How Can Electric and Fuel Trucks Form the Perfect Caravan?

Imagine a long line of trucks driving side by side, saving energy and cutting emissions. This is the idea of a "platoon", a convoy that exploits reduced aerodynamic drag. In a mixed fleet of electric and fuel trucks, the challenge grows: how many vehicles can safely travel together? The answer lies in a size limit, set for safety and management reasons.

The researchers turned the problem into a bounded‑size coalition game. They derived a closed‑form rule that tells how to split trucks into optimal groups, maximizing the total platooning benefit. Once the structure is fixed, they introduced a "least‑core payoff" scheme that ensures no subgroup has an incentive to leave.

If the perfect stability zone (the core) is empty, the model computes the minimal relaxation needed for approximate stability. Numerical tests show this strategy beats previous methods, delivering the highest overall benefit and a fairer profit split. In practice, trucks can travel closer, save fuel or electricity, and keep a stable collaboration.

The approach paves the way for smarter fleets where electric and diesel trucks coexist synergistically, lowering costs and environmental impact.

The platoon formation problem is modeled as a positive‑sum cooperative game where each truck is a player and coalitions represent groups traveling together. The maximum size constraint \(k\) introduces a combinatorial limitation: not all partitions of the truck set are feasible. The authors prove that, under this condition, the optimal coalition structure is a near‑uniform partition, i.e., groups have sizes \(k\) or \(k-1\) depending on the total number of vehicles \(n\). This characterization dramatically reduces the search space, shifting from exponential to quasi‑linear complexity.

For benefit allocation, the model employs the "least‑core" concept: it seeks the smallest \(\epsilon\) such that a payoff vector \(x_i\) satisfies \(\sum_{i\in S} x_i \ge v(S) - \epsilon\) for every admissible coalition \(S\), where \(v(S)\) is the coalition's value (platooning benefit). When \(\epsilon = 0\), the point lies in the core and the coalition is stable. If the core is empty, the minimal \(\epsilon\) provides the smallest deviation from perfect stability, still ensuring that no sub‑group can improve by more than \(\epsilon\) by leaving the formation.

The least‑core computation is solved via dual linear programming, exploiting the symmetric structure of \(k\)-sized coalitions. Moreover, the paper proposes a polynomial‑time algorithm based on a "type‑based" aggregation procedure, grouping trucks by energy type (electric or diesel) and load capacity, further reducing computational complexity. Experimental results show that, compared to greedy heuristics or Nash‑based solutions, the proposed method maximizes total benefit by roughly 12‑15% and cuts the \(\epsilon\) value by an order of magnitude, confirming near‑perfect stability even in highly heterogeneous energy scenarios.