Additive Data Envelopment Analysis Research Articles

Additive Integer-Valued DEA Models With Fuzzy Undesirable Outputs: Closest Benchmarking Targets and Super-Efficiency

Many production activities generate undesirable outputs apart from desirable outputs. In addition, the data related to undesirable outputs may be fuzzy (imprecise) in some cases. Based on the fuzzy data theory, we propose a group of additive integer-valued data envelopment analysis (DEA) models with fuzzy undesirable outputs. The advantages of the proposed models are as follows: (1) they enable decision-makers to evaluate the efficiency of decision making units (DMUs) with integer-valued variables and fuzzy undesirable outputs; (2) they can be easily solved without any transformation because they are linear programming models; (3) they are better than radial DEA models as they can identify inefficiencies in all the selected inputs and outputs. Particularly, minimum distance-based additive integer-valued DEA models with fuzzy undesirable outputs are developed in this paper to find the closest benchmarking targets for inefficient DMUs, and additive super-efficiency integer-valued DEA models with fuzzy undesirable outputs are presented to differentiate and rank efficient DMUs. The validity of the proposed models is examined by an empirical application in the pallet rental industry.

A common-weights approach for efficiency evaluation in fuzzy data envelopment analysis with undesirable outputs: Application in banking industry

Data Envelopment Analysis (DEA) is a non-parametric approach based on linear programming for evaluating the performance of decision making units (DMUs) with multiple inputs and multiple outputs. The lack of the ability to generate the actual weights, not considering the impact of undesirable outputs in the evaluation process and the measuring of efficiencies of DMUs based upon precise observations are three main drawbacks of the conventional DEA models. This paper proposes a novel approach for finding the common set of weights (CSW) to compute efficiencies in DEA model with undesirable outputs when the data are represented by fuzzy numbers. The proposed approach is based on fuzzy arithmetic which formulates the fuzzy additive DEA model as a linear programing problem and gives fuzzy efficiencies of all DMUs based on resulting CSW. We demonstrate the applicability of the proposed model with a simple numerical example. Finally, in the context of performance management, an application of banking industry in Iran is presented for analyzing the influence of fuzzy data and depicting the impact of undesirable outputs over the efficiency results.

Evaluation of Iranian electronic products manufacturing industries using an unsupervised model, ARAS, SAW, and DEA models

Iranian electronic products supplier industries are developing day by day and modern techniques and facilities are assigning as well as many promotions about green products supply chain as input materials introduced into the generation cycle of industries. Current cluster study of Iranian Electronic Products Manufacturing Industries (IEPMI) comprised a technical and hierarchical evaluation carried out as the objective of current research. It was used SPSS and Excel Software to classify and analysis about 33 IEPMI via an unsupervised model, Additive Ratio Assessment (ARAS), Simple Additive Weighting (SAW) and Data Envelopment Analysis (DEA) models. Finally, a hierarchical cluster classification has developed for the 33 industries pertaining to 5 main criteria as well as the total inventory of input, output materials and facilities employed. It was found that the ranking systems based on ARAS and SAW presented the same results for IEPMI. DEA model was also classified IEPMI in terms of efficiency score.

A unified extension of super-efficiency in additive data envelopment analysis with integer-valued inputs and outputs: an application to a municipal bus system

Conventional data envelopment analysis (DEA) may generate the non-integer targets for integer-valued inputs and outputs of decision-making units (DMUs). To derive the convincing projections, integer-valued DEA has attracted much attention. Given the integrality restriction, Du et al. (Eur J Oper Res 218(1):186–192, 2012) proposed the super-efficiency approach consisting of additive integer-valued and additive super-efficiency integer-valued models for the differentiation of efficient DMUs, thereby raising the discriminatory power. This paper extends their approach to develop a simpler but stricter version, which we refer to as the unified additive super-efficiency model. The newly-developed model has three advantages. First, the slacks of input excess, input saving, output shortage and output surplus can be directly computed in a single program to obtain the efficiencies of inefficient DMUs and super-efficiencies of efficient DMUs. Secondly, it suggests the strongly Pareto-efficient projections for efficient DMUs. Finally, the identified super-efficiencies allow for the property of continuity. A comparison of the proposed model, with Du et al.’s (2012) and standard additive super-efficiency approaches is discussed using a numerical example. In addition, the applicability of the proposed model is illustrated by a data set covering 13 bus companies operating in the municipal bus system of Taichung. Our work not only provides managerial insights into the primary sources of inefficiency and super-efficiency but also contributes to the current understanding of how super-efficiency would be effectively and accurately measured in the presence of integer-valued data.

