Chance-constrained data envelopment analysis modeling with random-rough data

2018 ◽  
Vol 52 (1) ◽  
pp. 259-284 ◽  
Author(s):  
Rashed Khanjani Shiraz ◽  
Madjid Tavana ◽  
Debora Di Caprio
Keyword(s):  
Data Envelopment Analysis ◽  
Deterministic Model ◽  
Equivalent Model ◽  
Management Tool ◽  
Data Envelopment ◽  
Output Data ◽  
Quadratic Constraints ◽  
Dea Model ◽  
Deterministic Equivalent ◽  
Input And Output

Data envelopment analysis (DEA) is a useful management tool for measuring the relative efficiency of decision making units (DMUs) which consumes multiple inputs to produce multiple outputs. Although precise input and output data are fundamentally indispensable in classical DEA models, real-world problems often involve random and/or rough input and output data. We present a chance-constrained DEA model with random and rough (random-rough) input and output data and propose a deterministic equivalent model with quadratic constraints to solve the model. The main contributions of this paper are fourfold: (3.1) we propose a DEA model for problems characterized by random-rough variables; (3.2) we transform the proposed chance-constrained model with random-rough variables into a deterministic equivalent non-linear form that could be simplified as a deterministic model with quadratic constraints; (3.3) we perform sensitivity analysis to investigate the stability and robustness of the proposed model; and (3.4) we use a numerical example to demonstrate the feasibility and richness of the obtained solutions.

A New Method for Solving Dual DEA Problems with Fuzzy Stochastic Data

2019 ◽  
Vol 18 (01) ◽  
pp. 147-170 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Madjid Tavana ◽  
Seyed Hadi Nasseri ◽  
Omid Gholami
Keyword(s):  
Real Life ◽  
Equivalent Model ◽  
Random Input ◽  
Output Data ◽  
Programming Technique ◽  
Dea Model ◽  
Deterministic Equivalent ◽  
Input And Output ◽  
Stochastic Dea ◽  
Dea Models

Data envelopment analysis (DEA) is a widely used mathematical programming technique for measuring the relative efficiency of decision-making units which consume multiple inputs to produce multiple outputs. Although precise input and output data are fundamentally used in classical DEA models, real-life problems often involve uncertainties characterized by fuzzy and/or random input and output data. We present a new input-oriented dual DEA model with fuzzy and random input and output data and propose a deterministic equivalent model with linear constraints to solve the model. The main contributions of this paper are fourfold: (1) we extend the concept of a normal distribution for fuzzy stochastic variables and propose a DEA model for problems characterized by fuzzy stochastic variables; (2) we transform the proposed DEA model with fuzzy stochastic variables into a deterministic equivalent linear form; (3) the proposed model which is linear and always feasible can overcome the nonlinearity and infeasibility in the existing fuzzy stochastic DEA models; (4) we present a case study in the banking industry to exhibit the applicability of the proposed method and feasibility of the obtained solutions.

scholarly journals Data Envelopment Analysis with Uncertain Inputs and Outputs

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Meilin Wen ◽  
Linhan Guo ◽  
Rui Kang ◽  
Yi Yang
Keyword(s):  
Data Envelopment Analysis ◽  
Deterministic Model ◽  
The Other ◽  
Data Envelopment ◽  
Decision Tool ◽  
Uncertain Measure ◽  
Dea Model ◽  
Dea Models ◽  
The One ◽  
Inputs And Outputs

Data envelopment analysis (DEA), as a useful management and decision tool, has been widely used since it was first invented by Charnes et al. in 1978. On the one hand, the DEA models need accurate inputs and outputs data. On the other hand, in many situations, inputs and outputs are volatile and complex so that they are difficult to measure in an accurate way. The conflict leads to the researches of uncertain DEA models. This paper will consider DEA in uncertain environment, thus producing a new model based on uncertain measure. Due to the complexity of the new uncertain DEA model, an equivalent deterministic model is presented. Finally, a numerical example is presented to illustrate the effectiveness of the uncertain DEA model.

