Different Decision Making Units Research Articles

Aggregation of meta-technology ratio in DEA framework using the evidential reasoning approach

The metafrontier data envelopment analysis (DEA) model is a popular evaluation technique when different decision-making units (DMUs) may exhibit production technology heterogeneity. In this framework, the group metatechnology ratio (MTR) is an important indicator to help measure the technology gap at the group level. The common approach to the group MTR aggregation is the arithmetic average approach, which requires the MTR of the DMU to satisfy the ‘additive independence’ condition. Because the MTRs are generated from the same data set and linked to each other, the MTRs do not meet the ‘additive independence’ condition. Therefore, a new aggregation approach is needed. This study applies the evidential reasoning (ER) approach to aggregate the group MTR by the transformation of the MTR of DMU to pieces of evidence. Moreover, this study proposes examples that verify the applicability and practicality of the MTR aggregation using the ER approach, including an empirical example of the evaluation practice of the transportation system of 30 provincial regions in mainland China for 2013–2019.

Modeling business partnerships: A data envelopment analysis approach

Strategic alliances and partnerships including mergers and acquisitions have been a growing trend in many industries in the past decades. There are many studies in the literature emphasizing the importance of business partnerships. However, literature on partnership optimization is quite limited. This paper defines various types of strategic alliance collaborations and partnerships between different decision making units (DMUs) and develops data envelopment analysis (DEA) models to guide partners on how redistributing their inputs and outputs could enhance their performance. The results of this study are useful for companies considering strategic alliances and partnerships to improve competitiveness. An application in banking is used to highlight the advantages of the proposed method in this paper.

A nonparametric distance function approach with endogenous direction for estimating marginal abatement costs of CO2 emissions

The directional distance function (DDF) framework has been widely used to estimate the marginal abatement cost (MAC) of CO2 emissions to support decision-making in environmental sustainability and climate change issues. In the use of DDF, an important task is mapping evaluated entities towards a realistic production technology frontier. This study develops a new nonparametric approach for estimating the MAC of CO2 emissions. The approach incorporates the optimal endogenous direction into an enhanced environmental production technology and has three advantages. First, it avoids the arbitrariness in mapping directions. Second, it captures the heterogeneity in optimization paths across different decision-making units (DMUs). Third, it generates more reliable benchmarks for estimating MAC by constructing an environmental technology frontier that is consistent with the material balance principle. We apply the approach to study China's thermal power industry and find clear heterogeneity in MACs and optimization paths at the province level. The results on the optimal endogenous directions show that the DMUs prefer to increase both desirable output and CO2 emissions when CO2 emissions are unregulated. Comparisons with other approaches reveal that arbitrarily mapping exogenous directions and technology representations are likely to generate distorted and unrealistic MACs.

A novel fuzzy non-radial data envelopment analysis: An application in transportation

The slack-based measure (SBM) DEA model is a non-radial model used to calculate the relative efficiency, input, and output targets of the different decision-making units (DMUs) based on their best peers or efficient frontier. The conventional SBM DEA model used crisp inputs and outputs. But, it can be observed in real-life problems that sometimes the available data is in linguistic forms such as “few”, “many”, “small”, or missing data. The DEA technique is frontier based, and therefore, imprecise data may lead to untenable results. Fuzzy theory, which is already established to handle uncertain data, can overcome this problem. Furthermore, the sensitivity and stability analysis have been checked the robustness of fuzzy DEA models. In this study, sensitivity and stability analysis of the fuzzy SBM DEA has been performed. The lower and upper sensitive bounds for inputs and outputs variables have been obtained for both the inefficient and efficient DMUs to calculate the input and output targets. Finally, a real-life transportation problem for the validity of the study is presented for its depiction.