Efficiency evaluation and ranking of supply chains based on stochastic multicriteria acceptability analysis and data envelopment analysis

AbstractEvaluating performance of supply chains has been an important topic in supply chain management for researchers and practitioners. In this study, we integrate stochastic multicriteria acceptability analysis (SMAA) technique and data envelopment analysis (DEA) methodology and propose a model, named “two‐stage SMAA‐DEA,” for efficiency evaluation and ranking of two‐stage supply chains (e.g., supplier–manufacturer) with stochastic criteria values. Two stochastic efficiency measures are defined for supply chain efficiency evaluation in the model. The maximum efficiency is the best efficiency score based on the optimistic criterion. The average efficiency is the expected efficiency score based on the average criterion. In addition, the model provides rank acceptability and holistic acceptability index for the supply chain ranking. The developed two‐stage SMAA‐DEA model has several advantages. First, it extends two‐stage DEA models to handle uncertain or imprecise inputs, intermediate measures, and outputs using stochastic distributions. Second, it allows for variable process weights and does not need any prior preference information on processes. Our study extends network DEA to address uncertain or stochastic measures, and the model can be considered as a multicriteria decision‐making method with a two‐stage additive DEA value function. An empirical study evaluating 27 supply chains is presented to illustrate the proposed models.

Benchmarking and Performance Evaluation Towards the Sustainable Development of Regions in Taiwan: A Minimum Distance-Based Measure with Undesirable Outputs in Additive DEA

Sustainable development (SD) governance for a better society has received considerable attention. The development of a robust benchmarking and performance evaluation approach is a matter of growing concern to accelerate the progress in achieving SD. In this study, a minimum distance-based additive data envelopment analysis model with window analysis is proposed to attain the closest benchmarking target in the presence of undesirable outputs. This novel extension not only focuses on the construction of a composite indicator to shed light on the efficiency of each decision-making unit but also provides convincing and realizable suggestions for improving efficiency. This study benchmarks the SD efficiency across 19 administrative regions of Taiwan covering the period from 2011 to 2016. The empirical results reveal that the average SD efficiency of Taiwan has experienced a gradual deterioration over the last 3 years, and the primary sources of regional SD inefficiency may vary with industrial structure. Potential directions of improvement for reinforcing sustainable practices in Taiwan are also discussed. The findings can provide local governments with holistic insights into the sources that degrade SD performance and further contribute to improving SD solutions by recommending appropriate policies to achieve a more sustainable society.

Two-stage additive integer-valued data envelopment analysis models

PurposeThe purpose of this paper is to propose a modified model in multi-stage processes when there are intermediate measures between the stages and in this sense, the new efficiency scores are more accurate. Conventional data envelopment analysis (DEA) models disregard the internal structures of peer decision-making units (DMUs) in evaluating their relative efficiency. Such an approach would cause managers to lose important DMU information. Therefore, in multistage processes, traditional DEA models encounter problems when intermediate measures are used for efficiency evaluation.Design/methodology/approachIn this study, two-stage additive integer-valued DEA models were proposed. Three models were proposed for measuring inefficiency slacks in each stage and in the system as a whole.FindingsThree models were proposed for measuring inefficiency slacks in each stage and in the system as a whole.Originality/valueThe advantage of the proposed models for multi-stage systems is that they can accurately determine the stages with the greatest weaknesses/strengths. By introducing an applied case in the Iranian power industry, the paper demonstrated the applications and advantages of the proposed models.

