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Hours-of-service-aware siting of charging and battery-swapping stations for long-haul electric trucks under adoption uncertainty

Elnaz Irannezhad, Jia Guo

arXiv:2610.08187v1cs.CE

TL;DR

Long-haul BET infrastructure planning must account for terrain-dependent energy use, operational schedules, and mandatory driver rest. This paper jointly plans charging or swapping stations and truck schedules, while staging investment under uncertain adoption. Across twelve Australian East Coast corridors, adoption changes alter the final charge-only network modestly, while uncertainty mainly changes site choice.

  • Problem

    Long-haul infrastructure planning must connect en-route station decisions with route-specific energy, charging or swapping schedules, capacity, and mandatory driver rest.

    Source: §1 · pp. 2–3

  • Method

    The framework jointly sites charging and swapping stations, schedules replenishment with driver rest, models terrain-based energy and multi-pack batteries, and stages investment under Markovian adoption uncertainty.

    Source: §1 · pp. 2–3, §7 · p. 39

  • Results

    A ±30% adoption change alters the final charge-only network by −12% to +13% of stations, over 95% are built by stage two, and charging-site overlap with a deterministic plan is 71%.

    Source: §7 · p. 39

  • Takeaways & Limitations

    On every charge-only route, the least-cost network satisfying range, capacity, and hours-of-service constraints is also the cost–delay optimum at the assumed value of time.

    Source: §6 · p. 38

    The adoption process is exogenous: the model does not capture infrastructure improvements feeding back to accelerate BET adoption.

    Source: §7 · p. 40

Abstract

from arXiv · show

Planning en-route charging and battery-swapping infrastructure for long-haul battery-electric trucks (BETs) requires models that reflect how trucks actually operate. This paper develops a mixed-integer programming framework that jointly sites charging or swapping stations and schedules each truck's charging, swapping and mandatory driver rest, so that charging time overlaps with regulated rest instead of being added to it. Energy use is derived segment by segment from road terrain with a tractive-force model, and the truck battery is modelled as a set of independently swappable packs. Staged investment under uncertain BET adoption is formulated as a multistage stochastic program with Markovian demand and solved by stochastic dual dynamic integer programming (SDDiP) with Lagrangian cuts; we show that the Lagrangian multipliers can be bounded by each station's annualised cost without weakening the cuts. Applied to twelve freight corridors on Australia's East Coast, the algorithm jointly optimises charging and battery-swapping events as well as mandatory break events. A +/- 30\% change in adoption alters the final charge-only network by only -12\% to +13\% of stations, with over 95\% of stations built by the second stage. Hedging against uncertainty mainly changes which sites are chosen (71\% overlap with a deterministic rolling-horizon model), not when they are built.

1 Introduction

Long-haul truck infrastructure planning must connect terrain-dependent energy use, station capacity and placement, charging or swapping schedules, and mandatory driver rest. This paper integrates those decisions and stages investment as BET adoption grows.

Terrain-based energy modelling

  • Road energy use is estimated on 1-kilometre segments from terrain-derived grades using a tractive-force model that includes regenerative braking on sufficiently steep descents.The model adds a constant auxiliary electrical load and sums segment energy between consecutive candidate facilities.Source: §1 · p. 3

Integrated planning framework

  • Charging and rest are scheduled jointly with station siting, so charging adds trip time only when it outlasts a required rest.The model uses a two-tier break rule: a 10-minute break after at most 2 hours of continuous driving and a 30-minute rest after at most 5 hours of cumulative driving.Source: §1 · pp. 2–3

Multi-pack batteries

  • Each truck is modelled with a fixed number of independently swappable battery modules, allowing a swapping event to replace one or multiple packs.During charging, the onboard system distributes power across the modules simultaneously.Source: §1 · p. 3

Stochastic investment planning

  • Investment is staged under Markovian adoption uncertainty using SDDiP, with stations opened as adoption is observed and never closed.Lagrangian multipliers can be bounded by each station’s annualised cost without weakening the cuts, and cuts remain valid when dual iterations or MILP solves stop early.Source: §1 · pp. 3–4

Capacity and peak demand

  • Peak-hour route flow can be split into parallel sub-flows that use different stations, allowing multiple capacity-constrained facilities to serve demand.Source: §1 · p. 4

2 Literature Review

The review traces how operational assumptions in BET deployment, energy use, charging, scheduling, and station placement shape infrastructure planning. It identifies a gap between operational realism and strategic investment decisions, motivating an integrated staged model.

