Weights In Data Envelopment Analysis Research Articles

Positive weights in data envelopment analysis

AbstractData Envelopment Analysis (DEA) models give each decision making unit freedom to assign values to the input-output weights maximising its efficiency score. However, there is no guarantee that the optimal weights obtained from a DEA model are always positive which poses a problem, in both theory and practice. This paper offers new linear programming models to deal with the zero weights problem without restricting the weights or placing prior value judgments on them while maintaining the original DEA frontier. These models generate a profile of weights with the maximum number of positive weights applicable to both envelopment and multiplier DEA settings. These linear programs still allow weight flexibility and are independent of the solver. We show how these models can be modified to provide unit-specific positive weights. We illustrate the relevance of our approach using artificial and real world data.

Financial efficiency of companies operating in the Kosovo food sector: DEA and DEAHP

Data Envelopment Analysis (DEA) evaluates a large number of input and output variables using mathematical programming techniques and analyzes the effectiveness of similar decision making units (DMU). Unlike traditional methods, the most important advantage of DEA is that the weights of input and output variables can be defined by the analyzer. In this study, the limitations of the DEA weights were determined using the AHP, which considers expert opinion. In addition, an alternative judgment scale was used for the Saaty judgment scale, which is used as a standard in the AHP method, and thus a more sensitive analysis was performed. There have been studies dealing with the comparison of judgment scales, but few studies on consistency sensitivity are needed. This point has also been addressed in this study. Subsequently, the financial efficiency of 27 companies operating in the food sector in Kosovo was evaluated with the weight-restricted DEA model, first created using the unweighted DEA model and then the AHP model, and the two models were compared. This paper is the first one of its kind since there are no previous studies regarding the examination of the financial efficiency of companies operating in the Kosovo food sector based on the DEAHP method.

Evaluating sustainable efficiency of decision-making units considering undesirable outputs: an application to airline using integrated multi-objective DEA-TOPSIS.

Sustainable development has gained significant attention in the literature due to the increased global awareness of environmental sustainability during the last decade. Sustainable development has three aspects, including economic, social, and environmental. The challenge of sustainable development is to establish a balance between these three aspects. Assessing the efficiency of a company contributes comprehensive information to improve its overall performance. Despite numerous studies in this field, the literature lacks studies that simultaneously consider all three aspects of sustainable development, especially the social aspect. The main objective of this paper is to calculate the technical, social, and environmental efficiency scores. We also introduce a new efficiency called sustainable efficiency that merges all three sustainable development aspects in one efficiency score. This study applies two existing data envelopment analysis (DEA) models to evaluate technical, social, environmental, and sustainable efficiencies. These models, namely the three-step method and the modified three-step method, are computationally intensive. Also, this paper introduces two new DEA models, namely the common weight goal programming DEA and the common weight DEA, to assess the efficiencies with much fewer computations. Each model produces results that are different from one another. Therefore, the TOPSIS approach is applied to provide an overall result by integrating the results obtained from the four presented models. For this purpose, the implementation of four TOPSIS models is required. To illustrate the capability and validity of the developed models in efficiency calculation, a case of Iranian airlines is presented. The selected airlines are evaluated in different aspects, and final results are obtained by applying TOPSIS. The findings show that using TOPSIS to combine the results of several DEA models leads to a fully ranking of airlines in four aspects of technical, social, environmental, and sustainable efficiencies. Also, it is recommended to managers to probe pairwise comparison between different efficiencies of airlines in order to find and improve the weak ones.

A composite indicator index as a proxy for measuring the quality of water supply as perceived by users for urban water services

• Development of a composite indicator to measure the quality of water supply based on variables that are considered to affect users' perceptions of the quality of water supply. • A CI that includes relevant aspects that determine users' perceptions of water supply quality. • A new CI application, using MCDA with common DEA weights, to calculate a proxy for water supply service quality. • A CI that combines economic, technical and service quality variables, as they may be perceived by users, into a single indicator for water managers. The objective of this study is to develop a composite indicator (CI) to measure the quality of water supply based on the variables that are considered to affect users’ perceptions of water supply quality. The proposed CI includes six relevant aspects that determine users’ perceptions of water supply quality (network quality, water quality, water price, complaints, inconvenience caused by upgrading the network, and continuity of service) in a simple, economical, and objective way, using multi-criteria decision analysis (MCDA) with weights based on data envelopment analysis (DEA). The CI was applied to 32 municipalities in the metropolitan area of Valencia (Spain). The results show the high quality of the water supply service in this area. The use of this CI to measure the quality of the water supply service may prove useful for public institutions and managers of urban water supply, giving them an instrument to improve the management, efficiency, and quality of the water services they provide.