Integration of Data Envelopment Analysis and Clustering Methods

Data Envelopment Analysis (DEA) has been applied creatively in various study domains to compare and evaluate different Decision Making Units (DMUs) based on multiple input–output attributes. In this paper, the performance of Jordanian public hospitals is assessed via a methodology combining DEA with data mining methods, specifically, clustering. Initially, inputs of inefficient hospitals were altered to check for waste in the allocated resources. Then, the number of inputs–outputs was manipulated to test if the number is strongly influencing the productivity of the DMUs. The number of DMUs used was 27 public hospitals and the applicable efficiency measurements used were constant return to scale (CRS) and variable return to scale (VRS) through the DEAP software. Experiments showed that the efficiency of a hospital might be more meaningfully assessed if it is compared with a group of hospitals that are similar in some factors. More specifically, results of applying the CRS model proved that 77% of the hospitals were efficient. Additionally, we found that the inefficiencies of some hospitals are linked to weak resource utilization. It is concluded that number of inputs–outputs inserted in the efficiency evaluation process impacts the resulted values.

Integration of Balanced Scorecard and Three- stage Data Envelopment Analysis Approaches

The Balanced Scorecard (BSC) provides an outlook of an organization’s general performance; it integrates financial perspective with other performance aspects, like learning and growth, internal processes, and customer perspectives. The momentous issue, in implementation of BSC, is the proper selection of measures. The main objective of this paper is to introduce a novel approach in an attempt to select the most appropriate measures by integrating BSC and three-stage Data Envelopment Analysis (DEA) model. To achieving this aim, the BSC’s measures are utilized as input and output variables of DEA model and the most appropriate measures in each BSC’s perspective are determined with interpretation of the efficiency variations in different stages. An experimental example containing six Iranian banks has been investigated to demonstrate the implementation of this approach. The results indicate that increased staff expertise (L2) and high speed services (P2), respectively in stage one and two are appropriate measures. Also, in this study, we cannot judge about the effect of customer satisfaction rate (C2), because the values of this measure are similar in different decision making units (DMUs). The proposed approach in the current paper helps managers to recognize appropriate measures for staff empowerment, internal process improvement, customer satisfaction increase, and organization’s financial outcomes improvement.

Energy and environmental efficiency evaluation based on a novel data envelopment analysis: An application in petrochemical industries

Petrochemical industry is a high energy consumption and heavy pollution industry. Therefore, energy and environmental efficiency evaluation becomes extremely important to achieve sustainable development of the petrochemical industry. This paper proposes a novel DEA model to estimate the energy and environmental efficiency of the petrochemical industry thoroughly. The proposed method introduces the efficiency variable to each energy input and undesirable output and uses environmental performance index (EPI) to represent the overall performance of different decision making units (DMUs). Moreover, the scores of efficiency variables reflect the environmental performance of energy inputs and undesirable outputs, and the larger score represents the greater performance of the DMUs. Meanwhile, the EPI synthesizes the environmental efficiency value of energy inputs and undesirable outputs to help us grasp the energy and environmental comprehensive performance of DMUs, which also contributes to measure the potential of energy saving and emission reduction of petrochemical industry simultaneously. Finally, the proposed model is applied to the energy and environmental efficiency analysis of different ethylene plants under different scales. The experimental results demonstrate the validity of the proposed model and reveal some implications for improving energy efficiency and carbon dioxide emissions reduction of ethylene plants in the petrochemical industry.

Linear robust data envelopment analysis: CCR model with uncertain data

Data envelopment analysis (DEA) traditionally assumes that input and output data of the different decision making units (DMUs) are measured with precision. However, in many real applications inputs and outputs are often imprecise. This paper proposes a linear robust data envelopment analysis (LRDEA) model using imprecise data represented by an uncertainty set. The method is based on the robust optimisation approach of Bertsimas and Sim to seek maximisation of efficiency under uncertainty (as does the original DEA model). In this approach, it is possible to vary the degree of conservatism to allow for a decision maker to understand the tradeoff between a constraint's protection and its efficiency. The method incorporates the degree of conservatism in the maximum probability bound for constraint violation. Application of the proposed model (LRDEA) to analyse the technical and scale efficiency of potato production in 23 Iranian provinces demonstrates the reliability and flexibility of the model.

