A mathematical programming model for the bus deviation route problem

In small towns, or in those peripherical metropolitan areas in which the demand for public transportation is relatively low, the objectives of the bus route planner are different from those faced in highly congested networks. Some towns, also in Italy, are experimenting with urban public transportation systems where regular bus routes are designed which allow users located at specific points outside the main line to signal their presence to the bust driver, who then deviates from the main route to satisfy this demand. This way the bus line is a mixture between a regular line and a dial-a-ride system. The bus deviation route problem is concerned with the design problem which arises in planning the location of the demand points outside the line. A model is presented which takes into account both the advantage of passengers served by this deviation device and the disadvantage suffered by passengers on the bus, whose travel time increases during deviations. and by passengers downstream of the deviation whose waiting time also increases. Through some modeling assumption we are able to represent this problem as a mixed integer linear programming problem, whose relatively low dimension allows for exact solution through standard simplex-based branch and bound code. The proposed model has been applied to a real case and some results of this are presented and discussed.