Ranking Of Decision Making Units Research Articles

Ranking DMUs by using interval efficiencies in data envelopment analysis

Efficiency is a relative measure that allows assessment across different ranges. Evaluating the performance of decision-making units (DMUs) from an optimistic perspective yields the best relative efficiency (optimistic efficiency), which establishes an efficiency frontier. Conversely, evaluating from a pessimistic perspective produces the worst relative efficiency (pessimistic efficiency) and creates an inefficiency frontier. This study examines the efficiency of DMUs in two scenarios and proposes models for adjustment coefficient. The pessimistic and optimistic efficiencies are adjusted to the lower and upper bounds of the DMUs based on the adjustment coefficient, enabling determination of efficiency intervals for all DMUs, as well as evaluation and ranking. A Hurwicz criterion-based approach is introduced and applied to compare and rank the interval efficiencies of DMUs. Two numerical examples are examined using the proposed DEA adjustment coefficient models to demonstrate its potential application and validity.

Assessing environmental and operational efficiencies: a multi-objective optimisation problem in a two-stage network data envelopment analysis

Abstract The environmental efficiency of industries plays an important role in economic development of countries. Accordingly, dividing the internal network structure of industries into two sub-processes, including green and operational stages enables decision-makers to assess both of the efficiencies simultaneously. Such assessment can be implemented using a non-parametric methodology termed data envelopment analysis (DEA). Standard DEA models consider the whole system of decision-making units (DMUs) as a single process (i.e., black-box). The black-box approach ignores modelling of the internal network structure of the assessed DMUs. This issue tackled by network DEA models since it considers the internal network structure of DMUs. In the network DEA, the efficiency evaluation of system stages is essential to identify its overall efficiency, resulting to a multi-objective optimisation problem. Therefore, the network DEA is a widely welcomed methodology proposed for solving multi-objective problems. This paper assesses the operational and environmental efficiencies of a network structure system by converting the multi-objective optimisation problem into a linear single objective function. In this investigation, a technique of tri-objective function problem is proposed. The proposed technique transforms into a single objective function by keeping one objective function and shifting the other two objective functions into the model’s constraints. The applicability and usefulness of the proposed technique have been tested using a data set of 20 industries. The developed approach provides valuable evaluations to decision-makers to rank DMUs by considering their green and operational efficiency simultaneously.

Combining bootstrap data envelopment analysis with social networks for rank discrimination and suitable potential benchmarks

Many studies have attempted to overcome the inherent relativity of data envelopment analysis (DEA), which gives rise to the existence of undiscriminated decision-making units (DMUs) or the changes in the reference relationships depending on how the DMUs are grouped. This study presents a new and intuitive algorithm based on the bootstrapping method for generating a network that reflects both the DMUs’ original reference relationships and their potential benchmarks in a way that does not violate DEA's theoretical and practical premises while enabling a fuller ranking of the DMUs. An in-depth discussion regarding the definition of two types of potential benchmarks that can be used to rank DMUs flexibly is provided to highlight the superiority of the proposed algorithm. The application of our proposed algorithm delivers significant advantages over existing network approach models and opens new possibilities for utilizing the bootstrap DEA method.

Efficiency evaluation for decision making units with fixed-sum outputs using data envelopment analysis and stochastic multicriteria acceptability analysis

The generalized equilibrium efficient frontier data envelopment analysis (GEEFDEA) approach, an extension of the DEA method, has been widely used to solve the problem of evaluating decision making units (DMUs) producing fixed-sum outputs. It constructs a common equilibrium efficient frontier through a minimum reduction strategy for fixed-sum outputs and uses this frontier as a benchmark to achieve a complete ranking of DMUs. However, the existence of multiple feasible equilibrium efficient frontiers may lead to inconsistency in the evaluation criteria, and this possibility limits the method’s usefulness. In this paper, an integrated framework for solving this problem is proposed to rank DMUs by using stochastic multicriteria acceptability analysis (SMAA-2) method combined with the GEEFDEA approach. Instead of using a certain common equilibrium efficient frontier as in conventional GEEFDEA approaches, we explore all possible frontiers to answer various robustness questions by computing rank acceptability indices and pairwise winning indices. Furthermore, we derive the complete ranking from the dominance relationships among the DMUs. Two numerical examples are used to demonstrate the effectiveness and rationality of the proposed hybrid approach.

