From diesel to electric: potential of drayage trucks transition in Southern California

Summary

Battery electric drayage trucks (BEDTs) offer an opportunity to decarbonize the drayage fleets. This article analyzes the potential of BEDTs using data on 1,051 drayage trucks in Southern California. A methodology is developed to evaluate energy and charger requirements across singleton, small, and large fleets. This study assesses the fraction of trucks that can be electrified using battery sizes from 100 to 1000 kWh. Our analysis reveals decreasing uncertainties for fleet electrification with increasing battery size and with offsite charging involved. Combining an 800-kWh battery with both depot and offsite charging using 350 kW chargers, approximately 95% of diesel drayage trucks can be electrified. However, singleton fleets demonstrate the lowest performance and experience substantial improvements through offsite charging. Preferred locations for depot and off-site chargers are identified near the Ports of Long Beach and Los Angeles, and the City of Ontario. These results provide essential guidance for electrifying drayage trucks.

Graphical abstract

Highlights

• •Larger battery sizes reduce uncertainty and enhance electrification feasibility
• •Offsite charging improves performance, especially for singleton fleets
• •800-kWh batteries with offsite charging enable about 95% of truck electrification
• •High charger demand concentrated near POLA, POLB, and the City of Ontario

Electrochemical energy storage; Energy Modelling; Energy transportation

Introduction

Greenhouse gas (GHG) emission reduction in the transportation sector is significant for mitigating climate change impacts. Transportation was the largest source (28%) of anthropogenic U.S. GHG emissions in 2022.¹ While medium and heavy-duty trucks represent only 5% of U.S. vehicles, they generate approximately 24% of transportation-related emissions.^2,3 The transportation sector is the largest source (40.1%) of GHG emissions in California, where heavy-duty trucks account for 8.4% of emissions.⁴ California has set ambitious climate targets to reduce GHG emissions by 40% by 2030 and 80% by 2050.⁵ Electrifying heavy-duty trucks is a critical step to meet these targets. Toward this end, the California Air Resources Board (CARB) developed the Advanced Clean Transportation (ACT) Regulation in June 2020 that mandated heavy-duty commercial fleets to be zero-emission vehicles (ZEVs) by 2045, and set a timeline for meeting heavy-duty ZEV market thresholds.⁶ After the CARB’s recent regulations, 14 other states and the District of Columbia signed a memorandum of understanding setting targets that 30% of new medium and heavy-duty vehicle sales to be ZEV by 2030, with the ultimate goal of 100% by 2050.⁷ This policy support and the decline in battery costs have prompted recent studies to investigate opportunities for the applications of Heavy-Duty Electric Trucks (HDETs).^8,9

The opportunity for deploying HDETs in heavy-duty operations is an attractive option to meet California’s GHG reduction targets, given that California will utilize more renewable energy sources for electricity generation and set a goal to ensure at least 60% of electricity is renewable by 2030 and to achieve zero-carbon electricity by 2045.^10,11,12 The initial electrification efforts will focus on high-priority fleets that are most suitable for the transition. The drayage truck fleet, which moves goods between ports and transshipment facilities, warehousing, and other points in the distribution system, is one of the earliest heavy-duty vocations to see pilot deployments of ZEV and offers significant potential for reducing GHG in California.

The San Pedro Bay Ports (SPBP) complex is the largest port system in California and the US, consisting of the Port of Los Angeles (POLA) and Port of Long Beach (POLB), accounting for about 40% of U.S. shipping containers imports and 31% and 74% of the market share in the U.S. and west coast, respectively.^13,14 Together they stand as Southern California’s largest fixed pollution generator.¹⁵ Heavy-duty drayage trucks serve a significant role, with each port having registered more than 17,000 heavy-duty drayage trucks to carry the majority of cargo between the ports, railyards, and warehouses.¹⁶ These drayage activities make up the largest contribution to port-related GHG emissions, responsible for approximately 40% of the SPBP-wide total according to the POLA and POLB inventories.¹⁷

As a result, the State of California has identified transitioning drayage trucks to ZEV technology as the main policy goal for mitigating GHG emissions, and has mandated 100% ZEVs in drayage by 2035–10 years earlier than other heavy-duty commercial fleets.¹⁸ Results from a 2020 survey by the SPBP as part of their Clean Air Action Plan found that BEVs were the most preferred technology option among the various ZEV technologies, being identified as the top choice for 35% of fleets when hybrid drivetrains are included.¹⁹ Battery Electric Drayage Trucks (BEDTs) were identified as potentially viable due to their typically regular daily duty cycles that are based in a depot location and with daily Vehicle-Miles Traveled (VMT) patterns that are often compatible with the ranges offered by batteries.²⁰

Recent studies investigating factors affecting Alternative Fuel Vehicle (AFV) adoption in categorized sizes of truck fleets have predominantly focused on general heavy-duty fleets and relied primarily on qualitative analyses based on survey data.^21,22 However, these studies have not specifically addressed drayage fleets, nor have they thoroughly explored the potential for observed operations. Given the significance of the ZEV for drayage fleets and the limited research in this area, this article aims to quantify the potential of BEDTs for drayage fleets and examine how it varies across different fleet size categories. The following research questions will be investigated in this study.

