Optimal and Heuristic Approaches for Platooning Systems with Deadlines

Efficient truck platooning is a key strategy for reducing freight costs, lowering fuel consumption, and mitigating emissions. Deadlines are critical in this context, as trucks must depart within specific time windows to meet delivery requirements and avoid penalties. In this paper, we investigate the optimal formation and dispatch of truck platoons at a highway station with finite capacity $L$ and deadline constraints $T$. The system operates in discrete time, with each arriving truck assigned a deadline of $T$ slot units. The objective is to leverage the efficiency gains from forming large platoons while accounting for waiting costs and deadline violations. We formulate the problem as a Markov decision process and analyze the structure of the optimal policy $\pi^\star$ for $L = 3$, extending insights to arbitrary $L$. We prove that the $\pi^\star$ is monotone in the state space $\mathcal{S}$ and identify classes of unreachable states. Moreover, since $\mathcal{S}$ grows exponentially with $L$ and $T$, we propose heuristics-including conditional and deep-learning based approaches-that exploit these structural insights while maintaining low computational complexity.