A robust DEA model in the presence of uncertain integer-valued parameters

PurposeUncertainty in data, whether in real-valued or integer-valued data, may result in infeasible optimal solutions or unreliable efficiency scores and ranking of decision-making units. To handle the uncertainty in integer-valued factors in data envelopment analysis (DEA) models, this study aims to propose a robust DEA model which is applicable in the presence of such factors.Design/methodology/approachThis research focuses on the application of fuzzy interpretation of efficiency to a mixed-integer DEA (MIDEA) model. The robust optimization approach is used to address the uncertain integer-valued parameters in the proposed MIDEA model.FindingsIn this study, the authors proposed an MIDEA model without any equality constraint to avoid the arise problem by such constraints in the construction of the robust counterpart of the conventional MIDEA models. We have studied the characteristics and conditions for constructing the uncertainty set with uncertain integer-valued parameters and a robust MIDEA model is proposed under a combined box-polyhedral uncertainty set. The applicability of the developed models is shown in a case study of Malaysian public universities.Originality/valueThis study develops an MIDEA model equivalent to the conventional MIDEA model excluding any equality constraint which is crucial in robust approach to avoid restricted feasible region or infeasible solutions. This study proposes a robust DEA approach which is applicable in cases with uncertain integer-valued parameters, unlike previous studies in robust DEA field where uncertain parameters are generally assumed to be only real-valued.

Evaluating the Efficiency of Decision Making Units in Fuzzy two-stage DEA Models

Data envelopment analysis (DEA) is an optimization method to assess the efficiency of decision-making units with multiple-inputs/multiple-outputs assumption. Most real-life issues contain more than one stage unit which needs multiple-stage data envelopment analysis models to be solved. Moreover, the inputs and outputs of the units are rarely measured accurately in real-life problems, hence fuzzy data envelopment analysis approaches can be significantly helpful in calculating efficiency scores. In this study, an approach for evaluating the performance of decision-making units (DMUs) in fuzzy two-stage DEA models is developed. The developed model is a parametric program based on alpha-cuts. The dependence on alpha allows the manager to compare and rank DMUs based on his/her degree of certainty and after the selection of alpha, our proposed model becomes linear. Furthermore, a theorem is proposed and proved for conventional multiplicative two-stage DEA models with the assumption of Variable Returns to Scale. This theorem can be used to evaluate the correctness of the results. Finally, by two illustrative examples, the ability of the proposed approach to solve fuzzy two-stage DEA models is shown, and the obtained results are compared to that of some other methods in this field.

Assessing the sustainability of transport supply chains by double frontier network data envelopment analysis

The transport industry is one of the main contributors to environmental pollution. Sustainable supply chain management (SSCM) is an essential subject in the transportation industry. Today, one of the important goals of organizations is to evaluate the sustainability of supply chain (SC) because assessing the efficiency of SCs helps organizations to enhance their awareness of performance and develop managerial strategies. Data envelopment analysis (DEA) is a common technique to assess the sustainability. The objective of this paper is to propose a Malmquist productivity index (MPI) based on network data envelopment analysis (NDEA) model in the presence of integer data, undesirable outputs, and non-discretionary inputs. The NDEA models deal with the internal structure of decision making units (DMUs). The MPI reflects the productivity change over time. The proposed model can fully rank DMUs. To prove the applicability of the proposed model, the sustainability of intercity passenger transportation is evaluated.

