Linear robust data envelopment analysis: CCR model with uncertain data

Sabouhi, Mahmood; Najafabadi, Mostafa Mardani

doi:10.1504/ijpqm.2017.086369

Cited by 10 publications

(5 citation statements)

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“…The CCR model was proposed to evaluate the effectiveness of scale and technology for DMUs . For n of DMUs, the efficiency θ of each DMU with m of inputs X and s of outputs Y is calculated as follows:

\begin{matrix} true \\ min θ \\ \begin{matrix} s . t . \sum_{j = 1}^{n} λ_{j} X_{j} + S^{-} = θ X_{j 0} \\ \begin{matrix} \sum_{j = 1}^{n} λ_{j} Y_{j} - S^{+} = Y_{j 0} \\ \begin{matrix} λ_{j} \geq 0, j = 1, 2, \dots, n \\ S^{-} \geq 0, S^{+} \geq 0 \end{matrix} \end{matrix} \end{matrix} \end{matrix},

where X j = ( x 1 j , x 2 j , … , x ij , … , x mj ) T ; Y j = ( y 1 j , y 2 j , … , y rj , … , y sj ) T ; x ij is the input of raw material (fuel) i of DMU j ; y rj is the input of product r of DMU j ; λ j is the combined weight of DMU j ; X j 0 and Y j 0 are the inputs and outputs of DMU j 0 ; and S + and S − are the slack variables.…”

Section: Evaluation Methods Of Energy Efficiency In the Isimentioning

confidence: 99%

“…59,60 Then, the energy efficiency is determined by the ratio of inputs to outputs of this evaluation group. At present, the Charnes, Copper and Rhodes model (CCR), 61 Banker, Charnes and Cooper model (BCC), 61,62 and slack-based model 62 are widely used to evaluate the energy efficiency of the ISI. These models will be highlighted below.…”

Section: Data Envelopment Analysismentioning

confidence: 99%

“…The CCR model was proposed to evaluate the effectiveness of scale and technology for DMUs. [61][62][63] For n of DMUs, the efficiency θ of each DMU with m of inputs X and s of outputs Y is calculated as follows:…”

Section: Ccr Modelmentioning

confidence: 99%

See 2 more Smart Citations

Review of evaluation methodologies and influencing factors for energy efficiency of the iron and steel industry

Sun

et al. 2019

Int J Energy Res

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Summary To promote the sustainable development of the iron and steel industry (ISI), evaluation methods and influencing factors of energy efficiency have been studied in the past decades. A systematic review of these methodologies and influencing factors is presented in this paper. Initially, this paper states the development, current situation, and energy consumption of the world's ISI. Then, the definition of energy efficiency is described. After that, the evaluation methods are categorized as single‐factor methods (including these indicators of thermodynamic, thermos‐physical, thermo‐economic, and economic) and multifactor methods (including parametric and nonparametric methods). Furthermore, typical evaluation methods are highlighted. Thermal analysis method and exergy analysis method are routinely combined to optimize the energy utilization. Data envelopment analysis (DEA) and stochastic frontier analysis (SFA) are widely concerned and well developed to gain a better economic benefit. Malmquist index method is often associated with DEA to analyze the technical process and return to scale. Some emerging methods are proposed, for example, the three‐stage DEA method together with DEA and SFA. Finally, the influencing factors of energy efficiency in the ISI are discussed, including industrial structure, technological level, energy consumption structure, price, and so on. It is suggested that optimizing energy structure and improving technology level are effective measures to improve the energy efficiency in the ISI.

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\begin{matrix} true \\ min θ \\ \begin{matrix} s . t . \sum_{j = 1}^{n} λ_{j} X_{j} + S^{-} = θ X_{j 0} \\ \begin{matrix} \sum_{j = 1}^{n} λ_{j} Y_{j} - S^{+} = Y_{j 0} \\ \begin{matrix} λ_{j} \geq 0, j = 1, 2, \dots, n \\ S^{-} \geq 0, S^{+} \geq 0 \end{matrix} \end{matrix} \end{matrix} \end{matrix},

Section: Evaluation Methods Of Energy Efficiency In the Isimentioning

confidence: 99%

Section: Data Envelopment Analysismentioning

confidence: 99%

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Review of evaluation methodologies and influencing factors for energy efficiency of the iron and steel industry