Additive slacks-based measure: Computational strategy and extension to network DEA

The current paper visits a set of data envelopment analysis (DEA) models that identify inefficiency by optimizing input and output slacks. These slacks are aggregated either in an additive or ratio form. Only the ratio slacks-based DEA models can be solved as a linear program and generate a DEA score between zero and unity. The additive slacks-based model can be equivalent to the Russell graph measure and converted into a second order cone programming (SOCP) problem whose solving procedure has become a mature technology. As such, the additive slacks-based model can also yield a DEA score between zero and unity. This study shows that the additive slacks-based model can be applied to modelling network DEA where the internal structures of decision making units (DMUs) are of interest. The additive slacks-based network DEA can be solved using SOCP technique and adapted to the preference of the decision maker by choosing the weights for aggregating individual components in the network structures. It is shown that the additive slacks-based approach can yield divisional efficiencies of Pareto optimal equivalences to be selected by the decision maker when compared to the existing ratio slacks-based measure. An example and solving codes are provided in the current study.

Sustainability Assessment of Taiwan’s Semiconductor Industry: A New Hybrid Model Using Combined Analytic Hierarchy Process and Two-Stage Additive Network Data Envelopment Analysis

Sustainable development has become the biggest concern of the semiconductor industry, which plays a vital role not only in technology breakthroughs, but also by serving as an enabler for sustainability. This study combines Analytic Hierarchy Process (AHP) and additive network Data Envelopment Analysis (DEA) to measure the sustainable performance which are derived from business growth stage and energy utilization stage through the parametric linear program. Meanwhile, this method makes up the disadvantage of the weighting technique used additive decomposition approach to the two-stage network and avoids biasing toward the second stage. The findings demonstrate that Taiwan’s semiconductor manufacturing sector has exhibited a steady increase in its overall trend of sustainability performance. According to the stage-level performance results, the performance of business growth is better than energy utilization. However, the changing trend of overall sustainability performance is through a steady increase from environmental efficiency and not from economic efficiency.

Multi-period additive efficiency measurement in data envelopment analysis with non-positive and undesirable data

The conventional data envelopment analysis (DEA) models make an assumption of non-negativity in the inputs and outputs data of the decision making units (DMUs) under analysis. In this paper, we present a non-radial measure of efficiency of DMUs by establishing a multi-period additive DEA model taking into consideration both desirable and undesirable inputs and outputs with positive and non-positive values. The proposed efficiency model possesses the requisite features of translation invariance and unit independence, obligatory when dealing with negative values in the data set. Furthermore, this paper contributes with the proposal of a multi-period additive super-efficiency DEA model to discriminate the performance of efficient decision making units. Finally, we present an efficiency evaluation 37 countries worldwide on economic parameters to demonstrate the applicability and efficacy of the proposed models.

Multistage network data envelopment analysis: Semidefinite programming approach

Additive efficiency aggregation is one of the important techniques measuring the relative efficiency of decision-making units under network data envelopment analysis (DEA). However, the modelling of additive network DEA is limited to parametric methods to approximate optimal solutions in previous literature. Under multistage network structure, if some outputs leave the system from a given stage while others become inputs to the next stage and some new inputs enter at any stage, the additive network models become extremely nonlinear and are impossible to be solved by linear program. The current paper proposes to solve general additive two-stage models by using semidefinite programming, which is known as effective as linear program. We then extend the methodology to general multistage network structures (including serial processes, parallel processes, multistage processes with non-immediate successor flows, and multistage processes with feedbacks). A numerical data set and the case of regional R&D processes in China are revisited by using the newly developed approach.

