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

Authors:
Thierry Garaix;Christian Artigues;Dominique Feillet;Didier Josselin
Affiliations:
Politecnico di Torino, DAUIN, Torino, Italy;CNRS/ LAAS/ 7 avenue du colonel Roche, F-31077 Toulouse, France and Université/ de Toulouse/ UPS, INSA, INP, ISAE/ LAAS/ F-31077 Toulouse, France;Ecole des Mines de Saint-Etienne, CMP Georges Charpak, F-13541 Gardanne, France;Université/ d'Avignon et des Pays de Vaucluse, UMR ESPACE 6012 CNRS, F-84911 Avignon, France
Venue:
Computers and Operations Research
Year:
2011

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Abstract

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.