Congestion-Aware Charging Coordination for Electric Ride-Hailing Fleets under Stochastic Demand

Francesco Viti; Richard D. Connors; Tai-Yu Ma

REVIEW 4 major objections 6 minor 2 references

Congestion-Aware Charging Coordination for Electric Ride-Hailing Fleets under Stochastic Demand

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A sequential MILP charging policy that anticipates station queues and end-of-day energy needs raises electric ride-hailing profit by 7.65%-15.05% and service rate by 7-12.3 percentage points over four benchmark policies.

desk verdict A detailed simulation study of a congestion-aware charging policy whose headline gains are plausible but rest on a day-ahead planner calibrated to a benchmark policy's waiting times, plus an abstract that doesn't match the tables. read the letter →

arxiv 2412.09978 v4 pith:ZW6ALWFX submitted 2024-12-13 math.OC cs.SYeess.SY

Tai-Yu Ma , Richard D. Connors , Francesco Viti This is my paper · ORCID

classification math.OCcs.SYeess.SY MSC 90B0690C1190C15

keywords ride-hailingelectricvehicleschargingschedulingmixedintegerlinearprogrammingcongestiontime-of-useenergypricesstochasticdemandfleetmanagement

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to show that an electric ride-hailing fleet can serve more customers and earn more profit without adding chargers, by scheduling charging around two things most earlier models ignore: queues at congested chargers and each vehicle's actual energy need to finish the day. It proposes a sequential mixed-integer linear program that first builds a day-ahead charging plan using expected waiting times and time-of-use energy prices, then reassigns vehicles to chargers online every minute. In simulations on a Manhattan-like grid with 100 EVs and 3,000 or 4,000 customers a day, the policy beats four benchmark charging rules on both profit and customer service rate, with profit gains of about 7.65% to 15.05% and service-rate gains of about 7 to 12.3 percentage points depending on scenario.

What carries the argument

The load-bearing object is a sequential MILP with three interacting models: a day-ahead charging plan (P1) that assigns vehicles to half-hour epochs and target SoCs to minimize energy, access, and opportunity costs subject to charger capacity and a minimum charging time; a reactive pool-and-target rule (Eq. 29) that sets each vehicle's post-charge energy to just cover its remaining driving needs to end of day; and an online vehicle-to-charger assignment (P3) solved every minute that minimizes access, waiting, and charging time. The day-ahead plan is calibrated with expected waiting times and average profit rate estimated from simulating the Fastest benchmark policy on training days, which is what lets it steer charging away from predicted afternoon congestion peaks.

What would settle it

Re-run the five validation days after re-estimating the day-ahead plan's waiting-time and profit-rate inputs from the CongestionAware policy's own realized queues, iterating until the plan's predicted waiting times match the simulated ones; if the profit gap over the DynaThreshold benchmark falls below the reported 7.65%-15.05% or disappears, the advantage is an artifact of benchmark-calibrated parameters rather than of the scheduling logic.

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Extended reading notes

Core claim

On its own terms, the paper's central claim is that charging congestion, not charger scarcity, is the main drag on electric ride-hailing profitability, and that it can be managed by coordinating vehicles' charging times, durations, and charger choices with an eye on expected queueing. The proposed CongestionAware policy replaces the usual 'charge when the battery is low, charge to 80%' rule with a day-ahead plan that minimizes charging cost, access cost, and opportunity cost of time under charger capacity and minimum charging-duration constraints, and then adapts that plan online. In the reported experiments it achieves the highest profit of all five policies in every demand scenario and battery-size case, cuts total charging waiting time by roughly half to two-thirds, and concentrates end-of-day batteries near the reserve level instead of leaving the fleet half full.

Load-bearing premise

The day-ahead plan trusts that waiting times and profit rates estimated by simulating a different (Fastest) charging policy on training days still describe the congestion the new policy will actually create; if those estimates are wrong, the schedules could be miscalibrated and the reported gains might not hold.

