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arxiv: 2605.21183 · v1 · pith:EQ7ROPMNnew · submitted 2026-05-20 · 📡 eess.SY · cs.SY

Collaborative Optimization of Battery Charging / Swapping Stations for eVTOLs Based on Closed-Loop Supply Chain and Space-Time Network

Pengfeng Lin , Miao Zhu , Jiahui Sun , Haoyang Cui , Xiaoyong Cao , Chuanlin Zhang , Yunda Yan This is my paper

Pith reviewed 2026-05-21 03:47 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords eVTOLbattery swappingbattery chargingclosed-loop supply chaintime-space networkoptimizationrange anxietypower distribution
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The pith

A closed-loop supply chain model with time-space networks optimizes battery swapping and charging for eVTOLs to maximize revenue.

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

The paper proposes a model for managing battery charging and swapping stations that serve electric vertical take-off and landing aircraft. It treats battery movements as a closed-loop supply chain and applies time-space network methods to schedule batteries, transport, and charging. The optimization maximizes operational revenue while coordinating eVTOL flights with station operations and the electricity distribution network. A sympathetic reader would care because the approach directly targets the energy limits that constrain how far and how frequently these aircraft can operate, potentially easing the path to practical commercial use.

Core claim

Following an investigation into battery energy replenishment strategies, a closed-loop supply chain-based model for eVTOL battery charging and swapping is proposed. Time-space network methods are utilized to characterize the scheduling of batteries and logistics throughout the system. Aiming to maximize the operational revenue of the model, optimized management of battery swapping, transportation, and charging processes is implemented, facilitating coordinated operation among eVTOLs, swapping stations, and charging stations. The model is solved by Gurobi, verifying its feasibility.

What carries the argument

Closed-loop supply chain model integrated with a time-space network that tracks battery locations, flows, and schedules across stations and aircraft.

Load-bearing premise

The time-space network formulation and closed-loop supply chain abstraction accurately capture real-world battery logistics, operational constraints, and electricity network interactions without additional unmodeled factors such as regulatory limits or stochastic demand.

What would settle it

Field data from an operating eVTOL battery network showing whether actual revenue, battery utilization rates, and observed range anxiety levels match the values predicted by the optimized schedule.

Figures

Figures reproduced from arXiv: 2605.21183 by Chuanlin Zhang, Haoyang Cui, Jiahui Sun, Miao Zhu, Pengfeng Lin, Xiaoyong Cao, Yunda Yan.