The Environmental Efficiency Analysis Based on the Three-Step Method for Two-Stage Data Envelopment Analysis

This paper suggests that the efficiency of a system (decision-making unit) and its subsystem cannot be properly measured using a two-stage data envelopment analysis (DEA) model either in cooperative or non-cooperative evaluation. Indeed, the existing methods subjectively determine the status of the subsystems in the whole system. The two-stage DEA models, either cooperative game or non-cooperative game, are used to analyze the environmental efficiency. However, when the actual relationship between the two subsystems is inconsistent with the subjective relationship assumptions, the overall efficiency of the system and the efficiency of each subsystem will be biased. The conventional two-stage DEA models require predetermining the relationship between the subsystems within the system based on the subjective judgment of the decision-maker. Based on this, this paper proposes a three-step method to solve the two-stage DEA. First, the position relation among subsystems is determined according to the optimal weights through the model. According to the status relationship among subsystems, the decision units are grouped, and the two-stage DEA model of cooperative game or non-cooperative game is used to analyze the efficiency in each group. This method reduces the subjectivity of decision making and analyzes the efficiency of each decision unit applying the most appropriate two-stage DEA model to find the source of inefficiency. Finally, this paper verifies the rationality and validity of the method by analyzing the water use efficiency of industrial systems in China. It is found that most regions in China value economic development more than environmental protection (as evidenced by the DEA weights). What is more, the method proposed by the paper can be generalized for any two-stage DEA problem.

A two-stage multi-objective second generation biodiesel supply chain design considering social sustainability: A case study

Undesirable environmental impacts caused by fossil fuel consumption have motivated governments to focus on biofuels production. Therefore, in our paper, we design a multi-objective biodiesel supply chain from Jatropha, which includes biomass cultivation center, pretreatment, and oil extraction center, biorefinery, and demand zone. In our study, a two-stage approach presented, which first specifies candidate locations for biomass cultivation with a common weight data envelopment analysis (CWDEA) method and then strategic and tactical decisions were made by a mathematical model. The presented multi-objective model focuses on cost minimization, besides social benefits and environmental impacts maximization while a life cycle assessment approach is used to model social indicators. The capability of the model is validated by proposing a case study of Iran and the augmented ε-constraint method is employed to reach a trade-off between three pillars of sustainability while managerial insights are provided by employing a Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method for the optimal solution selection. Model's results and sensitivity analysis on key parameters, specify the best locations for Jatropha Curcas L. (JCL) cultivation and facility construction as well as an optimal value of supply chain variables, which finally proves that Iran has a high potential for biodiesel production from JCL that leads improving balanced socio-economic development in this country.

Ground-level aircraft operations as a measure of sustainable airport efficiency: A weight-restricted DEA approach

Ground-level aircraft operations and landing and take-off cycle account for the vast majority of an airport’s total emission. Among other factors, planning skills are critical in minimizing the emissions produced and fuel burn through reducing taxi times during landing and take-off operations. This study examines the sustainable efficiencies of busiest European airports considering their success in reducing emissions during landing and take-off cycles and argues (i) emission per landing and take-off cycle is a good proxy for ground-level aircraft operation planning skills and provides more practical results than the total amount of annual emission, (ii) weight restriction procedure is necessary in Data Envelopment Analysis applications to ensure furnishing the impact of emission criteria on overall efficiency. A weight-restricted Data Envelopment Analysis model was constructed, and both physical and sustainable efficiencies of each airport were examined during nine years between 2010 and 2018. A combinative Analytic Hierarchy Process – Criteria Importance Through Intercriteria Correlation approach was used to define criteria weights, and a new modified approach was proposed and used to include these weights in Data Envelopment Analysis. Findings proved the necessity of weight restriction when one would examine the impact of emissions produced on sustainable airport efficiency. The Malmquist Productivity Index showed a great shift in physical output production; however, improvements to reduce landing and take-off cycle times have lagged behind the shift in physical output production.

