Data Envelopment Analysis Theory Research Articles

Two-stage network data envelopment analysis production games

<abstract> <p>DEA (Data Envelopment Analysis) production games combine DEA theory with cooperation games and assess the benefits to production organizations with single-stage structure. However, in practical production problems, the production organizations are always with network structures. The structure of the production organization not only affects its own benefits, but also relates to the cooperation among organizations. Therefore, it is necessary to study DEA production games with network structures. In this paper, we consider the production organizations with two-stage processes, wherein the organizations are assumed to possess available resources and own technologies. The technology level of each organization is reflected by the observed units based on the network DEA (NDEA) production possibility set. Suppose that the organizations can cooperate through the ways of pooling the initial resources and (or) sharing the technology in each production process. According to the different cooperation styles of each stage in the alliance, seven types of cooperation among organizations are considered. The models of maximizing the revenues of coalitions, namely the NDEA production games, are established corresponding to the seven types, by which the maximal revenue for each coalition can be calculated. We prove that two-stage DEA production games have the super-additive property, and can be expressed as linear programming games. Hence, they are equivalent to the linear production games, and they are totally balanced. Therefore, the proposed cooperative games have a non-empty core, and hence have nucleolus, and the Owen set belongs to the core. In addition, based on the basic conceptions of the nucleolus and the Owen set, the revenue can be allocated among organizations in the alliance. Finally, a numerical example and an empirical application to 17 bank branches of the China Construction Bank in the Anhui Province are presented to illustrate the applicability of the proposed approach, and the relationship between the cooperative manners and the revenue allocation is reflected in analytical results.</p> </abstract>

FIRM VALUATION WITH DATA ENVELOPMENT ANALYSIS: BORSA IṠTANBUL EXAMPLE

Objective of this study is to present an example of firm valuation with Data Envelopment Analysis (DEA), which is an alternative and new firm valuation method, and to contribute this limited field of research area with new findings. With this objective in mind, after giving information about the theory of valuation, market-based valuation, DEA and methodology of firm valuation with DEA, BIST 100 indexed firms in Borsa Istanbul are valued with DEA in this study. Results shows that 69% of the estimated value ranges and 73% of the maximum values estimated cover the market values of the relevant firms. It can be said that this method, which is understood to have more successful estimation results in case the number of firms in peer groups increases, is a very useful method for testing the results obtained from other firm valuation methods.

A new efficiency evaluation approach with rough data: An application to Indian fertilizer

<p style='text-indent:20px;'>In the world of chaos, nothing is certain. In such an unpredictable world, measuring the efficiency of any individual is inevitable. In a conventional data envelopment analysis (DEA) model, exact input and output quantity data are needed to measure the relative efficiencies of homogeneous decision-making units (DMUs). However, in many real-world applications, the exact knowledge of data might not be available. The rough set theory allows for handling this type of situation. This paper tries to construct a rough DEA model by combining conventional DEA and rough set theory using optimistic and pessimistic <inline-formula><tex-math id="M1">\begin{document}$ \beta $\end{document}</tex-math></inline-formula> confidence values of rough variables, all of which help provide a way to quantify uncertainty. In the proposed method, the same set of constraints (production possibility sets) is employed to build a unified production frontier for all DMUs that can be used to properly assess each DMU's performance in the presence of rough input and output data. Besides, a ranking system is presented based on the approaches that have been proposed. In the presence of uncertain conditions, this article investigates the efficiency of the Indian fertilizer supply chain for over a decade. The results of the proposed models are compared to the existing DEA models, demonstrating how decision-makers can increase the supply chain performance of Indian fertilizer industries.</p>

Strategic Alliances for Sustainable Development: An Application of DEA and Grey Theory Models in the Coal Mining Sector

Sustainable development is a global trend and an economic priority for many governments. Although new energies can be considered good investments in green growth, they may lead to financial barriers to developing countries. The purpose of the study concentrates on an alternative solution that increases the efficiency performance of current fossil energy industries. The study has combined two models of Data Envelopment Analysis (DEA) and Grey Theory in determining inefficient units to propose potential strategic alliances for sustainable development in the Vietnam Coal industry. Besides considering inputs and outputs in the models, the location of coal mines is also a key indicator in recommending good alliances. The results show that the collaborations between the Cao Son coal mine and the Coc Sau coal mine, and between the Nui Beo coal mine and the Vang Danh coal mine, bring the best improvement for sustainable development. The study suggests detailed strategies in action that enterprises and policymakers can refer to, to apply in practice.

