The Integrated Dial-a-Ride Problem

Abstract

In this paper we present a formulation of the Integrated Dial-a-Ride Problem (IDARP). This problem is to schedule dial-a-ride requests, where some part of each journey may be carried out by a fixed route service. The IDARP is a generalization of the Dial-a-Ride Problem. An arc-based formulation is proposed, and it is shown how the model can be made easier to solve by arc elimination, variable substitution and the introduction of subtour elimination constraints. Small instances of the IDARP can be solved using an exact solution method, and one such instance is studied. We also describe how input and output data can be created and visualized in a geographic information system.

The integrated dial-a-ride problem with timetabled fixed route service

“…This is reasonable and extends the applicability of the model but makes some of the arc elimination rules for the DARP and IDARP introduced in Cordeau (2006) and Häll et al (2009) invalid, since the triangle inequality for the demand responsive and fixed route vehicles is no longer true in all cases.…”

“…Based on an arc-flow formulation of the DARP from Cordeau (2006), a mathematical programming formulation of the IDARP is given in Häll et al (2009). Using this formulation the problem is solved exactly for small instances, up to 10 requests.…”

“…Some of these rules are specific to the IDARP while some are also used for the dial-a-ride, pick-up and delivery, vehicle routing, and travelling salesman problems. Häll et al (2009) assume that the frequency on the fixed route lines is so high that customer waiting times at transfer locations can be disregarded. As the real-world environments where an integrated demand responsive service for the elderly and/or disabled could be useful are likely to be low density urban areas and more rural areas, this assumption could well limit the practical applicability of the model.…”

“…Also, the fixed route lines that have the largest potential for lowering operational costs are lines covering large distances, making the assumption of short waiting times possibly unrealistic. Additionally, the travel times of all vehicles, both demand responsive and fixed route, are assumed to be the same in the model presented in Häll et al (2009). This is quite a rigid framework that does not allow for the introduction of, for example, commuter trains (possibly a lot faster than demand responsive vehicles) or bus lines with convoluted, non-direct, paths (possibly a lot slower than demand responsive vehicles taking the shortest path).…”

“…In the model presented in Häll et al (2009), each transfer location is modeled by one node for each request. Thus, each request adds 2 + g nodes to the network, where g is the number of physical transfer locations.…”