency of a set of decision-making units (DMUs). Conventional DEA models use definite and precise data while real-life problems often consist of some ambiguous and vague information, such as linguistic terms. Fuzzy sets theory can be effectively used to handle data ambiguity and vagueness in DEA problems. This paper proposes a novel fully fuzzified DEA (FFDEA) approach where, in addition to input and output data, all the variables are considered fuzzy, including the resulting efficiency scores. A lexicographic multi-objective linear programming (MOLP) approach is suggested to solve the fuzzy models proposed in this study. The contribution of this paper is fivefold: (1) both fuzzy Constant and Variable Returns to Scale models are considered to measure fuzzy efficiencies; (2) a classification scheme for DMUs, based on their fuzzy efficiencies, is defined with three categories; (3) fuzzy input and output targets are computed for improving the inefficient DMUs; (4) a super-efficiency FFDEA model is also formulated to rank the fuzzy efficient DMUs; and (5) the proposed approach is illustrated, and compared with existing methods, using a dataset from the literature.