Minimizing Carbon Footprint for Timely E-Truck Transportation: Hardness and Approximation Algorithm
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Carbon footprint optimization (CFO) is important for sustainable heavy-duty e-truck transportation. We consider the CFO problem for timely transportation of e-trucks, where the truck travels from an origin to a destination across a national highway network subject to a deadline. The goal is to minimize the carbon footprint by orchestrating path planning, speed planning, and intermediary charging planning. We first show that it is NP-hard even just to find a feasible CFO solution. We then develop a (1+ϵ_F, 1+ϵ_β) bi-criteria approximation algorithm that achieves a carbon footprint within a ratio of (1+ϵ_F) to the minimum with no deadline violation and at most a ratio of (1+ϵ_β) battery capacity violation (for any positive ϵ_F and ϵ_β). Its time complexity is polynomial in the size of the highway network, 1/ϵ_F, and 1/ϵ_β. Such algorithmic results are among the best possible unless P=NP. Simulation results based on real-world traces show that our scheme reduces up to 11% carbon footprint as compared to baseline alternatives considering only energy consumption but not carbon footprint.
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