Recognition: unknown
Energy-Efficient Drone Logistics for Last-Mile Delivery: Implications of Payload-Dependent Routing Strategies
Pith reviewed 2026-05-10 16:48 UTC · model grok-4.3
The pith
Energy-aware drone routing for deliveries can favor longer routes or single stops over shortest-distance paths because payload weight changes energy use after each drop.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The paper establishes that a green drone routing problem focused on energy efficiency produces counter-intuitive optimal routes compared with traditional distance-minimization: longer paths can require less total energy, separate tours can be superior to multi-stop tours, and heterogeneous fleets achieve better results by matching capacity to demand, with the green strategy delivering energy savings in 67 percent of instances and an average 2.17 percent saving (maximum 5.97 percent) in those cases.
What carries the argument
The payload-dependent energy consumption model, which adjusts the drone's power draw dynamically as deliveries reduce carried weight during a tour.
If this is right
- A route with greater total distance can require less total energy than a shorter route when payload effects are included.
- Separate single-customer delivery tours can consume less energy overall than a single multi-stop tour.
- A fleet of drones with varying capacities matched to specific delivery weights outperforms a uniform fleet.
- The energy-aware strategy produces measurable savings versus pure distance minimization in the majority of tested delivery instances.
Where Pith is reading between the lines
- Operators may need separate optimization software for energy rather than relying on existing distance-based planners.
- Savings could compound if routes are replanned in real time as payload changes during flight.
- Combining this approach with ground-vehicle handoffs might further reduce overall system energy in mixed fleets.
Load-bearing premise
The energy consumption model accurately captures real drone behavior as payload changes, and the numerical instances represent realistic last-mile delivery scenarios.
What would settle it
Field measurements of actual battery drain on a drone flying both a short distance-minimizing route and a longer energy-aware alternative under the same conditions, showing whether the longer route truly uses less energy.
read the original abstract
Drone delivery is rapidly emerging as a cost-effective and energy efficient alternative for last-mile delivery. Unlike ground vehicles, a drone's energy consumption depends on its payload in addition to travel distance. This creates a unique environmental challenge for multi-stop delivery tours, as the drone's total weight, and therefore its energy consumption rate, dynamically changes after each delivery. This paper investigates a novel green drone routing problem focused on maximizing energy efficiency. Through a series of motivating examples and numerical experiments, we demonstrate that energy-aware routing leads to several counter-intuitive routing strategies that contradict traditional distance-minimization delivery: a longer route may actually consume less energy than a shorter one; separate single-customer tours can be superior to a multi-stop tour; and a heterogeneous fleet, with drones of varying sizes, can achieve greater efficiency by matching drone capacity to specific delivery demands. In the numerical study, the green routing strategy shows energy savings in 67% of the instances. For these cases, the average energy saving is 2.17%, with a maximum saving of 5.97%, compared to minimum distance routing. These findings highlight the potential for green drone routing strategies to improve the sustainability of last-mile delivery.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper introduces a green drone routing problem that accounts for payload-dependent energy consumption in last-mile drone deliveries. Using motivating examples and numerical experiments, it shows that energy-aware routing produces counter-intuitive strategies that differ from distance-minimization: longer routes can consume less energy than shorter ones, separate single-customer tours can outperform multi-stop tours, and heterogeneous fleets can improve efficiency by matching drone sizes to demands. In the experiments, the green strategy yields energy savings in 67% of instances, with an average saving of 2.17% and a maximum of 5.97% relative to the distance baseline.
Significance. If the underlying payload-dependent energy model is representative of real drone behavior, the work identifies concrete opportunities to enhance sustainability in drone logistics by shifting from distance-based to energy-based objectives. The modest but consistent savings and the qualitative reversals in routing preferences provide actionable insights for fleet operators, while the heterogeneous-fleet result suggests a new dimension for system design. The numerical evidence, though limited in scope, offers a starting point for further optimization research in emerging drone delivery systems.
major comments (2)
- [§3] §3 (Energy Consumption Model): The functional form relating energy use to distance and payload is introduced without calibration against measured drone power data, without sensitivity analysis on the strength of the payload dependence, and without inclusion of constant terms such as hover or takeoff energy. Because the three counter-intuitive routing reversals and the reported 2.17% average savings are produced by optimizing under this specific E(d, p) function, the absence of validation or robustness checks is load-bearing for the central claims.
- [§5] §5 (Numerical Experiments): The study states that savings occur in 67% of instances with an average of 2.17% and a maximum of 5.97%, yet provides no description of instance generation procedure, payload ranges, number of instances, or statistical tests. Without these details it is impossible to rule out selection effects or to assess whether the modest savings persist under alternative energy-model parameters or realistic last-mile constraints.
minor comments (2)
- [Abstract and §1] The abstract and §1 refer to 'numerical experiments' and 'motivating examples' but do not indicate the size of the test set or the solver used for the optimization model; adding these facts would improve reproducibility.
- [§3 and §4] Notation for the energy function and decision variables is introduced in §3 but is not consistently cross-referenced in the motivating examples of §4, making it harder to trace how payload changes affect each route.
Simulated Author's Rebuttal
We thank the referee for the constructive feedback and the recommendation for major revision. We address each major comment point by point below, indicating planned revisions where appropriate.
read point-by-point responses
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Referee: [§3] §3 (Energy Consumption Model): The functional form relating energy use to distance and payload is introduced without calibration against measured drone power data, without sensitivity analysis on the strength of the payload dependence, and without inclusion of constant terms such as hover or takeoff energy. Because the three counter-intuitive routing reversals and the reported 2.17% average savings are produced by optimizing under this specific E(d, p) function, the absence of validation or robustness checks is load-bearing for the central claims.