A new method based on finding the weak and strong defining supporting hyperplanes to recognize the anchor points

One of the main important issues in Data Envelopment Analysis (DEA) is to recognize the set of anchor points which is the subset of the extreme efficient points of the production possibility set (PPS). An anchor point is an extreme efficient point which is located on the intersection of the strong efficient frontier and the weak efficient frontier. In the other word, each anchor point delineate the strong efficient frontier from the weak efficient frontier. So, if a decision making unit (DMU) is an anchor point, then there is at least one supporting hyperplane whose the gradient vector has some of zero components, and so some input\output factor does not play any role in the performance of the unit under evaluation. The concept of anchor point was used in DEA for the generation of unobserved DMUs in order to extend the DEA efficient frontier and so, this concept plays a critical role in the DEA theory and its applications. Given the importance of the anchor pints in the DEA literature, this study focuses on finding the anchor points and presents a new method to search the anchor points of the PPS under the variable returns to scale (VRS) assumption. For this purpose, we use the definition of the anchor points and present an approach to find the anchor points of the PPS. The proposed method is based on finding the weak and strong defining supporting hyperplanes passing through the unit under evaluation. The main advantage of the proposed method is that it exactly uses the definition of the anchor points to provide the approach and it is very simple to use and the anchor points can be easily identified by solving two simple models. In addition, the proposed approach is such that in addition to determining the anchor points, it also finds two important defining supporting hyperplanes on the PPS, which can be used in many problems in DEA. The potentially of the proposed method is illustrated by some numerical examples, reported in the literature to compare the proposed method with the existing methods.

An algorithm for the anchor points of the PPS of the BCC model

Anchor points play an important role in data envelopment analysis theory and applications; they delineate the efficient part of the production possibility set (PPS) frontier.In this paper, we propose an approach for finding the anchor points of the PPS of the Banker, Charnes and Cooper (BCC) model. This approach is based on a variant of super-efficiency models and their duals. The necessary and sufficient conditions for the characterization of the anchor points are also provided.Finally, the applicability of the proposed model is illustrated with some numerical examples.

A Two-Stage Rough Data Envelopment Analysis and Its Application in Three-Level Supply Chain Performance Evaluation

The measure of efficiency for the supply chain is necessary to show productivity and how it uses its resources. One of the most important efficiency measurements is Data Envelopment Analysis (DEA). The traditional DEA model treats the decision-making units (DMUs) as a black box. It considers only the initial inputs and the final outputs. But the internal interactions between subsystems are neglected. This type of DEA is used for straightforward systems, but the complex multistage systems like supply chains, traditional DEA get inaccurate efficiency indicators. As well as, one of the main challenges is the uncertainty of data. The inputs and outputs values are usually required to be deterministic in traditional DEA. Although, this is not a case of real-life problems. Therefore, we develop a mixed innovative approach from Two-stage DEA and rough set theory to produce a modified Two-stage RDEA. The proposed model can measure the efficiency of DMUs comprehensively by considering the internal structure of any supply chain and treating with incomplete and imprecise data. We applied the Two-stage RDEA model in a three-level supply chain to show its applicability to measure the efficiency for both a whole supply chain and all levels comprehensively.

Water pollutant discharge permit allocation based on DEA and non-cooperative game theory

Against the background of the ecological civilization system reform in the new era, the appropriate allocation of water pollutant discharge permits is an important policy for controlling the amount of wastewater discharge. Traditional allocation methods have disadvantages, such as high additional costs, an unfair allocation scheme, and market distortion. In the present study, a fixed-cost allocation model based on data envelopment analysis (DEA) and the Nash non-cooperative game theory is employed to allocate water pollutant discharge permits of totally 31 provinces in China from 2008 to 2017. The allocation scheme considers environmental efficiency. The results demonstrate regional differences in the allocation of water pollutant discharge permits. The eastern region has abundant allocations. The northeastern and central regions have insufficient allocations. Besides, the western region has a significant shortage of allocations. It indicates the higher the utilization efficiency of the water pollutant discharge permits, the higher the region's sustainable development is. Based on the analysis, we propose guidelines for industrial wastewater discharge reduction.