Achievements of the European Union member states toward the development of sustainable agriculture: A contribution to the structural efficiency approach

The ranking of decision-making units can be performed by measuring their efficiency. However, the discriminatory power of efficiency measures is sometimes compromised, and complete rankings are not attained. Additionally, environmental performance must be considered when assessing the sustainability of operations. This paper applies the “average contribution to structural efficiency” index to measure the environmental performance of the European Union Member States’ agricultural sectors. The contribution index considers all of the possible combinations of observations when assessing states’ environmental performance. This process allows for a complete ranking of the countries under consideration. The agricultural performance of Bulgaria, Denmark, France, the Netherlands, Romania, Slovakia and Slovenia, as measured by the conventional data envelopment analysis, approached the production frontier. Therefore, these countries could not be ranked based on the conventional data envelopment analysis model. The application of the contribution index showed that Romania, the Netherlands, Bulgaria, Slovakia and Slovenia were ranked as the best-performing countries. In addition, France and Belgium showed positive contributions to structural efficiency, although they were not classified as efficient countries. Therefore, cooperation with these countries would allow other countries to exploit their agricultural resources in a more productive and sustainable manner.

Performance measurement of decision making units through interval efficiency with slacks-based measure: an application to tourist hotels in Taipei

Data envelopment analysis (DEA) is widely used to evaluate the performance of a group of homogeneous decision making units (DMUs). Considering the uncertainty, interval DEA has been introduced to fit into more situations. In this paper, an interval efficiency method based on slacks-based measure is proposed to solve the uncertain problems in DEA. Firstly, the maximum and minimum efficiency values of the evaluated DMU are calculated by the furthest and closest distance from the evaluated DMU to the projection points on the Pareto-efficient frontier, respectively. Then, the AHP method is used for the full ranking of DMUs. The paper uses the pairwise comparison relationship between each pair of DMUs to construct the interval multiplicative preference relations (IMPRs) matrix. If the matrix does not meet the consistency condition, a method to obtain consistency IMPRs is introduced. According to the consistency judgment matrix, the full ranking of DMUs can be obtained. Finally, we apply our method to the performance evaluation of 12 tourist hotels in Taipei in 2019.

A new interval efficiency measure in data envelopment analysis based on efficiency potential

Abstract This study proposes a new approach for evaluating the efficiency of decision-making units (DMUs) with interval data. We define a potential-based measure of efficiency (PBM), analogous with the concepts of the vector field and the potential function in Physics that projects the DMUs onto the best and the worst frontiers defined by the best and the worst values of the inputs and outputs of the DMUs. This contrasts with the standard and arguably unfair approach that benchmarks the best performance of a DMU against the worst performance of all other DMUs or the worst performance of a DMU against the best performance of all other DMUs. We argue that it is more sensible to assume that all the DMUs perform at their best or at their worst. Then, in this way, a narrower efficiency interval is determined for each DMU. We show how to derive a numerical efficiency, and hence, how to rank DMUs from the efficiency interval. Our methodology is illustrated using a dataset that relates to the performance of the branches of an insurance company in Iran. We compare our methodology with other existing methods from the literature.

Assessing sustainability of supply chains by fuzzy Malmquist network data envelopment analysis: Incorporating double frontier and common set of weights

Sustainable supply chain management (SSCM) is one of the most significant topics. Today, assessing sustainability and choosing the best supply chain is an important goal for companies. One of the techniques that can be used for evaluating the sustainability of supply chains is data envelopment analysis (DEA). This study contributes to the knowledge of sustainability assessment by (i) proposing a double frontier network DEA (NDEA) model with common set of weights (CSW), (ii) dealing with fuzzy data to assess sustainability, and (iii) deriving a CSW model for Malmquist productivity index (MPI). The CSW models consider the same set of weights for all decision making units (DMUs) so that all DMUs get the highest sustainability score. The fuzzy MPI (FMPI) is used to assess the sustainability of supply chains with the trapezoidal fuzzy number. The FMPI reflects the productivity change over time. The proposed model can assess the sustainability of supply chains and takes into account different confidence levels in two periods and can fully rank DMUs. Our model can measure the sustainability of supply chains via fuzzy MPI. Using our proposed approach, the decision-makers can determine the optimistic, pessimistic, and double frontier sustainability of supply chains. To prove the applicability of the proposed model, the sustainability of customs centers is assessed.

