Department of Mathematics

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Author: search.filters.author.Mathur, TrilokSubject: search.filters.subject.Data envelopment analysis (DEA)

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Now showing 1 - 4 of 4
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    Solving extended assignment problem using stochastic DEA approach
    (IEEE, 2025-04) Agarwal, Shivi; Mathur, Trilok
    The assignment model is a particular application of linear programming problems where tasks are assigned to agents with the goal of either maximization of profit or minimization of cost (in terms of both money and time) with provided deterministic data. But in real-life cases, more than one attribute may occur. Also, all these attributes need not be deterministic; some attributes may be stochastic in nature. The existing assignment model cannot handle these types of issues. To overcome these drawbacks, the study proposes the integrated extended assignment model with stochastic theory and the data envelopment analysis (DEA) technique. To illustrate the suggested concept, a numerical example is provided.
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    An optimal criteria selection in efficiency assessment through integration of dea with rough set theory
    (Springer, 2025-09) Agarwal, Shivi; Mathur, Trilok
    Data Envelopment Analysis (DEA) is a prominent nonparametric technique used to assess the efficiency of decision-making units (DMUs) by using multi criteria. However, traditional DEA models can be significantly impacted by criteria that do not contribute significantly to the efficiency analysis, thereby reducing accuracy and discriminatory power. Additionally, for DEA models to produce reliable results, the number of DMUs should be greater than the number of criteria included. This paper introduces a Rough Data Envelopment Analysis (RDEA) approach, which integrates Rough Set Theory (RST) with DEA to effectively handle this problem. RST is used by the RDEA framework to find and remove less contributing criteria from the input and output data in efficiency analysis. RST generates lower and upper approximations which helps in identifying criteria that are not significantly contributing to the efficiency analysis. Once these criteria have eliminated from the data set, the DEA models may be utilized to provide a more accurate and reliable efficiency evaluation of DMUs. This theoretical framework leverages the capabilities of RST to streamline input and output data, enhancing the effectiveness of DEA in evaluating efficiency. Also, a numerical example is provided to show implementation of this method.
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    Expected credits approach for scale efficiency using fuzzy dea
    (Springer, 2024-07) Agarwal, Shivi; Mathur, Trilok
    Data envelopment analysis (DEA) is a technique that uses data to evaluate the relative efficiencies of decision-making units (DMUs). In real life, the collection of crisp data is onerous; some vagueness can occur due to inconvenient data. With vague data, conventional DEA models cannot be used, as DEA is very sensitive to data. To overcome this problem, the fuzzy theory is integrated with DEA. The new slack DEA model (NSM) concerns straight away with input and output slacks. To handle vague or qualitative data, a fuzzy new slack DEA model can be used. In this study, the fuzzy NSM technique with the expected credits approach is used to calculate the scale efficiencies of DMUs under the constant returns to scale (CRS) and variable returns to scale (VRS) assumptions. This approach converts the fuzzy NSM into a crisp linear programming model and provides a single, crisp efficiency score for each DMU. To illustrate the proposed fuzzy NSM technique with the expected credits approach, the scale efficiency of the Indian oil refineries is measured.
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    An integrated DEA-fuzzy AHP method for prioritization of renewable energy sources in India
    (Springer Nature, 2025-01) Agarwal, Shivi; Mathur, Trilok
    As India’s population grows and urbanization accelerates, energy demand is increasing sharply while conventional sources fall behind. To tackle energy shortages and climate change, India must prioritize renewable energy sources (RES), which offer sustainable solutions. The country is rich in RES, which can enhance fuel mix for electricity generation. This study analyzes various RES in India-solar, geothermal, hydro, biomass, wave, onshore, and offshore wind energy -using an integrated data envelopment analysis (DEA) and fuzzy analytic hierarchy process (Fuzzy AHP) methodology. Four main parameters-technical, economic, environmental, and socio-political -are identified and supported by 19 criteria, with environmental parameters including both desirable and undesirable criteria. In first phase, undesirable criteria are transformed into desirable criteria using Modified Ratio model. DEA is then applied to calculate initial efficiency score of RES under each parameter category. Fuzzy AHP determines weights for each parameter. The weights and initial efficiency scores are then combined to calculate overall efficiency score and ranking of RES. Sensitivity analysis shows that results obtained from proposed methodology are significant, and robust. Offshore wind ranks highest in efficiency, followed by hydro and onshore wind, while geothermal scores lowest. This methodology could benefit developing nations and guide policymakers in adopting RES.