scholarly journals A FUZZY DATA ENVELOPMENT ANALYSIS FOR CLUSTERING OPERATING UNITS WITH IMPRECISE DATA

2013 ◽  
Vol 21 (01) ◽  
pp. 29-54 ◽  
Author(s):  
SABER SAATI ◽  
ADEL HATAMI-MARBINI ◽  
MADJID TAVANA ◽  
PER J. AGRELL
Keyword(s):  
Data Envelopment Analysis ◽  
Parametric Method ◽  
Data Envelopment ◽  
Output Data ◽  
Fuzzy Environment ◽  
Input And Output ◽  
Fuzzy Data Envelopment Analysis ◽  
Human Decision ◽  
Fuzzy Dea ◽  
Operating Units

Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiency of peer operating units that employ multiple inputs to produce multiple outputs. Several DEA methods have been proposed for clustering operating units. However, to the best of our knowledge, the existing methods in the literature do not simultaneously consider the priority between the clusters (classes) and the priority between the operating units in each cluster. Moreover, while crisp input and output data are indispensable in traditional DEA, real-world production processes may involve imprecise or ambiguous input and output data. Fuzzy set theory has been widely used to formalize and represent the impreciseness and ambiguity inherent in human decision-making. In this paper, we propose a new fuzzy DEA method for clustering operating units in a fuzzy environment by considering the priority between the clusters and the priority between the operating units in each cluster simultaneously. A numerical example and a case study for the Jet Ski purchasing decision by the Florida Border Patrol are presented to illustrate the efficacy and the applicability of the proposed method.

scholarly journals Efficiency of the Slovak forestry in comparison to other European countries: An application of Data Envelopment Analysis

2018 ◽  
Vol 64 (1) ◽  
pp. 46-54 ◽  
Author(s):  
Miroslav Kovalčík
Keyword(s):  
Data Envelopment Analysis ◽  
European Countries ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Efficiency Improvement ◽  
Parametric Approach ◽  
Output Data ◽  
Average Efficiency ◽  
Input And Output ◽  
Forestry Sector

AbstractEfficiency improvement is important for increasing the competitiveness of any sector and the same is essential for the forestry sector. A non-parametric approach – Data Envelopment Analysis (DEA) was used for the assessment of forestry efficiency. The paper presents the results of the efficiency evaluation of forestry in European countries using DEA. One basic and two modified models (labourandwood sale) were proposed, based on available input and output data from Integrated Environmental and Economic Accounts for Forests and specific conditions of forestry also. The sample size was 22 countries and the data for 2005–2008 was processed. Obtained results show average efficiency in the range of 69 – 90% (depending on the model). Based on the results of the analysis following can be concluded: Slovak forestry achieved under average efficiency in comparison to other European countries, there were great differences in efficiency among individual countries; state of economy (advanced countries and countries with economy in transition) and region did not influence the efficiency statistically significant.

Generalized Fuzzy Sample DEA Model and its Application in the Evaluation of Projects

2011 ◽  
Vol 63-64 ◽  
pp. 407-411
Author(s):  
Ren Mu ◽  
Zhan Xin Ma ◽  
Wei Cui ◽  
Yun Morigen Wu
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Data Envelopment Analysis Model ◽  
Data Envelopment ◽  
Input Output ◽  
Output Data ◽  
Dea Model ◽  
Decision Making Unit ◽  
Fuzzy Input ◽  
Fuzzy Dea

Evaluating the performance of activities or organizations by traditional data envelopment analysis model requires crisp input/output data. However, in real-world problems inputs and outputs are often with some fuzziness. To evaluate DMU with fuzzy input/output data, researchers provided fuzzy data envelopment analysis (FDEA) model and proposed related evaluating method. But up to now, we still cannot evaluate a fuzzy sample decision making unit (SDMU) for FDEA model. So this paper proposes a generalized fuzzy DEA model which can evaluate a sample decision making unit and a numerical experiment is used to illustrate this model.

scholarly journals Dual frontiers data envelopment analysis: multiple ranking approaches from optimistic and pessimistic perspectives

