Rollout-Based Charging Scheduling for Electric Truck Fleets in Large Transportation Networks

Andreas A. Malikopoulos; Shaoyuan Li; Ting Bai; Xinfeng Ru

arxiv: 2604.02768 · v1 · submitted 2026-04-03 · 📡 eess.SY · cs.SY

Rollout-Based Charging Scheduling for Electric Truck Fleets in Large Transportation Networks

Ting Bai , Xinfeng Ru , Shaoyuan Li , Andreas A. Malikopoulos This is my paper

Pith reviewed 2026-05-13 19:52 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords electric truck fleetscharging schedulingrollout-based dynamic programmingoptimizationtransportation networkselectric vehiclesdynamic programming

0 comments

The pith

A rollout-based dynamic programming framework solves charging schedules for large electric truck fleets near-optimally in polynomial time.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the joint optimization of charging sequences and power levels for large electric truck fleets that share dedicated stations, where the coupling of discrete ordering choices with continuous control makes exact solutions intractable for real-time use. It introduces a rollout-based dynamic programming approach organized in an inner-outer two-layer structure that separates sequencing decisions from power allocation. This separation enables efficient evaluation of policies while preserving near-optimality and allows the method to respond to trucks arriving dynamically and to time-varying electricity prices. The resulting algorithm runs in polynomial time and delivers solutions that substantially improve upon standard heuristics in both quality and speed. A sympathetic reader would care because fleet operators need fast, high-quality schedules to keep costs low without relying on slow exact solvers that cannot scale.

Core claim

The rollout-based dynamic programming framework built on an inner-outer two-layer structure decouples discrete sequencing decisions from continuous power allocation, enabling efficient policy evaluation and approximation that yields near-optimal solutions with polynomial-time complexity for the fleet charging scheduling problem while adapting to dynamic arrivals and time-varying prices.

What carries the argument

Rollout-based dynamic programming framework with inner-outer two-layer structure that separates ordering decisions from schedule optimization.

If this is right

Real-time charging management becomes feasible for large-scale transportation networks.
The approach outperforms conventional heuristics in both solution quality and computational efficiency.
Schedules remain effective under dynamic truck arrivals and changing electricity prices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same two-layer decoupling could apply to other mixed discrete-continuous scheduling problems in transportation or energy systems.
For fleets much larger than those simulated, hybrid methods combining the rollout step with additional heuristics may be needed to maintain speed.
Direct coupling of the scheduler with live traffic data could further improve adaptation to network conditions.

Load-bearing premise

The inner-outer two-layer structure decouples sequencing from power allocation in a way that keeps solutions near-optimal for the fleet sizes and network conditions considered.

What would settle it

A simulation run on a fleet size or network larger than those tested where the rollout method's total cost exceeds the true optimum by more than a few percent, as measured against an exact solver run on a smaller instance.

Figures

Figures reproduced from arXiv: 2604.02768 by Andreas A. Malikopoulos, Shaoyuan Li, Ting Bai, Xinfeng Ru.

**Figure 1.** Figure 1: Comparison of the total cost (N = 8). 1) Comparison with the Exact Solution: We first evaluate the optimality and computational efficiency of the proposed approach by comparing it with the exact solution for small ET fleets, with N = 4, 5, 6, 7, 8 and C = 3. The slack parameter is set to S = 1.5, and all trucks are assumed to arrive within a 30-minute time window. The station-level charging power limit is … view at source ↗

**Figure 3.** Figure 3: presents the total operational cost of the fleet for N = 100, comparing the rollout-based policies with the heuristic methods. The results show that RO (FCFS) achieves the lowest total cost, where the cost caused by tardy penalties is reduced significantly compared with other approaches. Moreover, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Comparison of the total charging power ( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

read the original abstract

In this paper, we investigate the charging scheduling optimization problem for large electric truck fleets operating with dedicated charging infrastructure. A central coordinator jointly determines the charging sequence and power allocation of each truck to minimize the total operational cost of the fleet. The problem is inherently combinatorial and nonlinear due to the coupling between discrete sequencing decisions and continuous charging control, rendering exact optimization intractable for real-time implementation. To address this challenge, we propose a rollout-based dynamic programming framework built upon an inner-outer two-layer structure, which decouples ordering decisions from the schedule optimization, thus enabling efficient policy evaluation and approximation. The proposed method achieves near-optimal solutions with polynomial-time complexity and adapts to dynamic arrivals and time-varying electricity prices. Simulation studies show that the rollout-based approach significantly outperforms conventional heuristics with high computational efficiency, demonstrating its effectiveness and practical applicability for real-time charging management in large-scale transportation networks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The two-layer rollout method for electric truck charging scheduling is a practical extension that runs efficiently and outperforms heuristics in simulations.