• 1.What proportion of diesel drayage truck operations and trucks can be feasibly met by BEDTs for different battery sizes and fleet size categories?
• 2.What are the preferred locations for charger installations?
• 3.How does offsite charging impact the feasibility of BEDTs for different fleet sizes?

To address these questions, this study makes several key contributions to current literature. First, it focuses on operational requirements derived from observed behavior using a large real-world dataset and applies a novel approach to quantify the feasibility of BEDTs. The analysis utilizes commercially obtained stop telemetry data from conventionally diesel fleets operating in Southern California to identify truck tours (as sequences of stops), depot locations (as the most common terminus of tours for a truck), and fleets (as collections of trucks operating from the same depot). Second, the study examines three fleet size categories by determining required charging configurations that would be needed to satisfy charging schedules determined by a smart charging strategy. This approach provides a more granular understanding of the feasibility of BEDTs across different fleet sizes. Third, the findings are used to consider the feasibility of two charging scenarios: depot and offsite charging. The study also investigates energy demands, battery size configurations, and a methodology for formulating configurations of chargers to assess the potential of BEDTs by different fleet size categories. The framework proposed in this study can also be adapted to other fleets and in other port regions to understand the performance of BEDTs.

Not surprisingly, light-duty BEVs have seen more rapid deployment to date, and most research has focused on studying charging infrastructure and vehicle energy demand for the light-duty sector.^23,24,25,26 In general, BEV deployment is more challenging for heavy-duty than light-duty vehicles because of the range limitations of current battery technology. However, performance advancements in battery technology may mean that BEVs could soon be suitable for many heavy-duty applications.²⁷

A relatively small number of researchers have considered the feasibility of heavy-duty BEVs from several perspectives, including: simplifying refueling using overnight charging, calculating the trip-based energy demand, and analyzing the feasibility of BEV operations for small fleets. For example, Cabukoglu et al.²⁸ quantified BEV feasibility in Swiss heavy-duty fleets for countrywide freight applications and found that only 6 to 19% of heavy-duty trucks could be electrified by using depot-based charging with 50 kW overnight charging power. Tong et al.²⁹ discussed long-haul truck electrification in the U.S. based on trip-based energy consumption but did not consider truck tour-based movements. Forrest et al.³⁰ estimated BEV feasibility for California’s medium and heavy-duty sectors based on survey data for trips, which lacked detailed information on truck movements and tours. Brennan et al.³¹ explored the potential of short-haul HDETs and their impacts on electricity distribution systems with three real-world fleets, which assumed each truck had been assigned a unique plug at its depot. Alonso-Villar et al.³² assessed the potential of HDETs in harsh climates but overlooked the impact on different fleet sizes.

Despite the technical focus, few studies have considered the perspectives of fleet operators' decisions to adopt electric trucks. Bae et al.²¹ and Cantillo et al.³³ investigated the motivators and barriers to adopting HDETs based on surveys in California and Colombia, respectively. Anderhofstadt and Spinler^34,35,36 investigated the factors that influence the fleet’s decisions and willingness to purchase and operate electric trucks in Germany and China. Knostantinous and Gkritza³⁷ examine truck fleets’ intention to electrification. Sugihara et al.²² engaged with fleet operators through semi-structured interviews to identify perceived barriers to electric truck adoption in heavy-duty contexts in California. However, these studies lacked a quantitative analysis of the relationships between satisfied operation requirements, battery size, and infrastructure configuration.

Drayage trucks have received special attention in the literature. Ramirez-Ibarra and Saphores³⁸ highlighted the benefits of ZE drayage trucks in Southern California. However, feasibility analysis is a prerequisite for realizing these benefits. Tanvir et al.³⁹ proposed four truck fleet electrification scenarios with twenty trucks to analyze the feasibility of BEDTs and the impact of battery capacity. Bradley⁴⁰ estimated the charger cost and charger power demand with fixed daily VMT of BEDTs by overnight charging at fleet-level for the short and long term, which assumes that daily movement patterns can be satisfied by a specific battery size. Giuliano et al.^41,42 evaluated the potential of replacing diesel trucks with BEDTs for the years 2020, 2025, and 2030 with the assumption that each daily operation is limited by 8 h. Wu et al.⁴³ minimized the total cost and daily operating schedule to satisfy port delivery tasks with the optimal truck fleet size but relied on fixed truck trip distance/time, failing to reflect real-world conditions. Garrido et al.^44,45 analyzed the feasibility of BEDTs based on home-based charging for vehicles from the same fleet. Dessouky and Yao⁴⁶ explored the feasibility of using BEDTs in drayage operations, but the datasets were generated randomly to simulate the drayage system. These studies suggest that the feasibility of BEDTs to replace conventional trucks is dependent on their ability to meet operational requirements, which are generally a function of energy demand, allowable charging duration, charger power, and the number of chargers available. However, the findings for drayage fleets either lacked operational behaviors or were limited to the small fleet and lacked generalization for varying fleet sizes, which might impact operations. Additionally, these studies also lack a comparison between different fleet size categories.

