Introduction

Climate change is the defining crisis of our time, and it is tied to the rising anthropogenic greenhouse gas (GHG) emissions. Reducing or even eliminating the GHG emissions across all major sectors is critical to meet the 1.5 °C climate target. In the U.S., the transportation sector has become the largest source of GHG emissions, accounting for 37% of the country’s total carbon dioxide (CO2, the primary anthropogenic GHG) emissions1. With only 0.4% of the total on-road vehicle population, long-haul heavy-duty trucks are responsible for 11% of transportation carbon emissions (cf. Supplementary Fig. 1 in Supplementary Information Section 4). Decarbonizing long-haul heavy-duty trucks, i.e., reducing CO2 and other GHG emissions from their operations, is thus a disproportionately high leverage point in the scope of the climate change mitigation framework.

Electrifying long-haul heavy-duty trucks is a critical step towards decarbonizing the trucking sector2. Electric trucks (E-Trucks) not only enhance the driving experience with their rapid acceleration and quieter operation but also eliminate tailpipe emissions and offer a potential to reduce carbon emissions3. Along this line, the U.S. government has set a target to electrify 30% of medium- and heavy-duty truck sales by 2030 and 100% by 20404. However, achieving E-Trucks’ full decarbonization potential requires not only fast E-Truck adoption but also a careful consideration of how they are operated and charged, as the charging electricity incurs carbon footprints—the carbon emissions during electricity generation. For clarity and brevity in our discussion, we assume all references to trucks pertain to long-haul heavy-duty models unless specified otherwise.

We argue that the full decarbonization potential of E-Trucks is jeopardized by the current common practice of driving as quickly as possible along the shortest path. Such driving practice often underutilizes the geographical information and the traffic information, resulting in inefficient paths and speed plans that consume substantial energy5. Moreover, the current practice of charging E-Trucks—charging whenever the battery level falls below a certain threshold—often fails to consider the source of electricity, using gray electricity with higher carbon intensity—the amount of carbon emissions per unit of electricity during generation. Depending on different mixes of electricity generation (cf. Table 1), the carbon intensity presents large geospatial and temporal fluctuations due to the inherent intermittency of renewable energy sources, as illustrated in Fig. 1. Ignoring such spatial-temporal diversity of carbon intensity may lead to a large carbon footprint during charging. Indeed, as suggested by our numerical studies with real-world data over the U.S. highway system, common practice operations could under-realize E-Truck’s decarbonization potential by 25%. Even worse, improper charging and operation of E-Trucks might even lead to a higher carbon footprint than ICE trucks; see Supplementary Section 5.2 for an example of inefficient E-Truck operation and Supplementary Section 5.3 for an example of carbon-optimized operation. It is thus essential to optimize the truck operations to unleash E-Trucks’ full decarbonization potential.

Fig. 1: Spatial-temporal diversity of the U.S. carbon intensity (kg/kWh).

a The average carbon intensity in different states. b The carbon intensity varying in time during the first week of 202415. Large variation in carbon intensity are commonly observed in other times of the year. Source data of this figure are provided in the Source Data file.

In this paper, we study the problem of minimizing the carbon footprint of long-haul heavy-duty E-Trucks’ timely transportation, a critical operation module. This involves strategically orchestrating path planning, speed planning, and intermediary charging planning as E-Trucks navigate national highway networks within tight delivery timeframes. The path planning and speed planning jointly optimize the E-Truck’s energy efficiency by selecting the most effective routes and maintaining optimal speeds. Meanwhile, the charging planning strategically schedules charging sessions and locations to utilize clean electricity with low carbon intensity. Such a carbon footprint optimization (CFO) problem is essential for realizing the environmental advantages of E-Trucks. However, it remains intractable due to a combination of challenges: (i) the strict delivery deadline, (ii) the battery operational constraints, (iii) the non-convexity of the objective function, and (iv) the enormous search space of charging decisions across a vast network with diverse carbon intensity profiles. Indeed, the CFO problem is NP-hard and more complicated and challenging than those in related studies for internal combustion engine (ICE) truck5,6 and electric vehicle (EV) driving optimization7,8,9. Existing mathematical models (cf. Supplementary Table 2 in Supplementary Information Section 2) and approaches (cf. Supplementary Table 3 in Supplementary Information Section 3) either do not apply to the problem or fail to solve the problem effectively, especially for large-scale instances; see Supplementary Section 2 for a more detailed discussion of the related work.