read the letter

Rollout dynamic programming with a two-layer split looks like a solid way to handle charging schedules for big electric truck fleets without blowing up the computation time. The outer layer handles the ordering of which trucks charge when using a base policy, while the inner layer solves the continuous power allocation as a convex problem. This keeps the evaluation polynomial in fleet size and lets the method adapt to changing electricity prices and new truck arrivals. The construction is explicit and the stress-test note confirms the decoupling works without internal contradictions or hidden assumptions that would break the polynomial claim. What stands out is how they apply this to the specific problem of dedicated charging infrastructure for trucks in large networks. The simulations show clear gains over standard heuristics in both cost and speed, which is the practical payoff. The paper builds on established rollout ideas but tailors them cleanly to the coupling between sequence and allocation, and the results are consistent with the headline performance gap. The main limitation is that near-optimality is demonstrated through simulations rather than with theoretical guarantees on the approximation gap. That is common in this area but means the results are tied to the scenarios tested. There is also not much on how sensitive the method is to the choice of base policy or to variations in network topology. This paper is aimed at researchers and practitioners in transportation systems and fleet management who need scalable optimization tools for electrification. A reader working on similar scheduling problems would get value from the explicit algorithm and the performance numbers. It is coherent and engages the literature properly, so it deserves a serious referee. I would send it to peer review with the expectation that reviewers will ask for more on the base policy and perhaps additional test cases.

Referee Report

1 major / 1 minor

Summary. The paper proposes a rollout-based dynamic programming framework with an inner-outer two-layer structure for jointly optimizing charging sequences and power allocations for large electric truck fleets. The approach decouples discrete ordering decisions (via base-policy enumeration in the outer layer) from continuous convex power-allocation subproblems (in the inner layer) to minimize total fleet operational cost under time-varying electricity prices and dynamic arrivals, claiming polynomial-time complexity and near-optimal performance that significantly outperforms conventional heuristics in simulations.

Significance. If the near-optimality and polynomial scaling hold, the method would provide a practical, real-time solution for large-scale electric truck charging coordination, bridging the gap between intractable exact optimization and heuristic approaches in transportation networks with dedicated infrastructure.

major comments (1)

[Simulation studies (as referenced in the abstract)] The central claim of 'near-optimal solutions' rests entirely on simulation studies without reported quantitative error bounds, optimality gaps relative to exact solutions on small instances, or verification of the approximation quality for the inner-outer decoupling; this makes the performance assertion difficult to assess rigorously beyond the specific simulated regimes.

minor comments (1)

[Abstract] The abstract states 'polynomial-time complexity' without specifying the degree or explicit dependence on fleet size and network parameters, which would help clarify the scaling claims.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. The comment on strengthening the validation of near-optimality claims is well-taken, and we will revise the manuscript to incorporate quantitative assessments on small instances while clarifying the rationale for heuristic comparisons on large-scale problems.

read point-by-point responses

Referee: [Simulation studies (as referenced in the abstract)] The central claim of 'near-optimal solutions' rests entirely on simulation studies without reported quantitative error bounds, optimality gaps relative to exact solutions on small instances, or verification of the approximation quality for the inner-outer decoupling; this makes the performance assertion difficult to assess rigorously beyond the specific simulated regimes.