This article addresses these gaps by assessing the real-world behavior of a relatively large sample of drayage trucks to determine the necessary charging infrastructure (number of chargers and their geographic distribution) to satisfy energy requirements deriving from the observed behavior. By providing a comprehensive analysis of the relationships between operational requirements, battery size, and infrastructure configuration for varying fleet sizes, this research contributes to understanding the feasibility and requirements for transitioning drayage fleets to BEDTs.

Results

This section evaluates the potential for replacing diesel trucks with BEDTs for existing drayage operations. The primary focus is to assess the potential of observed diesel truck behaviors that can be replicated by BEDTs. The potential is quantified by the fraction of tours and trucks that can be effectively satisfied by BEDTs considering the depot and offsite charging. A heatmap analysis is conducted to identify candidate locations for charger installation. Furthermore, the evaluation results are presented for the entire truck population as well as categorized by fleet size, providing insights into the impact of BEDTs varies across different fleet sizes.

Tours and battery size analysis

This section presents the relationship between battery size and the feasibility of tours in the context of depot and offsite charging scenarios. The feasibility of BEDTs strongly depends on battery size and the feasibility increases as higher-capacity batteries are used.

Figure 1 shows the fraction of electrifiable tours per BEDT across battery sizes 100 to 1000 kWh, utilizing data from our one-month dataset. The error bar bands decrease for both depot charging and offsite charging scenarios as battery size increases, which indicates reduced variability in tour feasibility. Incorporating offsite charging into the analysis, we observe an increase in the average fraction of satisfied tours per BEDT and a decrease in error variation for certain battery sizes. Notably, there is a substantial improvement in the fraction of satisfied tours and a decrease in error deviation when the battery size falls within the range of 100–600 kWh. However, beyond a battery size of 700 kWh, the fraction of satisfied tours per BEDT does not experience a significant further increase, remaining consistently above 95%. Figure 2 shows the average number of offsite charging per tour per truck across battery sizes from 100 to 1000 kWh. The frequency of offsite charging decreases as battery size increases, with the most significant reductions within 100–600 kWh. Beyond 700 kWh, the offsite charging around stabilizes. This finding suggests that there is a critical battery size beyond which the benefits of offsite charging become less significant, as the majority of tours can already be successfully completed using depot charging alone. These findings highlight the importance of appropriately selecting battery sizes for BEDTs, as larger capacities lead to higher tour feasibility and reduced uncertainties, resulting in a greater proportion of tours being successfully completed.

Figure 1.

Fraction of satisfied tours per BEDT for all trucks

The fraction of satisfied tours per BEDT is calculated by averaging the proportion of tours successfully completed per truck, with error bars representing the distribution across trucks.

Figure 2.

Average number of offsite charging sessions per tour per truck

Data represents the mean number of offsite charging events per tour per truck across battery size from 100 to 1000 kW.

For each fleet category, as depicted in Figure 3, the fraction of satisfied tours is higher in large fleets compared to small fleets and singleton fleets, given the same battery size and considering both depot charging with and without offsite charging. The introduction of offsite charging significantly increases the fraction of satisfied tours and reduces uncertainties for all fleet categories. This is especially true for singleton fleets, which typically face greater challenges, with the average fraction increasing significantly and reaching 90% with a 500 kWh battery size when offsite charging is implemented. In contrast, with only depot charging, singleton fleets require a battery size of 1000 kWh to achieve a similar level of fraction. These findings highlight the significance of selecting appropriate offsite charging to maximize tour satisfaction for singleton fleets.

Figure 3.

Fraction of satisfied tours per BEDT in the categorized fleet for depot and with offsite charging

The fraction of satisfied tours per BEDT is calculated by averaging the proportion of satisfied tours per BEDT that can be successfully completed within that specific fleet category, with error bars representing the distribution across the same fleet category.

