Some approaches on checkpoint dial-a-ride problems

The aim of this paper is to present some modelling approaches related to a special form of advanced public transport operations and called with different names such as route deviation line, point deviation bus line, corridor deviation line and checkpoint dial-a-ride. A checkpoint dial-a-ride transit system combines characteristics both of traditional fixed route transit and of advanced door-to-door dial-a-ride service. It resembles fixed route operations because some users have to walk to and from at a finite number of stops located on a corridor and always visited. The checkpoint dial-a-ride system also resembles a door-to-door service because some users are picked up and dropped on demand at another finite number of special stops, called deviated stops or checkpoints, located near their trip ends. Such checkpoints are the main elements of a route deviation bus operations, which accepts user demands and, by communicating with a central control unit, makes the bus deviate from its regular route to serve the off-fixed-line request and then return on the regular route. Route deviation bus systems has been proposed and applied in several countries in order to enhance effectiveness of urban transit during off-peak periods, as well-suited service for small cities or as part of a larger integrated transit system. Nevertheless, mathematical modelling of problems associated to route deviation bus systems has received few research contributions. In this paper we describe some of the most recent mathematical approaches to the deviation bus route design problem.