Mathematics

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https://hdl.handle.net/20.500.14540/131

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Browsing Mathematics by Academic Level "Masters"

Now showing 1 - 5 of 5
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    Bottleneck Just-in-Time Sequencing for Mixed-Model Production Systems
    (Department of Mathematics, 2008) Poudyal, Chudamani
    Due to today’s competitive automotive industrial challenges of providing a variety of products at a very low cost by smoothing productions on a flexible transfer line, one of the most important and fertile research topic in industrial mathematics is to penalize jobs both for being early and for being tardy. A problem is to determine a production sequence for producing different types of products on the line. Just-in-Time (JIT) mixedmodel production system is used to address this problem, which involves producing only the right products of different models of a common base product in evenly balanced sequences in the exact quantities, at the right times, at the right place. Sequencing JIT production system can be formulated as a challenging nonlinear integer programming problem. The goal of such system is to balance the rate of production of products. Minimization of the variation in demand rates for outputs of supplying processes is the output rate variation problem (ORVP) and minimization of the variation in the rate at which different products are produced on the line is the product rate variation problem (PRVP). The problem for minimizing of deviations between actual and desired production for PRVP can be solved efficiently in pseudo-polynomial time complexity. However, the ORVPs for two or more levels are strongly NP-hard. Heuristic algorithms and dynamic programming to solve such NP-hard problems are summarized. But ORVPs with pegging assumption are solvable by reducing them to the corresponding weighted PRVPs. The cyclic sequences are optimal for both sum and max deviation PRVPs. For the bottleneck PRVP, a binary search technique is used to test the existence of a perfect matching and thereby to get optimal sequence. A feasible sequence always exists such that, at all times, the deviation of actual production from the desired level of production for every product is never more than one unit for the max-absolute and maxsquared PRVPs. An elegant algebraic concept of balanced words is used to deal the bottleneck PRVP. The max-absolute PRVP is shown to be Co-NP with leaving its general complexity open. In this thesis, we study several interesting algebraic structures, properties, existence of cyclic solutions and two applications of bottleneck PRVP. An optimal sequence for an instance of max-absolute PRVP is obtained. With considering two min-sum and maxabsolute objectives, a bicriterion objective for balancing the sequence is analyzed. A comparative study of different objectives is also summarized. Moreover, several directions for further research are also explored including some emerged conjectures.
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    Effect of Changing the Dimension of Initial Debris Mass in the Dynamics of Landslide Generated Tsunami
    (Department of Mathematics, 2021) Acharya, Grishma
    Debris ow is a traveling mass of loose mud, soil, air, water and sand that moves down a slope caused due to gravity. When debris ows, landslides, or any gravitational mass ows hit closed or partially open water sources such as seas, oceans, fjords, hydraulic reservoirs, mountain lakes, bays and landslide dams, it results in tsunami (impulse water waves) by transforming their impact energy to water body, potentially causing damages of infrastructures and human casualties both near eld and the distant coastlines. The degree of hazard depends on the scale, types, location and process of the landslide. Volume or size of the initial debris mass that fails in the slope, is one of the dominant factors in accelerating the splash strength or intensity, the propagation and amplitudes of the subsequent water waves and potential dam breach or water spill over. Here, we numerically integrate the two-phase mass ow model [61] for quasi three dimensional, high-resolution simulation results with variation of size of the two-phase initial landslide or debris both longitudinally and laterally. In our numerical experimental results, we observe fundamentally di erent solid and uid wave structures in the reservoir, and the dynamics of submarine mass ow for di erent volumes of the release mass by extending or contracting the base area along down-slope and/or cross-slope directions. The simulation results show that tsunami amplitudes and run out extents are rapidly increased when the volume of initial release mass in the form of a triangular wedge is enlarged by increasing the base area through the increment of the length and breadth of the release base. This study can be an instructive tool to develop and implement tsunami hazard mitigation measures to enhance public safety and reduce potential loss.
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    The Interplay Between Measure Theory and Topology
    (Department of Mathematics, 2016) Rana, Jit Bahadur
    A connection between measure theory and topology is established when a eld F is de ned in terms of topological properties. More precisely, we de ned F as the smallest eld containing all the open sets of a topological space , then there are interesting interrelation between measure theory and topology. We study the interrelation between topological space, open sets and continuous functions in one hand and measure space, measurable set and measurable function on the other.
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    Optimization models with exclusive bus lanes
    (Department of Mathematics, 2022) Chand, Gaurab
    Exclusively reserved lane for public buses in arterial road of the city is called exclusive bus lane (EBL). In this research study, we survey network optimization EBL models, then we review min-max dynamic optimization EBL model with three modes of vehicles. Major upgraded terms on reviewed model have been taken prior origin count of the bus travel time, bureau of public road (BPR) constraint to the car mode and maximum number of motorcycle rider constraint. Among them, BPR constraint has impacted signi cantly over objective function as well as planning of EBL on the transportation network. Tra c data related to the motorcycle mode had been estimated using statistical tool by increasing the capacity of arcs and without loss of generality with original data of buses and cars. We prefer parallel genetic algorithm (PGA) for the solution of the revised problem and proved that complexity is NP-hard. A numerical example is revealed as a reviewed optimization network model to achieve the feasibility and therefore yield optimal solution.
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    Visualization, Formulation and Intuitive Explanation of Iterative Methods for Transient Analysis of RLC Circuit
    (Department of Mathematics, 2021) Thakur, Bhogendra Kumar
    The time-varying currents and voltages resulting from the sudden application of sources usually due to switching are transients. An RLC circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series or in parallel. The transient response is dependent on the value of the di erent characteristics of the damping factor (i.e., overdamped, critically damped, and underdamped). The numerical solutions of rst and second-order di erential equations with initial value problem (IVP) have been computed by using the Explicit (Forward) Euler method, Implicit (Backward) Euler method, Classical second-order (Heun's or RK2) method, Third-order Runge-Kutta (RK3) method, Fourth order Runge-Kutta method and Butchers fth-order Runge-Kutta (BRK5) method. The observation compares this numerical solution of ODEs obtained by the above-mentioned methods among them with the necessary visualization and analysis of the error. These iterative methods will be extended and implement to analyze the transient analysis of an RLC circuit. The superiority of these methods over one another has been examined. The Butcher's fth-order Runge-Kutta (BRK5) method is found to be the best numerical technique to solve the transient analysis due to its high accuracy of approximations. Moreover, we consider the possibility of discussing and analyze above mentioned iterative methods in the cases of di erent characteristics of damping factors. Di erent methods are used di erent iterative methods to analyze the transient analysis of an RLC circuit and compared among them. The consequences of this work lend some limelight to the modern approaches to solving complicated mathematical problems.