2021 ◽  
Author(s):  
Abdullah Maraee Aldamak
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Efficiency Score ◽  
The Body ◽  
Data Envelopment ◽  
Free Disposal Hull ◽  
Dea Model ◽  
Ranking Models ◽  
Input And Output ◽  
Dea Models

The field of data envelopment analysis (DEA) has evolved rapidly since its introduction to decision-making science 40 years ago. DEA has since attracted the attention of many researchers because of its unique characteristic to measure the efficiency of multiple-input and multiple-output decision-making units (DMUs) without assigning prior weight to the input and output, unlike most available decision analysis tools. The body of research has resulted in a huge amount of literature and diverse DEA models with very many different approaches. DEA classifies all units under assessment into two groups: efficient with a 100% efficiency score and inefficient with a less than 100% efficiency score. This ability is considered both a strength and a weakness of the standard DEA model because, although it allows DEA to evaluate the efficiency of any dataset, it lacks the power to rank all DMUs, by giving full efficiency scores to many efficient units. This issue has attracted many researchers to investigate the weak discrimination power of classical DEA models, resulting in a subfield of research that focuses on DEA ranking. This thesis focuses on the development of the conventional DEA model, and an attempt has been made to study models that are considered as improved models, or approaches that bring a better ranking field, that may bring more accurate evaluation than the original DEA. After studying DEA ranking models, the thesis presents various models under the optimistic and pessimistic DEA ranking approaches. The first and fundamental contribution are the optimistic and pessimistic free disposal hull (FDH) models. In this study, authentic optimistic and pessimistic DEA models without convexity are developed from both input and output orientation. Further into the research investigation, extended models have been proposed, by combining the conventional and FDH ranking models with other different approaches in the literature. Chapter 4 of this thesis presents three extended FDH models: an FDH slack-based model, an FDH superefficiency model, and a dual frontier without infeasibility super-efficiency FDH model. Chapter 5 shows the development of extended models when virtual DMUs are considered. Improved virtual DMU models and improved FDH virtual DMU models are proposed in order to develop the DEA ranking ability from both optimistic and pessimistic approaches. The final model is an optimistic and pessimistic forecasting approach using regression analysis. The forecasting model can be used by decision makers to determine the resources needed for future planning to build an efficient new unit with reference to the current DMU set.

scholarly journals Efficiency Distribution Analysis with Data Envelopment Analysis (DEA) Approach Fertilizer

Tibuana ◽  
2021 ◽  
Vol 4 (02) ◽  
pp. 91-98
Author(s):  
Titiek Koesdijati ◽  
Andarmadi Jati Abdhi Wasesa
Keyword(s):  
Data Envelopment Analysis ◽  
Relative Efficiency ◽  
Environmental Changes ◽  
Distribution Channels ◽  
Data Envelopment ◽  
Distribution Analysis ◽  
Output Data ◽  
Input And Output ◽  
Level Of Use ◽  
Output Efficiency

Distribution channels have an important meaning for achieving company success in the field of marketing so that company management is required to always be responsive and able to adapt to environmental changes. Input and output data processing is done by giving weights to the input and output using the DEA CCR primal model by maximizing the input-oriented-based objective function. The results of processing the efficiency scale show the relative efficiency level of the scale of each DMU in the company. The efficiency scale is obtained through the formulation of the DEA CCR primal model between each DMU input and output. If the DMU gets an input and output efficiency value of less than 100%, then the DMU is said to be relatively inefficient. Meanwhile, if the efficient value is equal to 100%, then the DMU is said to be relatively efficient. Of the 5 distribution cities, Sidoarjo, PaluKendari, Bandung and Lamongan which were analyzed, there were 2 cities that were inefficient or experiencing waste in their input and output variables, so the company needed to reorganize the level of use of inputs and outputs it achieved and utilize them optimally to get output that is optimal. targeted.

scholarly journals Dual frontiers data envelopment analysis: multiple ranking approaches from optimistic and pessimistic perspectives

2021 ◽  
Author(s):  
Abdullah Maraee Aldamak
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Efficiency Score ◽  
The Body ◽  
Data Envelopment ◽  
Free Disposal Hull ◽  
Dea Model ◽  
Ranking Models ◽  
Input And Output ◽  
Dea Models