A DEA integrated grey factor analysis approach for efficiency evaluation and ranking in uncertain systems

Efficiency evaluation and ranking in manufacturing systems involves complex and multiple input/output criteria. As a well-established non-statistical method for relative efficiency evaluation, data envelopment analysis (DEA) is questioned for the lack of discriminatory capability and the sensitivity to measurement error. Traditional multivariate statistical analysis used for multiple criteria performance evaluation has the prerequisite of underlying hypotheses and shows poor resolution facing up to insufficient amounts of sample data. We consider that the grey theory is a systematic analysis methodology that focuses on information insufficiency and model uncertainty. Thus, this study combines the advantages of DEA, factor analysis (FA), and grey theory to deal with the deficiencies. A DEA integrated grey factor analysis (GFA-DEA) efficiency evaluation and ranking model for uncertain systems is established. It is structured on the absolute degree of grey incidence (ADGI) matrix instead of the correlation matrix. Therefore, the underlying factors that explain a substantial proportion of the variance will be extracted, and the overall efficiency of all the identities will be evaluated and ranked. Furthermore, the model is employed to evaluate and rank the utilization efficiency of organizational quality infrastructure (QI) in 22 manufacturing enterprises in China, which is an important driver of business and operational performance improvement. According to Spearman rank correlation, the proposed method gives a higher correlation with super efficiency compared to other methods. The results indicate the adaptability of the GFA-DEA algorithm, which is able to offer a computationally easy and reliable result for small and uncertain data sets.

DEA game for internal cooperation between an upper-level process and multiple lower-level processes

Cooperation is an important strategy to improve companies’ profitability. As a data-driven tool for performance evaluation, data envelopment analysis (DEA) is often used to measure the benefits from cooperation between independent decision making units (DMUs) or systems, but few involve the internal cooperation in a network structure system. For a double-level system that consists of an upper- and multiple lower-level processes, prior to cooperation, its internal processes are independent and fail to yield profit. Once the upper-level process cooperates with at least one lower-level process, the system can operate to obtain profit. At present, no research explores the internal cooperation in a double-level system from the perspective of relative performance, considering such dependency between upper- and lower-level processes. To fill this gap, we propose a double-level DEA game by integrating network DEA and cooperative game theory, and prove this new game is monotone, super-additive, and has non-empty core. We use an example of 15 supply chains including one supplier and three retailers to validate our approach and provide an example as a real-life application. Results show the Shapley value and nucleolus have the best performance in allocating the total profit in terms of fairness and stability, respectively.

Using optimization algorithms of DEA and Grey system theory in strategic partner selection: An empirical study in Vietnam steel industry

In the current market economy, alliances play a key role in developing strategies across fields. In order to have a good partner, managers have used both qualitative and quantitative methodologies. This paper proposes a mathematical model to figure out the most suitable strategic partners. With input data from published financial reports, the authors use the data envelopment analysis (DEA) to evaluate the business efficiency of the steel companies in the period of 2011–2019. Then, Grey system theory is applied to predict their performance in the future period. The findings recommend the two leading steel manufactures but having ineffective performance, the Hoa Sen Group, and the Pomina Steel Corporation, as the most feasible beneficial partnership. Managers and the government can take advantages of the model in order to implement and have overall plans of steel enterprise in the future.