Sun

et al. 2019

Int J Energy Res

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“…The CCR ratio model calculates the unit's overall efficiency by merging its scale efficiency and pure technical efficiency into a single number, as shown from Equations ( 2)- (11). The efficiency obtained is never absolute because it is constantly judged in respect to the field [29].…”

Section: Ccr (Ratio) Modementioning

confidence: 99%

Contextual Comparative Analysis of Dar es Salaam and Mombasa Port Performance by Using a Hybrid DEA(CVA) Model

Kunambi,

Zheng

2024

Logistics

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Background: This research conducts a contextual comparative analysis between Dar es Salaam and Mombasa ports, employing a hybrid data envelopment analysis (DEA) model that integrates the contextual value-added approach (CVA). The assessment incorporates various inputs (quay length, number of cranes, and storage area) and outputs (number of ship calls and cargo throughput) to compute efficiency scores, offering nuanced insights into the strengths, weaknesses, and areas for improvement of both ports. Methods: The hybrid DEA model with CVA is applied to calculate efficiency scores, considering the diverse inputs and outputs. This approach allows for a comprehensive evaluation of the relative performance of Dar es Salaam and Mombasa ports. The study also explores the influence of trade-related externalities on port efficiency, providing a holistic understanding of the factors shaping the ports’ operational effectiveness. Results: The efficiency scores depict distinctive performance trends between Dar es Salaam and Mombasa ports. Notably, Dar es Salaam exhibits maximum efficiency (efficiency value of 1) in 2018 and 2021, while Mombasa attains optimal performance (efficiency value of 1) in 2021. However, efficiency values fluctuate for both ports in other years, ranging between 0.895 and 0.985 for Mombasa and 0.924 and 0.960 for Dar es Salaam. Conclusions: This study highlights the dynamic efficiency levels of Dar es Salaam and Mombasa ports over multiple years and identifies critical factors influencing their performance. The findings contribute valuable insights to the field of port analysis, offering guidance to port management and policymakers in optimizing the efficiency and competitiveness of these vital maritime hubs.

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“…In the mid-1990s, the issue of creating conservatism in mathematical programming models was introduced by limiting uncertain parameters (Ben-Tal & Nemirovski, 2000). The benefits of using robust optimization are reporting point-based optimal solution (confronting the optimal interval solutions in interval programming) (M. Sabouhi & Mardani, 2017) and lack of awareness of the data distribution (the challenge of coping with the need to be aware of the data distribution in the stochastic programming) (Mardani Najafabadi & Taki, 2020).…”

Section: Introductionmentioning

confidence: 99%

Mathematical Programming Approaches for Modeling a Sustainable Cropping Pattern under Uncertainty: A Case Study in Southern Iran

Najafabadi¹,

Ashktorab²

2021

Preprint

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In recent years, the excessive and unreasonable use of chemicals, the occasional use of water, and the use of improper irrigation methods have created a worrying and unstable situation in developing countries' agricultural activities. In the present study, the robust multi-objective fractional linear programming model (RMOLFP) was introduced to determine the sustainable optimal cropping pattern. This model was presented in the Gotvand irrigation and drainage network located in Khuzestan province, southern Iran, under two scenarios with and without considering the uncertainty to evaluate the ability of the model. The results showed that in the first scenario, the consumption of critical disruptive inputs of sustainable agriculture such as fertilizers and chemical pesticides decreased by 5.9% and 8.19%, respectively. On the other hand, the model's uncertainty condition was applied in the second scenario in which the increase in gross margin was reduced. There is a trade-off between protecting the optimization model against system uncertainty and gross margin. Finally, the ability of the proposed model to apply uncertainty conditions was verified by the Monte Carlo simulation method. The results of this simulation confirmed the use of the RMOLFP method in determining the sustainable optimal cropping pattern for the study area.

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Linear robust data envelopment analysis: CCR model with uncertain data

Cited by 10 publications

References 0 publications

Review of evaluation methodologies and influencing factors for energy efficiency of the iron and steel industry

Review of evaluation methodologies and influencing factors for energy efficiency of the iron and steel industry

Contextual Comparative Analysis of Dar es Salaam and Mombasa Port Performance by Using a Hybrid DEA(CVA) Model

Mathematical Programming Approaches for Modeling a Sustainable Cropping Pattern under Uncertainty: A Case Study in Southern Iran

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