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Author(s): Achaku D. T., Sani B..

Volume/Issue: Volume 7 , Issue 2 (2024)

Abstract:

Vehicle Routing Problem with Time Windows (VRPTW) is an NP hard combinatorial scheduling optimization problem in which a minimum number of routes have to be determined so as to serve each of the destinations within their specified time windows. In this paper, the mail delivery of the Nigerian Postal Services (NIPOST) is modelled as a VRPTW in order to address the problem of delay in mail delivery occurring regularly in NIPOST. The Abuja Post Office is used as a case study and the Model of a related literature is applied with modifications to solve the problem. The problem is solved by applying Lexisearch algorithm using data that was obtained from Abuja Post Office and computational results on Solomon’s 100 instances were used to validate the algorithm.

Keywords:

Vehicle routing problem, Branch and bound algorithm, Time windows, Optimal and mail clearance.

No. of Downloads: 0

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Author(s): George Obed Samuel, P. O. Ekoko (Prof.).

Volume/Issue: Volume 7 , Issue 2 (2024)

Abstract:

Game theory is the examination of strategic interactions between two or more individuals known as players who act based on their individual self-interest within a framework known as the game. Every player possesses a set of possible actions referred to as strategies, from which they make selections. In a two-person zero sum game, each of the two players has at least two strategies. In such a game problem where both players have no inferior strategies, we can determine the optimal mixed strategies of the game problem by converting it to a linear programming problem and solving it using the simplex method or variations of it. In this paper, consideration of some existing models along with our proposed model on the conversion of game problem to LPP was made. We compared the results across the various models considered. The results obtained revealed that our proposed model on the conversion of game problem to LPP produced a higher value of the game compared to the others considered; and thus, produced better performance.

Keywords:

Game Theory, Linear Programming Formulation, linear programming problem, simplex method.

No. of Downloads: 0

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Author(s): Awoyemi Samson Oyebode, Taiwo Abass Ishola, Olatayo Timothy Olabisi.

Volume/Issue: Volume 7 , Issue 2 (2024)

Abstract:

The study proposed a Trend-Fourier Regression (TFR) model to handle time series datasets with simultaneous trend and cyclical variations. The model steps involve identification, estimation, diagnosis and forecasting. The Nigerian monthly Crude Oil Price (NMCOP) was used to implement the model and NMCOP was identified as trend-cyclical. The model estimation using Ordinary Least Squares method indicates that an increase in time will result in changes in NMCOP. Durbin-Watson statistics, histogram and autocorrelation function of residual plots were used to diagnose and specify the model to be stable. The coefficient of determination (R^2) indicates that over 80% of dependent variable variations were explained, with an adjusted (R^2) indicating a predictive ability exceeding 80%. The model efficiency was confirmed through out-sample and forecast evaluations, revealing superiority due to its smaller MAE, RMSE, and MAPE values, indicating minimal error. Conclusively, the TFR model is suitable for datasets that exhibit trend-cyclical variations simultaneously.

Keywords:

Trend-cyclical variation, Diagnostic checking, Trend-Fourier regression, Nigerian monthly crude oil price, Forecasting, Estimation.

No. of Downloads: 0

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Author(s): Adagba T. Titus, Ben O. Johnson, Auta T. Jonathan.

Volume/Issue: Volume 7 , Issue 2 (2024)

Abstract:

The structure of groups plays an important role in the study of the nature of the groups. We examine some basic properties and structural characteristics of the dihedral group of degree n, where n is a natural number, by group-theoretic approach. We begin the exploration by providing a foundational understanding of dihedral groups, elucidating their definitions and essential properties. Furthermore, we investigated the algebraic and geometric aspects of these groups, highlighting their role in describing symmetries of n-gons and other mathematical entities. Special attention is given to the distinctive features that differentiate dihedral groups from other algebraic structures. The analytic expressions for the order of subgroups are obtained and the commutativity investigated. The groups are all represented for further analysis and applications.

Keywords:

Algebraic Structure, Permutation Group, Dihedral Group, Subgroups, Isomorphism, Generators.

No. of Downloads: 0

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Author(s): Onuoha N.O..

Volume/Issue: Volume 7 , Issue 2 (2024)

Abstract:

This paper presents the theoretical study of forced Van der Pol oscillator equation. Oscillatory systems are studied to know measures that can reduce the amplitude of oscillation of the oscillatory system. Here, multiple two-timing regular parameter perturbation is applied since it is a kind of perturbation among other perturbation techniques that enables the study of the behaviour of a system under certain conditions. Asymptotic expansion technique was also applied. Excel Microsoft was used to analyse the uniformly valid asymptotic solution of the Van der Pol oscillator equation obtained. The uniformly valid asymptotic solution in the independent variable obtained, showed that damping alters the amplitude of the oscillatory system thereby affecting its motion. Increase in damping decreases the amplitude of oscillation of the system. With damping incorporated in the system though very small damping, the amplitude of oscillation reduces with time.

Keywords:

Oscillatory system, Regular parameter perturbation, asymptotic expansion, damping, amplitude, oscillation.

No. of Downloads: 0

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Author(s): Oti Eric U, Olusola Michael O..

Volume/Issue: Volume 7 , Issue 2 (2024)

Abstract:

The agglomerative hierarchical clustering methods are the most popular type of hierarchical clustering used to group objects in clusters based on their similarity. The methods are represented by a bottom-up approach where each object starts in its cluster and pairs of clusters are merged as it moves up the hierarchy. In this paper, we present six agglomerative hierarchical clustering methods namely: the single linkage method, complete linkage method, average linkage method, centroid method, median method, and Ward’s method. We also evaluated how these methods work on a practical basis using a matrix of distance pairs of five points. It was observed that the single linkage method through its dendrogram produced the most similarity measure between x_i and x_j, while Ward’s method produced the highest distance measure between x_i and x_j.

Keywords:

Agglomerative methods; Dendrogram; Distance matrix; Objects; Similarities.

No. of Downloads: 0