Linear robust data envelopment analysis: CCR model with uncertain data

Data envelopment analysis (DEA) traditionally assumes that input and output data of the different decision making units (DMUs) are measured with precision. However, in many real applications inputs and outputs are often imprecise. This paper proposes a linear robust data envelopment analysis (LRDEA) model using imprecise data represented by an uncertainty set. The method is based on the robust optimisation approach of Bertsimas and Sim to seek maximisation of efficiency under uncertainty (as does the original DEA model). In this approach, it is possible to vary the degree of conservatism to allow for a decision maker to understand the tradeoff between a constraint's protection and its efficiency. The method incorporates the degree of conservatism in the maximum probability bound for constraint violation. Application of the proposed model (LRDEA) to analyse the technical and scale efficiency of potato production in 23 Iranian provinces demonstrates the reliability and flexibility of the model.

Efficiency improvement based upon overall value judgment and weight restriction

Purpose – The purpose of this paper is to consider the following problem: the authors consider a new constructed unit system to indicate the characteristics of the inputs and outputs of different decision-making units (DMUs) and propose several modified models to calculate their efficiencies based on overall value judgment and weight restriction in the production process. Design/methodology/approach – This paper applies principal component analysis (PCA) to analyze the original value judgment information, and the key indices in the production process are extracted. The modified data envelopment analysis (DEA) models are proposed and DEA efficiencies and their projections are calculated. Findings – By incorporate PCA and DEA, the authors propose new virtual DMUs composed of unique optimal multipliers of each DMU. Crucial indexes are extracted and the weights of inputs and output are ranked through using PCA by taking the preference and value judgments of all DMUs into consideration. Weight constraints from the ranking are utilized to improve the traditional CCR-DEA model. The empirical results validate the feasibility of the approach. Practical implications – The method can be used in many organizations which have excessive amounts of inputs and outputs variables, such as banks, chain stores, car factory, etc. Originality/value – This paper presents an integrated methodology of using PCA and DEA for considering the preferences of the inputs and outputs and value judgment of all DMUs and ranks the importance of the indicators from the overall perspectives.

Effectiveness of maritime safety control in different navigation zones using a spatial sequential DEA model: Yangtze River case

This paper aims to analyze the effectiveness of maritime safety control from the perspective of safety level along the Yangtze River with special considerations for navigational environments. The influencing variables of maritime safety are reviewed, including ship condition, maritime regulatory system, human reliability and navigational environment. Because the former three variables are generally assumed to be of the same level of safety, this paper focuses on studying the impact of navigational environments on the level of safety in different waterways. An improved data envelopment analysis (DEA) model is proposed by treating the navigational environment factors as inputs and ship accident data as outputs. Moreover, because the traditional DEA model cannot provide an overall ranking of different decision making units (DMUs), the spatial sequential frontiers and grey relational analysis are incorporated into the DEA model to facilitate a refined assessment. Based on the empirical study results, the proposed model is able to solve the problem of information missing in the prior models and evaluate the level of safety with a better accuracy. The results of the proposed DEA model are further compared with an evidential reasoning (ER) method, which has been widely used for level of safety evaluations. A sensitivity analysis is also conducted to better understand the relationship between the variation of navigational environments and level of safety. The sensitivity analysis shows that the level of safety varies in terms of traffic flow. It indicates that appropriate traffic control measures should be adopted for different waterways to improve their safety. This paper presents a practical method of conducting maritime level of safety assessments under dynamic navigational environment.

Slacks-Based Efficiency Measurements with Undesirable Outputs in Data Envelopment Analysis

Data envelopment analysis (DEA) has recently gained great popularity in modeling environmental performance because it provides condensed information to decision makers when the production process includes undesirable outputs. In this paper, we develop a new slacks-based efficiency measurement for modeling environmental performance using the environmental DEA technology. The proposed index has more theoretical justification, and distinguishes among different decision making units (DMUs) better in practice. Then we further extend it to the nonoriented index with double aim of increasing desirable outputs and reducing undesirable outputs. Finally, we calculate the index for each of 25 OECD European countries in a model of CO2emission performance from 2007 to 2009 and the results obtained are presented.