Considering the current state of technology and CCCV charging, our findings suggest that a battery die of 800 kWh is most appropriate for drayage operations. At this capacity, the average fraction of satisfied tours per BEDT is approximately 86%, 96%, and 98% for singleton, small, and large fleets with only depot charging, respectively. The average fraction of satisfied tours per BED increases to around 95%, 98%, and 99% for singleton, small, and large fleets, respectively, when offsite charging is utilized. This insight highlights the potential for offsite charging to level the playing field and enable more widespread adoption of BEDTs across various fleet sizes.

Electrifiable drayage truck analysis

In this article, we assume that a conventional diesel truck that produces the observed behavior for a full month can be electrified if 100% of the observed tours can be satisfied by a certain battery size of BEDT. Accordingly, we have investigated the relationship between battery size and the fraction of electrifiable drayage trucks.

Figure 4 shows that the fraction of electrifiable drayage trucks is highly dependent on battery size, with a notable increase in the proportion as larger battery capacities are utilized. Moreover, the introduction of offsite charging further enhances the fraction of electrifiable trucks. Specifically, our analysis reveals that BEDTs could potentially replace 80% of conventional diesel trucks when equipped with an 800 kWh battery size, and it rises to 95% when offsite charging is incorporated. These findings offer reference values regarding the fraction of diesel trucks that could be replaced by BEDTs and offer valuable insights into the feasibility of using larger battery sizes for BEDTs within drayage operations.

Figure 4.

Fraction of electrifiable drayage trucks across different battery sizes

Data shows the proportion of diesel trucks that could be replaced by BEDTs.

Figure 5 presents the fraction of electrifiable drayage trucks within specific fleet categories, including singleton fleets, small fleets, and large fleets, across various battery sizes. According to the results, the fraction of electrifiable trucks is lower in singleton fleets compared to small and large fleets, irrespective of whether offsite charging is implemented. However, the introduction of offsite charging has a more significant impact on singleton fleets, leading to a greater increase in the fraction of electrifiable trucks and reduced uncertainties compared to other fleet categories.

Figure 5.

Fraction of electrifiable trucks in fleets for depot charging and with offsite charging

The fraction of electrifiable drayage trucks within a specific fleet is determined by averaging the fractions calculated for each fleet within that category, with error bars capturing the distribution across the same fleet category.

For a specific battery size of 800 kWh, the fraction of electrifiable trucks is 49%, 71%, and 86% for singleton, small, and large fleets, respectively, when relying solely on depot charging. With the inclusion of offsite charging, these fractions increase to 80%, 89%, and 97% for singleton, small, and large fleets, respectively. These findings highlight the potential benefits of offsite charging for all fleet categories, particularly singleton fleets, as it substantially increases the fraction of trucks that can be feasibly replaced with BEDTs. The findings suggest that specific challenges are faced by different fleet categories when developing electrification plans. While large fleets may be able to achieve high levels of electrification with depot charging alone, singleton fleets and small fleets may require additional support, such as the deployment of offsite charging infrastructure, to maximize their electrification potential and ensure a more equitable transition to electric drayage trucks.

Number of chargers and charging location

The number of chargers is generated for battery capacities between 200 kWh and 1000 kWh, as the fraction of electrifiable trucks does not show significant improvement with offsite charging when the battery size is 100 kWh in Figure 5. Figure 6 displays the number of chargers for all fleets under both depot charging and offsite charging scenarios.

Figure 6.

Number of chargers for depot and offsite charging for all trucks

The figure displays the total number of chargers needed for the depot and offsite charging for all drayage fleets.

The number of chargers for depot charging remains relatively constant across different battery sizes. This is due to the fixed location of the depot and the ability to meet the charging demand with a specific number of chargers. When aggregated across all fleets, the total number of depot chargers remains relatively consistent across battery sizes, especially when compared to the greater variation observed in offsite charging, where the number of chargers decreases as battery size increases. This decrease can be attributed to the reduction in required locations for offsite charging as battery sizes grow. This decrease can be explained by the reduction in the number of locations required for offsite charging as battery sizes grow. With larger battery capacities, BEDTs can cover greater distances and complete more trips before needing to recharge, thus reducing the need for a dense network of offsite charging stations. As a result, fewer chargers are required to support the fleet as battery sizes increase.

Figure 7 presents a heatmap illustrating the distribution of chargers across various fleets for 800kWh battery size, which highlights the preferred locations for depot charger installation. The analysis reveals that the POLA, POLB, and the City of Ontario are the primary concentration areas for charger deployment. The City of Ontario ranked as the top hub for logistics warehouses in Southern California in 2022,⁴⁷ which makes it a strategic location for charger deployment. The concentration of chargers in these areas aligns with the high density of drayage operations and the proximity to key logistics centers, ensuring convenient access to charging infrastructure for fleet operators.

Figure 7.