2 Literature Review

  • The review organises prior work around deployment evidence, energy estimation, charging and scheduling, and infrastructure placement, identifying inherited assumptions and remaining gaps.Source: §2 · p. 4

2.1 Operational Feasibility and Deployment Evidence

  • BET feasibility and economic competitiveness vary with duty cycle, vehicle class, battery capacity, ambient conditions, electricity price, and infrastructure; this study does not perform a full total-cost-of-ownership comparison.The review also notes that electrification coverage varies by vehicle and charging strategy, and that network availability can bind long-haul electrification.Source: §2.1 · p. 4

2.2 Energy Consumption Modelling

  • Physics-based energy models reflect vehicle dynamics and route grade, while data-driven approaches can capture empirical interactions but need detailed training data that remain difficult to obtain for emerging long-haul fleets.Source: §2.2 · p. 5

2.3 Charging Behaviour and Non-linear State-of-Charge Dynamics

  • Nonlinear charging profiles taper at high state of charge, so linear charging-time approximations may underestimate dwell; piecewise-linear models require documented breakpoints and approximation error.Source: §2.3 · p. 5

2.4 Charging Scheduling and Grid Interaction

  • Scheduling, charger capacity, and grid impacts interact, but this model captures vehicle schedules and charger capacity while leaving electrical-network constraints outside its formulation.Prior work also indicates that concurrent arrivals can strain capacity; the present model does not explicitly represent stochastic queues or first-come, first-served service.Source: §2.4 · pp. 5–6

2.5 Charging and Battery-Swapping Infrastructure Placement

  • Prior siting studies variously address capacity, swapping, and driver rules, but en-route location models do not schedule mandatory rest and many scheduling studies treat station locations as given.The review frames joint station location, capacity, and regulated rest as the central integration need.Source: §2.5 · p. 6

2.6 Research Gaps and Study Contributions

  • The literature separates operational realism from strategic planning: terrain-based energy, rest scheduling, multi-pack batteries, and staged investment under uncertain demand are not jointly represented in prior models reviewed.This study combines these layers and allows multiple capacity-constrained stations to jointly serve peak-hour route demand.Source: §2.6 · pp. 7–8

3 Models

The section develops models for locating charging and battery-swapping facilities and scheduling truck energy replenishment and driver rest, accounting for station costs, delay, operational constraints, and segment-level energy use. It couples staged infrastructure decisions under Markov demand with route-level scheduling through an SDDiP procedure using bounded-multiplier Lagrangian cuts.

3 Models

  • The model jointly selects station locations and infrastructure, truck visits and replenishment schedules, and driver breaks or rests to minimise annualised establishment and delay costs subject to energy, capacity and HoS constraints.Delay includes time for charging or swapping and applicable mandatory rest; because rest is required regardless, the model can reduce only dwell time beyond that rest.Source: §3 · pp. 8–9

3.1 Assumptions

  • Charging may be partial, arrival SoC must respect a minimum reserve, and swapped modules are assumed fully charged; experiments use a fixed ten-minute swap event regardless of modules exchanged.All battery modules start at 100% SoC in the experiments, and the fixed swap-time assumption requires validation for a specific swapping technology.Source: §3.1 · p. 9
  • The model treats peak-hour demand as divisible, uses fixed segment speeds and predetermined routes, and derives energy use from terrain-sensitive tractive force; it excludes congestion, weather variation, incidents and rerouting.Battery modules discharge in parallel, and charging duration uses a convex piecewise-linear approximation of a CC-CV curve rather than a constant rate.Source: §3.1 · p. 9