An evaluation of cross-efficiency methods: With an application to warehouse performance

Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a selection of methods popular in the literature. These methods are applied to performance measurement of European warehouses. We develop a cross-efficiency method based on a rank-order DEA model to accommodate the ordinal nature of some key variables characterizing warehouse performance. This is one of the first comparisons of methods on a real-life dataset and the first time that a model allowing for qualitative variables is included in such a comparison. Our results show that the choice of model matters, as one obtains statistically different rankings from each one of them. This holds in particular for the multiplicative and game-theoretic methods whose results diverge from the classic method. From a managerial perspective, focused on the applicability of the methods, we evaluate them through a multidimensional metric which considers their capability to rank DMUs, their ease of implementation, and their robustness to sensitivity analyses. We conclude that standard weight-restriction methods, as initiated by Sexton et al. [48], perform as well as recently introduced, more sophisticated alternatives.

Presenting a data envelopment analysis model based on Goal programming and weight Restriction in order to evaluate the efficiency and ranking of decision-making units in Ghavamin Bank

هدف: هدف این مقاله ارزیابی کارایی واحدهای تصمیم‌گیرنده با به‌کارگیری مدل برنامه‌ریزی آرمانی تحلیل پوششی داده‌ها با محدودیت وزنی و رتبه‌بندی واحدها با یک روش منحصربه‌فرد در بانک قوامین می‌باشد. روش: در این پژوهش برای تعیین کارایی مدیریت شعب استان‌ها در بانک قوامین نخست مدل CCR کلاسیک به‌کارگیری شد. به‌منظور افزایش قدرت تفکیک‌پذیری واحدهای تصمیم‌گیرنده کارا از ناکارا، مدل برنامه‌ریزی آرمانی با محدودیت وزنی ترکیب‌شده و یک مدل جدید تحت عنوان برنامه‌ریزی آرمانی تحلیل پوششی داده‌ها با محدودیت وزنی ارائه گردید. یافته‌ها: بر اساس مقادیر خروجی مدل CCR کلاسیک، 16 واحد از 32 واحد تصمیم‌گیرنده کارا و 16 واحد ناکارا شدند. در مرحله بعد برای تفکیک‌پذیری بیشتر واحدها مدل برنامه‌ریزی آرمانی تحلیل پوششی داده‌ها با محدودیت وزنی به‌کارگیری شد که نتایج حاصل از آن با نرم اقلیدسی مرتبه اول، از بین 32 واحد تصمیم‌گیرنده 7 واحد کارا و بقیه ناکارا شدند و نتایج حاصل از نرم بی‌نهایت، 1 واحد از 32 واحد کارا و بقیه واحدهای تصمیم‌گیرنده ناکارا شدند. نتیجه‌گیری: نتایج نشان دادند که مدل برنامه‌ریزی آرمانی تحلیل پوششی داده‌ها با محدودیت وزنی مربوط به نرم بی‌نهایت در تفکیک و رتبه‌بندی واحدهای تصمیم‌گیرنده کارا از ناکارا، دارای قدرت تفکیک‌پذیری بالایی نسبت به مدل CCR کلاسیک و نرم اقلیدسی مرتبه اول است

DEA Cross-Efficiency Aggregation with Deviation Degree Based on Standardized Euclidean Distance

Data envelopment analysis (DEA) has been extended to cross-efficiency to provide better discrimination and ranking of decision-making units (DMUs). Current researches about cross-efficiency mainly focus on the non-uniqueness of optimal solution of linear programming and information aggregation. As a common distance metric, standardized Euclidean distance is introduced to define the discrimination power between two vectors and the deviation degree for measuring the difference between the individual preference and group ideal preference. Based on above definitions, an alternative method is presented to compare multiple optimal solutions, and further, a universal weighted cross-efficiency model considering both dynamic adjustment of weights and preference formulation is constructed for evaluation and ranking. Two numerical examples are given to illustrate the effectiveness of the comparison method for multiple optimal solutions and weights determination method of DMUs, respectively. At last, a practical application aimed at evaluating environmental treatment efficiency in western area of China is given. Comparative analysis shows that our model could be more moderate, flexible, and general than some available models and methods, which can extend the theoretical research of cross-efficiency evaluation.