Chargers density map for depot charging

The map displays the distribution of chargers across various fleets.

Figure 8 depicts a charger heatmap specifically designed for offsite charging, considering battery sizes between 200 kWh and 1000 kWh. The heatmap reveals that larger battery sizes correlate with a reduction in the overall density of required chargers across the map. The concentrated areas of charger demand remain near the POLA, POLB, and the City of Ontario areas, consistent with the patterns observed in depot charging.

Figure 8.

Chargers heatmap as a function of battery capacity for offsite charging

Charger heatmap specifically designed for offsite charging considering battery sizes between 200 kWh and 1000 kWh.

Interestingly, the results suggest that the depot chargers could potentially serve as offsite charging options for other fleets. However, it is worth noting that utilizing depot chargers for offsite charging by different fleets may affect the optimization results for its fleet depot charging. However, this article does not consider collaborative charging among different fleets, which could be investigated in future research. This observation highlights the need for careful consideration and analysis to strike a balance between depot and offsite charging. This study improves our understanding of the spatial distribution of charger requirements for offsite charging, enabling more informed decision-making regarding the selection and allocation of charging infrastructure for effective operations.

Discussion

This study quantitatively assessed the potential for electrifying drayage trucks based on real-world drayage operational data from over 1,000 drayage trucks in Southern California. By developing and implementing algorithms for detecting valid stops, generating depots, tours, and fleets from collected telemetry data, the study established a robust methodology for evaluating the energy requirements of drayage fleets and applying smart charging strategies to meet these demands. The study also developed a method for optimizing the charger requirements, considering both depot-based and offsite charging scenarios. The application of these strategies and methodologies to the observed fleet data enables an evaluation of the potential of BEDTs to be used without changing existing drayage operations performed with diesel trucks.

A quantitative analysis of how varying battery sizes influence electrified observed drayage behaviors emphasizes that the battery size significantly impacts the feasibility of BEDTs. Specifically, this study provides reference values for the fraction of satisfied tours by BEDTs and the proportion of trucks that can be shifted to BEDTs across a range of battery capacities, from 100 kWh to 1000 kWh. These insights serve as valuable guidance for fleet schedulers in planning and managing drayage electrification. Notably, the study revealed that BEDTs can successfully complete 97% of observed drayage tours per truck, and 80% of trucks can be effectively replaced by BEDTs, with an 800 kWh battery size and depot-only charging. With the inclusion of offsite charging, these percentages increase to approximately 98% of tours and 95% of trucks that can be performed with BEDTs. The error bar analysis provided critical insights into the variability of performance across different fleet sizes and charging scenarios. As battery size increases, the error bar bands decrease for both depot and offsite charging, indicating reduced variability in tour feasibility. The incorporation of offsite charging led to a substantial increase in the average fraction of satisfied tours per BEDT and the fraction of electrifiable trucks, as well as a noteworthy decrease in uncertainties, particularly for singleton fleets. These findings underscore the significant benefits of offsite charging for BEDTs in small fleets, as it improves overall performance and reduces uncertainties, highlighting the need for offsite charging infrastructure to support the successful transition to BEDTs. The study also identified preferred locations for depot and offsite charger installations for charger infrastructure planning, primarily concentrated near the POLA and POLB areas and the City of Ontario, which was the largest hub for logistics warehouses in Southern California in 2022.

Furthermore, this study reveals disparities among the categorized fleet sizes, particularly with singleton fleets exhibiting lower performance compared to other fleet size categories. For example, the fraction of satisfied tours per BEDT in singleton fleets exhibited slower improvement as battery size increased, and the fraction of tours satisfied by a BEDT with a specific battery capacity in singleton fleets was slightly lower than in other fleet categories. Additionally, the proportion of trucks that can be replaced by BEDTs diminishes as fleet size gets smaller. Specifically, with an 800 kWh battery size and depot charging, the percentage of trucks that could be replaced was 86% for large fleets, 71% for small fleets, and 49% for singleton fleets. However, with the inclusion of offsite charging, these percentages increased to 97% for large fleets, 89% for small fleets, and 80% for singleton fleets. These findings highlight the potential for substantial improvements in the performance of singleton fleets through the utilization of offsite charging.

In conclusion, this study suggests that there are feasible pathways for decarbonizing the drayage sector by electrifying drayage diesel trucks. The findings highlight the importance of battery size and the potential benefits of integrating offsite charging into the electrification process, which significantly improves the performance of singleton fleets. Overall, these findings offer valuable insights into the feasibility of transitioning from diesel drayage trucks to BEDTs. These insights can inform policy decisions and infrastructure planning, supporting California’s efforts to electrify drayage fleets and meet its greenhouse gas reduction goals.

