Coordination of Bus Departures by Mathematical Programming

Abstract

This paper deals with coordination of bus arrivals. A quality criterion of this problem is to minimize waiting time of passengers, to make public transport more attractive. One possibility for solving is to increase the number of arrivals with associated investments. Another possibility, without investment, is the coordination of bus arrivals. The latter possibility is analyzed and solved in this paper. Mathematical formulation of this problem leads to a quadratic programming model which is hard to solve. Our approach is based on piecewise linearization of the quadratic objective function. This integer programming model enables to include to the problem some other non-trivial aspects of arrival coordination. These additional aspects are the necessity of safety break compliance and order rearrangement of bus arrivals at a given bus stop. In this paper, integer programming models of the above mentioned problems are presented and the associated numerical experiments are reported to enable comparison of the suggested approaches.