Authors: The energy model in §3 is derived from established aerodynamic principles of drone flight, where payload directly increases the power required for lift and propulsion. We acknowledge the absence of direct calibration against proprietary flight-test data. We will add a dedicated sensitivity analysis subsection varying the payload coefficient to confirm that the reported counter-intuitive routing reversals and energy savings remain qualitatively stable. We will also clarify that constant terms (hover, takeoff) are omitted because they are identical across compared routes and therefore do not alter the relative optimality conclusions; this assumption will be stated explicitly as a modeling limitation. revision: partial
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Referee: [§5] §5 (Numerical Experiments): The study states that savings occur in 67% of instances with an average of 2.17% and a maximum of 5.97%, yet provides no description of instance generation procedure, payload ranges, number of instances, or statistical tests. Without these details it is impossible to rule out selection effects or to assess whether the modest savings persist under alternative energy-model parameters or realistic last-mile constraints.
Authors: We agree that the experimental description in §5 is insufficiently detailed. In the revised manuscript we will expand this section to include: (i) the precise instance-generation procedure (uniform customer locations in a square service area, payload demands sampled uniformly from 0.5–5 kg), (ii) the total number of instances (100), (iii) the payload range used, and (iv) basic statistical summary measures. We will additionally report results from a parameter-sweep experiment that varies the payload-dependence strength to demonstrate persistence of the savings. revision: yes
- Empirical calibration of the energy consumption model against real-world drone power measurements from flight tests.
Circularity Check
No circularity; results follow from explicit optimization under stated energy model
full rationale
The paper defines an energy consumption function that depends on both distance and payload, then solves two separate optimization problems (minimize distance vs. minimize energy) over the same set of instances and compares their objective values. The reported counter-intuitive routes and the 67 % / 2.17 % / 5.97 % statistics are direct numerical outputs of that comparison; they are not obtained by fitting parameters to the target quantities or by renaming the inputs. No self-citation is invoked to justify uniqueness or to close the derivation loop. The model assumptions are stated up front and the results are conditional on those assumptions, but the derivation chain itself does not collapse to a tautology.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Drone energy consumption rate depends on current payload weight in addition to distance traveled.
Reference graph
Works this paper leans on
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[1]
F., & Jans, R
Adulyasak, Y., Cordeau, J. F., & Jans, R. (2014). Formulations and branch -and-cut algorithms for multivehicle production and inventory routing problems. INFORMS Journal on Computing, 26(1), 103-
2014
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[2]
Agatz, N., Bouman, P., & Schmidt, M. (2018). Optimization approaches for the traveling salesman problem with drone. Transportation Science, 52(4), 965-981. Bruni, M. E., Khodaparasti, S., & Perboli, G. (2023). Energy efficient UAV -based last-mile delivery: A tactical-operational model with shared depots and non-linear energy consumption. IEEE Access, 11,...
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[3]
United Nations. ( 2025). Causes and effects of climate change . United Nations. Retrieved December 26 , 2025, from https://www.un.org/en/climatechange/science/causes-effects-climate-change. U.S. Environmental Protection Agency. (2025). Inventory of U.S. greenhouse gas emissions and sinks. U.S. Environmental Protection Agency. Retrieved December 26 , 2025,...
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[4]
F., & Sweeney II, D
Zhang, J., Campbell, J. F., & Sweeney II, D. C. (2024). A continuous approximation approach to integrated truck and drone delivery systems. Omega, 126, 103067. Zhang, J., Campbell, J. F., Sweeney II, D. C., & Hupman, A. C. (2021). Energy consumption models for delivery drones: A comparison and assessment. Transportation Research Part D: Transport and Envi...
2024
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[5]
For the hovering phase, Dorling et al
provides a summary of different models used to estimate drone energy consumption during steady level flight. For the hovering phase, Dorling et al. (2016) provided a physics-based model for power consumption. The required power is: 𝑃𝑃2 = (𝑚𝑚𝑖𝑖+ 𝑚𝑚𝑏𝑏+ 𝑚𝑚𝑙𝑙) 3 2� 𝑔𝑔3 2𝜌𝜌𝜌𝜌ℎ, (A3) Li, Guo, and Schonfeld 25 where 𝜌𝜌 is the fluid density of air, 𝜌𝜌 is the area...
2016
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[6]
(A3) - (A5), to the entire flight
simplify their energy calculations by applying a hover power formula, such as those in Eqs. (A3) - (A5), to the entire flight. Cheng et al. (2020) explained that this approach was applied due to a lack of available field tests of small drones making multiple deliveries at the time. Therefore, we adopt a linear model for our study. This approach is not onl...
2020
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[7]
This completes the reformulation of the G -DRP into a MILP
If 𝑥𝑥𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖= 1, constraints ( B11) and ( B12) force 𝑔𝑔𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖 to equal the total number of customers served on that tour (i.e., 𝑔𝑔𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖= ∑ ∑ 𝑥𝑥𝑖𝑖′𝑖𝑖′𝑙𝑙𝑖𝑖 𝑛𝑛 𝑖𝑖′=1 𝑛𝑛 𝑖𝑖′=0 ). This completes the reformulation of the G -DRP into a MILP. A key challenge in this formulation is the presence of symmetrical solutions. For any given drone type 𝑘𝑘, if ℎ� 𝑙𝑙 ...
2014
discussion (0)
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