Editorial extensions

If this is right

Operators can raise profit by 7.65%-15.05% and service rate by 7-12.3 percentage points without buying more chargers.
The advantage over benchmarks widens when charging infrastructure is scarce and when battery capacity is larger, so the policy is most valuable in exactly the conditions where naive charging rules break down.
Total charging waiting time drops to roughly a third to a half of benchmark levels, and fast chargers run near full occupancy during peak hours while slow chargers are mostly unused.
The method scales: online assignment solves in about 0.03 seconds even for 20,000 requests/day, while the day-ahead plan can be solved approximately within a one-hour time limit.
Replacing full 80% charges with energy-need-based partial charges is the main driver of the gain; time-of-use price awareness contributes only a small additional saving.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The reported gains depend on calibrating the day-ahead plan with waiting times from a benchmark policy; a self-consistent calibration using the CongestionAware policy's own realized queues could either shrink or enlarge the advantage, and the paper does not provide that fixed-point check.
The partial-recharge rule effectively aims every vehicle's end-of-day battery at the reserve level; the same 'charge just enough to finish the shift' principle could apply to other shift-based fleets, from delivery vans to airport shuttles.
Because slow chargers are rarely used, the policy suggests that adding fast chargers, not slow ones, is the binding investment lever; a testable extension is to re-run the sensitivity analysis with fast-only expansions.
The day-ahead model's dependence on historical average waiting times could be replaced by a learned predictor that accounts for the policy's own feedback, connecting this approach to model-based RL without changing the online MILP core.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Plainly: this is a serious engineering paper with a genuine equilibrium-calibration problem. The authors build a three-layer MILP scheme — day-ahead charging plan (P1), reactive go-charge pool with end-of-day energy anticipation, and online vehicle-charger assignment (P3) — and they add realistic details that most prior work omits: minimum charging duration, maximum queue waiting with charger-chasing, partial recharge targets, ToU prices. The simulation description is detailed enough to be replicable in principle, and the online solve times are convincing.

The main claim, that CongestionAware beats four benchmarks in profit and service rate, is supported by Table 4: roughly 8-15% profit and 8-12 percentage-point service-rate gains. The sensitivity analysis is extensive — battery sizes, charger counts, demand from 1000 to 6000 customers/day, overnight charging costs, charger-type prices, plus a scaling study to 20,000 customers/day. That is real work, and the conclusion that the policy helps most when chargers are scarce is consistent with the mechanism.

The soft spot the stress-test note identifies is genuine. P1 uses expected waiting times Wbar_hs and average profit rate gamma estimated by simulating the Fastest benchmark on ten training days. Under CongestionAware, realized waiting times are much lower (36-48 hours vs 77-136 for benchmarks), so the cost coefficients in P1 are not the ones the policy induces. There is no fixed-point check, no sensitivity analysis over Wbar. If the planner were re-solved with self-consistent waiting times, the schedule would likely change. The direction of the bias actually works in the paper's favor — overestimating waiting costs makes the plan conservative about congestion — so the qualitative story probably holds. But the magnitude of the gains could move, and I would not treat the headline numbers as established.

There is also an abstract inconsistency that needs fixing. The top-of-paper abstract claims +19.32% profit and +20.03% service rate for 4000 customers, and +3.91%/+4.60% against something called 'OptChg'. The full-text abstract says up to +15.06% profit and +19.16% service, and Table 4 shows the strongest benchmark is DynaThreshold. 'OptChg' never appears in the paper. This is a version-control slip, but it makes the headline claim unreproducible from the tables.

Also worth noting: no code or data is shipped, and the validation uses five days without significance tests. The standard deviations in Table 5 are small, so the differences are probably real, but a test would be cheap to add.

Recommendation: send to review. The contribution is new, the modeling is detailed, and the issues are addressable — a self-consistency check on Wbar, a significance test, and a corrected abstract. I'd want those before the numbers are cited, but the paper deserves referee time.

Referee Report

4 major / 6 minor

Summary. The paper proposes a sequential mixed-integer linear programming approach, named CongestionAware, for coordinating dispatching and charging of an electric ride-hailing fleet under stochastic demand, time-of-use energy prices, and congested charging stations. A day-ahead plan (Model P1) determines which vehicles charge, when, and to what target state of charge, using expected charger waiting times and average profit rates. During the day, an online vehicle-to-charger assignment (Model P3) and a batch dispatch model (Model P2) are solved every minute. The policy is tested in a Manhattan-like simulation with 100 vehicles, 12 chargers, and two demand scenarios (3000 and 4000 customers/day), and compared against four benchmark charging policies. The authors report that CongestionAware yields higher total profit and customer service rates, with lower charging waiting times, and support this with sensitivity analyses over battery capacity, charger counts, demand levels, and pricing schemes.

