Mathematical Formulation Model for a School Bus Routing Problem with Small Instance Data

This paper aims to describe the mathematical formulation model and an exact optimal solution analyses for a school bus routing problem with small instance data. The formulated model has been used to compute the optimal solution of time spent by students at all bus stops, apart from that the bus stops are not necessary be linearly ordered. We also listed down five procedures of mathematical formulation model to reach an exact optimal solution for a school bus routing problem with small instance data. We assume that each bus has fixed pick up points, these generates the many possible routes for a bus, the number of routes that generated is equal to permutation of pick up points, for each route of a bus we computing the objective function and the route with smallest objective function value can be optimal route of a bus. The sample data from two schools located at Dar es Salaam are collected and validated in the model to shows the good performing of that model. The optimal solution results obtained shows that the students spent minimal minutes in new planned routes compared to current routes. Keywords: bus stop, students, buses, optimal value, optimal solution, set, pick up