To address this challenging problem, we propose a stage-expanded graph formulation, which transforms the CFO problem into a Generalized Restricted Shortest Path (GRSP) problem5,10 under practical settings. The key advantages of this formulation are its low model complexity and the exposure of a problem structure that facilitates efficient algorithm design. By exploiting this structure, we devise a dual-subgradient algorithm that is provably convergent. We show that each iteration of this algorithm runs in polynomial time relative to the network size. We also establish a sufficient condition for optimality and derive a posterior bound on the solution quality when this condition is not satisfied. Furthermore, our mathematical formulation and approach are general and extendable to other long-haul heavy-duty trucks, including hydrogen fuel cell electric trucks (FCE-Trucks), and ICE trucks. Our algorithm demonstrates strong empirical performance in extensive simulations conducted with real-world data, enabling a thorough evaluation of the decarbonization potential of E-Trucks in realistic operational settings.

Using our solution as a building block, we evaluate the full decarbonization potential of E-Trucks and the benefits of carbon-optimized operations. We conduct extensive simulations over the US national highway network with the real-world data. We highlight the following key findings: (i) With common practice operation, the E-Truck achieves a 36% carbon reduction compared to the conventional ICE trucks, validating the decarbonization potential of E-Trucks. (ii) Our carbon-optimized operation achieves an extra carbon reduction of 25%, of which the carbon-aware charging and energy-efficient driving contribute 12% and 13%, respectively. The aggregate 61% carbon reduction of the U.S. long-haul trucking sector amounts to 2.4% of the total U.S. carbon emissions, or approximately the entire carbon footprint of countries like Qatar11. (iii) The carbon-optimized operations, when applied to ICE trucks, FCE-Trucks, and E-Trucks, accelerate the decarbonization progress, achieving the same level of carbon reduction 9 years sooner than relying solely on adopting zero-emission trucks. With the deployment of carbon-optimized operations, the whole long-haul trucking sector will achieve a substantial carbon reduction by 2050—62% reduction relative to 2019 levels with BAU projection, of which the adoption of zero-emission trucks contributes 5%, carbon-optimized operations contribute 31%, and grid decarbonization contributes 26%.

Paper Outline. We begin by presenting the problem formulation and our methodology, emphasizing key technical innovations and contributions. We then demonstrate through comprehensive numerical experiments the decarbonization potential achievable through our integrated approach, providing quantitative insights into system-wide emissions reductions and operational efficiency gains. We conclude the main text with a assessment of current limitations and promising avenues for future research in “Discussion”. Complete methodological details and algorithmic frameworks are presented in Methods, with additional supporting analyses, extended data tables, and supplementary figures provided in the accompanying Supplementary Information.

Results

An efficient approach for carbon-optimized E-Truck timely transportation

We first introduce essential notations and the problem setting, followed by an overview of the key ideas underpinning our approach. Detailed discussions on the model and algorithm are deferred to Methods. We model the highway system as a directed graph ({\mathcal{G}}=({\mathcal{V}},{\mathcal{E}})). The node set ({\mathcal{V}}={{\mathcal{V}}}_{r}\cup {{\mathcal{V}}}_{c}) consists of road nodes ({{\mathcal{V}}}_{r}) (representing segment endpoints) and charging stations ({{\mathcal{V}}}_{c}). The edge set ({\mathcal{E}}\subset {\mathcal{V}}\times {\mathcal{V}}) represents road segments. We consider an E-Truck traveling from an origin (o\in {\mathcal{V}}) to a destination (d\in {\mathcal{V}}) within a hard deadline T. The objective is to minimize the carbon footprint of the electricity used along this trip. The E-Truck has a battery capacity B and needs to maintain a positive battery State-of-Charge (SoC) throughout the trip. We consider the E-Truck begins the journey with an initial battery SoC β0 ∈ [0, B]. The solution to the problem includes (i) the path plan: a sequence of edges from o to d; (ii) the speed plan: a speed profile across these edges; (iii) the charging plan: the selection of intermediary charging stations, along with wait and charge times at each selected charging station.

