Units In Data Envelopment Analysis Research Articles

Analyzing efficiency of decision-making units in data envelopment analysis

A variety of irrigation management systems are evaluated using Data Envelopment Analysis (DEA) to see which one is the most cost-effective, environmentally friendly, and socially responsible. Accordingly, an irrigation management project report serves as the basis for the comparison of different ranks in MCDM and DEA. There are DEA approaches termed CCR, BCC, and RCCR that use criterion weights integrated with the inclusion of assurance areas to increase the analysis' discriminating power and reach the ranking of strategies. The findings show that DEA is a good alternative or supplement to MCDM, and including management preferences into the DEA methodology yields comparable outcomes to MCDM procedures.

Identifying the closest most productive scale size unit in data envelopment analysis

Identifying the closest most productive scale size unit in data envelopment analysis

Finding the single efficient unit in data envelopment analysis with flexible measures

Efficiency evaluation is crucial for providing decision support in both target setting and competency recognition. In many practical applications, flexible measures that can be classified as either input or output often lead to inconsistent results due to distinct classifications. Conventional classification methods may identify many efficient decision making units (DMUs), which cannot provide us with the best alternative and reduces the discriminating power of associated models. In this study, we develop a novel integrated approach by identifying the single efficient DMU considering flexible measures. Specifically, our proposed approach guarantees the feasibility of the associated efficiency estimation model under relatively mild conditions. Moreover, the weight scheme and non-dominated classification result can be uniquely determined via a revised min-max computational procedure. We validate and illustrate the proposed approach by applying it to evaluate the efficiencies of Chinese commercial banks before and during the pandemic. Our findings suggest that the pandemic does have an impact on bank efficiency, and different banks respond differently to the pandemic shock. More specifically, the best-performing bank that stands out before and during the pandemic can be identified as a unique benchmark, and the others could learn from this alternative to mitigate the pandemic shock.

Some comments on improving discriminating power in data envelopment models based on deviation variables framework

Ghasemi, Ignatius, and Rezaee (2019) (Improving discriminating power in data envelopment models based on deviation variables framework. European Journal of Operational Research 278, 442– 447) propose a procedure for ranking efficient units in data envelopment analysis (DEA) based on the deviation variables framework. They claim that their procedure improves the discriminating power of DEA and can be an alternative to the super-efficiency model that is well-known to have the infeasibility problem and the cross-efficiency approach which suffers from the presence of multiple optimal solutions. However, we demonstrate, in this short note, that their procedure is developed based upon inappropriate use of deviation variables which leads to the development of a ranking approach that does not meet their expectations and as a result, an unreasonable ranking of decision making units (DMUs). We also show that the use of deviation variables, if interpreted and used correctly, can lead to developing a cross-inefficiency matrix and approach.

The determination of the most suitable inertia weight strategy for particle swarm optimization via the minimax mixed-integer linear programming model

Purpose This paper aims to consider each strategy of the particle swarm optimization (PSO) as a unit in data envelopment analysis (DEA) and uses the minimax mixed-integer linear programming DEA approach to find the most suitable inertia weight strategy. A total of 15 inertia weight strategies were empirically examined in a suite of 42 benchmark problems in the view of DEA. Design/methodology/approach PSO is very sensitive to inertia weight strategies, and therefore, an important amount of research attempts has been concentrated on these strategies. There is no research into the determination of the most suitable inertia weight strategy; however, there are a large number of comparisons related to the inertia weight strategies. DEA is one of the performance evaluation methods, and its models classify the set of strategies into two distinct sets as efficient and inefficient. However, only one of the strategies should be used in the PSO algorithm. Some effective models were proposed to find the most efficient strategy. Findings The experimental studies demonstrate that an approach is a useful tool in the determination of the most suitable strategy. Besides, if the author encounters a new complex problem whose properties are known, it will help the author to choose the best strategy. Practical implications A heavy oil thermal cracking three lumps model for the simplification of the reaction system was used because it is an important complicated chemical process. In addition, the soil water retention curve (SWRC) plays an important role in diverse facets of agricultural engineering. As the SWRC can be regarded as a nonlinear function between the water content and the soil water potential, Van Genuchten model is proposed to describe this function. To determinate these model parameters, an optimization problem is formulated, which minimizes the difference between the measured and modeled data. Originality/value In this paper, the PSO algorithm is integrated with minimax mixed-integer linear programming to find the most suitable inertia weight strategy. In this way, the best strategy could be chosen for a new more complex problem.

