´ ´ BERNAT GACIAS AND FREDERIC MEUNIER
Abstract. The deployment of electric taxi ﬂeets is highly desirable from a sustainable point of view. Nevertheless, the weak autonomy of this kind of vehicles requires a careful operation. The way of managing such a ﬂeet and the question of locating charging terminals for the vehicles are addressed in this paper. Methods for dealing with these tasks are proposed and their eﬃciency is proved through simulations.
1. Introduction 1.1. Context. Centrale OO 1 is a pioneering project aiming to deploy in Paris a ﬂeet of 100 % electric taxis. The company in charge of the management of the ﬂeet is the Soci´t´ du Taxi Electrique Parisien (STEP). ee The deployment of such ﬂeets ﬁnds is main motivation in sustainable issues: electric vehicles release almost no air pollutants at the place where they are operated and have less noise pollution than internal combustion engine vehicles. However, the main drawback of an electric vehicle is its weak autonomy – 80 km in the case of the Centrale OO project. In taxi ﬂeet management, two kinds of requests can be diﬀerentiated: booking requests and opportunistic requests. The ﬁrst ones can be immediate or in advance of travel and have to be processed by the taxi dispatching system which assigns the request to a taxi. The opportunistic requests correspond to the traditional taxi services picking up passengers at cab-ranks or from the side of the road. Of course, this kind of requests is not processed by the dispatching system. The constraints of the management, as expressed by the STEP, are • A taxi must never break down • An opportunistic demand inside Paris and its suburbs must always be satisﬁed (legal environment of Paris) • The number of booking demands accepted has to be maximized The charging problem of the taxis must therefore be carefully addressed. At a tactical level, a good assignment of the trips to the taxis is crucial. We propose an eﬃcient way to manage the electric ﬂeet in real-time while taking into account the charging tasks. At a strategic level, the charging problem includes the determination of the best location for the charging terminals. The signiﬁcant initial investment (the cost of an electrical charging terminal is about 20.000 euros) and the restricted vehicle autonomy give a high relevancy to the charging terminal location task. Indeed, a wrong placement may in eﬀect lead to a poor ﬂeet management with vehicles having diﬃculties to charge the batteries due to charging terminals saturation or even with vehicles constantly running out of charge to keep operating. Our purpose is to propose a practical way for computing the “best” locations for the charging terminals. 1.2. Model. We describe now formally the model we deal with in this paper. We derive also some elementary relations, which gives some informations on the capacity of a given system (in terms of number of trips that can be realized by unit of time). 1.2.1. Input description. A complete directed graph G = (V, A) models the network. The vertices are points in the city at which trips start and ﬁnish. They can moreover be used to locate vehicle charging terminals. The arcs model the possible trips. The duration of a trip is a random variable Ta of expectation τa . The Key words and phrases. charging terminal location; electric vehicles; ﬂeet management system; mixed integer programming; simulation; taxi dispatching. This project has been funded by R´gion Ile de France. e 1 See the website http://taxioo.com/index.html for an artistic view. 1
hal-00721875, version 2 - 31 Jul 2012
demand for each possible trip a ∈ A is assumed to follow a Poisson process of rate λa . Actually, this demand is split between a booking demand and an opportunistic demand, see Section 5 for a more accurate description. There are n taxis. A taxi consumes γ Wh by unit of time when it is moving. It stores ρ Wh by unit of time when it is charging. The...