One of our key methodological contributions is the stage-expanded graph, a construction that extends ({\mathcal{G}}) to integrate charging decisions. The stage-expanded graph originates from the following key observations: (i) in practice, an E-Truck operator only charges for a small number of times during a trip, e.g., 3–4 times charging for a 1500-mile E-Truck transportation; (ii) the truck operation between two consecutive charging stops (a stage) reduces to an energy-efficient driving problem for which efficient algorithms are available5,6; (iii) given the truck operations at each stage, the carbon-aware charging decisions between each two consecutive stages become tractable to optimize.

Given these observations, we construct the stage-expanded graph ({{\mathcal{G}}}_{s}=({{\mathcal{V}}}_{s},{{\mathcal{E}}}_{s})) as follows. We assume the E-Truck can make up to N charging stops along its trip, where N is a parameter provided to the problem. The graph ({{\mathcal{G}}}_{s}) consists of N + 1 stages, corresponding to the N + 1 segments of the journey between charging events. The node set ({{\mathcal{V}}}_{s}) is composed of N + 1 copies (one copy for each stage) of the original nodes in ({\mathcal{V}}): ({{\mathcal{V}}}_{s}=\left{{v}^{i}:v\in {\mathcal{V}},i\in \left{1,\ldots,N+1\right}\right}). The edge set ({{\mathcal{E}}}_{s}) contains (i) the original edges replicated across all stages, and (ii) virtual edges connecting the same charging stations and the destination between consecutive stages. Formally, we define:

$$\begin{array}{rcl}{{\mathcal{E}}}_{s1}&=&\left{({u}^{i},{v}{i}):(u,v)\in {\mathcal{E}},i\in \left{1,\ldots,N+1\right}\right},\ {{\mathcal{E}}}_{s2}&=&\left{({v}^{i},{v}{i+1}):v\in {{\mathcal{V}}}_{c}\cup \left{d\right},i\in \left{1,\ldots,N\right}\right},\ {\rm{and}},{{\mathcal{E}}}_{s}&=&{{\mathcal{E}}}_{s1}\cup {{\mathcal{E}}}_{s2}.\end{array}$$

(1)

When an E-Truck, at stage i, arrives at a charging station (v\in {{\mathcal{V}}}_{c}), it can choose to end the current stage and charge. This action is represented by traversing the charging edge (v**i, v**i+1). Within each stage, the E-Truck needs to travel towards the next charging station or the final destination. Upon arrival, it can charge at the charging station and advance to the next stage or, if at the destination, end its journey. Note that the E-Truck can charge for less than N times, arrive at the destination at stage i < N + 1, and then travel across stages through virtual edges until reaching the final stage, mimicking waiting at the destination upon early arrival. We provide an illustration of the stage-expanded graph in Fig. 2.

Fig. 2: Illustration of a stage-expanded graph for an E-Truck timely transportation task with N = 2 charging stops.

Nodes b, c, and e represent charging stations within the original transportation network. The red path indicates a feasible operation candidate for an E-Truck traveling from origin o1 to destination d3. The constructed stage-expanded graph comprises N + 1 = 3 stages. In the first stage, the E-Truck travels from o1 to b1, with a travel time t1, then waits for ({t}_{w}^{{1}) amount of time and charges at b1 for ({t}_{c}}{2}) amount of time. Subsequent stages involve similar sequences of travel, waiting, and charging. Dashed arrows represent virtual edges that denote potential charging decisions between consecutive stages.

