Fuzzy stochastic Data Envelopment Analysis with application to NATO enlargement problem

2019 ◽  
Vol 53 (2) ◽  
pp. 705-721 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Seyed Hadi Nasseri ◽  
Omid Gholami
Keyword(s):  
Data Envelopment Analysis ◽  
Data Envelopment ◽  
Threshold Values ◽  
Discrimination Power ◽  
Dea Model ◽  
Nato Enlargement ◽  
Proposed Model ◽  
Stochastic Dea ◽  
Dea Models ◽  
Stochastic Data

Data Envelopment Analysis (DEA) is a widely used technique for measuring the relative efficiencies of Decision Making Units (DMUs) with multiple deterministic inputs and multiple outputs. However, in real-world problems, the observed values of the input and output data are often vague or random. Indeed, Decision Makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. Hence, we formulate a new DEA model to deal with fuzzy stochastic DEA models. The contributions of the present study are fivefold: (1) We formulate a deterministic linear model according to the probability–possibility approach for solving input-oriented fuzzy stochastic DEA model, (2) In contrast to the existing approach, which is infeasible for some threshold values; the proposed approach is feasible for all threshold values, (3) We apply the cross-efficiency technique to increase the discrimination power of the proposed fuzzy stochastic DEA model and to rank the efficient DMUs, (4) We solve two numerical examples to illustrate the proposed approach and to describe the effects of threshold values on the efficiency results, and (5) We present a pilot study for the NATO enlargement problem to demonstrate the applicability of the proposed model.

scholarly journals Modifying the convexity condition in Data Envelopment Analysis (DEA)

2020 ◽  
Vol 33 (02) ◽  
pp. 454-467
Author(s):  
Roghyeh Malekii Vishkaeii ◽  
Behrouz Daneshian ◽  
Farhad Hosseinzadeh Lotfi
Keyword(s):  
Data Envelopment Analysis ◽  
Real Data ◽  
Data Envelopment ◽  
Convexity Condition ◽  
Discrimination Power ◽  
Data Set ◽  
Step Procedure ◽  
Proposed Model ◽  
Dea Models ◽  
Production Possibility Set

Conventional Data Envelopment Analysis (DEA) models are based on a production possibility set (PPS) that satisfies various postulates. Extension or modification of these axioms leads to different DEA models. In this paper, our focus concentrates on the convexity axiom, leaving the other axioms unmodified. Modifying or extending the convexity condition can lead to a different PPS. This adaptation is followed by a two-step procedure to evaluate the efficiency of a unit based on the resulting PPS. The proposed frontier is located between two standard, well-known DEA frontiers. The model presented can differentiate between units more finely than the standard variable return to scale (VRS) model. In order to illustrate the strengths of the proposed model, a real data set describing Iranian banks was employed. The results show that this alternative model outperforms the standard VRS model and increases the discrimination power of (VRS) models.

Measuring Performance of a Three-Stage Network Structure Using Data Envelopment Analysis and Nash Bargaining Game: A Supply Chain Application

2018 ◽  
Vol 17 (05) ◽  
pp. 1429-1467 ◽  
Author(s):  
Mohammad Amirkhan ◽  
Hosein Didehkhani ◽  
Kaveh Khalili-Damghani ◽  
Ashkan Hafezalkotob
Keyword(s):  
Supply Chain ◽  
Data Envelopment Analysis ◽  
Nash Bargaining ◽  
Data Envelopment ◽  
Second Stage ◽  
Proposed Model ◽  
Nash Bargaining Game ◽  
Dea Models ◽  
Overall Efficiency