Significance. If the reported gains are robust, the paper offers a practically relevant tool: fleet operators could improve profit and service rates without adding charging infrastructure. The paper's strengths include explicit queueing modeling, minimum charging duration constraints, a day-ahead/online decomposition, comparison against four benchmark policies, and extensive sensitivity and scalability experiments. The main weaknesses are that the day-ahead plan is calibrated using waiting times and profit rates from a benchmark policy rather than from the proposed policy itself, the validation is based on only five days per scenario without significance testing, and the abstract's headline numbers are not reproduced in the body of the paper. These issues leave the central claim plausible but not yet established.

major comments (4)

[§4.2.a, Eq. (1)] The day-ahead planning model P1 uses expected waiting times Wbar_hs and average profit rate gamma that are estimated by simulating the Fastest benchmark policy on 10 training days (Section 4.2.a). However, under the proposed CongestionAware policy the realized charging waiting times are much smaller than under Fastest (Table 4: TW = 36.0/48.4 h for CongestionAware versus 77.1–136.1 h for the benchmarks). Therefore the cost coefficients in Eq. (1) do not correspond to the congestion regime that the proposed policy actually induces. The paper provides no fixed-point or consistency check (re-estimating Wbar_hs and gamma under CongestionAware and re-solving P1), and no sensitivity analysis to these input estimates. Since P1's output is the distinguishing component of the method, the reported profit and service-rate advantages could shift if the plan were re-solved self-consistently. Please provide such a check or a sensitivity analysis over Wbar_hs and gamma.
[Abstract vs. Section 5 / Table 4] The quantitative claims in the abstract are not reproduced in the full text. The abstract states gains of up to +19.32% profit and +20.03% service rate, and relative to a benchmark called 'OptChg' gains of +3.91% profit and +4.60% service rate. Section 5 instead reports profit increases of 7.65%–10.69% (c3000) and 8.76%–15.05% (c4000), and service-rate increases of 7–10.8 and 7.9–12.3 percentage points (Table 4). The benchmark 'OptChg' is never defined in the full text, and no results for it appear in any table. These inconsistencies make the paper's main quantitative claims not reproducible from the manuscript; the authors should reconcile the abstract with the reported results and either define OptChg or remove it.
[§3.3, Eqs. (27)–(28)] The stated replacement constraints for P3 in the case where the number of to-charge vehicles is smaller than the number of chargers require every charger to be assigned exactly one vehicle (sum_v x̂_vs = 1 for all s in Eq. (28)). This is infeasible whenever |Ω̃_t| < |S|, a case that occurs in the simulation. The intended constraints appear to be reversed or the implemented formulation differs from the text. Because P3 is the online assignment model used in every simulation step, this discrepancy is load-bearing for the reported results. Please clarify the correct formulation and confirm that the implemented model matches it.
[§4.2, Tables 4–5] All performance comparisons rest on five validation days per demand scenario, and no statistical significance tests are reported. While the standard deviations in Table 5 suggest that the largest differences are not noise, formal paired tests or confidence intervals are needed to support the claim of systematic outperformance, especially for the smaller differences among benchmark policies. This is particularly relevant because the validation sample is small and the demand process is stochastic. Please add significance tests or at least confidence intervals for the main KPIs (profit and service rate) in Tables 4 and 9–11.

minor comments (6)

[Figures 1–2] The figure numbering is inconsistent: the timeline in Section 3.1 is called Figure 1, but the charging station map in Section 4.1 is also called Figure 1 while the displayed figure is numbered 'Figure 2. Charging station distribution in the study area.' Please re-number the figures in order of appearance.
[Table 2 and P2/P3 notation] The energy consumption rate is denoted μ in the models (Eqs. (15), (21)) but is listed as φ in Table 2; harmonize the notation.
[§4.1, Table 2] Charging power should be expressed in kW, not kWh: '50 kWh' should be '50 kW' and '11kWh' should be '11 kW' in the text and Table 2.
[§4.3.c and Appendix B] The paper reports that P1 is solved with optimality gaps of about 5%–14% within a one-hour time limit; please add an explicit caveat in the conclusions that the day-ahead plan is an approximate, not exact, solution, and discuss whether higher-quality solutions could change the results.
[Title] The title on the first page of the manuscript ('Coordinated vehicle dispatching and charging scheduling for an electric ride-hailing fleet under charging congestion and dynamic prices') differs from the title under which the paper is listed ('Congestion-Aware Charging Coordination for Electric Ride-Hailing Fleets under Stochastic Demand'). Please align these before publication.
[§3.3, P2 constraints] In constraints (15) and (16), the set of requests is written as r_t in some places and R_t in others; the notation should be consistently R_t.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported profit and service-rate gains are simulation outcomes, not algebraic consequences of the fitted planning parameters.

