Time coordination of bus arrivals on a set of bus stops

This paper deals with a time coordination of bus arrivals on a set of bus stops. A quality criterion of this problem is to minimize the waiting time of passengers to make public transport more attractive. One possible solution to this problem is to coordinate bus arrivals. This problem can be formulated as a mathematical model with the quadratic objective function and a set of equality or inequality constraints. Nevertheless, this quadratic programming model can be difficult to solve. Our approach introduced in this paper is based on a piecewise linearization of the quadratic objective function. This integer programming model enables to include to the problem some other significant aspects of time coordination of bus arrivals. Therefore, the attention is aimed at the importance of continuity of bus arrivals on a set of bus stops. Integer programming model of the above mentioned problem will be presented in the following text and associated numerical experiments with real data will be presented too.