Department of Mathematics

Permanent URI for this collectionhttp://localhost:4000/handle/123456789/1920

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Author: search.filters.author.Kulshrestha, Rakhee

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    A comparative study of ε-constraint, lp-metric, and weighted sum multi-objective optimization methods in a circular economy
    (Elsevier, 2024) Kulshrestha, Rakhee; Sangwan, Kuldip Singh
    Approximately 74.7 Mt (Million Metric Tonnes) of e-waste is expected to be produced in 2030, and laptop e-waste is one of the major constituents of this. The goal of this paper is to develop and optimize a mixed-integer linear programming (MILP) mathematical model for a laptop manufacturer in India, based on a framework that integrates secondary reuse concept associated with traditional circular economy waste avoidance strategies. The multi-objective solution techniques of ε-constraint, LP-metric, and weighted sum methods are used to optimize the circular economy model. The proposed model aids as a policy tool to decide the optimum number of inspection/collection centers, sales/distribution centers, disassembly centers, refurbishing centers, recycling centers, and their optimum locations and allocations. This study results suggest that reuse, secondary customer centers, refurbishing, and recycling of the laptops is not only economically beneficial to the organization but also environment friendly and helps to create more jobs in the rural economy.
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    Transient analysis of energy-saving strategy for cognitive radio networks using G-queue with heterogeneity
    (Elsevier, 2024-02) Kulshrestha, Rakhee
    Energy efficiency, high data speeds, and effective spectrum utilization stand as the primary factors governing 5G and beyond networks. A base station (BS) in a cognitive radio network (CRN) that conserves energy during sleep periods is a promising contender for achieving more effective spectrum allocation. An efficient energy-saving strategy is offered in this study to achieve greener communication in wireless cellular networks. This study aims to propose and analyze an energy-saving scheme for the BS, taking into account the heterogeneity and reliability of networks. The entire system is modeled as a three-dimensional Markov chain by establishing a discrete-time preemptive priority queueing model with single vacation, heterogeneous packets, and negative packets such as viruses. Then, the transient analysis of the Markov chain is performed using the recursive method. Utilizing the transient probability distribution, we present numerical results derived from reliability analysis and queueing analysis to substantiate the validity of the proposed model. Furthermore, results based on the energy-saving degree are showcased to affirm the effectiveness of the proposed scheme. Finally, a reward cost function is obtained depending on the successful transmission of secondary packets, and the Quasi-Newton method is used to determine the optimal reward cost.
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    Modelling and simultaneous optimization of environmental, economic, and technological factors in machining
    (Springer, 2023-10) Sangwan, Kuldip Singh; Kulshrestha, Rakhee
    In the current era, manufacturing industries are facing multifaceted challenges related to increasing environmental awareness, decreasing economic gains, and technology obsolesce. These challenges become more apparent during the machining of difficult-to-machine materials due to high tool wear rates, high cutting forces, undesirable surface quality, high tool replacement costs, and a stagnating productivity. The developed approach aims at improving environmental, economic, and technological factors by optimizing four performance characteristics–energy demand, surface roughness, tool wear, and material removal rate during the milling of H13 tool steel by using an integrated artificial neural network and genetic algorithm. The proposed methodology provides Pareto solutions for minimum energy demand, surface roughness, & tool wear, and maximum material removal rate. The novelty of this work lies in generating Pareto fronts for analyzing conflicting responses, and determining preferred solutions without sacrificing environmental, technological, and economic considerations, simultaneously. The present work will be significant to practitioners in adopting better management strategies and simultaneously dealing with these challenges. The potential of the research lies in directly integrating the proposed optimization module with the machine tool system to serve as an online tool for machine tool process optimization.