Efficiency evaluation of parallel interdependent processes systems: an application to Chinese 985 Project universities

Data envelopment analysis (DEA) has been widely applied in measuring the efficiency of homogeneous decision-making units. Network DEA, as an important branch of DEA, was built to examine the internal structure of a system, whereas traditional DEA models regard a system as a ‘black box’. However, only a few previous studies on parallel systems have considered the interdependent relationship between system components. In recent years, parallel interdependent processes systems commonly exist in production systems because of serious competition among organisations. Thus, an approach to measure the efficiency of such systems should be proposed. This paper builds an additive DEA model to measure a parallel interdependent processes system with two components which have an interdependent relationship. Then, the model is applied to analyse the ‘985 Project’ universities in China, and certain policy implications are explained.

Efficiency measures of the Chinese biogas project subsidy policy using an additive two stage DEA

In this study, based on the perspective of effectiveness, the entire process of the biogas project is divided into two sub-processes (biogas production and biogas consumption). We utilize the additive two-stage Data Envelopment Analysis to evaluate the efficiency of biogas project subsidy policy. Our finding indicates that from the perspective of input-output efficiency, the efficiency of biogas project subsidy policy is low in China. There are two main reasons for this result: the subsidy is inadequate and its purpose deviates from the actual demand. First, because the subsidy is inadequate and the construction cost of the rural biogas project is high, farmers are unable to build rural household biogas digesters by raising funds themselves. Second, the biogas project subsidy policy only stimulates the increase in biogas production through increasing the construction of large and middle scale biogas projects. But the construction of a household biogas digester is ignored. Furthermore, macro-affecting factors have a significant influence on the implementation of biogas project subsidy policy. When formulating new biogas project subsidy policy, the government should consider the influence of urbanization, per capita annual income, and international oil price fluctuations. The above analysis could provide theoretical guidance for the government to formulate new biogas project subsidy policy.

Hierarchical network systems: An application to high-technology industry in China

In real world situations, there is a hierarchical structure exists in a specific organization and each component has its network process. However, such hierarchical network system has not been well studied in previous literature, and misleading results often are produced. The current paper discusses a data envelopment analysis (DEA) modelling technique for a network structure where a hierarchical system consists of components having two-stage series processes. An additive network DEA is proposed to evaluate the performance of this type of network structure. The overall and divisional efficiencies of the system and each component can be derived, and the relationship between system efficiency, divisional efficiency and the ones of components is discussed. The newly developed additive network DEA is nonlinear and cannot be converted into a linear program. A semidefinite programming (SDP) approach is developed for effectively solving this model and the global solution can be guaranteed. Another linear multiplicative network DEA also developed for this hierarchical system. The two newly developed models are illustrated with a case of the performance evaluation of high-technology industry in China.

A DEA‐based method of allocating the fixed cost as a complement to the original input

AbstractThis paper focuses on the problem of how to divide a fixed cost as a complement to an original input among decision‐making units (DMUs) equitably. Using the data envelopment analysis (DEA) technique, this paper concerns the problem from the perspective of efficiency analysis. It is found that not all DMUs can become efficient under common weights if a low enough fixed cost is assigned. Therefore, the global modified additive DEA (MAD) model is introduced. By optimizing the global MAD‐efficiency, a new allocation method and the corresponding algorithm to ensure the uniqueness of the allocation result is designed. The proposed method can be used under both constant returns to scale and variable returns to scale for nonnegative data; it is suitable for the situation where the costs play a great role in the production of DMUs. Numerical results show the validity and advantages of our method.

Dynamic network data envelopment analysis based upon technology changes

ABSTRACTThe existing dynamic models assume the technology is unchanged in which the same factor should have the same multiplier, no matter which process it is associated with. The internal network structures embedded in a multi-period system are ignored in the literature. The current paper considers that the technology is changed in the dynamic system The same factor may have different multipliers in different periods, except for the variables of intermediate measures connecting two stages in one period and flows connecting two consecutive periods. An additive aggregation dynamic network data envelopment analysis is developed to measure the multi-period systems with a two-stage process embedded in each period. The system efficiency, overall efficiency and stage efficiencies of each period can be derived, and the relationship between the system efficiency and period efficiencies can be identified. The newly developed dynamic network model is nonlinear, and can be transformed to a semi-definite programming problem. A case of high-tech industry in China is illustrated to the approach.