Limitations of the study

This article provided a quantitative potential analysis of BEDTs in Southern California using real-world data. The same methodology could be applied to other regions, but several limitations should be considered. Firstly, this research optimizes the number of chargers without the consideration of the collaborative charging by fleets. In collaborative charging, multiple fleets can share private chargers, which could have implications for charger installation and infrastructure planning. Secondly, the data did not capture seasonal effects on drayage operations, which are influenced by import and export product types and patterns at different times of the year and potentially impact the transferability of the results.⁴⁴ The data used in this study focuses on October 2020, which recorded the second-highest container traffic at the POLB that year.⁴⁸ To enhance the transferability of results, future research should take into consideration seasonal influences on drayage. Thirdly, this study focuses on the feasibility of plug-in charging for battery electric drayage trucks. Future research should conduct a comparative total cost of ownership (TCO) analysis across different charging strategies, such as battery swapping, to evaluate their economic benefits and operational viability.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Guoliang Feng (guolianf@uci.edu).

Materials availability

This study did not generate new materials.

Data and code availability

• •Data: All data reported in this article will be shared by the lead contact upon request.
• •Code: This article does not report any original code.
• •Additional information: Any additional information required to reanalyze the data reported in this article is available from the lead contact upon request.

Acknowledgments

This study was made possible with funding received by the University of California Institute of Transportation Studies through the Road Repair and Accountability Act of 2017 (Senate Bill 1). This document is disseminated under the sponsorship of the State of California in the interest of information exchange and does not necessarily reflect the official views or policies of the State of California. The contents of this article reflect the views of the authors who are responsible for the facts and the accuracy of the data presented herein.

Author contributions

The authors confirm their contribution to the article as follows: study conception and design: Guoliang Feng, Craig Ross Rindt, Stephen Ritchie; analysis and interpretation of results: Guoliang Feng, Craig Ross Rindt; draft article preparation: Guoliang Feng, Craig Ross Rindt, Stephen Ritchie. All authors reviewed the results and approved the final version of the article.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Software and algorithms
Python	Python Software Foundation	3.8.5
Pyomo	Pyomo	6.2
Gurobi	Gurobi	9.5.0
Other
GPS data	GeoStamp	N/A
Research Region	Southern California Association of Governments	N/A

Method details

Characterizing drayage behavior using stop telemetry

Drayage operations move containers and bulk freight to and from near-port locations. We want to investigate the potential of using BEDTs in terms of vehicle range and charging requirements, which are dictated by the drayage patterns carried out as daily driver shifts that consist of a departure from the depot (the between shifts parking location) to conduct one or more pick-up and delivery tours, as Figure S1 shows, followed by a return to the home depot consistently when the shift ends with long “dwell” periods (usually overnight).⁴⁹ The "freight tour" lacks a standardized definition, as there is no clear consensus on defining the start and end of a tour.^50,51,52,53 Because our focus is drayage, we define a tour as a series of stops that begins and ends at a depot with a dwell time of more than 30 minutes. We select 30 minutes because short breaks of less than 30 minutes (e.g., food break, restroom) are typically unplanned and maybe partially planned.^54,55 Driver surveys about shift patterns have found that drivers tend to operate 6-14 hours per shift and that they typically conduct 3 pick-up and delivery tours during a shift.⁴⁹

As noted, the dwell periods, coupled with the relatively short length of their daily near-port patterns of behavior, make drayage trucks an attractive target for electrification amongst heavy-duty applications.³⁹ As such, because our focus is the potential of BEDTs for existing drayage operations, we are interested in identifying typical drayage tour characteristics including the VMT as well as the available dwell periods. The tour VMT can then be used to explore how replacing these trucks with BEDT might alter the potential of the observed tours through range restrictions dictated by battery capacity and temporal charging constraints. Furthermore, by analyzing dwell periods from the fleet perspective, we can explore the strategic question of how many chargers would be needed by fleets of varying sizes and the operational question of how to schedule the charging. These questions are also directly linked to how the electrification of these fleets would place a geographically and temporally distributed load on the grid. The tactical question of fleet sizing is not considered because we are analyzing the feasibility of reproducing the observed behavior of a fixed set of fleets.

The analysis reported here is based upon stop telemetries obtained for 1,051 drayage trucks operating within the Southern California Association of Governments (SCAG) region (Figure S2) from Sep 30^th to Oct 31^st of 2020. The actual truck telemetry (time and position at 1 second intervals) was not directly available but was processed by the vendor into a series of time-stamped stops as described next.

Figure S3 demonstrates the framework employed for conducting our analysis of the potential for electrifying drayage trucks, comprising two primary components: data processing and analysis of electrification potential. Initially, the stop telemetry data is processed to identify valid stops, depots, fleets, and tours. Subsequently, the analysis of electrification potential is performed, focusing on tour operations. Examination of the relationship between the feasibility of BEDTs and factors such as battery size, charger demand, and offsite charging is then conducted. Finally, the results are aggregated and summarized by trucks and fleets.