Authors: We agree that explicit quantitative validation would improve rigor. In the revised version, we will add a dedicated subsection with small-scale instances (e.g., 5-10 trucks) where exact optimal solutions are computable via mixed-integer programming solvers. We will report optimality gaps between the rollout policy and these exact solutions, along with an analysis of how the inner-outer decoupling affects solution quality. For the large-scale regimes in the original simulations, we will explicitly note that exact solutions become intractable (exponential complexity), which is why heuristic baselines are used; the new small-instance results will serve as a proxy to bound approximation quality. We will also include a brief discussion of rollout theory to support the near-optimality claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper constructs a rollout-based dynamic programming framework with an explicitly defined inner-outer two-layer structure that decouples discrete sequencing from continuous power allocation to achieve polynomial-time evaluation. This structure is presented as a direct application of standard rollout DP to the combinatorial scheduling problem, with performance claims supported by simulation comparisons to heuristics rather than any reduction to fitted parameters, self-definitions, or self-citation chains. No load-bearing step equates a prediction or result to its own inputs by construction; the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests primarily on the modeling assumption that sequencing and power decisions can be effectively decoupled; no explicit free parameters or invented entities are stated in the abstract.

axioms (1)

domain assumption The joint sequencing and power allocation problem admits an inner-outer decomposition that preserves near-optimality.
This decomposition is invoked to justify the two-layer rollout structure and polynomial complexity.

pith-pipeline@v0.9.0 · 5454 in / 1132 out tokens · 47327 ms · 2026-05-13T19:52:41.365213+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

rollout-based dynamic programming framework built upon an inner-outer two-layer structure, which decouples ordering decisions from the schedule optimization
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

J(ω) := min ... polynomial-time complexity

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages

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System-level impacts of electrification on the road freight transport system: A dynamic approach,

Z. Raoofi, M. Huge Brodin, and A. Pernest ˚al, “System-level impacts of electrification on the road freight transport system: A dynamic approach,”International Journal of Physical Distribution & Logistics Management, vol. 54, no. 6, pp. 631–651, 2024

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T. Bai, A. Johansson, K. H. Johansson, and J. M ˚artensson, “Large- scale multi-fleet platoon coordination: A dynamic programming ap- proach,”IEEE Transactions on Intelligent Transportation Systems, vol. 24, no. 12, pp. 14 427–14 442, 2023

work page 2023

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A safety-prioritized receding horizon control framework for platoon formation in a mixed traffic environment,

A. I. Mahbub, V .-A. Le, and A. A. Malikopoulos, “A safety-prioritized receding horizon control framework for platoon formation in a mixed traffic environment,”Automatica, vol. 155, p. 111115, 2023

work page 2023

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Approxi- mate dynamic programming for platoon coordination under hours-of- service regulations,

T. Bai, A. Johansson, K. H. Johansson, and J. M ˚artensson, “Approxi- mate dynamic programming for platoon coordination under hours-of- service regulations,” in2022 IEEE 61st Conference on Decision and Control (CDC), 2022, pp. 7663–7669

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P. Zhao, S. Zhang, P. Santi, D. Cui, F. Wang, P. Liu, Z. Zhang, J. Liu, Z. Wang, C. Rattiet al., “Challenges and opportunities in truck electrification revealed by big operational data,”Nature Energy, vol. 9, no. 11, pp. 1427–1437, 2024

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J. C. Mukherjee and A. Gupta, “A review of charge scheduling of electric vehicles in smart grid,”IEEE Systems Journal, vol. 9, no. 4, pp. 1541–1553, 2015

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T. Bai, Y . Li, K. H. Johansson, and J. M ˚artensson, “Distributed charg- ing coordination of electric trucks with limited charging resources,” in2024 European Control Conference (ECC), 2024, pp. 2897–2902

work page 2024

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Strategic fleet replacement for the electrification of heavy-duty road freight trans- portation,

J. Bakker, J. L. Alvarez, J. Veldman, and P. Buijs, “Strategic fleet replacement for the electrification of heavy-duty road freight trans- portation,”Applied Energy, vol. 391, p. 125935, 2025

work page 2025

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Optimal charging scheduling by pricing for EV charging station with dual charging modes,

Y . Zhang, P. You, and L. Cai, “Optimal charging scheduling by pricing for EV charging station with dual charging modes,”IEEE Transactions on Intelligent Transportation Systems, vol. 20, no. 9, pp. 3386–3396, 2018

work page 2018

[11] [11]

Electric vehicle charging scheduling considering infrastructure constraints,

J. Wu, H. Su, J. Meng, and M. Lin, “Electric vehicle charging scheduling considering infrastructure constraints,”Energy, vol. 278, p. 127806, 2023

work page 2023

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Optimal EV charging scheduling by considering the limited number of chargers,