Sources of provincial carbon intensity reduction potential in China: A non-parametric fractional programming approach

With the increasing prominence of the global climate change, China's carbon intensity reduction has attracted considerable worldwide concern. This study proposes a fractional programming model to evaluate Chinese provincial carbon intensity reduction potential based on data envelopment analysis theory, which is superior to the common directional distance function approach in identifying global optimal solutions and improving the robustness of the estimation. To avoid the biased estimation, a meta-frontier is constructed according to the convergence of provincial carbon intensity, and then the overall potential is decomposed from the perspective of ineffective management, spatial technological gap and intertemporal technological gap. The results show that the carbon intensity of 30 Chinese provinces cannot converge to a common equilibrium and that 5 clubs that converge to different equilibria are clustered. Moreover, different clubs have diversified potentials for carbon intensity reduction, and spatial technological gaps contribute the most potential for clubs 3, 4 and 5. Even worse, the spatial technological gaps have not been significantly narrowed over time. This study provides not only a theoretical tool to investigate carbon intensity reduction potentials but also empirical evidence to guide China's carbon intensity reduction.

Bounded and discrete data in data envelopment analysis with assurance regions

PurposeThe purpose of this paper is to evaluate design performance of 51 gear shaping machines by using data envelopment analysis (DEA).Design/methodology/approachExisting studies extend traditional DEA by handling bounded and discrete data based on envelopment models. However, value judgment is usually neglected and fail to be incorporated in these envelopment models. In many cases, there is a need for prior preferences. Using existing DEA approaches as a backdrop, the current paper presents a methodology for incorporating assurance region (AR) restrictions into DEA with bounded and discrete data, i.e. the assurance region bounded discrete (AR-BD) DEA model. Then, the AR-BD DEA model is combined with a context-dependent DEA to obtain an efficiency stratification.FindingsThe authors examine different AR restrictions and calculate efficiency scores of five scenarios of AR restrictions by using the proposed AR-BD DEA model. It shows that AR restrictions have a great impact on the efficiency scores. The authors also identify nine efficient frontiers in total. For each decision-making unit, it could set benchmarks and improve its performance based on each higher efficient frontier.Originality/valueThis paper first evaluates efficiency of gear shaping machines by considering different (bounded and discrete) variable types of data and including AR restrictions. The AR-BD DEA model and context-dependent AR-BD DEA model proposed in this paper further enrich the DEA theory. The findings in this paper certainly provide useful information for both producers and consumers to make smart decisions.

Using optimization algorithms of DEA and Grey system theory in strategic partner selection: An empirical study in Vietnam steel industry

In the current market economy, alliances play a key role in developing strategies across fields. In order to have a good partner, managers have used both qualitative and quantitative methodologies. This paper proposes a mathematical model to figure out the most suitable strategic partners. With input data from published financial reports, the authors use the data envelopment analysis (DEA) to evaluate the business efficiency of the steel companies in the period of 2011–2019. Then, Grey system theory is applied to predict their performance in the future period. The findings recommend the two leading steel manufactures but having ineffective performance, the Hoa Sen Group, and the Pomina Steel Corporation, as the most feasible beneficial partnership. Managers and the government can take advantages of the model in order to implement and have overall plans of steel enterprise in the future.

How public environmental concern affects the sustainable development of Chinese cities: An empirical study using extended DEA models

China is now facing the formidable tasks of saving energy and reducing emissions, so it is very important to analyze China's energy and environmental efficiency. However, previous studies have rarely paid attention to the cross-impacts that different forms of public environmental concern (PEC) have simultaneously on energy and environmental efficiency. To investigate how these two types of efficiency change along with PEC variations, this paper employs six extended programming models which are developed based upon the theory of Data Envelopment Analysis (DEA) and the directional distance function (DDF). An empirical analysis of data from 239 Chinese prefecture-level cities demonstrates the techniques. The empirical results show that PEC variations can significantly affect the environmental efficiency only if the city is experiencing unsustainable development. This work also shows that PEC about input resources may exaggerate the environmental efficiency, implying that the public may be more tolerant of resource over-consumption than of pollutant over-emission.

An efficiency analysis of food distribution system through data envelopment analysis

The specific quality and safety requirements, typical of the food supply chain, force to strong action on implementing distribution networks, reducing transport and delivery costs, improving distribution efficiency and performance, increasing carriers control and flexibility. In this context, the selection and evaluation of third-party logistics has become a crucial aspect in order to realise an efficient food products distribution, with both a high level of service and competitive costs. This paper implements data envelopment analysis theory to analyse the case of an Italian food producer, which distributes its products on the national territory, through several third-party logistic carriers. This study made possible to define the most efficient carrier among those responsible for the distribution process, analysing the retail trade and large-scale retail trade. This paper represents a reference guideline to all the food companies involved in the process of evaluation and improvement of the distribution process.

