A Continuous Approximation for Demand Responsive Transport with Meeting Points

Abstract

Optimisation of demand responsive transport requires solving a vehicle routing problem (VRP), a computationally demanding discrete combinatorial problem that can be challenging to integrate within a bi-level network design framework. Continuous approximations are therefore appealing, yielding tractable analytic formulae for key performance indicators of discrete routing problems. It is well known that the optimal tour length, V , of the travelling salesman problem for N points randomly distributed in area A has asymptotic 1 1 formula V ∼ N 2 A 2 . Established continuous approximations for more complex VRPs have the same, separable, functional form. In this paper we consider a first mile demand responsive transport problem characterised by the use of meeting points, with customer ride time constrained by a maximum detour factor. We show that the total tour length of this VRP cannot be described by existing continuous approximations. We propose a new continuous approximation functional form and demonstrate its effectiveness.