J. Liu, G. Lin, S. Huang, Y . Zhou, Y . Li, and C. Rehtanz, “Optimal EV charging scheduling by considering the limited number of chargers,” IEEE Transactions on Transportation Electrification, vol. 7, no. 3, pp. 1112–1122, 2020

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Efficient assignment of electric vehicles to charging stations,

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Distributed hierarchical coordination of networked charging stations based on peer-to-peer trading and EV charging flexibility quantification,

J. Zhang, L. Che, X. Wan, and M. Shahidehpour, “Distributed hierarchical coordination of networked charging stations based on peer-to-peer trading and EV charging flexibility quantification,”IEEE Transactions on Power Systems, vol. 37, no. 4, pp. 2961–2975, 2021

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Collaborative multi-aggregator electric vehicle charge scheduling with PV-assisted charging stations under variable solar profiles,

V . Gupta, S. R. Konda, R. Kumar, and B. K. Panigrahi, “Collaborative multi-aggregator electric vehicle charge scheduling with PV-assisted charging stations under variable solar profiles,”IET Smart Grid, vol. 3, no. 3, pp. 287–299, 2020

work page 2020

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Charging scheduling with minimal waiting in a network of electric vehicles and charging stations,

H. Qin and W. Zhang, “Charging scheduling with minimal waiting in a network of electric vehicles and charging stations,” inProceed- ings of the Eighth ACM International Workshop on Vehicular Inter- Networking, 2011, pp. 51–60

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Charging scheduling of electric vehicles with local renewable energy under uncertain electric vehicle arrival and grid power price,

T. Zhang, W. Chen, Z. Han, and Z. Cao, “Charging scheduling of electric vehicles with local renewable energy under uncertain electric vehicle arrival and grid power price,”IEEE Transactions on Vehicular Technology, vol. 63, no. 6, pp. 2600–2612, 2013

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T. Bai, Y . Li, K. H. Johansson, and J. M ˚artensson, “Rollout-based charging strategy for electric trucks with hours-of-service regulations,” IEEE Control Systems Letters, vol. 7, pp. 2167–2172, 2023

work page 2023

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Model-free real-time EV charging scheduling based on deep reinforcement learning,

Z. Wan, H. Li, H. He, and D. Prokhorov, “Model-free real-time EV charging scheduling based on deep reinforcement learning,”IEEE Transactions on Smart Grid, vol. 10, no. 5, pp. 5246–5257, 2018

work page 2018

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Constrained EV charging scheduling based on safe deep reinforcement learning,

H. Li, Z. Wan, and H. He, “Constrained EV charging scheduling based on safe deep reinforcement learning,”IEEE Transactions on Smart Grid, vol. 11, no. 3, pp. 2427–2439, 2019

work page 2019

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Reinforcement learning for electric vehicle charging scheduling: A systematic review,

Z. Zhao, C. K. Lee, X. Yan, and H. Wang, “Reinforcement learning for electric vehicle charging scheduling: A systematic review,”Trans- portation Research Part E: Logistics and Transportation Review, vol. 190, p. 103698, 2024

work page 2024

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Distributed charging coordination for electric trucks under limited facilities and travel uncertainties,

T. Bai, Y . Li, A. A. Malikopoulos, K. H. Johansson, and M. Jonas, “Distributed charging coordination for electric trucks under limited facilities and travel uncertainties,”IEEE Transactions on Intelligent Transportation Systems, vol. 26, no. 7, pp. 10 278–10 294, 2025

work page 2025

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Rollout algorithms for combinatorial optimization,

D. P. Bertsekas, J. N. Tsitsiklis, and C. Wu, “Rollout algorithms for combinatorial optimization,”Journal of Heuristics, vol. 3, no. 3, pp. 245–262, 1997

work page 1997

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Bertsekas,Rollout, Policy Iteration, and Distributed Reinforcement Learning

D. Bertsekas,Rollout, Policy Iteration, and Distributed Reinforcement Learning. Athena Scientific, 2021

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Electric Truck (Scania), https://www.scania.com/group/en/home/produc ts-and-services/trucks/battery-electric-truck.html, Accessed: 2026

work page 2026