ALGORITHM

Efficient route planning plays a crucial role in logistics management because it directly affects transportation cost, delivery time, and operational efficiency. Many delivery operations experience inefficiencies due to poorly structured routing strategies, particularly when multiple locations must be served from a single depot. This study focuses on optimizing delivery routes for Viboi Ventures, a Coca Cola distribution depot located in Benin City, Nigeria. The primary aim of the research is to determine the most efficient delivery sequence that minimizes total travel distance while ensuring that each destination is visited exactly once. To achieve this aim, the study obtained delivery location data, determined inter-location distances using Google Maps, and developed an optimization model to evaluate alternative delivery routes. The study adopts a quantitative modelling approach based on the Travelling Salesman Problem (TSP), a well established optimization model used to determine the shortest possible route through multiple locations. Distance data between the depot and nine delivery points were collected using Google Maps and organized into a distance matrix. Manual computations were first conducted to evaluate feasible route combinations. To enhance the reliability of the results, the Branch and Bound optimization algorithm was subsequently applied to systematically evaluate route alternatives and validate the optimal solution. The analysis showed that the manually derived route produced a total travel distance of 13.7 km, while the algorithm based solution generated a shorter distance of 12.2 km both was significantly lower than that of the company’s existing delivery route which is 18.7km. This result demonstrates the effectiveness of algorithmic optimization in improving delivery efficiency and reducing travel distance. The study concludes that applying computational optimization techniques such as the Branch and Bound algorithm, combined with real world geographic data, can significantly improve logistics planning and operational performance for delivery based businesses.

This study evaluated and compared the performance of three statistical methods for hypothesis testing when comparing means between two populations: the t-test, Welch's t-test, and the z-test. The t-test assumes normally distributed data and equal variances, while Welch's t-test accounts for unequal variances, and the nonparametric Mann- Whitney U test is an alternative for non-normal data. The research aimed to determine the optimal test by formulating hypotheses, selecting appropriate test statistics, determining sample sizes, and implementing the tests using R programming. The data analyzed were the mean heights of NBA guards and forwards during the 2022-2023 season. A power analysis assessed the reliability, validity, and assumptions of the tests. The results indicated a significant difference in mean heights between guards and forwards, with guards being slightly taller on average. Importantly, the Welch's t-test consistently outperformed the standard t-test and z-test across varying sample sizes, demonstrating higher power and a greater ability to detect true effects while minimizing Type I and Type II errors. This superior performance is attributed to the robustness of Welch's t-test in handling unequal variances between groups, a common scenario in real -world data analysis.