Optimization of occupancy rate in dial-a-ride problems via linear fractional column generation

Thierry Garaix (1, 2) , Christian Artigues (3) , Dominique Feillet (4) , Didier Josselin (5)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
2 CIS-ENSMSE - Centre Ingénierie et Santé
3 LAAS-MOGISA
4 LIA - Laboratoire Informatique d'Avignon
5 ESPACE - Études des Structures, des Processus d’Adaptation et des Changements de l’Espace

In this paper, we consider a dial-a-ride problem where the objective is to maximize the passenger occupancy rate. The problem arises from an on-demand transportation system developed in a rural zone in France, where the objective of encouraging people meeting is pursued. We address the solution of the problem with a column generation approach, applied to a set partitioning formulation where the objective function is fractional. Based on the literature on linear fractional programming, two methods are developed to deal with this fractional objective. Experiments permit to compare these two approaches and to evaluate the impact of the new objective compared to a standard min-cost or min-time optimization.

Mots clés: dial-a-ride problem; column generation; vehicle routing; on-demand transportation; linear fractional program; dial-a-ride problem

Domaines: Recherche opérationnelle [math.OC]

Thierry Garaix, Christian Artigues, Dominique Feillet, Didier Josselin. Optimization of occupancy rate in dial-a-ride problems via linear fractional column generation. Computers and Operations Research, 2011, 38 (10), pp.1435 - 1442. ⟨10.1016/j.cor.2010.12.014⟩. ⟨hal-01904436⟩