Siting of water borehole at Tamale Islamic senior high school using the absolute 1-centre problem

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This thesis seeks to model the location of water borehole at Tamale Islamic Senior High School in the Tamale Metropolis. The Absolute 1-centre algorithm is used to identify the optimal water borehole location at Tamale Islamic Senior High School. The Absolute 1-centre problem seeks to minimize the maximum weighted distance necessary for both students and masters to access the water borehole facility. We focus on the residence of masters and students and other places of importance in the school. We collected data on the road distances between the structures in the school and developed it into a network. We compute the matrix of shortest paths for all pairs of nodes using the Floyd Warshall Algorithm from which the vertex centre was found. The local centre for each edge of the network developed was computed and the least of all the local centres was compared to the vertex centre. The solution to the Absolute 1-centre problem was obtained by locating the vertex centre to be node A (school administration) with cost 353metres.The local centre was also found to be 25m from node A and 228m from node B (Boys dormitory) with a cost of 340m.Since the local centre had a least cost compared to the vertex centre, it is taken as the absolute centre of the network.
A thesis submitted to the Department of Mathematics Institute of distance Learning Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirements for the award of the degree of MASTER OF SCIENCE, September 2011