A Linear Programming Relaxation DEA Model for Selecting a Single Efficient Unit with Variable RTS Technology

The selection-based problem is a type of decision-making issue which involves opting for a single option among a set of available alternatives. In order to address the selection-based problem in data envelopment analysis (DEA), various integrated mixed binary linear programming (MBLP) models have been developed. Recently, an MBLP model has been proposed to select a unit in DEA with variable returns-to-scale technology. This paper suggests utilizing the linear programming relaxation model rather than the MBLP model. The MBLP model is proved here to be equivalent to its linear programming relaxation problem. To the best of the authors’ knowledge, this is the first linear programming model suggested for selecting a single efficient unit in DEA under the VRS (Variable Returns to Scale) assumption. Two theorems and a numerical example are provided to validate the proposed LP model from both theoretical and practical perspectives.

Forecast of the efficiency confidence interval of decision-making units in data envelopment analysis

Data Envelopment Analysis (DEA) is a well-known method for calculating the efficiency of Decision-Making Units (DMUs) based on their inputs and outputs. When the data is known and in the form of an interval in a given time period, this method can calculate the efficiency interval. Unfortunately, DEA is not capable of forecasting and estimating the efficiency confidence interval of the units in the future. This article, proposes a efficiency forecasting algorithm along with 95% confidence interval to generate interval data set for the next time period. What’s more, the manager’s opinion inserts and plays its role in the proposed forecasting model. Equipped with forecasted data set and with respect to data set from previous periods, the efficiency for the future period can be forecasted. This is done by proposing a proposed model and solving it by the confidence interval method. The proposed method is then implemented on the data of an automotive industry and, it is compared with the Monte Carlo simulation methods and the interval model. Using the results, it is shown that the proposed method works better to forecast the efficiency confidence interval. Finally, the efficiency and confidence interval of 95% is calculated for the upcoming period using the proposed model.

A simplistic approach without epsilon to choose the most efficient unit in data envelopment analysis

Data envelopment analysis is a very effective mathematical instrument in assessing the performance of decision-making units. In most real cases, the decision-maker need to identify a single most efficient unit. Several approaches were proposed for this necessity in the literature using data envelopment analysis. This study, based on the two steps model suggested by Toloo and Salahi (2018), proposes a new model without epsilon to choose the most efficient unit. The proposed model has fewer constraints than their model and is solved by a one-step linear programming model without epsilon. The proposed model determines exactly one DMU as the most efficient one and other decision-making units have efficiency scores strictly less than one. A simulation study was designed to test the proposed model in terms of some criteria such as correlation. In addition, the examples of real cases whose real rank is known and frequently used in literature of the most efficient unit were preferred for the validity of the proposed model. The results illustrated that the discrimination power problem was experienced in the previous models whereas no such problem was observed in the new proposed model for the same real cases.