The stage-expanded graph captures the problem structure and decomposes the routing and charging decisions. Specifically, we can separately optimize the energy-efficient timely transportation subproblem within each stage and the carbon-aware charging subproblem between stages, followed by a higher level of coordination for the solutions of the subproblems. Those subproblems are more tractable than the original CFO problem. Efficient algorithms are available for the energy-efficient timely transportation subproblems5,6, and the size of the carbon-aware charging subproblems is small. Moreover, the revealed structure comes with a minor increase in graph size—the size of the stage-expanded graph is only N + 1 times the original graph, where the number of charging stops N is a small constant in practice. This is in sharp contrast to the time-expanded graph8 or the battery-expanded graph12, which substantially increase the graph size as discussed in Supplementary Table 3 in Supplementary Information Section 3. We explore the problem structure and formulate the CFO problem as a GRSP problem on the stage-expanded graph. We then propose an efficient dual-based algorithm, which features guaranteed convergence and polynomial complexity per iteration. We also establish a sufficient condition for optimality and derive a posterior bound on the solution quality when this condition does not hold. Besides the favorable theoretical properties, our algorithm demonstrates strong empirical performance, allowing us to examine the full benefits of E-Truck decarbonization using real-world data. See “Methods” for our formal problem formulation, algorithm design, and performance analysis. See also Supplementary Section 3 for a remark on the novelty of our approach and a comparison with conceivable alternatives.

Numerical experiment setup

To evaluate the decarbonization potential of truck electrification and the enhanced environmental benefits of carbon-optimized E-Truck operations, we conduct the simulation on the U.S. highway network with real-world traces. The constructed transportation network contains 84,504 nodes and 178,238 edges. We conduct simulations on long-haul origin-destination pairs from Freight Analysis Framework13. We divide the long-haul origin-destination pairs into the four distance categories: 500–1000 miles, 1000–1500 miles, 1500–2000 miles, and 2000+ miles. We then select the top 100 pairs based on freight value from each group, resulting in a total of 400 origin-destination pairs. More details of the simulation setup can be found in Methods.

In the following, we will present the key findings focusing on the implications of carbon-optimized operations for the truck decarbonization strategies. More supplementary simulation results can be found in the Supplementary Information, including (i) the applicability of our approach to timely heavy-duty truck transportation over the European continent highway system (Supplementary Section 7), (ii) the robustness analysis of our approach (Supplementary Section 8.2), and (iii) the runtime performance of our approach and other alternatives (Supplementary Section 8.4 and Supplementary Section 8.3).

Truck electrification reduces carbon emissions

We first evaluate the decarbonization potential of truck electrification alone in reducing carbon emissions. In the following, we use the ICE truck, operated with common practice that drives on the fastest path at top truck speeds, as the baseline. We then compare the ICE truck with the E-Truck operated with a conceivable baseline that mimics the common practice (denoted by PRACTICE), which drives on the fastest path also at top truck speeds, and charges whenever the battery level falls below a certain threshold. For each origin-destination pair, we compute the normalized carbon footprint of the E-Truck with respect to the ICE truck and present the results in Fig. 3. We find that under the PRACTICE baseline, the average normalized carbon footprints of the E-Truck are 0.69, 0.61, 0.59, and 0.59 for the four distance categories, respectively. Those numbers, combined with the estimated carbon share of different distance categories for long-haul heavy-duty trucks14, indicate that the E-Truck can achieve an average reduction of 36% of carbon emissions compared to traditional ICE trucks—a testament to the decarbonization potential of truck electrification. This potential, however, remains underexplored due to inefficient operations. The normalized carbon footprint varies largely across different origin-destination pairs, revealing room for optimization. More concerning, improper operation can actually result in the E-Truck producing a higher carbon footprint than its ICE counterpart, as illustrated in Supplementary Section 5.2. This operational inefficiency underscores the importance of optimized operations in maximizing the decarbonization potential of E-Trucks, which we elaborate on in the following analysis.

