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This paper deals with the Electric Vehicle (EV) Scheduling and Optimal Charging Problem. More precisely, given a fleet of EVs and Combustion Engine Vehicles (CVs), a set of tours to be processed by vehicles and a charging infrastructure, the problem aims to optimise the assignment of vehicles to tours and minimise the charging cost of EVs while considering several operational constraints mainly related to chargers, electricity grid and EVs driving range. We prove that the Electric Vehicle Scheduling and Charging Problem (EVSCP) is NP-hard in the ordinary sense. We provide a mixed-integer linear programming formulation to model the EVSCP and use CPLEX to solve small and medium instances. To solve large instances, we propose two heuristics: a Sequential Heuristic (SH) and a Global Heuristic (GH). The SH considers the EVs sequentially. To each EV, it assigns a set of tours and guarantees the feasibility of a charging schedule. Then, it generates an optimal charging schedule for this EV. However, the GH computes, in the first step, a feasible assignment of tours to all EVs. In the second step, it applies a global Min-Cost-Flow-based charging algorithm to minimise the charging cost of the EVs fleet. To evaluate the efficiency of our solving approaches, computational results on a large set of real and randomly generated test instances are reported and compared.

Abstract-Although there are few efficient algorithms in the literature for scientific workflow tasks allocation and scheduling for heterogeneous resources such as those proposed in grid computing context, they usually require a bounded number of computer resources that cannot be applied in Cloud computing environment. Indeed, unlike grid, elastic computing, such as Amazon's EC2, allows users to allocate and release compute resources on-demand and pay only for what they use. Therefore, it is reasonable to assume that the number of resources is infinite. This feature of Clouds has been called "illusion of infinite resources". However, despite the proven benefits of using Cloud to run scientific workflows, users lack guidance for choosing between multiple offering while taking into account several objectives which are often conflicting.On the other side, the workflow tasks allocation and scheduling have been shown to be NP-complete problems. Thus, it is convenient to use heuristic rather than deterministic algorithm. The objective of this paper is to design an allocation strategy for Cloud computing platform. More precisely, we propose three complementary bi-criteria approaches for scheduling workflows on distributed Cloud resources, taking into account the overall execution time and the cost incurred by using a set of resources.