full rationale

The paper's derivation chain is a simulation study: parameters (delta_h, gamma, Wbar_hs) are estimated from historical/training data, the day-ahead MILP P1 is solved with those parameters, and the online policies P2/P3 are executed in a discrete-event simulator whose KPIs (profit, service rate, waiting time) are measured, not computed from Eq. (1). There is no equation in the paper that makes the reported Z equal to the optimized Z1, and no fitted parameter is renamed as a predicted outcome. The planning parameters Wbar_hs and gamma are estimated by simulating the Fastest benchmark on 10 training days; this creates a calibration concern because the realized waiting times under CongestionAware differ substantially from those under Fastest, and the paper does not check fixed-point consistency between planned and realized waiting times. However, miscalibration or an unfair comparison is a correctness/validity risk, not a circular reduction: the central claim is not forced by how the parameters were set. The paper also contains an internal reporting inconsistency: the abstract cites an undefined baseline 'OptChg' and headline gains (+19.32% profit, +20.03% service rate; +3.91%/+4.60% vs OptChg) that do not appear in Table 4 or anywhere in the body. This is a reproducibility defect, not a circularity. There is no load-bearing self-citation chain: the authors' prior work is used mainly for benchmarks (e.g., MinChgOpT) and related literature, not to justify the central result. Thus no specific circular step can be quoted, and the appropriate finding is no significant circularity with score 0.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a simulation whose planning inputs are partly estimated from the same simulation environment. The main free parameters are expected waiting time, average consumption, and opportunity cost inputs to P1, plus hand-chosen thresholds; none are independently calibrated to field data. No new physical entities are introduced.

free parameters (8)

gamma (average profit per minute traveled) = estimated per scenario from Fastest-policy simulation, values not tabulated
Used in P1 objective Eq. (1) to convert charging time and waiting time into opportunity cost. Estimated from simulated historical days, so the planned schedules inherit behavior of the benchmark policy.
Wbar_hs (expected waiting time at charger s in epoch h) = estimated per scenario, not tabulated
Central congestion signal in P1 Eq. (1). Obtained by simulating the Fastest charging policy on 10 training days, so it is not an independently measured quantity.
delta_h (average energy consumption per epoch) = estimated values not reported
Used in P1 SoC dynamics and in the target-SoC rule Eq. (29). Estimated from simulation of historical trips with an internal combustion engine proxy.
C (average charging access cost) = approximately 2.7 USD
Estimated from average distance to charging stations; enters P1 Eq. (1) as fixed access cost per charging operation.
E_tilde_v (random target SoC cap) = uniform random in [0.5B, E_max]
Eq. (29) sets the target SoC cap as a random draw. This injects randomness into the reactive charging policy and is not derived from data.
m (number of epochs approximating E_min) = integer satisfying m*delta_h <= E_min
Appears in Eq. (29) to estimate remaining energy need. Chosen by hand rather than estimated.
maximum waiting time at a queuing charger = 30 minutes in base case
Policy parameter for the reactive model. Sensitivity analysis in Table 8 shows profit and service rate vary with this threshold.
theta (SoC threshold for adding vehicles to charging pool) = 20% of battery capacity
Determines which vehicles are forced to charge in Algorithm 1 Step 9. Fixed by hand, not calibrated.

assumptions (7)

standard math Gurobi solves MILP models P1 to P3 correctly to the stated gaps
The paper relies on commercial solver correctness for all reported KPIs and computational times.
domain assumption Linear charging power assumption
P1 and P3 use y/phi_s for charging time, so charging speed is constant up to E_max. The paper acknowledges nonlinear charging above 80% but models it linearly.
domain assumption Energy consumption proportional to distance with constant rate mu
Used in SoC update equations and in P2/P3 constraints. Ignores traffic, speed variation, and auxiliary loads.
domain assumption Customer demand realizations are faithfully represented by randomly drawn NYC taxi zone trips
Origins and destinations are generated randomly in a 4x20 km rectangle with minimum trip length 5 km, not actual GPS coordinates, and destinations may lie outside the area.
domain assumption Vehicles start fully charged and overnight charging restores full battery at low cost
Removes end-of-day charging decisions from P1. Sensitivity with overnight costs in Section 4.3.d partially relaxes this.
ad hoc to paper Expected waiting times from the Fastest policy are valid inputs for planning under the proposed policy
Wbar_hs is estimated under one benchmark regime and used to plan schedules for a different policy. No fixed-point or consistency check is provided.
domain assumption Operator has full control of dispatch and charging
Assumes a central fleet operator controls all vehicles. Driver behavior and individual preferences are not modeled.

