Time-dependent shortest path with discounted waits

Jérémy Omer (1) , Michael Poss (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 MAORE - Methods, Algorithms for Operations REsearch

We study a variant of the shortest path problem in a congested environment. In this setting, the travel time of each arc is represented by a piecewise continuous affine function of departure time. Besides, the driver is allowed to wait at nodes to avoid wasting time in traffic. While waiting, the driver is able to perform useful tasks for her job or herself, so the objective is to minimize only driving time. Although optimal solutions may contain cycles and pseudo-polynomially many arcs, we prove that the problem is N P-Hard under a mild assumption. We introduce a restriction of the problem where waits must be integer and propose pseudo-polynomial algorithms for the latter. We also provide a fully polynomial time approximation scheme for a special case of the problem where the total wait is not too large. Finally, we discuss harder variants of the problem and show their inapproximability.

Domaines: Recherche opérationnelle [math.OC]

Jérémy Omer, Michael Poss. Time-dependent shortest path with discounted waits. 2018. ⟨hal-01836007v1⟩