Valid stops detection

The vendor identified valid stops using the following algorithm to process the 1 second telemetry data. If a drayage truck does not move more than 150 meters for at least a 10-minute duration, the stationary period is identified as a valid stop and the geocode of the location is recorded. If the stop location is within the threshold distance of any warehouse location as identified by SCAG, where the threshold distance is 200 meters for the area of warehouses under 50,000 square feet and 400 meters for the area of warehouses above 50, 000 square feet, then the stop is matched to that warehouse. If multiple warehouses are within threshold distance, then the stop is matched to the nearest one. Additionally, if no warehouse match is found for a stop, and the stop is detected, then the stop is considered to have happened in the broader traffic zone as defined by SCAG’s Port Transportation Analysis Model (PortTAM) model.⁵⁶

If a drayage truck enters any POLA and POLB terminal it is identified as a valid port stop. Vehicle movements inside the terminal area are ignored and the stop continues until the truck leaves the terminal irrespective of time and distance traveled. Moreover, if a stop is detected inside the terminal, then the duration of the stop must be no less than 5 minutes, which avoids unnecessary stops that can happen when the truck is on its way to another location by passing through the terminal. If a stop occurs outside of all the SCAG zones, then we ignore that stop.

Depot, fleet, and tour identification

Given the valid stops identified for each truck in the sample, we can turn to the problem of identifying depots, fleets, and tours. As we describe below, depots are determined by analyzing the long duration of stops for each truck. Our data does not provide organizational affiliations of sampled trucks for fleet grouping. However, because our potential analysis is focused on charging behaviors and the associated range provided by various temporal charging strategies, the co-location of depot location is sufficient for defining fleets and their depot-based charging behavior even if the observed trucks belong to different organizations. We did not have data on where the depots for individual trucks were, so we estimated depot locations by looking for places where trucks consistently stopped for longer than the dwell time threshold.

With the valid stops provided by the vendor as detailed in Section 3.1, our purpose is to group the stops for each truck into sequences performed during a single shift corresponding to a driver’s working day. To facilitate this analysis, we make two assumptions. First, we assume that the depot for a given truck is the same throughout the course of the month of observed data. Second, we assume that the stop at the depot will generally be the longest stop (i.e., with the longest dwell period) observed for a truck within a given day. Combining these assumptions, our approach is to identify the depot location for each truck for each day by defining a dwell time threshold that indicates when a stop is long enough to represent the end-of-shift. A given threshold will identify a set of end-of-shifts for each truck. To keep the homogeneous of the depots and fleets, the locations of the end of shifts are then spatially clustered for each truck using a radius of 0.1 miles by haversine distance, which formula (Equation 1) is computed between two pairs of coordinates $\left({lat}_1,{lon}_1\right)$ and $\left({lat}_2,{lon}_2\right)$.⁵⁷ The most frequent end-of-shift location is then selected as its depot. Though the dwell threshold might conceivably vary for each truck, we assume for simplicity that a single threshold can effectively characterize all trucks in the population. With the depots identified for the trucks in the sample, the end-of-tour is defined as the stop location is less than 1 mile from the depot with a dwell time of more than 30 minutes.^54,55

$$d=2R·\mathit{arcsin}\left(\sqrt{{\sin }^2\left(\frac{{lat}_2-{lat}_1}{2}\right)+\cos \left({lat}_1\right)\cos \left({lat}_2\right){\sin }^2\left(\frac{{lon}_2-{lon}_1}{2}\right)}\right)$$ (Equation 1)

where R is the average earth radius (3959 miles) and all coordinates are expressed in radians, $\left({lat}_1,{lon}_1\right)$ and $\left({lat}_2,{lon}_2\right)$ are coordinates for two pairs of stops.

The following algorithm was applied to characterize the relationship between the dwell duration threshold and the selected depot for all trucks, which we can then use to select the best dwell threshold.

