BITS Faculty Publications
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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 Analyzing unemployment dynamics: a fractional-order mathematical model(Wiley, 2025-03) Mathur, TrilokThe persistent rise in unemployment rates poses a significant threat to global economic stability. Addressing this challenge effectively requires a deeper understanding of workforce dynamics, particularly through the integration of an individual's employment history into analytical models. This research introduces a fractional mathematical model, leveraging the Caputo fractional derivative and three key variables: the number of skilled unemployed individuals, the number of employed individuals, and the number of available job vacancies. The model's well-posedness and global stability are rigorously established using fixed-point theory. Additionally, the basic reproduction number is analyzed to identify critical factors that facilitate the creation of new job opportunities. Real-world data from India are employed for MATLAB simulations, offering predictions of unemployment trends in the coming years. A graphical analysis highlights the impact of the COVID-19 pandemic on unemployment rates. The model's predictive accuracy is demonstrated through error analysis, showing that fractional-order forecasts achieve less than 5% error, outperforming integer-order models in capturing the nuances of unemployment dynamics. Sensitivity analysis reveals that the employment rate is the most influential parameter; a 40% increase in this rate could lead to 192,200 additional employed individuals. The fractional-order model further exhibits superior performance metrics, including lower root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) values, alongside a higher correlation coefficient ( ). These findings underscore the model's potential to enhance the understanding and mitigation of unemployment challenges.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 Short-term wind speed prediction with adaptive signal processing based hybrid statistical models(Springer, 2025-03) Pasari, SumantaThe inherent nonlinearity, intermittency, and chaotic nature of wind speed make accurate forecasting challenging. Traditional approaches like standalone time series models and frequency domain analysis struggle to capture these complex characteristics effectively. In light of this, the present study utilizes three self-adaptive signal processing methods, namely empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and variational mode decomposition (VMD) and combines with ARIMA or window-sliding ARIMA (WSARIMA) to develop six hybrid models, namely EMD–ARIMA, EEMD–ARIMA, VMD–ARIMA, EMD–WSARIMA, EEMD–WSARIMA, and VMD–WSARIMA. To illustrate the efficacy of the proposed hybrid models in daily wind speed prediction, four study sites from India with different climates are considered. Based on the analysis of 7 years (08-2015–03-2023) of wind speed data, it is found that: (i) the extracted components of VMD overcome the limitations of EMD and EEMD methods; (ii) the combination of VMD and WSARIMA outperforms any other comparative model, such as ARIMA, WSARIMA, EMD–ARIMA, EEMD–ARIMA, VMD–ARIMA, EMD–WSARIMA, or EEMD–WSARIMA; the VMD–WSARIMA model reduces RMSE by 70–80% compared to the conventional ARIMA model; (iii) finally, as a part of post-processing, the residual analysis of the best fit VMD–WSARIMA model shows desirable characteristics. Therefore, the present study strongly recommends to consider adaptive decomposition based hybrid models in wind speed forecasting at shorter time horizon.Item Earthquake cycle progression in major city regions of Taiwan through nowcasting technique(Springer, 2025-05) Pasari, SumantaThe complex tectonic framework of Taiwan makes it susceptible to devastating earthquakes that originate on both mapped faults, and at times, on unmapped faults. The unmapped faults especially highlight the limitation of conventional fault–based hazard assessment methods, emphasizing the need for alternative approaches. In this context, we implement a surrogate area–based earthquake nowcasting technique to assess the seismic cycle progression in 10 densely populated cities across Taiwan. We utilize the notion of natural times, the inter–event counts of small earthquakes between successive large events, to calculate the Earthquake Potential Score (EPS) for each city region. To derive natural time statistics, we analyze eight reference probability models, including exponential distribution and its variants, exponentiated group of distributions, and heavy–tailed distributions. Statistical inference of 114 observed natural times shows that the exponentiated exponential distribution provides the best fit. As of April 24, 2025, the EPS values (%) for M 6.0 earthquakes in the 10 cities range from 53% to 69%, with the following values: Taipei (69%), Hsinchu (68%), Keelung (67%), Hualien (59%), Nantou (58%), Taitung (57%), Chiayi (56%), Pingtung (55%), Tainan (54%), and Kaohsiung (53%). These EPS values indicate the progression in current earthquake cycle toward a M 6.0 earthquake in the corresponding city region. Moreover, there is a consistency in the nowcast scores despite some variations in threshold magnitudes and city regions. The studied approach and results therein offer valuable insights to decision makers to enhance earthquake preparedness and risk management across Taiwan.Item Numerical simulation and convergence analysis for Riemann-Liouville fractional initial value problem involving weak singularity(Inder Science, 2023-11) Santra, SudarshanThe present work considers a Riemann-Liouville fractional initial value problem (IVP) associated with homogeneous initial condition involving a weak singularity near the origin. Due to presence of initial singularity, an initial layer occurs at t = 0. The L1 scheme is introduced on a uniform mesh to approximate the solution. The convergence analysis shows that the present method is more accurate and produces less error compared to some existing methods on any subdomain away from the origin while the proposed method is comparable over the entire region. Numerical examples and comparison results are provided in order to show the effectiveness of the proposed method.Item Numerical simulation for time fractional integro partial differential equations arising in viscoelastic dynamical system(CRC Press, 2023) Santra, SudarshanThe study on fractional calculus gains more attention of many researchers in recent times, due to its immense applicability to define various models, such as viscoelastic damped structure [1], the model due to radiative transfer [2], the theory of linear transport [3], and the mathematical structure due to kinetic energy of gases [4]. A detailed investigation about the application of fractional differential as well as fractional integro-differential equation is available in [5–7]. The general form of a fractional derivative viscoelastic models can be written as: 8.1 https://www.w3.org/1998/Math/MathML" display="block"> X ( t ) + ∑ m = 1 M a m D t α m X ( t ) = E 0 Y ( t ) + ∑ n = 1 N E n D t β n Y ( t ) , https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003328032/39998614-bd30-4270-a56c-d58717d36a18/content/math8_1.tif"/>Item Higher order approximations for fractional order integro-parabolic partial differential equations on an adaptive mesh with error analysis(Elsevier, 2023-11) Santra, SudarshanThis work deals with a higher order numerical approximation for analyzing a class of multi-term time fractional partial integro-differential equations involving Volterra integral operators. The solutions to these problems have a mild singularity at the initial time, due to which an initial layer appears, which becomes more sharper as the highest order time fractional derivative decreases. This behaviour reduces the rate of convergence by standard approaches. We start the present work by considering the existence and uniqueness of a class of generalized partial integro-differential equations and then, present the L1 discretization on a graded mesh in time which is adapted towards the initial time level. This discretization leads to a higher order accuracy than the solutions obtained on a time uniform mesh. The convergence analysis corresponding to the Volterra integral operator is nontrivial as it uses a repeated quadrature rule. This analysis can also be extended for weakly singular kernels. The stability analysis of the present scheme with a sharp error estimation is also provided. The analysis with extensive experiments shows that a higher rate of accuracy can be attained for several suitable choices of the grading parameters for solving several classes of time fractional integro-differential equations.