A tabu search based heuristic for the transportation of mentally disabled people
Résumé
Transportation of mentally disabled persons is subject to many specific constraints due to medical or organisational reasons. We consider the problem of the daily transportation of persons from their home to specialized medical or social institutions. This concerns either mentally disabled children who attend specialised schools, or adults working in vocational rehabilitation centres. Most of them are unable to travel on their own, so that a dedicated transportation system must be managed by the centres. Daily inbound and return trips for dozens of persons are generally performed by costly taxis or minibuses. We model the underlying optimisation problem as a multi-periodic vehicle routing problem with time windows, heterogeneous fleet and additional constraints. The main characteristic of the model is to mix closed routes (that form loops from the centre) and open routes from the driver's home to the centre. We propose two objective functions aimed at minimising the transportation cost or finding a trade-off between the cost and the quality of service respectively. Our approach for solving this problem efficiently and rapidly is a three phase heuristic. The first phase addresses a so called standard problem where every person is located at their main address with the most classical time window. Initial routes are built through a best insertion procedure based on a regret calculation. The second phase is a tabu search that combines several classical moves of the literature: customer relocation, customer exchange, cross-exchange, string exchange etc. The third step considers the real daily demand of every person. This step integrates possible daily variations in the demand: possible absence, variations in the time windows, daily changes in the addresses (pick-up or delivery at the parents, home family, nurse, etc.). The algorithm has been embedded in a decision support system called Marika. This decision support system seeks both technical efficiency and the satisfaction of human concerns. We present numerical results obtained from both test instances from the VRP literature and real instances. We show that the average of the individual travelling times as well as the total travelling time of the vehicles can be reduced by around 15% for real instances. We finally enumerate some research perspectives. A first improvement is to obtain consistent schedules for every person. The idea is that daily variations in the demand of some transported persons should have limited impact on the schedules of other persons. This issue is important when applied to a fragile population. A second objective is to look for a trade-off between the cost, the quality and the consistency of service through a multi-objective optimization. The last project research concerns the possibility for distinct centres to organize common transportation services in order to reduce the costs.