Mathematical formulation of the Nigeria road network model of multiple sources to multiple destinations

In this research work, we examine Nigeria road network of multiple sources-to-multiple destinations from the coastal towns of Lagos, Warri/Asaba, Port Harcourt and Calabar through the intermediary routes to multiple destinations of the border town of Sokoto, Katsina and Maiduguri. The mathematical model was developed using positive edge weights based on the current road distances between state capitals obtained from Nigeria kilometer chart of state capitals. Lingo computer application package was used to solve the formulated problem consisting of 1 objective function, 75 constraints and 441 variables to identify the shortest routes from given multiple sources-to-multiple destinations. The shortest routes obtained compared favorably with the actual ones and were found to be the best