The field of data envelopment analysis (DEA) has evolved rapidly since its introduction to decision-making science 40 years ago. DEA has since attracted the attention of many researchers because of its unique characteristic to measure the efficiency of multiple-input and multiple-output decision-making units (DMUs) without assigning prior weight to the input and output, unlike most available decision analysis tools. The body of research has resulted in a huge amount of literature and diverse DEA models with very many different approaches. DEA classifies all units under assessment into two groups: efficient with a 100% efficiency score and inefficient with a less than 100% efficiency score. This ability is considered both a strength and a weakness of the standard DEA model because, although it allows DEA to evaluate the efficiency of any dataset, it lacks the power to rank all DMUs, by giving full efficiency scores to many efficient units. This issue has attracted many researchers to investigate the weak discrimination power of classical DEA models, resulting in a subfield of research that focuses on DEA ranking. This thesis focuses on the development of the conventional DEA model, and an attempt has been made to study models that are considered as improved models, or approaches that bring a better ranking field, that may bring more accurate evaluation than the original DEA. After studying DEA ranking models, the thesis presents various models under the optimistic and pessimistic DEA ranking approaches. The first and fundamental contribution are the optimistic and pessimistic free disposal hull (FDH) models. In this study, authentic optimistic and pessimistic DEA models without convexity are developed from both input and output orientation. Further into the research investigation, extended models have been proposed, by combining the conventional and FDH ranking models with other different approaches in the literature. Chapter 4 of this thesis presents three extended FDH models: an FDH slack-based model, an FDH superefficiency model, and a dual frontier without infeasibility super-efficiency FDH model. Chapter 5 shows the development of extended models when virtual DMUs are considered. Improved virtual DMU models and improved FDH virtual DMU models are proposed in order to develop the DEA ranking ability from both optimistic and pessimistic approaches. The final model is an optimistic and pessimistic forecasting approach using regression analysis. The forecasting model can be used by decision makers to determine the resources needed for future planning to build an efficient new unit with reference to the current DMU set.

scholarly journals Operational Efficiency of Chinese Provincial Electricity Grid Enterprises: An Evaluation Employing a Three-Stage Data Envelopment Analysis (DEA) Model

2018 ◽  
Vol 10 (9) ◽  
pp. 3168 ◽  
Author(s):  
Haoran Zhao ◽  
Huiru Zhao ◽  
Sen Guo
Keyword(s):  
Data Envelopment Analysis ◽  
Environmental Variables ◽  
Market Competition ◽  
Environmental Values ◽  
Operational Efficiency ◽  
Data Envelopment ◽  
Electricity Grid ◽  
Frontier Analysis ◽  
Dea Model ◽  
Statistical Noise

With the implementation of new round electricity system reform in China, the provincial electricity grid enterprises (EGEs) of China should focus on improving their operational efficiency to adapt to the increasingly fierce market competition and satisfy the requirements of the electricity industry reform. Therefore, it is essential to conduct operational efficiency evaluation on provincial EGEs. While considering the influences of exterior environmental variables on the operational efficiency of provincial EGEs, a three-stage data envelopment analysis (DEA) methodology is first utilized to accurately assess the real operational efficiency of provincial EGEs excluding the exterior environmental values and statistical noise. The three-stage DEA model takes the amount of employees, the fixed assets investment, the 110 kV and below distribution line length, and the 110 kV and below transformer capacity as input variables and the electricity sales amount, the amount of consumers, and the line loss rate as output variables. The regression results of the stochastic frontier analysis model indicate that the operational efficiencies of provincial EGEs are significantly affected by exterior environmental variables. Results of the three-stage DEA model imply that the exterior environmental values and statistical noise result in the overestimation of operational efficiency of provincial EGEs, and the exclusion of exterior environmental values and statistical noise has provincial-EGE-specific influences. Furthermore, 26 provincial EGEs are divided into four categories to better understand the differences of operational efficiencies before and after the exclusion of exterior environmental values and statistical noise.

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