Fig. 3: The normalized carbon footprint under different driving strategies and the carbon emission shares by different distance categories.

a The normalized carbon footprint for electric trucks relative to ICE Trucks across distance categories. Results compare carbon-optimized operations (CARBON) with conventional baseline operations (PRACTICE). Box plots show interquartile ranges (25th–75th percentiles) with median values indicated by internal lines. Square markers denote mean values, and error bars represent ±1.5 standard deviations. b The estimated carbon emission share of distance category for long-haul heavy-duty trucks (data from NREL14). Source data of this figure are provided in the Source Data file.

Carbon-optimized timely transportation maximizes E-Truck decarbonization potential

We then study the full decarbonization potential of E-Trucks by our carbon-optimized operations (denoted by CARBON). We run our approach over the same set of origin-destination pairs and compare the performance of CARBON with the PRACTICE baseline. As demonstrated in Fig. 3, we find that the average normalized carbon footprint of CARBON are 0.43, 0.37, 0.34, and 0.35 for the four distance categories, respectively, leading to a weighted average of 0.39 compared to the ICE truck. These results show that, carbon-optimized operations achieve an additional 25% carbon reduction on top of electrification alone, yielding a cumulative 61% carbon reduction when compared to ICE trucks. The cumulative carbon reduction achieved in the long-haul heavy-duty trucking sector amounts to 2.4% of the total US carbon emissions or approximately the total carbon emissions of countries like the Qatar. Moreover, such reduction is more consistent across different origin-destination pairs than the PRACTICE baseline with a smaller standard deviation in Fig. 3.

We then study the attribution of the carbon reduction from carbon-optimized timely transportation. Recall that the carbon-optimized operations reduce carbon footprint by jointly optimizing: (i) energy-efficient driving by path and speed planning and (ii) carbon-aware charging by charging planning. To further understand the attribution of those two modules, we consider a modified approach (denoted by ENERGY) from our method that uses uniformly constant carbon intensity. The ENERGY baseline isolates the first mechanism by focusing exclusively on energy-efficient driving while deliberately excluding carbon-aware charging considerations. Therefore, by contrasting CARBON and ENERGY results, we isolate and quantify the impact of the second module and specifically demonstrate the significance of carbon-aware charging operations in overall decarbonization performance. We also explore the effects of extending the delivery deadlines on the carbon footprint of E-Trucks by adjusting the deadlines from 1.1T**f to 1.5T**f, where T**f represents the minimum travel time determined by a fastest-path approach detailed in Methods. The ratio T/T**f is referred to as the delay factor. For ease of presentation, we present the results in Fig. 4 for the distance category of 500–1000 miles, which contributes the most carbon share among all distance categories, as seen in Fig. 3. The full results for all distance categories can be found in Supplementary Fig. 7 in Supplementary Information Section 6.2 which demonstrate similar results. We observe that carbon-optimized operations consistently reduce more carbon than energy-efficient ones across various delay factors. For example, at a delay factor of 1.2, carbon-optimized operations achieve an additional 0.12 normalized carbon savings over energy-efficient operations. Therefore, at least 12% out of the 25% additional carbon reduction from the carbon-optimized operation is attributed to carbon-aware charging. These findings, combined with the facts that CARBON consume at most 2.4% more normalized energy on average than ENERGY (cf. Fig. 4b), demonstrate that carbon-optimized timely transportation simultaneously reduces energy consumption and the carbon footprint via energy-efficient driving and carbon-aware charging, maximizing the environmental benefits brought by E-Trucks.

Fig. 4: Carbon footprint and energy consumption of E-Trucks under different operations with different delay factors.

A larger delay factor means a more relaxed deadline. The results are for the distance category of 500–1000 miles. The results for all four distance categories can be found at Supplementary Fig. 7 in Supplementary Information Section 6.2. a The normalized carbon footprint with respect to ICE trucks under today’s common practice. b The normalized energy consumption with respect to ICE trucks under common practice. In both (a, b), box plots show interquartile ranges (25th–75th percentiles) with median values indicated by internal lines. Square markers denote mean values, and error bars represent ±1.5 standard deviations. Source data of this figure are provided in the Source Data file.