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    Transient analysis of enhanced hybrid spectrum access for QoS provisioning in multi-class cognitive radio networks
    (Springer, 2024-04) Kulshrestha, Rakhee
    Cognitive radio networks (CRNs) offer a promising solution for improving spectrum utilization. However, ensuring quality of service (QoS) for heterogeneous secondary users (SUs) during spectrum handoff, particularly under high primary network traffic, poses challenges. This study develops a Markov-based analytical model to evaluate the gain of a non-switching spectrum handoff technique using a hybrid interweave-underlay spectrum access strategy, considering sensing errors. The proposed model assesses the effects of the hybrid spectrum access method for prioritized traffic across multiple SU classes, aiming to meet QoS requirements for delay-sensitive traffic. The study examines the CRN’s short-term behavior and realistic queueing scenarios by analyzing the system’s transient dynamics. Different spectrum access methods are compared for evaluation purposes. The analysis focuses on evaluating the effectiveness of the enhanced hybrid spectrum access scheme compared to individual interweave and hybrid interweave-underlay spectrum access strategies in terms of QoS provisioning for heterogeneous SUs. The results demonstrate increased throughput and improved spectrum utilization with the suggested scheme, affirming its suitability for satisfying QoS requirements for both delay-sensitive and delay-tolerant users.
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    A multi-objective fuzzy mathematical model for circular economy with leasing as a strategy
    (Emerald, 2024-05) Kulshrestha, Rakhee; Sangwan, Kuldip Singh
    This paper proposes multi-objective fuzzy mixed integer linear programming mathematical model considering multi-product, multi-echelon and multi-capacitated concepts of the circular economy. The three objectives of the proposed model, namely, economic, environmental and social are solved simultaneously using constraint approach to obtain balanced trade-off between the objective functions. The model is validated by solving a case study from the literature. The proposed model is made pragmatic for industrial application by considering multi-external suppliers multi-customer zones, multi-disassembly centers, multi-collection centers and multi-refurbishing centers and accounting for purchasing, processing, transportation, set-up costs and capacity constraints at the same time.
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    Comparative study on spectrum sensing and modulation techniques in cognitive radio network
    (IEEE, 2025-03) Kulshrestha, Rakhee
    This paper conducts a comparative analysis of two prominent spectrum sensing methods, energy detection (ED) and matched filter detection (MFD), under different modulation schemes, specifically binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), and 64-quadrature amplitude modulation (QAM), in an Additive White Gaussian Noise (AWGN) channel. The study evaluates the performance of ED and MFD in terms of probability of detection, false alarm, and sensitivity to signal-to-noise ratio (SNR). Simulation results indicate that 64-QAM is the preferred modulation scheme for achieving superior spectral efficiency. The analysis leverages receiver operating characteristic (ROC) curves to highlight the trade-offs between the probability of detection and probability of false alarm. These findings provide critical insights into the selection of appropriate spectrum sensing techniques, enhancing overall spectrum utilization in cognitive radio network.
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    Cost scrutiny of discrete-time priority queue with cluster arrival and Bernoulli feedback
    (Springer, 2024-03) Kulshrestha, Rakhee
    This work describes the economic feasibility of a single server discrete-time queueing model, (Geo/G/1) where interarrival times have a geometric distribution, and service times have a general distribution. This work is motivated by the case of discrete-time queueing models under priority scheme for solving many congestion issues of the telecommunication system wherein few calls are treated as prioritized calls and system manager may handle it properly. Herein a state-dependent arrival policy is used. It is assumed that the clients arrive in groups of varying sizes, and incorporates only one server queueing system with unlimited capacity. Under a discrete-time system with Markovian service practice, clients are serviced one at a time. If a client is dissatisfied with his service, he will most likely be directed back to the front of the queue. This concept is commonly referred to as Bernoulli feedback (BF) in queueing scenario. Just after every service, it is presumed that the server either starts to identify the next client to be serviced with some probability, or the server starts a solo vacation procedure with its complementary probability and this process is referred as Bernoulli vacation (BV). In addition, preferred and impatient clients are examined too. We investigate the Markov chain that underpins the queueing system in question, and its normalizing condition. The average number of consumers in the queue and the system are found using a generating function method. The numeral expositions are ascertained to delve the impact of different parameters on various performance metrics which can give information to system management in order to monitor the system's functioning condition and decrease congestion. We then used direct search method (DSM) and Particle Swarm Optimization (PSO) approaches to present a comparative study to assist system administrators or decision-makers by economically regulating the system. Furthermore, the results of the provided model are contrasted to those of a soft computing approach termed as ANFIS (Adaptive Neuro-Fuzzy Inference System).