The issue of efficiency analysis of network and multi-stage systems, as one of the most interesting fields in data envelopment analysis (DEA), has attracted much attention in recent years. A pure serial three-stage (PSTS) process is a specific kind of network in which all the outputs of the first stage are used as the only inputs in the second stage and in addition, all the outputs of the second stage are applied as the only inputs in the third stage. In this paper, a new three-stage DEA model is developed using the concept of three-player Nash bargaining game for PSTS processes. In this model, all of the stages cooperate together to improve the overall efficiency of main decision-making unit (DMU). In contrast to the centralized DEA models, the proposed model of this study provides a unique and fair decomposition of the overall efficiency among all three stages and eliminates probable confusion of centralized models for decomposing the overall efficiency score. Some theoretical aspects of proposed model, including convexity and compactness of feasible region, are discussed. Since the proposed bargaining model is a nonlinear mathematical programming, a heuristic linearization approach is also provided. A numerical example and a real-life case study in supply chain are provided to check the efficacy and applicability of the proposed model. The results of proposed model on both numerical example and real case study are compared with those of existing centralized DEA models in the literature. The comparison reveals the efficacy and suitability of proposed model while the pitfalls of centralized DEA model are also resolved. A comprehensive sensitivity analysis is also conducted on the breakdown point associated with each stage.

scholarly journals A Range Adjusted Measure of Super-Efficiency in Integer-Valued Data Envelopment Analysis with Undesirable Outputs

2021 ◽  
Vol 9 (4) ◽  
pp. 378-398
Author(s):  
Chunhua Chen ◽  
Haohua Liu ◽  
Lijun Tang ◽  
Jianwei Ren
Keyword(s):  
Data Envelopment Analysis ◽  
Transportation Systems ◽  
Decision Makers ◽  
Data Envelopment ◽  
Undesirable Outputs ◽  
Super Efficiency ◽  
Dea Model ◽  
Dea Models ◽  
Analysis Models ◽  
Transport Accidents

Abstract DEA (data envelopment analysis) models can be divided into two groups: Radial DEA and non-radial DEA, and the latter has higher discriminatory power than the former. The range adjusted measure (RAM) is an effective and widely used non-radial DEA approach. However, to the best of our knowledge, there is no literature on the integer-valued super-efficiency RAM-DEA model, especially when undesirable outputs are included. We first propose an integer-valued RAM-DEA model with undesirable outputs and then extend this model to an integer-valued super-efficiency RAM-DEA model with undesirable outputs. Compared with other DEA models, the two novel models have many advantages: 1) They are non-oriented and non-radial DEA models, which enable decision makers to simultaneously and non-proportionally improve inputs and outputs; 2) They can handle integer-valued variables and undesirable outputs, so the results obtained are more reliable; 3) The results can be easily obtained as it is based on linear programming; 4) The integer-valued super-efficiency RAM-DEA model with undesirable outputs can be used to accurately rank efficient DMUs. The proposed models are applied to evaluate the efficiency of China’s regional transportation systems (RTSs) considering the number of transport accidents (an undesirable output). The results help decision makers improve the performance of inefficient RTSs and analyze the strengths of efficient RTSs.

scholarly journals An Integrated Analytic Hierarchy Process—Slack Based Measure-Data Envelopment Analysis Model for Evaluating the Efficiency of Logistics Service Providers Considering Undesirable Performance Criteria

2019 ◽  
Vol 11 (8) ◽  
pp. 2330 ◽  
Author(s):  
Patricija Bajec ◽  
Danijela Tuljak-Suban
Keyword(s):  
Data Envelopment Analysis ◽  
Service Providers ◽  
Performance Criteria ◽  
Data Envelopment ◽  
Analytic Hierarchy ◽  
Dea Model ◽  
Logistics Service ◽  
Logistics Service Providers ◽  
Proposed Model ◽  
Hierarchy Process

Sustainable concerns are reputed to be of the utmost priority among governments. Consequently, they have become more and more of a concern among supply chain partners. Logistics service providers (LPs), as significant contributors to supply chain success but also one of the greatest generator of emissions, play a significant role in reducing the negative environmental impact. Thus, the performance evaluations of LPs should necessarily involve such a measure which, firstly, represents a balance between all three pillars of sustainability and, secondly, consider the desirable and undesirable performance criteria. This paper proposes an integrated analytic hierarchy process (AHP) and slack-based measure (SBM) data envelopment analysis (DEA) model, based on the assumption of a variable return to scale (VRS). An AHP pairwise comparison enables selecting the most influential input/output variables. Output-oriented SBM DEA provides simultaneously evaluation of both the undesirable and desirable outputs. The proposed model was tested on a numerical example of 18 LPs. The comparison of output Charnes, Cooper and Rhodes (CCR) and SBM DEA models resulted in a higher number of inefficient LPs when the SBM DEA model was applied. Moreover, efficiency scores of inefficient LPs were lower in SBM DEA model. The proposed model is fair to those LPs that are environmentally friendly.

