Department of Mathematics
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Item Solving extended assignment problem using stochastic DEA approach(IEEE, 2025-04) Agarwal, Shivi; Mathur, TrilokThe 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.Item Fuzzy DEA model with exogenously fixed variables for ranking of renewable energy sources(Springer, 2025-09) Agarwal, Shivi; Mathur, TrilokAs the global population grows, so does the demand for energy. India, with its fast growth, industrialization, and urbanization, is struggling to meet energy needs using traditional sources. To tackle energy shortages, pollution, and climate change, it’s important to find cost-effective and environment friendly alternatives. Renewable energy sources (RESs) offer a promising solution, making it important to prioritize them. India has strong potential in technologies like solar, geothermal, hydro, biomass, wave energy, and onshore and offshore wind energy. However, prioritizing these energy options involves considering many factors, often with conflicting priorities. This study proposed a fuzzy Data Envelopment Analysis (DEA) method to prioritize renewable energy sources in India, considering exogenously fixed variables that can’t be controlled, and handling undesirable variables. The proposed model ranks RESs effectively. It is revealed from results that Offshore wind energy is found to be the most efficient, followed by onshore wind and hydro energy, while geothermal energy ranks the lowest. The proposed methodology and findings can help developing nations and policymakers make better decisions when adopting renewable energy sources.Item An optimal criteria selection in efficiency assessment through integration of dea with rough set theory(Springer, 2025-09) Agarwal, Shivi; Mathur, TrilokData 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.Item Advancements of solar energy research in the context of SDG-7 attainment: a bibliometric analysis using spar-4-slr protocol(IEEE, 2025-05) Agarwal, Shivi; Mathur, TrilokRenewable energy sources, free of environmental risks, are vital for achieving net-zero CO2 emissions and addressing climate change to meet Sustainable Development Goals. This study explores the evolution of solar energy research using bibliographic coupling and keyword co-occurrence analysis of 6,460 articles from 1988 to 2024. The findings reveal a significant increase in solar power-related publications, with China leading in research output, followed by the United States and India. Top journals include Renewable Energy and Energies, with a growing focus on Energy and Engineering. This analysis serves as a vital reference for solar energy researchers and professionals.Item Assessment of offshore wind farm site suitability in India using GIS and MCDM methods(Springer, 2025-03) Agarwal, Shivi; Mathur, TrilokThe growing demand for sustainable energy sources has prompted investigation of offshore wind farms (OfWF) as viable options. This study proposes an innovative framework combining GIS with MCDM methods to identify highly suitable sites and efficiently prioritize alternative sites for OfWF, specifically focusing on regions viable for fixed foundations within the Indian EEZ. It takes into account technical, economic, and socio-environmental criteria to identify the optimal sites for OfWF. Two types of criteria are involved: exclusion criteria, refining study area by excluding areas unsuitable for renewable energy projects, and evaluation criteria, influencing the viability of specific sites in line with defined objective. The methodology involves screening criteria from existing literature, preprocessing data through GIS, and calculating criteria weights with AHP and CRITIC methods. This is followed by ranking potential sites using TOPSIS and VIKOR, offering structured decision support. The final phase of the analysis involved evaluating the consistency between individual site rankings using the Spearman rank correlation, ensuring reliability in the ranking outcomes across selected methods. The findings suggest the top fifteen sites for installing wind farms, ranging in offshore regions from Pallam town in Kanyakumari to Kooduthalai in Tirunelveli district, Tamil Nadu. This study’s insights on offshore renewable energy site selection in India are invaluable for policymakers, investors and sustainability initiatives, offering a roadmap for a cleaner and more sustainable energy future worldwide.Item A DEA-based approach for optimizing the extended transshipment problem(Elsevier, 2025-09) Agarwal, Shivi; Mathur, TrilokTransshipment issues represent a distinct category of transportation challenges that commonly arise in practical contexts. The conventional transshipment model typically focuses on a single variable (predominantly cost), with decision-makers endeavoring to enhance this variable. Nevertheless, in practical contexts, numerous cost-related and revenue-related variables significantly influence the transshipment process, necessitating their optimization to augment the efficacy of the transshipment strategy. To our knowledge, a deficiency exists in addressing such a transshipment problem characterized by multiple variables. To address this deficiency, the present study advances the conventional transshipment model to accommodate scenarios wherein various variables are present within the transshipment framework. To illustrate the validity of the proposed methodology, a numerical example is provided, utilizing empirical data concerning wheat production in Iran.Item Inhomogeneous generalized fractional Bessel differential equations in complex domain(Elsevier, 2026-03) Mathur, Trilok; Agarwal, ShiviThis paper explores inhomogeneous generalized fractional-order Bessel differential equations in the complex domain with arbitrary-order δ () using Riemann-Liouville (R-L) fractional operators. The study establishes the existence of holomorphic solutions through the power series method, considering the concept of radius of convergence. Conditions for the unique existence of holomorphic solutions in the complex domain are identified using fixed point theory and the Rouche theorem. Additionally, the paper demonstrates that the solution, particularly for infinite series of fractional power, satisfies the generalized Ulam-Hyers stability. Furthermore, when , the solution to the inhomogeneous Bessel differential equation takes the form of Bessel functions of the first kind, denoted as .Item Performance evaluation of public transport sector with missing data(Springer, 2024-07) Agarwal, Shivi; Mathur, TrilokEfficiency analysis is vital for decision-making in service sectors such as public transport and public health, aiding policy formulation and understanding competition. This study focuses on evaluating the efficiency of India's public transport sector, particularly State Road Transport Undertakings (SRTUs), utilizing Data Envelopment Analysis (DEA). However, a key challenge in real-life efficiency analysis is the unavailability or absence of certain data points. To address this issue, the study proposes the integration of DEA models and fuzzy numbers. By incorporating non-symmetrical fuzzy data, the study measures the efficiency of SRTUs and provides a ranking based on fuzzy efficiency.Item Expected credits approach for scale efficiency using fuzzy dea(Springer, 2024-07) Agarwal, Shivi; Mathur, TrilokData 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.Item Assessment of working capital management efficiency – a two-stage slack-based measure of data envelopment analysis(Emerald, 2024-06) Chadha, Saurabh; Agarwal, ShiviThis study aims to assess the efficiency of managing working capital in 1,388 Indian manufacturing firms from 2008 to 2019 and investigate the effects of firm-specific and macro-level determinants on working capital management (WCM) efficiency.