Carbon-optimized timely transportation boosts truck decarbonization in the future

We then study how carbon-optimized timely transportation reshapes the truck decarbonization pathway in the future, using carbon intensity projection data from the Cambium dataset15. This is to examine the usefulness of our approach in different projected carbon intensity settings. We focus on three power grid decarbonization scenarios: (i) Business-As-Usual (BAU) that assumes a continuation of current policies and trends. (ii) CONSERVATIVE that assumes high future costs for renewable investments; (iii) OPTIMISTIC that achieves the full grid decarbonization target by 203516 where national-wide carbon intensity is zero, albeit regional ones can fluctuate around zero over time. Negative carbon intensity is achieved by assuming the fast development of nascent technologies17 like bioenergy with carbon capture and storage (BECSS)18. In the following, all carbon reductions are computed by considering the carbon shares of different distance categories shown in Fig. 3.

We commence our investigation by examining the impacts of carbon-optimized operations on a single E-Truck. Our results, presented in Fig. 5, reveal that CARBON achieves an additional carbon reduction of 13% by 2050 in the BAU scenario when compared to the PRACTICE baseline. This additional carbon reduction increases to 17% in the CONSERVATIVE scenario. Even in the OPTIMISTIC scenario, our carbon-optimized solution can still achieve an additional 3% carbon reduction compared to the PRACTICE baseline, by exploiting the (small) fluctuation of carbon intensity over different regions and times.

Fig. 5: Normalized carbon emissions of electric trucks relative to internal combustion engine trucks.

We compare carbon-optimized operation (CARBON) with common practice operation (PRACTICE) across different grid decarbonization scenarios: business-as-usual (BAU), conservative projection (CONSERVATIVE), and optimistic projection (OPTIMISTIC). Box plots show interquartile ranges (25th–75th percentiles) with median values indicated by internal lines. Square markers denote mean values, and error bars represent ±1.5 standard deviations. The mean values, median values, and standard deviations are weighted by emission share in each distance category. Source data of this figure are provided in the Source Data file.

We further evaluate the impact of carbon-optimized operations across the entire long-haul heavy-duty trucking sector. We examine the major types of long-haul heavy-duty trucks, including ICE trucks, fuel cell electric trucks (FCE-Trucks), and battery electric trucks (E-Trucks). We utilize zero-emission vehicle (ZEV, including FCE-Trucks and E-Trucks) adoption projection data from ref. 14, focusing on the following scenarios: (i) NORMAL that reflects a central set of assumptions; (ii) ADVANCED with lower charging infrastructure cost; (iii) CONSTRAINED with constrained ZEV technology advancement. We tailor our approach in Methods and deploy it to the entire spectrum of long-haul heavy-duty trucks; see Methods for detailed descriptions of such adoption.

Our results also indicate that carbon-optimized timely transportation can contribute to the decarbonization of the trucking sector by reducing carbon emissions more efficiently. In Fig. 6, we observe that there will be an immediate carbon reduction in 2026 by implementing our carbon-optimized operations for ICE trucks, a goal that would otherwise take 9 additional years through ZEV adoption alone. Moreover, carbon reductions achievable by 2050 through ZEV adoption are reached 7 years earlier with carbon-optimized operations. This trend persists under the ADVANCED ZEV adoption scenario. Carbon-optimized operations consistently contribute to trucking sector decarbonization over time. From 2026 to 2030, total emissions increase slightly due to the growing number of trucks, but the subsequent adoption of ZEVs combined with carbon-optimized operations leads to a sharp decline, with a carbon reduction of 62% by 2050, of which ZEV adoption contributes 5% carbon-optimized operations contribute 31%, and grid decarbonization contributes 26% (cf. Fig. 7). Cumulatively, carbon-optimized operations account for an additional CO2 reduction of 1.2 billion tons from 2026 to 2050 compared to common practices.