Efficiency evaluation with cross-efficiency in the presence of undesirable outputs in stochastic environment

Data envelopment analysis (DEA) is a useful tool for efficiency evaluation of decision making units (DMUs). The classical DEA models deal with exact data while in real world problems we concern with uncertain data such as fuzzy, stochastic and etc. In this paper, using input oriented CCR model (ICCR) in the presence of undesirable outputs with specific risk (α), a new stochastic model called Expected Ranking Criterion is proposed. Based on this, the stochastic cross-efficiency evaluation is presented for robust ranking and discrimination of DMUs. Given the non-uniqueness of resulting optimal solutions, a model is introduced for ranking by which stochastic cross-efficiency is performed using aggressive approach. The proposed model provides ranking of all DMUs whereas current stochastic DEA models in literature fail in this regard. Finally, the proposed models are implemented for 32 thermal power plants with stochastic inputs and undesirable outputs. The results show the applicability of proposed models.

Forecasting the Confidence Interval of Efficiency in Fuzzy DEA

Data Envelopment Analysis (DEA) is a well-known method that based on inputs and outputs calculates the efficiency of decision-making units (DMUs). Comparing the efficiency and ranking of DMUs in different time periods lets the decision makers to prevent any loss in the productivity of units and improve the production planning. Despite the merits of DEA models, they are not able to forecast the efficiency of future time periods with known input/output records of the DMUs. With this end in view, this study aims at proposing a forecasting algorithm with a 95% confidence interval to generate fuzzy data sets for future time periods. Moreover, managers’ opinions are inserted in the proposed forecasting model. Equipped with the forecasted data sets and with respect to the data sets from previous periods, this model can rightly forecast the efficiency of the future time periods. The proposed procedure also employs the simple geometric mean to discriminate between efficient units. Examples from a real case including 20 automobile firms show the applicability of the proposed algorithm.

A robust cross-efficiency data envelopment analysis model with undesirable outputs

Degenerate optimal weights and uncertain data are two challenging problems in conventional data envelopment analysis (DEA). Cross-efficiency and robust optimization are commonly used to handle such problems. We develop two DEA adaptations to rank decision-making units (DMUs) characterized by uncertain data and undesirable outputs. The first adaptation is an interval approach, where we propose lower- and upper-bounds for the efficiency scores and apply a robust cross-efficiency model to avoid problems of non-unique optimal weights and uncertain data. We initially use the proposed interval approach and categorize DMUs into fully efficient, efficient, and inefficient groups. The second adaptation is a robust approach, where we rank the DMUs, with a measure of cross-efficiency that extends the traditional classification of efficient and inefficient units. Results show that we can obtain higher discriminatory power and higher-ranking stability compared with the interval models. We present an example from the literature and a real-world application in the banking industry to demonstrate this capability.

An adjustable fuzzy chance-constrained network DEA approach with application to ranking investment firms

This paper presents a novel approach for performance appraisal and ranking of decision-making units (DMUs) with two-stage network structure in the presence of imprecise and vague data. In order to achieve this goal, two-stage data envelopment analysis (DEA) model, adjustable possibilistic programming (APP), and chance-constrained programming (CCP) are applied to propose the new fuzzy network data envelopment analysis (FNDEA) approach. The main advantages of the proposed FNDEA approach can be summarized as follows: linearity of the proposed FNDEA models, unique efficiency decomposing under ambiguity, capability to extending for other network structures. Moreover, FNDEA approach can be applied for ranking of two-stage DMUs under fuzzy environment in three stages: 1) solving the proposed FNDEA model for all optimistic-pessimistic viewpoints and confidence levels, 2) then plotting the results and drawing the surface of all efficiency scores, 3) and finally calculate the volume of the three-dimensional shape in below the efficiency surface. This volume can be as ranking criterion. Remarkably, the presented fuzzy network DEA approach is implemented for performance appraisal and ranking of investment firms (IFs) with two-stage processes including operational and portfolio management process. Illustrative results of the real-life case study show that the proposed approach is effective and practically very useful.