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Cite this review

Pith. "Pith review of Congestion-Aware Charging Coordination for Electric Ride-Hailing Fleets under Stochastic Demand." pith.science (2026). https://pith.science/paper/ZW6ALWFX

@misc{pith2026241209978,
  author       = {Pith},
  title        = {Pith review of: Congestion-Aware Charging Coordination for Electric Ride-Hailing Fleets under Stochastic Demand},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZW6ALWFX}},
  note         = {Machine review of arXiv:2412.09978}
}

read the original abstract

Charging-station capacity strongly affects the profitability of electric ride-hailing systems. In this study, we develop a dynamic charging scheduling method that anticipates vehicles' energy needs and coordinates their charging operations with real-time energy prices to avoid long waiting time at charging stations and increase the total profit of the system. A sequential mixed integer linear programming model is proposed to devise vehicles' day-ahead charging plans based on their experienced charging waiting times and energy consumption. The developed charging policy is tested on a Manhattan-like study area using synthetic data drawn from NYC yellow taxi data with a fleet size of 100 vehicles given the scenarios of 3000 and 4000 customers/day. The computational results show that our method outperforms different benchmark policies with up to +19.32% profit and +20.03% service rate for 4000 customers relative to the weakest benchmark; relative to the strongest benchmark (OptChg), the corresponding gains are +3.91% profit and +4.60% service rate. Sensitivity analysis is conducted with different system parameters and managerial insights are discussed.

Figures

Figures reproduced from arXiv: 2412.09978 by the authors.

**Figure 1.** Timeline of day-ahead charging schedule, vehicle dispatch, and vehicle-charger assignment. The online vehicle-charger assignment (Model P3) and vehicle dispatch (Model P2) are solved and executed at the beginning of each minute. Based on the executions, the system states (𝑆̃ 𝑡 ,𝑉𝑡 ,Ω𝑡 , 𝑒𝑣𝑡, 𝑅𝑡 ,𝑊𝑅𝑡 , and vehicle locations) are updated accordingly, i.e., either unchanged until t+1 if vehicles remain idle, or updated… view at source ↗

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Reference graph

Works this paper leans on

2 extracted references · 1 canonical work pages

[52]

https://doi.org/10.1016/j.trc.2019.01.011 Jamshidi, H., Correia, G.H.A., van Essen, J.T., Nökel, K. , 2021. Dynamic planning for simultaneous recharging and relocation of shared electric taxis: A sequential MILP approach. Transp. Res. Part C Emerg. Technol. 125. https://doi.org/10.1016/j.trc.2020.102933 Jenn, A., 2019. Electrifying Ride-sharing: Transitio...

work page arXiv 2019
[1389]

Comparison of different modeling approaches for vehicle queuing at chargers for the benchmark charging policies

https://doi.org/10.1109/ICRA.2016.7487272 33 Appendix A. Comparison of different modeling approaches for vehicle queuing at chargers for the benchmark charging policies. In the literature, existing studies assume a simplified vehicle queuing behavior modeling at chargers/charging stations, i.e., vehicles wait in a queued charger/charging station for charg...

arXiv 2016

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [52]

https://doi.org/10.1016/j.trc.2019.01.011 Jamshidi, H., Correia, G.H.A., van Essen, J.T., Nökel, K. , 2021. Dynamic planning for simultaneous recharging and relocation of shared electric taxis: A sequential MILP approach. Transp. Res. Part C Emerg. Technol. 125. https://doi.org/10.1016/j.trc.2020.102933 Jenn, A., 2019. Electrifying Ride-sharing: Transitio...

work page arXiv 2019

[2] [1389]

Comparison of different modeling approaches for vehicle queuing at chargers for the benchmark charging policies

https://doi.org/10.1109/ICRA.2016.7487272 33 Appendix A. Comparison of different modeling approaches for vehicle queuing at chargers for the benchmark charging policies. In the literature, existing studies assume a simplified vehicle queuing behavior modeling at chargers/charging stations, i.e., vehicles wait in a queued charger/charging station for charg...

arXiv 2016