Developing a new super-efficiency DEA model in the presence of both zero data and stochastic data: a case study in the Iranian airline industry

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammad Tavassoli ◽  
Amirali Fathi ◽  
Reza Farzipoor Saen
Keyword(s):  
Airline Industry ◽  
Returns To Scale ◽  
Content Type ◽  
Super Efficiency ◽  
Dea Model ◽  
Proposed Model ◽  
Stochastic Dea ◽  
Stochastic Data ◽  
Constant Returns To Scale

PurposeThe purpose of this study is to propose a novel super-efficiency DEA model to appraise the relative efficiency of DMUs with zero data and stochastic data. Our model can work with both variable returns to scale (VRS) and constant returns to scale (CRS).Design/methodology/approachThis study proposes a new stochastic super-efficiency DEA (SSDEA) model to assess the performance of airlines with stochastic and zero inputs and outputs.FindingsThis paper proposes a new analysis and contribution to the knowledge of efficiency assessment with stochastic super-efficiency DEA model by (1) using input saving and output surplus index for efficient DMUs to get the optimal solution; (2) obtaining efficiency scores from the proposed model that are equivalent to original stochastic super-efficiency model when feasible solutions exist. A case study is given to illustrate the applicability of our proposed model. Also, poor performance reasons are identified to improve the performance of inefficient airlines.Originality/valueFor the first time, a new SSDEA model for ranking DMUs is proposed. The introduced model produces a feasible solution when dealing with zero input or output. This paper applies the input saving and output surplus concept to rectify the infeasibility problem in the stochastic DEA model.

Eco-innovation analysis of OECD countries with common weight analysis in data envelopment analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Reza Kiani Mavi ◽  
Neda Kiani Mavi ◽  
Reza Farzipoor Saen ◽  
Mark Goh
Keyword(s):  
Sustainable Development ◽  
Data Envelopment Analysis ◽  
Oecd Countries ◽  
Malmquist Productivity Index ◽  
Productivity Index ◽  
Environmental Research ◽  
Data Envelopment ◽  
Discrimination Power ◽  
Content Type ◽  
Dea Models

PurposeDespite unanimity in the literature that eco-innovation (EI) leads to sustainable development, evidence remains limited on measuring EI efficiency with the Malmquist productivity index (MPI). In conventional data envelopment analysis (DEA) models, decision-making units (DMUs) are inclined to assign more favorable weights, even zero, to the inputs and outputs to maximize their own efficiency. This paper aims to overcome this shortcoming by developing a common set of weights (CSW). Design/methodology/approachUsing goal programming, this study develops a CSW model to evaluate the EI efficiency of the organization for economic co-operation and development (OECD) countries and track their changes with MPI during 2010–2018. FindingsAchieving a complete ranking of DMUs, findings show the higher discrimination power of the proposed CSW compared with the original DEA models. Furthermore, results reveal that Iceland, Latvia and Luxembourg are the only OECD countries that have incessantly improved their EI productivity (MPI > 1) from 2010 to 2018. On the other hand, Japan is the OECD country that has experienced the highest yearly EI efficiency during 2010–2018. This paper also found that Iceland has the highest MPI over 2010–2018. Practical implicationsMore investment in environmental research and development (R&D) projects instead of generic R&D enables OECD members to realize more opportunities for sustainable development through minimizing energy use and environmental pollution in any form of waste and greenhouse gas emissions. Originality/valueIn addition to developing a novel common weights model for DEA-MPI to measure and evaluate the EI of OECD countries, this paper develops a CSW model by including the undesirable outputs for EI analysis.