A new methodology to measure efficiencies of inputs (outputs) of decision making units in Data Envelopment Analysis with application to agriculture

This paper aims at developing a new methodology to measure and decompose global DMU efficiency into efficiency of inputs (or outputs). The basic idea rests on the fact that global DMU's efficiency score might be misleading when managers proceed to reallocate their inputs or redefine their outputs. Literature provides a basic measure for global DMU's efficiency score. A revised model was developed for measuring efficiencies of global DMUs and their inputs (or outputs) efficiency components, based on a hypothesis of virtual DMUs. The present paper suggests a method for measuring global DMU efficiency simultaneously with its efficiencies of inputs components, that we call Input decomposition DEA model (ID-DEA), and its efficiencies of outputs components, that we call output decomposition DEA model (OD-DEA). These twin models differ from Supper efficiency model (SE-DEA) and Common Set Weights model (CSW-DEA). The twin models (ID-DEA, OD-DEA) were applied to agricultural farms, and the results gave different efficiency scores of inputs (or outputs), and at the same time, global DMU's efficiency score was given by the Charnes, Cooper and Rhodes (Charnes et al., 1978) [1], CCR78 model. The rationale of our new hypothesis and model is the fact that managers don't have the same information level about all inputs and outputs that constraint them to manage resources by the (global) efficiency scores. Then each input/output has a different reality depending on the manager's decision in relationship to information available at the time of decision. This paper decomposes global DMU's efficiency into input (or output) components' efficiencies. Each component will have its score instead of a global DMU score. These findings would improve management decision making about reallocating inputs and redefining outputs. Concerning policy implications of the DEA twin models, they help policy makers to assess, ameliorate and reorient their strategies and execute programs towards enhancing the best practices and minimising losses.

Number of performance measures versus number of decision making units in DEA

Sufficient numbers of decision-making units (DMUs) in comparison to the number performance measures that are classified as inputs and outputs has been a concern when applying data envelopment analysis (DEA) in real world settings. As the number of DMUs decreases (or the numbers of inputs and outputs increases) the discrimination power and accuracy of DEA with respect to the performance of DMUs decreases. The current study proposes a technique which increases the discrimination power of DEA and allows for increasing the numbers of inputs and outputs even if the number of DMUs is relatively small. An adjusted DEA methodology is proposed which is stronger and more accurate than the routine DEA methodology, and permits one to identify the reference units for each best-practice unit (more than the DMU itself) and to distinguish the performance and rank of DMUs relative to one another, thereby enhancing the discrimination power of DEA. The scores from the adjusted methodology are logically meaningful. The pros of the new approach are demonstrated by several examples and simulation experiments in controlled environments. The results show that the proposed technique significantly improves the discrimination power over that of the conventional DEA model when the number of DMUs decreases or the number of inputs and outputs increases. In addition, the proposed technique is used to evaluate the quality-of-life related to twelve input–output combinations for two sets of DMUs, namely fifteen USA cities and five international cities, where none of the rules of thumb are satisfied.

Discriminating extreme efficient decision making units in DEA using random weight vectors

Data Envelopment Analysis (DEA) is a linear programming based model which evaluates the relative efficiency of Decision Making Units (DMUs), with multiple inputs and outputs. Conventional DEA evaluates DMUs with their own weights and separates them into efficient and inefficient. To provide a full ranking of DMUs or select one of them (as the most preferred one), more discrimination is necessary. This paper presents a method that ranks extreme efficient units by comparing the volumes of their optimal weight sets, approximately, through generating some random weight vectors. To illustrate the proposed method, some numerical examples are provided.

Robust Russell and enhanced Russell measures in DEA

Russell measure is among non-radial measures for efficiency evaluation of decision making units in data envelopment analysis. Due to the nonlinearity of its objective function, an enhanced version of it is proposed that can be linearized using the known Charnes–Cooper change of variables. In this article, we give equivalent formulations of the robust Russell measure and its enhanced models under interval and ellipsoidal uncertainties in their best- and worst-cases. We show that the built formulations stay convex for both best- and worst-cases under interval uncertainty as well as worst-case with ellipsoidal uncertainty. In other words, these formulations are nonconvex only for ellipsoidal uncertainty in their best-case. Some illustrative examples are provided to validate the new models.

