Phase-type distributions and their applications to the vehicle routing problem with stochastic travel and service times

Andrés Gómez (1) , Raha Akhavan-Tabatabaei (1) , Andrés Medaglia (1) , Jorge E. Mendoza (2)

1 COPA - Centro para la Optimización y Probabilidad Aplicada, Departamento de Ingeniería Industrial
2 LIFAT - Laboratoire d'Informatique Fondamentale et Appliquée de Tours

The vehicle routing problem with stochastic travel and service times (VRPSTT) consists in designing routes of minimal expected cost over a network where travel and service times are represented by random variables. Most of the existing approaches for VRPSTT are conceived to exploit the properties of the distributions assumed for the random variables. Therefore, these methods are tied to a given family of distributions and subject to strong modeling assumptions. We propose an alternative way to model travel and service times in VRPSTT while making few assumptions regarding such distributions. To illustrate our approach, we embed it into a state-of-the-art routing engine and use it to conduct experiments on instances with dierent travel and service time distributions.

Domaines: Recherche opérationnelle [math.OC]

Andrés Gómez, Raha Akhavan-Tabatabaei, Andrés Medaglia, Jorge E. Mendoza. Phase-type distributions and their applications to the vehicle routing problem with stochastic travel and service times. ODYSSEUS 2015, May 2015, Ajaccio, France. ⟨hal-01179357⟩