Revealing potential of energy-saving behind emission reduction

PurposeThe purpose of this paper is to generate quantitative managerial insights for the improvement of the energy-saving potential and the coordinated development between economic growth and environmental protection.Design/methodology/approachA novel data envelopment analysis (DEA) model, based on the classical DEA theory, is developed from the perspective of emission reduction.FindingsThe empirical results indicate that China’s overall environmental efficiency is low and that there is huge improvement space for energy saving. Under the concerns of emission reduction, the energy-saving potential of the central region exceeds that of both the eastern and western regions. With regard to water, electricity and gas consumption, the electricity-saving potential exceeds the potential for both water saving and gas saving.Originality/valuePrevious studies rarely focused on the energy-saving potential, while considering environmental pollution. This paper applies a novel DEA method to evaluate the energy-saving potential of 30 Chinese provinces for 2015 with a focus on emission reduction concerns. Furthermore, both regional differences and energy type differences of the saving potential were analyzed.

A DEA model to evaluate Brazilian container terminals

This study aims to evaluate the main Brazilian port terminals specialized in the operation of containers between the years 2010 and 2014. Therefore, it was applied Data Envelopment Analysis (DEA) and some of its complementary models, represented by the Cross Evaluation, in order to implement a peer-evaluation and improve the discrimination of the 100% efficient terminal; and a current model known as DEA-Game Cross Efficiency that combines DEA and Game Theory. This article proposes an adaptation to the original model, since it considers a radial output orientation, regarded as more compatible with the problem under analysis. DEA-Game was applied for the first time in port performance measurement and it was shown more suitable than the others, since the Decision Making Units (DMU) are seen from the perspective of a non-cooperative game and the results proved to be a Nash equilibrium.

Common weights in dynamic network DEA with goal programming approach for performance assessment of insurance companies in Iran

PurposeConventional data envelopment analysis (DEA) models permit each decision-making unit (DMU) to assess its efficiency score with the most favorable weights. In other words, each DMU selects the best weighting schemes to obtain maximum efficiency for itself. Therefore, using different sets of weights leads to many different efficient DMUs, which makes comparing and ranking them on a similar basis impossible. Another issue is that often more than one DMU is evaluated as efficient because the selection of weights is flexible; therefore, all DMUs cannot be completely differentiated. The purpose of this paper is to development a common weight in dynamic network DEA with a goal programming approach.Design/methodology/approachIn this paper, a goal programming approach has been proposed to generate common weights in dynamic network DEA. To validate the applicability of the proposed model, the data of 30 non-life insurance companies in Iran during 2013-2015 have been used for measuring their efficiency scores and ranking all of the companies.FindingsFindings show that the proposed methodology is an effective and practical approach to measure the efficiency of DMUs with dynamic network structure.Originality/valueThe proposed model delivers more knowledge of the common weight approaches and improves the DEA theory and methodology. This model makes it possible to measure efficiency scores and compare all DMUs from multiple different standpoints. Further, this model allows one to not only calculate the overall efficiency of DMUs throughout the time period but also consider dynamic change of the time period efficiency and dynamic change of the divisional efficiency of DMUs.

Research on PM2.5 emission reduction path of China ‘s electric power industry based on DEA model

Based on the theory of data envelopment analysis, this study constructs the environmental performance evaluation model of the power industry, analyzes the performance of development of clean energy, the implementation of electricity replacement, and the development of coal-fired energy-saving and emission-reducing measures. Put forward technology path to reduce emission in the future. The results show that (1) improving the proportion of coal for power generation, speeding up the replacement of electricity is the key to solve the haze in China. (2) With the photovoltaic and other new energy power generation costs gradually reduced and less limit from thermal energy, by final of “thirteenth five-years plan”, the economy of clean energy will surpass thermal energy-saving emission reduction. (3) After 2025, the economy of the electricity replacement will be able to show.