3.2 Mathematical Formulation

  • Although the general model permits either facility type at each location, experiments use separate charge-only and swap-only specialisations with the corresponding infrastructure decisions fixed to zero.The facility-capacity, energy and HoS constraints otherwise remain unchanged.Source: §3.2 · p. 13
  • The charging formulation represents the convex CC-CV time curve through piecewise-linear interpolation, while enforcing a minimum arrival SoC and assigning exchanged modules 100% SoC.At most two consecutive charge-curve breakpoints are active, making the interpolation exact and continuous over the SoC range.Source: §3.2 · pp. 14–15
  • Peak-hour route demand can be split into parallel sub-flows so multiple capacity-contended stations can serve it simultaneously within each SDDiP stage.The number of sub-flows is the smallest number that keeps each evenly divided flow within the bottleneck candidate station’s throughput.Source: §3 · p. 8, §3.2 · p. 15
  • Energy balance and battery synchronisation apply independently within each truck sub-flow, and a driver cannot take both a long rest and a short break at one visit.Charging capacity is counted per truck, whereas swap capacity is counted per battery.Source: §3.2 · pp. 16–17
  • The four-stage, per-route model uses open stations and the observed demand state as its dynamic state; charger and battery counts and truck schedules are re-optimised at each stage.Station opening is irreversible, while policies use only current and past information, not future demand realisations.Source: §3.2 · pp. 18–19
  • Each stage cost combines annualised costs for newly opened stations with daily truck-delay costs valued at AUD 3 per truck-minute.The capital recovery factor is 6% over 20 years, and delay is multiplied by 365 operating days.Source: §3.2 · p. 19
  • Lagrangian cuts provide lower bounds on expected cost-to-go for every incoming station state when the next-stage approximation is a lower bound and stage problems are feasible.The validity result is not limited to the trial state where a cut was generated.Source: §3.2 · pp. 20–21
  • Multipliers can be restricted without loss to 0 ≤ π_i ≤ ρC_i, the nonnegative value of an already-open station capped by its annualised opening cost.The bounded box also keeps the cutting-plane model in the level method bounded.Source: §3.2 · pp. 21–22

3.3 Solution Algorithm

  • SDDiP reuses child-state dual solutions across parent states and scales per iteration with stages rather than scenario paths, enabling finer stage and branch resolution.For T = 4 and three demand states, the scenario tree has 40 nodes and 27 scenario paths; the authors say it could be solved as an extensive form.Source: §3.3 · p. 23
  • Policy evaluation simulates 200 independently sampled demand paths after freezing cuts, and the sample mean plus its 95% confidence-interval half-width gives a valid expected-cost upper bound.Training stops when the lower bound changes by less than 10^-4 relative for three consecutive iterations or after 50 iterations; time-limited forward solves use feasible incumbent decisions.Source: §3.3 · pp. 23–24

3.4 Energy Consumption Model

  • Road-route energy is estimated on contiguous nominal 1 km segments using grade, rolling resistance, and aerodynamic drag, with NASADEM elevation and posted/design speed.Positive net force draws battery energy subject to drivetrain losses; sufficiently steep descents return energy through regenerative braking, subject to round-trip efficiency.Source: §3.4 · p. 24
  • Segment battery demand adds constant auxiliary power over drive time to traction energy, so auxiliary loads also offset energy recovered during regenerative braking.Segment energies are signed and aggregated over routes and facility-to-facility legs; payload, weather, traffic, acceleration, and battery-temperature effects are not calibrated.Source: §3.4 · pp. 24–25
  • Charging from 0% to 100% SoC is assumed to take 90 minutes, swapping 10 minutes, and each truck carries 4 battery packs.Each pack charges at up to 120 kW in the 10–80% SoC range, and removed swap batteries are recharged to 100% at the station.Source: §3.4 · p. 25

4 Data

The case study represents East Coast freight corridors with route-specific candidate sites and assumed peak-hour demand. Site costs and driver-rest rules are parameterised to evaluate infrastructure deployment under those conditions.