The role of hyperplanes for characterizing suspicious units in DEA

In this paper, the suspicious units including anchor, terminal, and exterior units are investigated as important subsets of vertex units. Based on the concept of separating hyperplanes, an alternative definition of vertex units in data envelopment analysis is presented. Moreover, an advanced mathematical model for obtaining the separating hyperplane that splits up a vertex unit from the other units is proposed. Utilizing the core concept of separating hyperplanes, the special geometry of terminal units enables us to introduce a new definition for terminal units. Thus, some theorems have been proved which provide necessary and sufficient conditions for obtaining terminal units. We made use of the concept of supporting hyperplanes to provide a basic definition for exterior units and present a careful model for discovering exterior units. Also, based on the concept of supporting hyperplanes, different definitions of anchor units have been represented. Finally, the relationship between the sets of exterior, terminal and anchor units have been demonstrated in a theorem.

The new ranking method of the decision making units in DEA: with an approach to modifying the cross efficiency method

There is no doubt that organisations need an operation evaluation and measurement for having more efficiency and an optimal usage of their limited sources. One of the most practical methods for evaluating the operation is using the data envelopment analysis. Hence, data envelopment analysis (DEA) and ranking decision making units (DMU) are the most favourite subjects for the researchers. This method has modified on a different style on this article that has removed the existence of multiple optimal answers in the CCR (Chames-Cooper and Rhodes). In other words, the acquired ranks of the units are particular and have achieved with a special delicacy. In order to show the efficiencies of the method, some examples have presented that had achieved the more desirable and accurate ranking. The calculated results of performing this method have compared with the Anderson-Peterson method and its flexibility has studied according to the analysis of variance (ANOVA).

A powerful discriminative approach for selecting the most efficient unit in DEA

Abstract Data envelopment analysis (DEA) is a mathematical approach deals with the performance evaluation problem. Traditional DEA models partition the set of units into two distinct sets: efficient and inefficient. These models fail to get more information about efficient units whereas there are some applications, known as selection-based problems, where the concern is selecting only a single efficient unit. To address the problem, several mixed integer linear/nonlinear programming models are developed in the literature using DEA. The aim of all these approaches is formulating a model with more discriminating power. This paper presents a new nonlinear mixed integer programming model with significantly higher discriminating power than the existing ones in the literature. The suggested model lets the efficiency score of only a single unit be strictly greater than one. It is observed that the discrimination power of the model is high enough for fully ranking all units. More importantly, a linearization technique is used to formulate an equivalent mixed integer linear programming model which significantly decreases the computational burden. Finally, to validate the proposed model and also compare with some recent approaches, two numerical examples are utilized from the literature. Our founding points out the superiority of our model over all the previously suggested models from both theoretical and practical standpoints.

Efficiency ranking of decision making units in data envelopment analysis by using TOPSIS-DEA method

Data envelopment analysis methods classify the decision making units into two groups: efficient and inefficient ones. Therefore, the fully ranking all DMUs is demanded by most of the decision makers. However, data envelopment analysis and multiple criteria decision making units are developed independently and designed for different purposes. However, there are some applications in problem solving such as ranking, where these two methods are combined. Combination of multiple criteria decision making methods with data envelopment analysis is a new idea for elimination of disadvantages when applied independently. In this paper, first the new combined method is proposed named TOPSIS-DEA for ranking efficient units which not only includes the benefits of both data envelopment analysis and multiple criteria decision making methods, but also solves the issues that appear in former methods. Then properties and advantages of the suggested method are discussed and compared with super efficiency method, MAJ method, statistical-based model (CCA), statistical-based model (DR/DEA), cross-efficiency—aggressive, cross-efficiency—benevolent, Liang et al.’s model, through several illustrative examples. Finally, the proposed methods are validated.