Estimation of potential energy saving and carbon dioxide emission reduction in China based on an extended non-radial DEA approach

In the process of setting operational targets to achieve sustainable development of economy, environment and natural resources, estimation of potential energy saving and potential CO2 emission reduction becomes extremely important. This estimation can be conducted based on the energy efficiency evaluation for different decision-making units (DMUs) by data envelopment analysis (DEA). Non-fossil energy is an important component of energy consumption in China, and it has great impacts on energy efficiency and energy-related carbon dioxide (CO2) emissions. This paper proposes a non-radial DEA model to evaluate regional energy efficiencies in China. In the proposed model, non-fossil energy is treated as a fixed input. Based on the model, a method of measuring potential energy saving and CO2 emission reduction for efficiency improvement is also presented. The proposed approaches are illustrated by using a regional dataset in China. Based on the application results, some implications for improving energy efficiency and reducing CO2 emissions in China are provided.

Some clarifications on the DEA clustering approach

This paper clarifies the role of alternative optimal solutions in the clustering of multidimensional observations using data envelopment analysis (DEA). The paper shows that alternative optimal solutions corresponding to several units produce different groups with different sizes and different decision making units (DMUs) at each class. This implies that a specific DMU may be grouped into different clusters when the corresponding DEA model has multiple optimal solutions.

NEW DEA PERFORMANCE EVALUATION INDICES AND THEIR APPLICATIONS IN THE AMERICAN FUND MARKET

The data envelopment analysis (DEA) method is a mathematical programming approach to evaluate the relative performance of portfolios. Considering that the risk input indicators of existing DEA performance evaluation indices cannot reflect the pervasive fat tails and asymmetry in return distributions of mutual funds, we originally introduce new risk measures CVaR and VaR into inputs of relevant DEA indices to measure relative performance of portfolios more objectively. To fairly evaluate the performance variation of the same fund during different time periods, we creatively treat them as different decision making units (DMUs). Different from available DEA applications which mainly investigate the American mutual fund performance from the whole market or industry aspect, we analyze in detail the effect of different input/output indicator combinations on the performance of individual funds. Our empirical results show that VaR and CVaR, especially their combinations with traditional risk measures, are very helpful for comprehensively describing return distribution properties such as skewness and leptokurtosis, and can thus better evaluate the overall performance of mutual funds.

The relative efficiency of decision-making units: a case study of TFT-LCD industry in Taiwan

The Thin-Film Transistors Liquid-Crystal Display (TFT-LCD) industry has played an important role for Taiwan in the worldwide LCD market share competition. This paper reports the study of the performance as well as the productivity changes of the TFT-LCD industry in Taiwan from 1999 to 2004. In this study, Data Envelopment Analysis (DEA), a technique for measuring relative efficiency of different Decision-Making Units (DMUs) with non-preset production function, is utilised to measure relative efficiency. The Malmquist Productivity Index (MPI), an extension technique of DEA, is used to measure the productivity changes of one DMU during different periods by different production functions. The results show that with the input of Taiwan's government support, the efficiency of the TFT-LCD industry in Taiwan is increasing through 1999?2004, and net operation income and scales are the key performance indicators of TFT-LCD industry.

The necessary and sufficient conditions for returns to scale properties in generalized data envelopment analysis model

We give definitions on increasing, constant and decreasing returns to scale under the generalized data envelopment analysis (GDEA) model. The GDEA model prossesses cone structures for describing evaluators’ preferences toward different decision making units (DMU) and toward different input / output categories. The GDEA model contains many important DEA models as its subclasses. Based upon the definition, we discuss and rigorously prove the necessary and sufficient conditions for a DMU to have increasing, constant and decreasing returns to scale under a GDEA model, and discuss and clarify the differences and relationships of these conditions under different subclasses of the GDEA model. Furthermore, we describe a method based on a two-stage linear program to test returns to scale properties.