4 Data

  • The case covers east-coast corridors connecting Brisbane, Sydney and Melbourne in both directions, with only direction-accessible rest areas, passenger-EV charging sites and fuel-service stations retained.The candidate set is route-specific, not a complete national infrastructure inventory.Source: §4 · p. 25, Table 4 · p. 26
  • Charging demand uses current corridor flows and future growth, with deliberately higher assumed peak-hour volumes than existing heavy-vehicle volumes on the corridors.Demand is based on government traffic counts; the assumptions allow for dual-purpose passenger-and-truck stations and possible traffic growth.Source: §4 · pp. 25–26
  • Candidate-site costs reflect existing infrastructure: passenger-EV sites require the lowest upgrades, rest areas moderate upgrades, and fuel-service stations the highest investment.Rest-area establishment costs are discounted using a readiness score based on existing amenities and assumed weights.Source: §4 · p. 26, Table 5 · p. 27
  • Upfront costs are annualised at a 6% discount rate over a 20-year lifetime, while charging and swapping stations share fixed costs and technology-specific equipment costs are excluded.Directional candidate sites are physically distinct locations.Source: §4 · p. 27
  • The model uses a stylised two-tier rest rule—10 minutes after at most 2 driving hours and 30 minutes after at most 5—and assumes unattended charging and automated swapping can overlap with rest.The 24-hour limit and its 7-hour rest are not modelled; the assumption about unattended charging should be confirmed for attended charging.Source: §4 · p. 28

5 Experimental Results

The experiments compare separate charge-only and swap-only networks across twelve routes, under staged low, mid, and high BET-adoption scenarios. Adoption uncertainty changes the final charging network's size modestly, while site choices, driver schedules, and cost-delay outcomes vary across the analyses.

5 Experimental Results

  • Experiments analyse charge-only and swap-only networks separately despite an integrated formulation; adoption uncertainty uses four penetration stages and low, mid, and high branches.The transition probabilities are hypothesised for methodological demonstration because real BET adoption data are unavailable.Source: §5 · pp. 28–29

5.1 Station-siting Decisions in SDDiP against Deterministic Rolling Horizon Model

  • 83, 94, and 106 final-stage charging stations on low, mid, and high branches mean ±30% adoption variation changes station count by only −12% to +13%; over 95% are built by stage two.Demand not met through additional sites is partly absorbed by increasing charger counts and utilisation at existing sites.Source: §5.1 · p. 33
  • Charge-only SDDiP and deterministic networks build 87 vs 88 stations at 5% penetration and 95 vs 94 at 20%, with 71% stage-four site overlap.Peak charger requirements are identical on every route and stage, reaching 243 chargers on Route 4 at 20% penetration.Source: §5.1 · p. 33
  • At 20% penetration, swap-only SDDiP builds 53 vs 59 deterministic stations, raising Route 4's peak battery requirement from 162 to 284.The SDDiP policy spends 5.8% more in the first two stages but 3.0% less by the final stage, consistent with anticipating high demand.Source: §5.1 · p. 33
  • Swap-only policy-evaluation confidence bounds range from 2.62% to 5.35% (mean 3.35%), with only Route 9 above 5%; charge-only bounds are 3.07–7.9%, with four routes above 5%.The paper reports looser charge-only convergence as consistent with larger, harder stage subproblems and greater policy-cost variability.Source: §5.1 · p. 35

5.2 Driver Hours of Service and Charging Schedule

  • On Route 1 at 5% penetration, charging coincides with mandatory breaks or rests, and dwell extends only when charging outlasts required rest.Batteries are charged only as much as needed for the next stop or destination while preserving the minimum SoC reserve.Source: §5.2 · p. 36