Figure 1
Figure 1. Figure 1: CLSC-based charging and swapping system for eVTOL batteries(taking Shanghai city as an example) . III. OPTIMAL OPERATION MANAGEMENT FOR THE CLSC￾BASED EVTOL BATTERY CHARGING AND SWAPPING SYSTEM Based on the BCSS described in the previous section and the scenario illustrated in [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Logistics system operation model based on TSN. The operational model for the logistics system proposed in this paper comprises a vehicle scheduling model and a battery scheduling model for each truck. The vehicle scheduling model is presented in Equations (1)-(4). The real-time status of each truck serves as a critical basis for the BCSS to assign tasks for the next time step. Therefore, it must be ensured… view at source ↗
Figure 2
Figure 2. Figure 2: Transportation network of BCSS. In [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Electricity purchase price of BCS. TABLE I. PARAMETERS OF BCSS Parameter Name Value Parameter Name Value Ctru,cap (pack) 300 pri,back ($/pack) 5 tru,tran ($/h) 10 pri,batt ($/kWh) 0.01 labor ($/pack) 0.1 Ebatt,en (kWh) 30 ,ini BSS,DB,stor n S (pack) 200 effi,char 0.95 ,ini BSS,WB,stor n S (pack) 200  (pack) 30 batt_swap ($/pack) 6 Pmax,char (kW) 120 TABLE II. OPERATIONAL RESULTS OF BCSS Pobj,tran Po… view at source ↗
Figure 6
Figure 6. Figure 6: Driving trajectory and change in battery inventory of Truck1 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Driving trajectory and change in battery inventory of Truck3. Number of DBs carried by Truck 4(pack) Time(h) 0 4 8 12 16 20 24 (a)Truck 4's travel path and the number of DBs it carries 0 100 200 300 400 Truck's travel path and the number of DBs it carries Truck's travel path Number of DBs carried by the truck Node 4 Node 5 Node 3 Node 2 Node 1 Number of WBs carried by Truck 4(pack) Time(h) 0 4 8 12 16 20 2… view at source ↗
Figure 7
Figure 7. Figure 7: Driving trajectory and change in battery inventory of Truck2. 0 100 200 Number of WBs carried by Truck 3(pack) 300 400 Time(h) 0 4 8 12 16 20 24 (b)Truck 3's travel path and the number of WBs it carries Truck's travel path and the number of WBs it carries Truck's travel path Number of WBs carried by the truck Node 4 Node 5 Node 3 Node 2 Node 1 0 100 200 Number of DBs carried by Truck 3(pack) 300 400 Time(h… view at source ↗
Figure 9
Figure 9. Figure 9: Driving trajectory and change in battery inventory of Truck4. B. Analysis of BSS Simulation Results Combining [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 12
Figure 12. Figure 12: Operational results of BSS2. As shown in [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 11
Figure 11. Figure 11: Operational results of BSS1. As shown in [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 14
Figure 14. Figure 14: BCS's DB inventory and its related variables. 0 4 8 12 16 20 24 Time(h) 300 600 900 Number of batteries(pack) WB inventory of BCS BCS provides the number of WBs to the logistics system BCS retrieves the number of batteries from the charging piles [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
Figure 13
Figure 13. Figure 13: Operational results of BSS3. C. Analysis of BCS Simulation Results As shown in [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
read the original abstract

Against the backdrop of the burgeoning global low-altitude economy, countries have successively introduced a series of policies to accelerate the application and commercialization of electric vertical take-off and landing (eVTOL) aircraft. Nevertheless, purely electric eVTOLs confront constraints including limited battery energy density, high operational power requirements, and challenges associated with rapid energy replenishment, which collectively restrict their flight endurance and application scenarios. Furthermore, while eVTOL deployment is scaling up, supporting charging infrastructure and regulations remain underdeveloped. This situation presents emerging power distribution networks with new challenges in maintaining adequate electricity supply and ensuring operational continuity. To tackle these issues, following an investigation into battery energy replenishment strategies, a closed-loop supply chain-based model for eVTOL battery charging and swapping is proposed. Time-space network methods are utilized to characterize the scheduling of batteries and logistics throughout the system. Subsequently, aiming to maximize the operational revenue of the model, optimized management of battery swapping, transportation, and charging processes is implemented, facilitating coordinated operation among eVTOLs, swapping stations, and charging stations. Finally, the model is solved by Gurobi, verifying its feasibility. Simulation results further indicate that the model alleviates range anxiety for eVTOLs, offering strong support for their commercialization. Moreover, it enables coordinated scheduling between eVTOLs and the distribution network, thereby facilitating the network's gradual improvement and upgrading.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a closed-loop supply chain model for eVTOL battery charging and swapping stations, incorporating time-space network methods to represent battery scheduling and logistics. The optimization maximizes operational revenue through coordinated management of swapping, transportation, and charging, solved via Gurobi, with simulations claimed to demonstrate alleviation of range anxiety and improved coordination with the distribution network.

Significance. If the modeling assumptions hold under operational conditions, the framework could inform infrastructure planning for the low-altitude economy by providing a structured optimization approach to battery logistics. The application of established time-space network techniques to eVTOL energy replenishment represents a domain extension that may yield practical scheduling insights.