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    Blockchain-enabled solution for transparency and waste minimization in pharmaceutical supply chains
    (Elsevier, 2025) Sangwan, Kuldip Singh; Kulshrestha, Rakhee
    The pharmaceutical supply chain is a complex network involving multiple stakeholders and processes, making it susceptible to various inefficiencies and challenges such as counterfeiting, drug expiry, and inefficient inventory management. These challenges may lead to compromised patient safety and financial losses. Blockchain technology is a promising solution to these problems. This study develops a blockchain-enabled mathematical model for pharmaceutical supply chains. A distributed ledger is used to acquire the real-time drug transaction status throughout the supply chain. The study uses real-time data gathered from the distributed ledgers across the supply chain, ensuring optimum inventory with the minimization of expired drugs and transportation costs. By leveraging the proposed model, stakeholders can eliminate counterfeiting, reduce drug expiry, and ultimately ensure the integrity and safety of pharmaceutical products throughout their lifecycle. This model also helps manufacturers in decision making for drug manufacturing based on real-time data. Novelty of the study lies in real-time tracing and managing the drugs across the supply chain.
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    Overcoming the extended producer responsibility challenges of packaging material through integrated refurbishing and recycling
    (Springer, 2024-11) Sangwan, Kuldip Singh; Kulshrestha, Rakhee
    This paper proposes a model to integrate the refurbishing and recycling activities with the forward supply chain aiming to overcome the recent challenges faced by the organizations while implementing extended producer responsibility (EPR) regulations. The proposed model is easy to use, and the decision-makers can visualize the effects of their decisions on economic health of the organization to fulfil the growing needs of environmental conservation and social obligations by trading-off the number, location, and capacity of the recycling, refurbishing, collection, and disposal centers. The proposed model has been validated in a process industry (paint production). The results of the case organization suggest that integrating the refurbishing and recycling of the paint packaging is not only economically beneficial to the organization but is also environment friendly and helps to create jobs for low-skilled labor. Two novelties of the research work are the following: (i) the proposed model has been developed to handle carbon footprints generated in the recycling, refurbishing, and disposal processes as well as transportation, and (ii) the ε-constraint and LP-metric methods have been used to generate a set of Pareto-optimal solutions unlike single optimal solution. These Pareto-optimal solutions provide the flexibility to the organization to pick up optimal solutions with different environmental, social, and economic requirements to provide the government agencies data for EPR obligations.
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    Reliability and transient analysis of discrete-time multi-class priority queue with energy saving vacation policy
    (EDP Sciences, 2025-06) Kulshrestha, Rakhee
    The wireless communication systems can be modeled using discrete-time multi-class priority queues. Also, it is desired to reduce energy consumption in these systems, which can be achieved by implementing a vacation policy with priority queues. This study investigates a Geo/Geo/1 multi-class priority G-queue system featuring a vacation policy and server breakdowns. In this model, customers arrive at discrete time intervals and are classified into three priority classes. Virus attacks (considered hostile customers) may disrupt the server’s functionality during the service, leading to interruptions. If the server has completed serving all classes of customers and no customers are waiting in the queues, it will go on vacation. The entire system is represented as a three-dimensional Markov chain, and its transient behavior is analyzed using the recursive method. By utilizing transient probability distribution, we compute various performance metrics for the system, taking both reliability and queueing analyses into account. In conclusion, we develop a cost function based on successful customer transmissions, and then the quasi-Newton method and particle swarm optimization (PSO) algorithm are used to determine the optimal reward cost.