MEASURING LOW CARBON ENERGY, ECONOMIC AND ENVIRONMENTAL SUSTAINABILITY PERFORMANCE OF BRICS

Formulating a robust low-carbon strategy has now been critical to achieving sustainable economic development amid broad carbon emissions across the BRIC region thanks to rapid industrialization and international trade growth. Developing such a strategy requires measuring actual sustainability performance from the energy, economy and ecological perspectives in this region. Therefore, this study explores the relationship among BRIC countries’ energy, economic and environmental sustainability performance by applying a common weight data envelopment analysis (DEA)-like composite indicator approach. The indicators encompass a comprehensive, latest, appropriate and applicable set of indicators. The results reveal that China and Brazil outperform against other underlined countries of the region in achieving sustainability with an overall index score of 0.96. India stands in ranking on second with a steady and unchanged score in the region, followed by South Africa and Russia, standing in ranking on fourth and fifth, respectively, in this study. Inclusive scores of both countries indicate the actual and robust possible potential for better sustainability performances in the region. This study proposes a policy by lifting the cross-border trade for renewable energy to achieve long-term environmental sustainability in the BRICS region.

Erratum: A Cross-Efficiency Method with Common Restrictions on Weights in Data Envelopment Analysis

Erratum: A Cross-Efficiency Method with Common Restrictions on Weights in Data Envelopment Analysis

Fuzzy clustering of homogeneous decision making units with common weights in data envelopment analysis

Data Envelopment Analysis (DEA) is the most popular mathematical approach to assess efficiency of decision-making units (DMUs). In complex organizations, DMUs face a heterogeneous condition regarding environmental factors which affect their efficiencies. When there are a large number of objects, non-homogeneity of DMUs significantly influences their efficiency scores that leads to unfair ranking of DMUs. The aim of this study is to deal with non-homogeneous DMUs by implementing a clustering technique for further efficiency analysis. This paper proposes a common set of weights (CSW) model with ideal point method to develop an identical weight vector for all DMUs. This study proposes a framework to measuring efficiency of complex organizations, such as banks, that have several operational styles or various objectives. The proposed framework helps managers and decision makers (1) to identify environmental components influencing the efficiency of DMUs, (2) to use a fuzzy equivalence relation approach proposed here to cluster the DMUs to homogenized groups, (3) to produce a common set of weights (CSWs) for all DMUs with the model developed here that considers fuzzy data within each cluster, and finally (4) to calculate the efficiency score and overall ranking of DMUs within each cluster.

Restricting the relative weights in data envelopment analysis

AbstractIn this paper, we address the problem of relative weight restriction in data envelopment analysis (DEA). A fuzzy‐based approach to restricting the relative weights is proposed in this study. Unlike the classical weight restriction methods, the proposed approach has an interactive orientation. That is, similar to analytical hierarchy process, the proposed method shares the decision maker (DM) in weight restriction process. Here, the preferences of DM are asked via pairwise comparison matrices. Then, the weights of factors (inputs/outputs) are extracted from these matrices. These weights, finally, are incorporated in multiplier DEA models as the parametric triangular fuzzy numbers, in which, the parameter value indicates the degree of conformity of the relative weights according to DM views. To best of our knowledge, no one has been yet utilized fuzzy set theory to control the relative weights in DEA. Putting in another word, the contribution of this study is that the authors propose a new approach based on fuzzy set theory to weight restriction in DEA. A last, a real case on financial banking efficiency is used to illustrate the proposed approach.

Ranking with a Euclidean common set of weights in data envelopment analysis: with application to the Eurozone banking sector

This paper provides a new method to define a Euclidean common set of weights (ECSW) in data development analysis (DEA) that (1) allows ranking both efficient and inefficient firms, (2) is more realistic in terms of determination of weights, and (3) generates rankings for banks consistent with their credit ratings. We first use DEA to determine the efficient frontier and then estimate a common set of weights that can minimize the Euclidean distance between the firms and that frontier. This process is illustrated by a simple numerical example and is extended to a real-life situation using the Eurozone banking sector. Our ECSW approach outperforms other common set of weights approaches in both numerical and real-life examples, and in terms of providing rankings consistent with banks’ credit ratings.

Common set of weights in data envelopment analysis under prospect theory

AbstractData envelopment analysis (DEA) is a data‐driven tool for performance evaluation, measuring decision‐making units (DMUs) and designating them with specific weightings. The standard DEA model typically sets up that decision‐makers (DMs) are wholly rational to select the most favourable weights to obtain the maximum performance score, but does not take into account their attitude toward risk during the assessment. The prospect theory generally matches humans' psychological behaviours. Thus, our study captures the non‐rational behaviours of DMs, performing under risk scenarios, in order to construct a novel common‐weights DEA model that maximizes the total prospect value, which can vary more steeply for losses than for gains, hence obtaining a more realistic common weight scheme. Our proposed model not only generates DMUs, with higher total prospect values, but also greater degrees of satisfaction. The current study shows that the prospect theory can be aptly extended to the DEA research area, supplying a proper guideline for future DEA research.