5.3 Cost–delay Trade-off: Single-objective Extremes

  • At 3 AUD per truck-minute, the cost-only network matches the combined optimum on every charge-only route and 11 of 12 swap-only routes; delay-only builds 2–7× as many charging stations and 6–38× as many swapping stations.The authors attribute the inactive trade-off to charging being absorbed into mandatory rest, leaving little delay for added stations to remove.Source: §5.3 · p. 37

6 Discussion

At the assumed value of time, the least-cost network satisfying range, capacity, and hours-of-service constraints is already the cost–delay optimum on every charge-only route. Under adoption uncertainty, differences from deterministic planning center on site choice and swapping investment patterns, while computational effort varies with route complexity; the authors call for sensitivity experiments before policy or investment use.

6 Discussion

  • At the assumed value of time, the cost–delay trade-off is inactive: the least-cost feasible network is optimal on every charge-only route, while a delay-only objective multiplies charging station counts by 2–7 and opens nearly every swapping candidate site.The delay-only extreme is described as a diagnostic, not a plausible investment target.Source: §6 · p. 38
  • For charge-only, deterministic and SDDiP models select similar total station counts and identical peak charger requirements in several stages, although selected sites and early-stage costs differ.The comparison indicates that uncertainty chiefly affects site choice and investment timing rather than uniformly increasing station counts.Source: §6 · p. 38
  • For swapping, SDDiP sometimes builds fewer, more concentrated stations as demand grows, increases replacement inventory at the busiest sites, and shifts some investment earlier.These changes reflect the policy's consideration of possible higher-demand branches.Source: §6 · p. 39
  • 19 of 24 instances reached policy-evaluation confidence bounds of 5% or less; computational effort varies by route complexity, with high-demand routes needing more iterations and costly backward-pass dual solves.The authors recommend allocating network-wide SDDiP budgets by route complexity rather than uniformly across routes.Source: §6 · p. 39
  • Terrain, charging-curve, rest, and capacity assumptions can affect feasibility and delay, so systematic ablation and sensitivity experiments are needed before policy or investment decisions.The discussion says the magnitude of these effects remains to be established.Source: §6 · p. 39

7 Conclusion

The study integrates terrain-based energy use, driver-rest scheduling, and staged infrastructure investment under uncertain demand. Across twelve East Coast corridors, adoption changes mainly affect site selection, while most stations are built early.

7 Conclusion

  • The framework integrates terrain-derived energy use, mandatory HoS rest, independently swappable battery packs, staged investment under uncertain demand, and multi-site service of peak-hour route demand.The framework uses a multistage stochastic SDDiP model with Lagrangian cuts to time investment under uncertain demand growth.Source: §7 · p. 39
  • A ±30% adoption change alters the final charge-only network by −12% to +13% of stations, with over 95% built by stage two; uncertainty yields 71% overlap with a deterministic charging plan.For swapping, overlap with the deterministic plan is about half.Source: §7 · p. 39
  • SDDiP cuts remain valid lower bounds when dual iterations or MILP solves stop early, and restricting multipliers to [0, ρCi] preserves cuts while bounding the level-method master problem.Training stops on lower-bound stability; solution quality is assessed separately using a larger-sample policy evaluation.Source: §7 · p. 39
  • Energy use assumes fixed speed and fixed vehicle mass, omitting traffic, weather, payload variation, and battery thermal effects on efficiency.Traffic counts stand in for payload data; the paper identifies trip-level payload data as a natural refinement.Source: §7 · pp. 39–40
  • The model uses equal fixed station costs, hypothesised adoption transitions, stagewise-resolved capacities without ratchets, and exogenous adoption that ignores infrastructure-induced uptake.The paper proposes technology-specific, time-varying costs, calibrated adoption probabilities, and endogenous demand as future extensions.Source: §7 · p. 40
  • The case study uses routes under 12 hours, optimises routes separately with simultaneous peak-hour station loading, and assumes fixed site interconnections without modelling grid capacity.A joint network model with time-shifted station arrivals could capture shared stations and may reduce required capacity; grid constraints are also proposed for future work.Source: §7 · p. 40
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