A novel mixed binary linear DEA model for ranking decision-making units with preference information

Several mixed binary linear programming models have been proposed in the literature to rank decision-making units (DMUs) in data envelopment analysis (DEA). However, some of these models fail to consider the decision-makers’ preferences. We propose a new mixed binary linear DEA model for finding the most efficient DMU by considering the decision-makers’ preferences. The model proposed in this study is motivated by the approach introduced by Toloo and Salahi (2018). We extend their model by introducing additional assurance region type I (ARI) weight restrictions (WRs) based on the decision-makers’ preferences. We show that direct addition of assurance region type II (ARII) and absolute WRs in traditional DEA models leads to infeasibility and free production problems, and we prove ARI eliminates these problems. We also show our epsilon-free model is less complicated and requires less effort to determine the best efficient unit compared with the existing epsilon-based models in the literature. We provide two real-life applications to show the applicability and exhibit the efficacy of our model.

Integrated data envelopment analysis and multicriteria decision-making ranking approach based on peer-evaluations and subjective preferences: case study in banking sector

PurposeThis paper is focused on developing an integrated algorithmic approach named as data envelopment analysis and multicriteria decision-making (DEA-MCDM) for ranking decision-making units (DMUs) based on cross-efficiency technique and subjective preference(s) of the decision maker.Design/methodology/approachSelf-evaluation in data envelopment analysis (DEA) lacks in discrimination power among DMUs. To fix this, a cross-efficiency technique has been introduced that ranks DMUs based on peer-evaluation. Different cross-efficiency formulations such as aggressive and benevolent and neutral are available in the literature. The existing ranking approaches fail to incorporate subjective preference of “one” or “some” or “all” or “most” of the cross-efficiency evaluation formulations. Therefore, the integrated framework in this paper, based on DEA and multicriteria decision-making (MCDM), aims to present a ranking approach to incorporate different cross-efficiency formulations as well as subjective preference(s) of decision maker.FindingsThe proposed approach has an advantage that each of the aggressive, benevolent and neutral cross-efficiency formulations contribute to select the best alternative among the DMUs in a MCDM problem. Ordered weighted averaging (OWA) aggregation is applied to aggregate final cross-efficiencies and to achieve complete ranking of the DMUs. This new approach is further illustrated and compared with existing MCDM approaches like simple additive weighting (SAW) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to prove its validity in real situations.Research limitations/implicationsThe choice of cross-efficiency formulation(s) as per subjective preference of the decision maker and different orness levels lead to different aggregated scores and thus ranking of the DMUs accordingly. The proposed ranking approach is highly useful in real applications like R and D projects, flexible manufacturing systems, electricity distribution sector, banking industry, labor assignment and the economic environmental performances for ranking and benchmarking.Practical implicationsTo prove the practical applicability and robustness of the proposed integrated DEA-MCDM approach, it is applied to top twelve Indian banks in terms of three inputs and two outputs for the period 2018–2019. The findings of the study (1) ensure the impact of non-performing assets (NPAs) on the ranking of the selected banks and (2) are enormously valuable for the bank experts and policy makers to consider the impact of peer-evaluation and subjective preference(s) in formulating appropriate policies to improve performance and ranks of underperformed banks in competitive scenario.Originality/valueTo the best of the authors’ knowledge, this is the first study that has integrated both DEA and MCDM via OWA aggregation to present a ranking approach that can incorporate different cross-efficiency formulations and subjective preference(s) of the decision maker for ranking DMUs.