Maintaining production while reducing local and global environmental emissions in dairy farming

While milk is a major agricultural commodity, dairy farming also supports a large share of global beef production. In Life Cycle Assessment (LCA) studies of dairy farming systems, dairy-beef production is often ignored or ‘allocated off’, which may give a distorted view of production efficiencies. This study combines LCA with Data Envelopment Analysis (DEA) to develop an indicator of eco-efficiency for each of 738 UK dairy farms (3624 data points in 15 years) that aggregates multiple burdens and expresses them per unit of milk and dairy-beef produced. Within the DEA framework, the importance (weight) of dairy-beef relative to milk is iteratively increased to quantify the environmental losses from heavily focussing on milk-production, via e.g. higher yields per cow, with consequent lower burdens per unit of milk, yet with lower dairy-beef production levels, where burdens for beef production are externalized. Then, the relationship between DEA eco-efficiency and a series of indicators of dairy farming intensity at animal- and farm-levels was studied with Generalized Additive Models (GAM). For all sets of DEA weights (proportion of deviance explained ranged between 68% and 82%) indicate that milk yield per cow and forage area, and larger dairy herds all have a positive effect on eco-efficiency, while concentrate fed per unit of milk and the forage area both have a negative effect (p < 0.05 for all modelled relationships). These findings suggest that more intensive and consolidated dairy farms can positively impact on eco-efficiency. However, as the DEA weight for dairy-beef relative to milk increases, the relationship between environmental efficiency and farming specialization (expressed as L milk per kg dairy-beef produced) reverses from positive to negative. In conclusion, dairy-beef production is pivotal in determining the wider environmental efficiency of dairy (and ruminant food) systems, and its under-representation in efficiency studies has generated a misleading approach to meeting emission targets.

Determining a common set of weights in data envelopment analysis by bootstrap

Data envelopment analysis (DEA) is a model for measuring the efficiency of decision-making units (DMUs). The majority of DEA models suffer from drawbacks, in particular, changes in the weights of inputs and outputs. Consequently, the efficiency of DMUs is measured with different weights and so it is important to establish how to evaluate all DMUs using a common weight to optimize their efficiency at the same time. This study provides a new algorithm to overcome the weaknesses of the previous model. The proposed algorithm based on the bootstrap simulation establishes a bound for the input and output weights. Common weights are obtained by solving this model using bounded weights. According to the results of a numerical example solved by this model, it outperforms conventional models in terms of ranking DMUs.

A slacks-based measure model for calculating cross efficiency in data envelopment analysis

Cross efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of decision making units (DMUs) calculated from different weights in data envelopment analysis, and is helpful for ranking. Conventional cross efficiency is a radial measure, and the radial measure has some weaknesses. First, it is not able to provide appropriate efficiency scores for weakly efficient DMUs. Second, the efficiencies measured from the input and output sides under variable returns to scale are different which may cause difficulties in subsequent analyses. Third, negative values may appear when the efficiency is measured from the input side. To solve these problems, this paper proposes a slacks-based measure to calculate efficiency. The basic idea is the same as that of the radial measure using the frontier corresponding to a DMU to measure the efficiency of all DMUs, except that the efficiency measure is slacks-based instead of radial. Due to the nature of the slacks-based efficiency measure, the problems caused by weak efficiency and difference in input and output radial measures do not exist. More importantly, negative efficiencies are not produced. The proposed method is applied to a real case involving the selection of the most efficient robot to use for production. The results help identify the top-ranked robot.

Measuring environmental sustainability performance of South Asia

Abstract Sustainability and low-carbon economy strategies have been widely studied in the past; nevertheless, researchers often ignore the effects of combining energy, economic, and environmental factors when assessing sustainability performance. To fill this gap, we measure the environmental sustainability performance of South Asia using a common weight Data Envelopment Analysis (DEA)-like mathematical model encompassing a comprehensive, up-to-date, and relevant set of indicators. In this paper, we present a measurement of South Asia’s environmental sustainability performance for the years 2001–2015. Our results reveal that Bhutan outperforms the rest of the countries in South Asia, with an overall index score of 0.72. Nepal comes second in the region, with a stable score, followed by the Maldives. Afghanistan and Bangladesh are ranked fourth and fifth, respectively, and their overall scores indicate strong potential sustainability performances. India, Sri Lanka and Pakistan follow this list, with poor scores, with Pakistan having the lowest scores during the study period. Based on these findings, we propose a policy to boost the cross-border renewable energy trade for long-term environmental sustainability.

