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Logistics has gained great attentions with the prosperous development of e-commerce, which is often seen as the classic optimal vehicle routing problem. Meanwhile, electric vehicle (EV) has been widely used in logistic fleet to curb the emission of green house gases in recent years. Thus, solving the optimization problem of joint routing and charging of multiple EVs is in a urgent need, whose objective function includes charging time, charging cost, EVs travel time, usage fees of EV and revenue from serving customers. This joint problem is formulated as a mixed integer programming (MIP) problem, which, however, is NP-hard due to integer restrictions and bilinear terms from the coupling between routing and charging decisions. The main contribution of this paper lies at proposing an efficient two-stage algorithm that can decompose the original MIP problem into two linear programming (LP) problems, by exploiting the exactness of LP relaxation and eliminating the coupled term. This algorithm can achieve a nearoptimal solution in polynomial time. In addition, another variant algorithm is proposed based on the two-stage one, to further improve the quality of solution. Compared with the state-of-theart algorithm, extensive simulations are implemented to validate the effectiveness of the proposed algorithm. Index Terms-Electric vehicle, routing problem, mixed integer programming, linear programming NOMENCLATURE Given Parameters KThe set of EVs RThe set of transportation request nodes M i Revenue from serving requests when i ∈ R c v EVs' usage cost d ij Travel distance from node i to j where i, j ∈ V e ij Energy consumption traveling from node i to node j, e ij = d ij , where is the energy consumption rate g i Charging time per unit power(1 kWh) at node i, i ∈ V

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General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research.  You may not further distribute the material or use it for any profit-making activity or commercial gain  You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

No abstract