Eco-efficiency measurement and improvement of Chinese industry using a new closest target method

PurposeThe purpose of this paper is to measure Chinese industries’ eco-efficiency during 2006-2013. The Chinese industry attained rapid achievement in recent decades, but meanwhile, overconsumption of energy and environmental pollution have become serious problems. To solve these problems, many research studies used the data envelopment analysis (DEA) to measure the Chinese industry’s eco-efficiency. However, because the target set by these works is usually the furthest one for a province to be efficient, it may hardly be accepted by any province.Design/methodology/approachThis paper builds a new “closest target method” based on an additive DEA model considering the undesirable outputs. This method is a mixed-integer programming problem which can measure the ecological efficiency of provinces and more importantly guide the province to perform efficiently with minimum effort.FindingsThe results show that the eco-efficiency of Chinese provinces increased at the average level, but the deviations remained at a larger value. Compared to the “furthest” target methods, the targets by the approach proposed by this study are more acceptable for a province to improve its performance on both economy and environment counts.Originality/valueThis study is the first attempt to introduce the closest targets concept to measure the eco-efficiency and set the target for each provincial industry in China.

Evaluating operation and coordination efficiencies of parallel-series two-stage system: A data envelopment analysis approach

Abstract Our motivation of this study is to provide a data envelopment analysis (DEA) approach for evaluating and decomposing the operation efficiency, moreover, computing the coordination efficiency of systems with complex internal structure. We consider a two-stage system composed of three sub-systems, where the first stage is comprised of two independent sub-systems in parallel and then linked to the second stage or the third sub-system in series. Additive and multiplicative DEA efficiency measures are proposed to be jointly applied to illustrate the efficiency formation mechanism of the parallel-series system. The definition of coordination efficiency is inspired by the “gap” between accomplished optimal efficiency and idealized maximal efficiency of relevant systems. This study contributes in creating novel means to consider the different structural characteristics in the efficiency assessment of complex network systems, and to measure the externalities in terms of efficiency within their interior. The proposed models are demonstrated by revisiting the case of Taiwanese non-life insurance companies studied by Kao and Hwang. Corresponding implications of the empirical application are also discussed.

Comparison of the multicriteria decision-making methods for equity portfolio selection: The U.S. evidence

This paper compares the efficacy of four multicriteria decision-making (MCDM) methods in identifying the future best-performing stocks in two comprehensive samples of U.S. stocks. This is the first time that median-scaling (MS), the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), the Analytic Hierarchy Process (AHP), and the additive Data Envelopment Analysis (add.DEA) have been used to combine value and momentum indicators into a single efficiency score. The results show that the MCDM methods examined can successfully be applied to equity portfolio selection. As a robustness check, we repeat all the main sample tests for the sample of the largest-cap stocks included in the two biggest size quintiles (i.e., stocks above 40% NYSE market-cap breakpoint) and find that the overall results are surprisingly robust to size effect. However, the best-performing portfolios formed on the basis of different MCDM methods have remarkably different exposures to the style factors that are commonly used to explain the abnormal returns of active equity portfolios. As a practical implication of this study, investors following certain investing styles could take these different style exposures into account when choosing the MCDM criteria that best fit their portfolio-selection purposes.

Equivalent solutions to additive two-stage network data envelopment analysis

In the additive approach of two-stage network data envelopment analysis (DEA), the non-linear DEA model is transformed into a parametric linear model and then solved by computing a series of linear programs. Lim and Zhu (2013; Integrated data envelopment analysis: Global vs. local optimum.European Journal of Operational Research, 229(1), 276–278) and Ang and Chen (2016; Pitfalls of decomposition weights in the additive multi-stage DEA model. Omega, 58, 139–153) propose two parametric linear approaches to solve additive two-stage network DEA model. The current study shows that the two approaches are equivalent and use the same parameter in searching for the global optimal solution.