The holding problem at multiple holding stations.

*(English)* Zbl 1169.90329
Hickman, Mark (ed.) et al., Computer-aided systems in public transport. Selected papers based on the presentations at the 9th international conference, San Diego, CA, USA, August 9–11, 2004. Berlin: Springer (ISBN 978-3-540-73311-9/pbk). Lecture Notes in Economics and Mathematical Systems 600, 339-359 (2008).

Summary: Inherent stochasticity within the transit operating environment suggests there may be benefits of holding vehicles at more than one holding station on a route. In this paper, the holding problem at multiple holding stations considers holding vehicles at a given subset of stations on the route. By approximating the vehicle dwell time as the passenger boarding time, the holding problem at multiple holding stations can be modeled as a convex quadratic programming problem, with the objective function as a convex quadratic function subject to many linear constraints. This particular problem can be solved by a heuristic that decomposes the overall problem into sub-problems which can be solved to optimality. Also, a hypothetical numerical example is presented to illustrate the effectiveness of the problem formulation and heuristic.