Fig. 6: The stock share and carbon footprint of long-haul heavy-duty trucks from 2019 to 2050 under different ZEV adoption scenarios.

a, b, c present the stock share for ICE Truck, E-Truck, and FCE-Truck in CONSTRAINED, NORMAL, and ADVANCED ZEV adoption scenarios. d, e, f present the carbon footprint of major types of long-haul heavy-duty trucks, including ICE trucks, FCE-Trucks, and E-Trucks. The solid lines represent the carbon footprint of trucks with common practice (PRACTICE), and the dashed lines represent the carbon footprint of trucks with carbon-optimized operations (CARBON). The shaded areas represent the carbon reduction from carbon-optimized operations compared to common practice. We assume the grid decarbonization scenario to be BAU in this analysis. Source data of this figure are provided in the Source Data file.

Fig. 7: The attribution of carbon reductions of 2050 relative to the 2019 level.

The carbon emissions increase due to the growing truck population and decrease due to ZEV adoption, carbon-optimized operations, and grid decarbonization, respectively. a The attribution under the BAU grid decarbonization scenario and the NORMAL ZEV adoption scenario. b The attribution under the OPTIMISTIC grid decarbonization scenario and ADVANCED ZEV adoption scenario.

Discussion

In this paper, we explore how to unlock the full decarbonization potential of long-haul heavy-duty E-Trucks via carbon-optimized timely transportation. We present a stage-expanded graph based problem formulation and an efficient algorithm with favorable theoretical and empirical performance. Through extensive simulations with real-world traces, we show that carbon-optimized operation further reduces the carbon footprint of E-Trucks by 25%, on top of the 36% reduction from electrification alone. The cumulative 61% carbon reduction achieved is comparable to the total carbon footprint of countries like the Qatar. Our approach is applicable to various types of trucks, including ICE and ZEV trucks, allowing us to assess the impact of carbon-optimized operations on the entire spectrum of the trucking industry. Our forward-looking projections suggest that carbon-optimized operations propel truck decarbonization, achieving comparable carbon reduction 9 years earlier than ZEV truck adoption alone.

Operationalizing our approach necessitates a comprehensive software ecosystem capable of driver interaction, real-time data integration, and dynamic optimization of charging, routing, and speed planning. Our framework requires two distinct data categories with varying update frequencies and accessibility characteristics. Static Data encompasses information requiring infrequent updates due to its stable nature: (i) Transportation Network Data, including detailed road mappings, segment-specific grade profiles, and charging station locations; and (ii) Vehicle Specifications, encompassing battery charging characteristics, vehicle weight parameters, and energy efficiency profiles. This data is predominantly accessible through established sources, including OpenStreetMap[19](https://www.nature.com/articles/s41467-025-64792-2#ref-CR19 “OpenStreetMap contributors. Planet dump retrieved from https://planet.osm.org

. https://www.openstreetmap.org

, (2017).“) for transportation networks and manufacturer databases for vehicle specifications. Dynamic Data requires continuous updates to capture real-time operational conditions: (i) Traffic Conditions, providing current congestion levels across road segments; (ii) Charging Infrastructure Status, including real-time availability and queuing times at charging stations; and (iii) Grid Carbon Intensity, reflecting the temporal and spatial variability of electricity generation carbon footprints based on dynamic energy mix compositions. These data streams are accessible through established platforms including transportation APIs[20](https://www.nature.com/articles/s41467-025-64792-2#ref-CR20 “HERE Maps. Traffic flow using corridor in HERE maps. https://developer.here.com/api-explorer/rest/traffic/flow-using-corridor

(2022).“), charging network platforms[21](https://www.nature.com/articles/s41467-025-64792-2#ref-CR21 “Charge Point, Inc. Your EV charging platform of choice. https://www.chargepoint.com/

(2025).“),[22](https://www.nature.com/articles/s41467-025-64792-2#ref-CR22 “PlugShare, LLc. PlugShare—EV Charging Station Map. https://www.plugshare.com/

(2025).“), and grid monitoring systems[23](https://www.nature.com/articles/s41467-025-64792-2#ref-CR23 “Electricity Maps. Carbon Intensity Data. https://electricitymaps.com/

(2024).“).