major comments (2)
  1. [Simulation Results] Simulation Results section: The headline claim that simulations alleviate range anxiety and support commercialization rests on deterministic time-space network paths with fixed parameters for eVTOL schedules and battery flows. This is load-bearing for the central result because, without stochastic demand, variable arrival times, or scenario-based optimization, the revenue-maximizing solution can yield overly optimistic availability metrics that do not translate to reduced range anxiety under real uncertainties such as weather-dependent demand or electricity price volatility.
  2. [Model Formulation] Model Formulation section: The closed-loop supply chain abstraction and time-space network representation treat battery logistics as deterministic flows without explicit incorporation of regulatory limits, stochastic elements, or additional operational constraints. This choice directly affects the validity of the coordinated scheduling claim with the distribution network, as the abstract notes challenges in electricity supply but the formulation does not appear to include sensitivity analysis or robust variants.
minor comments (2)
  1. [Abstract and Simulation Results] The abstract and simulation description provide limited details on data sources, specific constraint formulations, or validation against real eVTOL operations, which reduces clarity for readers attempting to reproduce or extend the Gurobi-based results.
  2. [Notation and Time-Space Network] Notation for battery states and flows in the time-space network could be supplemented with an explicit legend or small example diagram to improve readability of the scheduling variables.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the scope and limitations of our deterministic optimization framework. We address each major comment below and indicate the revisions planned for the next manuscript version.

read point-by-point responses

  1. Referee: [Simulation Results] Simulation Results section: The headline claim that simulations alleviate range anxiety and support commercialization rests on deterministic time-space network paths with fixed parameters for eVTOL schedules and battery flows. This is load-bearing for the central result because, without stochastic demand, variable arrival times, or scenario-based optimization, the revenue-maximizing solution can yield overly optimistic availability metrics that do not translate to reduced range anxiety under real uncertainties such as weather-dependent demand or electricity price volatility.

    Authors: We agree that the model is deterministic with fixed eVTOL schedules and battery flow parameters. This choice enables a tractable formulation that demonstrates revenue maximization and coordinated battery logistics under the assumed conditions, providing a baseline for how the closed-loop supply chain can improve availability. We acknowledge that the absence of stochastic demand or scenario analysis means the results do not directly quantify performance under weather or price uncertainties. In the revised manuscript we will add a subsection to the Simulation Results discussing these limitations and outlining extensions to stochastic or robust optimization. revision: yes

  2. Referee: [Model Formulation] Model Formulation section: The closed-loop supply chain abstraction and time-space network representation treat battery logistics as deterministic flows without explicit incorporation of regulatory limits, stochastic elements, or additional operational constraints. This choice directly affects the validity of the coordinated scheduling claim with the distribution network, as the abstract notes challenges in electricity supply but the formulation does not appear to include sensitivity analysis or robust variants.

    Authors: The deterministic abstraction was selected to focus on the core integration of swapping, transportation, and charging processes within the time-space network. We recognize that this omits explicit stochastic elements, regulatory limits, and sensitivity analysis, which limits the direct applicability to real electricity supply variability. We will revise the Model Formulation section to explicitly state these modeling choices and their implications, and we will add sensitivity analysis on electricity prices and demand variations to the numerical experiments in the revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper proposes a closed-loop supply chain model using time-space networks to represent battery flows, swapping, and charging for eVTOLs. It then formulates an optimization problem to maximize operational revenue, solves it via Gurobi, and reports simulation outcomes such as alleviated range anxiety. This constitutes a standard forward modeling, optimization, and validation workflow. No equations reduce to self-definitions, no fitted parameters are relabeled as predictions, and no load-bearing claims rest on self-citations or imported uniqueness theorems. The results are computed outputs rather than tautological restatements of the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim depends on the modeling abstraction that closed-loop supply chain concepts and space-time networks sufficiently represent battery flows and station operations for optimization purposes; these are standard domain assumptions rather than new entities or fitted constants.

axioms (2)
  • domain assumption Time-space network methods can accurately characterize the scheduling of batteries and logistics throughout the system.
    Invoked to represent battery movements between eVTOLs, swapping stations, and charging stations.
  • domain assumption Maximizing operational revenue through coordinated scheduling produces the reported benefits for range anxiety and grid coordination.
    Links the optimization objective directly to the commercialization and network-improvement outcomes.

pith-pipeline@v0.9.0 · 5812 in / 1392 out tokens · 47695 ms · 2026-05-21T03:47:08.752574+00:00 · methodology

discussion (0)

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Reference graph

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