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 Fuzzy Data envelopment Analysis with SBM using α-level Fuzzy Approach

2019 ◽  
pp. 481-501
Author(s):  
Qaiser Farooq Dar ◽  
Ahn Young Hyo ◽  
Gulbadian Farooq Dar ◽  
Shariq Ahmad Bhat ◽  
Arif Muhammad Tali ◽  
...  
Keyword(s):  
Data Envelopment Analysis ◽  
Data Envelopment ◽  
Fuzzy Data ◽  
Fuzzy Approach ◽  
Discrimination Power ◽  
Sbm Model ◽  
Fuzzy Data Envelopment Analysis ◽  
Dea Models ◽  
Α Level ◽  
Fuzzy Dea

The applications of fuzzy analysis in data-oriented techniques are the challenging aspect in the field of applied operational research. The use of fuzzy set theoretic measure is explored here in the context of data envelopment analysis (DEA) where we are utilizing the fuzzy α-level approach in the three types of efficiency models. Namely, BCC models, SBM model and supper efficiency model in DEA. It was observed from the result that the fuzzy SBM model has good discrimination power over fuzzy BCC. On the other side, both the models fuzzy BCC and fuzzy SBM are not able to make the genuine ranking which is acceptable for all. So this weakness is overcome with the help of fuzzy super SBM model and all three models are applied to illustrate the types of decisions and solutions that are achievable when the data are vague and prior information is in imprecise. In this paper, we are considering that our inputs and outputs are not known with absolute precision in DEA and here, we using Fuzzy-DEA models based on an α-level fuzzy approach to assessing fuzzy data.

Data envelopment analysis with interactive variables

2015 ◽  
Vol 53 (10) ◽  
pp. 2390-2406 ◽  
Author(s):  
Aibing Ji ◽  
Hui Liu ◽  
Hong-jie Qiu ◽  
Haobo Lin
Keyword(s):  
Data Envelopment Analysis ◽  
Special Form ◽  
Design Methodology ◽  
Data Envelopment ◽  
Content Type ◽  
Dea Model ◽  
Proposed Model ◽  
Choquet Integrals ◽  
Practical Implications ◽  
Decision Making Units

Purpose – The purpose of this paper is to build a novel data envelopment analysis (DEA) model to evaluate the efficiencies of decision making units (DMUs). Design/methodology/approach – Using the Choquet integrals as aggregating tool, the authors give a novel DEA model to evaluate the efficiencies of DMUs. Findings – It extends DEA model to evaluate the DMU with interactive variables (inputs or outputs), the classical DEA model is a special form. At last, the authors use the numerical examples to illustrate the performance of the proposed model. Practical implications – The proposed DEA model can be used to evaluate the efficiency of the DMUs with multiple interactive inputs and outputs. Originality/value – This paper introduce a new DEA model to evaluate the DMU with interactive variables (inputs or outputs), the classical DEA model is a special form.

Randomizing DEA Efficiency Scores with Beta Distribution

2014 ◽  
pp. 1977-1985
Author(s):  
P. Sunil Dharmapala
Keyword(s):  
Data Envelopment Analysis ◽  
Order Statistic ◽  
Beta Distribution ◽  
Data Envelopment ◽  
Random Errors ◽  
Input Output ◽  
Stochastic Dea ◽  
Dea Models ◽  
Dea Efficiency ◽  
Statistical Results

A criticism leveled against Data Envelopment Analysis (DEA) is that it is incapable of handling input/output data contaminated with random errors, and therefore, efficiency scores reported by DEA do not reflect reality. Several researchers have addressed this issue by incorporating statistical noise into DEA modeling, thus giving birth to Stochastic DEA. In this chapter, utilizing well known DEA models, we propose a method to randomize efficiency scores by treating each score as an order statistic of an underlying Beta distribution. In an application to a set of banks, we demonstrate how to do this randomization and derive some statistical results.

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