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

TL;DR

This paper addresses the complex problem of minimizing the carbon footprint in timely e-truck transportation by developing a bi-criteria approximation algorithm that balances carbon reduction with computational efficiency.

Contribution

It introduces the first approximation algorithm for the CFO problem with guarantees on carbon footprint and battery capacity violations, along with polynomial time complexity.

Findings

Algorithm reduces carbon footprint by up to 11% in simulations.

Proves CFO problem is NP-hard even for feasibility.

Provides near-optimal solutions with theoretical guarantees.

Abstract

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 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.