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 Analysis of the L1 scheme for a time fractional parabolic–elliptic problem involving weak singularity(Wiley, 2020-09) Santra, SudarshanA time fractional initial boundary value problem of mixed parabolic–elliptic type is considered. The domain of such problem is divided into two subdomains. A reaction–diffusion parabolic problem is considered on the first domain, and on the second, a convection–diffusion elliptic type problem is considered. Such problem has a mild singularity at the initial time t = 0. The classical L1 scheme is introduced to approximate the temporal derivative, and a second order standard finite difference scheme is used to approximate the spatial derivatives. The domain is discretized with uniform mesh for both directions. It is shown that the order of convergence is more higher away from t = 0 than the order of convergence on the whole domain. To show the efficiency of the scheme, numerical results are provided.Item Numerical analysis of volterra integro-differential equations with caputo fractional derivative(Springer, 2021-07) Santra, SudarshanThis article deals with a fully discretized numerical scheme for solving fractional order Volterra integro-differential equations involving Caputo fractional derivative. Such problem exhibits a mild singularity at the initial time . To approximate the solution, the classical L1 scheme is introduced on a uniform mesh. For the integral part, the composite trapezoidal approximation is used. It is shown that the approximate solution converges to the exact solution. The error analysis is carried out. Due to presence of weak singularity at the initial time, we obtain the rate of convergence is of order on any subdomain away from the origin whereas it is of order over the entire domain. Finally, we present a couple of examples to show the efficiency and the accuracy of the numerical scheme.Item A novel finite difference technique with error estimate for time fractional partial integro-differential equation of Volterra type(Elsevier, 2022-01) Santra, SudarshanThe main purpose of this work is to study the numerical solution of a time fractional partial integro-differential equation of Volterra type, where the time derivative is defined in Caputo sense. Our method is a combination of the classical L1 scheme for temporal derivative, the general second order central difference approximation for spatial derivative and the repeated quadrature rule for integral part. The error analysis is carried out and it is shown that the approximate solution converges to the exact solution. Several examples are given in support of the theoretical findings. In addition, we have shown that the order of convergence is more high on any subdomain away from the origin compared to the entire domain.