Minimizing Carbon Footprint for Timely E-Truck Transportation: Hardness and Approximation Algorithm

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
$(1+\epsilon_{F}, 1+\epsilon_{\beta})$
bi-criteria approximation algorithm that achieves a carbon footprint within a ratio of
$(1+\epsilon_{F})$
to the minimum with no deadline violation and at most a ratio of
$(1+\epsilon_{\beta})$
battery capacity violation (for any positive
$\epsilon_{F}$
and
$\epsilon_{\beta}$
). Its time complexity is polynomial in the size of the highway network,
$1/\epsilon_{F}$
, and
$1/\epsilon_{\beta}$
. Such algorithmic results are among the best possible unless
$\mathbf{P}=\mathbf{NP}$
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.