Ranking efficient decision making units in data envelopment analysis based on reference frontier share

Data envelopment analysis (DEA) is a powerful technique for performance evaluation of decision making units (DMUs). Ranking efficient DMUs based on a rational analysis is an issue that yet needs further research. The impact of each efficient DMU in evaluation of inefficient DMUs can be considered as additional information to discriminating among efficient DMUs. The concept of reference frontier share is introduced in which the share of each efficient DMU in construction of the reference frontier for evaluating inefficient DMUs is considered. For this purpose a model for measuring the reference frontier share of each efficient DMU associated with each inefficient one is proposed and then a total measure is provided based on which the ranking is made. The new approach has the capability for ranking extreme and non-extreme efficient DMUs. Further, it has no problem in dealing with negative data. These facts are verified by theorems, discussions and numerical examples.

Cross efficiency based heuristics to rank decision making units in data envelopment analysis

This paper proposes two cross-efficiency based heuristics (CEHs) for ranking decision making units (DMUs) in Data Envelopment Analysis (DEA). This paper also suggests a stratification-based consistency evaluation framework (SCEF) to evaluate the performance of the proposed heuristics and several DEA-based full ranking methods in terms of consistency. Several cross-efficiency (CE) methods have been developed as a DEA extension to rank efficient and inefficient DMUs with the main idea of using DEA to do peer evaluation. However, it has been well known that they all suffer from lack of discrimination since efficiency scores from those methods may not be unique due to the non-uniqueness of the DEA optimal weights in the Linear Programming (LP) models. The proposed CEH methods overcome this issue since they do not use any LP models but show comparable consistency level to other DEA-based full ranking methods based on SCEF. Numerical examples from the literature and simulation indicate that CEHs are a good surrogate for CE method.

Convex cone-based ranking of decision-making units in DEA

One of the major research streams in data envelopment analysis (DEA) is ranking decision-making units (DMUs). Utilizing a multicriteria decision-making technique, we develop a novel approach to fully rank all units. Motivated by the convex cone-based total order for multiple criteria alternatives proposed by Dehnokhalaji et al. (Nav Res Logist 61(2):155–163, 2014), we consider DMUs in DEA as multiple criteria alternatives and obtain their total ordering. Initially, some pairwise preference information is provided by the decision maker for units and the concepts of convex cones and polyhedral sets are defined in a DEA framework, correspondingly. We apply a modification of Dehnokhalaji et al. method to extract additional preference information for each pair of units and consequently obtain a full ranking (strict total ordering) of DMUs. The benefit of our approach to their method is that we apply non-radial models to overcome the instability drawback of radial models and their infeasibility occurring in DEA applications. The proposed approach is implemented for two numerical examples, and the accuracy of it is investigated through a computational test.

A full ranking methodology in data envelopment analysis based on a set of dummy decision making units

In this paper, we propose a new methodology for ranking decision making units in data envelopment analysis (DEA). Our approach is a benchmarking method, seeks a common set of weights using a proposed linear programming model and is based on the TOPSIS approach in multiple attribute decision making (MADM). To this end, five artificial or dummy decision making units (DMUs) are defined, the ideal DMU (IDMU), the anti-ideal DMU (ADMU), the right ideal DMU (RIDMU), the left anti-ideal DMU (LADMU) and the average DMU (AVDMU). We form two comprehensive indexes for the AVDMU called the Left Relative Closeness (LRC) and the Right Relative Closeness (RRC) with respect to the RIDMU and LADMU. The LRC and RRC indexes will be used in the new proposed linear programming model to estimate the common set of weights, the new efficiency of DMUs and finally an overall ranking for all the DMUs. The change of the ratio between LRC and RRC indexes is capable to be provoked alternative rankings. One of the best advantages of this model is that we can make a rationale ranking which is demonstrated by the realized correlation analysis. Also, the new proposed efficiency score of the DMUs is close to the efficiency score of the DEA (CCR) methodology. Three numerical examples are provided to illustrate the applicability of the new approach and the effectiveness of the new approach in DEA ranking in comparison with other conventional ranking methods. Also, an "error" analysis proves the robustness of the proposed methodology.