Incorporating decision makers’ preferences into DEA and common weight DEA models based on the best–worst method (BWM)

Incorporating decision makers’ (DMs’) judgments and preferences into DEA models is very important in some real-world problems. This paper presents an integrated data envelopment analysis (DEA)—best–worst method (BWM)—for considering DMs’ preferences in DEA and reducing flexibility in weights of inputs and outputs. First, the preferences vectors are designed using BWM, and then, a multi-objective DEA-BWM model is introduced. The proposed DEA-BWM model simultaneously maximizes the efficiency scores of DMUs and considers DMs’ preferences about weights of inputs and outputs. Finally, a goal programming model is suggested for extending the DEA-BWM model and finding common weights of inputs and outputs based on the DMs’ judgments. The proposed common weight DEA-BWM (CWDEA-BWM) model maximizes the efficiencies of DMUs, considers DMs’ preferences and uses a set of common weights. In order to illustrate the capability of proposed models, a numerical example is solved. Moreover, the proposed DEA-BWM and common weight DEA-BWM models are applied to evaluate 39 Iranian electricity distribution companies, and the results are analyzed and compared. The results indicate that the proposed DEA-BWM and CWDEA-BWM models are suitable for incorporating DMs’ preferences into DEA and fully ranking of DMUs.

A bargaining approach to determine common weights in DEA

In this paper Data Envelopment Analysis (DEA) is used to assess the relative efficiency of a set of decision-making units (DMUs). Each DMU is evaluated on the basis of the ratio of its weighted output (i.e. virtual output) over its weighted input (i.e. virtual input). Conventional DEA models allow each DMU to select the weighting scheme which optimizes its own evaluation. However, this total flexibility has drawbacks and in certain contexts may not be desirable. In such cases, it may be more appropriate to consider a common set of weights to benchmark and rank the alternatives using a common platform. In this paper, bargaining theory is used to determine a common set of weights in DEA. The advantage of using a bargaining approach is that the weights emerge bottom-up as the result of an agreement between the DMUs, instead of using an exogenous criterion imposed from above. The novelty of the proposed approach is that we consider two players per DMU, one whose utility function corresponds to its virtual input, and another whose utility is the negative of the virtual input. Thus, each DMU wants to choose the output weights so as to maximize its virtual output, and the input weights so as to minimize its virtual input. In this way, all DMU try to appear under the best possible light but the input and output weights are common and agreed. Models based on the Nash and the Kalai–Smorodinsky solutions are formulated and an application to a supplier selection problem is presented.

A 2-tuple integrated DEA-based approach for neuromarketing technology evaluation

Purpose Neuromarketing, which is an interdisciplinary area, concentrates on evaluating consumers’ cognitive and emotional reactions to different marketing stimuli. In spite of advantages, neuromarketing still requires development and lacks a strong theoretical framework. Techniques that are used in neuromarketing studies have different superiorities and limitations, and thus, there is a need for the evaluation of the relevance of these techniques. The purpose of this study is to introduce a novel integrated approach for the neuromarketing research area. Design/methodology/approach The proposed approach combines 2-tuple linguistic representation model and data envelopment analysis to obtain the most efficient neuromarketing technique. It is apt to handle information provided by using both linguistic and numerical scales with multiple information sources. Furthermore, it allows managers to deal with heterogeneous information, without loss of information. Findings The proposed approach indicates that functional magnetic resonance imaging (fMRI) is the best performing neuromarketing technology. Recently, fMRI has been widely used in neuromarketing research. In spite of its high cost, its main superiorities are improved spatial and temporal resolutions. On the other hand, transcranial magnetic stimulation (TMS) and positron emission tomography (PET) are ranked at the bottom because of their poor resolutions and lower willingness of participants. Originality/value This paper proposes a common weight data envelopment analysis (DEA)-based decision model to cope with heterogeneous information collected by the experts to determine the best performing neuromarketing technology. The decision procedure enables the decision-makers to handle the problems of loss of information and multi-granularity by using the fusion of 2-tuple linguistic representation model and fuzzy information. Moreover, a DEA-based common weight model does not require subjective experts’ opinions to weight the evaluation criteria.