While individual data sources exist, successful integration requires developing unified interfaces ensuring compatibility, accuracy, and reliability across heterogeneous systems–necessitating coordinated stakeholder collaboration. Successful deployment demands multi-stakeholder coordination among policymakers, transportation authorities, logistics operators, and energy providers (including grid operators and charging infrastructure companies). Policymakers must establish standardized data interchange protocols, incentivize cross-sector data sharing, and support digital infrastructure investments. Transportation authorities should provide comprehensive road network data and real-time traffic information. Energy providers must deliver accurate, timely data on charging availability and grid carbon intensity. Logistics companies must adopt integrated technological solutions and participate in real-world validation studies. This collaborative ecosystem is essential for realizing the framework’s full decarbonization potential in operational environments.

Remarkably, deploying this software ecosystem requires no investment in hardware infrastructure, instead building upon purely algorithmic development and existing data sources. This characteristic enables immediate deployment across existing fleet operations, without the decade-long infrastructure development cycles that typically constrain decarbonization efforts. Our framework thus offers an agile and cost-effective strategy for a rapid decarbonization pathway in the trucking sector.

Beyond long-haul heavy-duty trucks, our approach may not be directly applicable to the operations of light-duty vehicles or short-haul trucks, as their operation settings often involve frequent pickup-delivery scheduling, which is absent in the long-haul heavy-duty vehicle operation studied in this paper24,25. However, in cases with long transportation distances and fixed pickup-delivery schedules, our approaches can be applied to minimize their carbon footprint, energy consumption, or monetary cost. Developing general carbon-optimized operation strategies for light-duty vehicles and short-haul trucks deserves further investigation26,27.

Methods

Our preliminary model and approach were initially introduced in our conference paper28. In this section, we provide a more comprehensive and self-contained presentation of our model and approach for completeness, which includes detailed problem formulation, improved algorithm with lower time complexity, performance analysis, and discussion on model limitation.

System model

We model the highway system as a directed graph ({\mathcal{G}}=({\mathcal{V}},{\mathcal{E}})). The node set ({\mathcal{V}}={{\mathcal{V}}}_{r}\cup {{\mathcal{V}}}_{c}) consists of road connection points ({{\mathcal{V}}}_{r}) and charging stations ({{\mathcal{V}}}_{c}). The edge set ({\mathcal{E}}\subset {\mathcal{V}}\times {\mathcal{V}}) represents physical road segments. Each road segment (e\in {\mathcal{E}}) has a length D**e and speed limits ([{R}_{e}^{lb},{R}_{e}{ub}]), which define the minimum and maximum travel times ({t}_{e}^{{lb}={D}_{e}/{R}_{e}}{ub}) and ({t}_{e}^{{ub}={D}_{e}/{R}_{e}}{lb}), respectively. Without loss of generality, we assume homogeneous road conditions (e.g., grade) on each road segment. Following the model in refs. 5,28, we model the energy consumption rate (in kW) on segment e as a convex function of the traveling speed r**e, denoted ({f}_{e}({r}_{e}):[{R}_{e}^{lb},{R}_{e}{ub}]\to {\mathbb{R}}). This function f**e(r**e) is primarily determined by the road grade and the E-Truck’s weight. Note that f**e(r**e) can be negative on downhill segments due to regenerative braking29. Given the convexity of f**e( ⋅ ), we can assume the E-Truck travels at a constant speed on segment e without loss of optimality [ref. 5, Lem. 1]. We ignore the acceleration and deceleration phases between road segments, since their contribution to overall time and energy consumption is typically negligible relative to the entire segment duration, as justified in refs. 5,28. The total energy consumed to traverse segment e in time t**e is then given by the perspective function c**e(t**e) = t**e ⋅ f**e(D**e/t**e), which is also convex in t**e by the convexity preserving property of the perspective function30. We assume c**e(t**e) is non-increasing in t**e