• 1.Input: valid stops coordinates, associated with truck id and destination duration.
• 2.
  For each candidate dwell duration threshold is from 60 to 960 minutes with 60-minute steps:

  • a.
    For each truck:

    • i.
      Identify the end-of-shifts as all stops longer than the dwell duration threshold.
    • ii.
      Haversine Grouping algorithm: compute the haversine grouping of all end-of-shifts as follows:

      • 1.
        Calculate the haversine distance between all pairs of end-of-shifts to produce a distance matrix. For example, in Equation 2, there is a truck t, which has m EOSs during the month for the threshold, where d_2m refers to the haversine distance between the second end-of-shift and mth end-of-shift.

        $$\left|\begin{array}{ccccc}& 1& 2& \cdots & m\\ 1& d_{11}& d_{12}& \cdots & d_{1m}\\ 2& d_{12}& d_{22}& \cdots & d_{2m}\end{array}\right|$$ (Equation 2)
      • 2.
        Group all end-of-shifts’ locations that are within a certain distance threshold (0.1 miles) of each other into candidate depots.
    • iii.
      Calculate the fraction of end-of-shift’s location for each candidate depot as the fraction of the truck’s end-of-shifts occurring at that location.
    • iv.
      Select the candidate depot as the depot that has the highest end-of-shift location fraction.
  • b.
    Compute the Haversine Grouping algorithm of the depots of all trucks to identify trucks that operate from the same depot as the candidate charging fleets and define these as the final depots and the trucks operating out of the same final depot as belonging to the same fleet.
  • c.
    Compute the minimum distance between the stop of each trip and the depot for each truck and identify tours for each truck.
  • d.
    Output: depot location, truck fleet, and truck tour.

As shown in Figure S4, we note that the average end-of-shift location fraction of the selected depots across all trucks (the black line) stabilizes after 480 minutes, after which the percentage of shifts in the same depot increases by less than 1%. Figure S5 shows the histogram of shift’s hours per operation when 480 minutes is chosen as the dwell threshold. This is consistent with the 6-14 hours per shift reported in the literature for drayage truck operations at POLA and POLB.⁴⁹

Using the dwell threshold of 480 minutes determines the depots for every truck and we find 83% of trucks end more than 90% of their shifts at the depot, as shown in Figure S6. This indicates our algorithm consistently identifies the depot locations of trucks in the sample. Upon the identification of depots for the sampled trucks, the corresponding fleets, and tours were subsequently determined. Any incomplete tours at the end of the month that do not end at a truck’s identified depot are removed from the data.

Routes and distance estimation

Because telemetry data is limited to stop sequences, we need to infer the distances traveled between each stop to estimate the VMT of the trips that make up tours. To do this, we extracted the SCAG-region transportation network from Open Street Map (OSM)⁵⁸ and assumed the drayage truck trajectories followed the shortest paths between each pair of origin and destinations as computed by the Open Source Routing Machine (OSRM).⁵⁹ This is assumed to be reasonable since drayage trucks are likely to use the shortest path or near-shortest path routes to minimize costs. OSRM uses pre-defined scripts called profiles to generate routes. These profiles allow for customization of routing properties such as vehicle type, dimensions, weight, speed limits for different roads such as vehicle type, dimensions, weight, speed limits for different roads, and additional penalties for road features like U-turns and traffic lights. In this paper, a truck profile⁶⁰ was attached to OSRM to generate the shortest path for drayage trucks, incorporating restrictions on vehicle size and highway penalties.

Data summary

The original vendor-supplied data is a table of moves that includes the source and destination coordinates, and the dwell time at source and destination. Applying the algorithms described above added the travel distance to each movement and grouped the 1,051 trucks into 147 fleets. The resulting augmented move table is summarized in Table S1. Figure S7 shows the proportion of trucks and fleets in the processed dataset belonging to different fleet sizes. In this paper, we categorize fleet size into singleton fleets (1 truck, such as an independent owner operator), small fleets (2-30 trucks), and large fleets (over 30 trucks). We find that 8.9% of trucks belong to singleton fleets, which make up 63.9% of all fleets. 34.1% of trucks are allied to small fleets, which is 30.6% of all fleets. 57.0% of the trucks belong to large fleets, which make up 5.4% of all fleets.

Formulation preparation

With our processed data, we now turn to investigate whether BEDTs could perform the observed diesel drayage truck behavior without requiring any changes to fleet operations, considering two key constraints: 1) energy consumption during each tour does not surpass the available battery size; 2) the charger power needed to meet the requirements of charging events is reasonable given current technology. If both conditions are met, we can conclude that it is feasible that BEDTs could be used in place of the diesel trucks in the dataset.

Calculation of energy demand

The energy consumption for each BEDT at each tour is calculated based on the traveled distance and fuel efficiency factor. This estimation captures the consumption rate surrounding different power drive performances and fuel efficiencies across different drayage truck payloads. The energy that would be required for a BEDT to complete each tour is calculated by estimating the energy that would be consumed to complete the on-road and in-port distance traveled. Processing the observed data into equivalent energy demand for BEDTs requires several assumptions. The energy consumption rate is significant to calculate on-road energy demand. For general on-road movements, the energy consumption of heavy-duty trucks ranges from 1.6 to 2.2 kWh/mile with no road gradient.⁶¹ Previous research assumes that short-haul heavy-duty trucks consume 1.8 kWh/mile computed over a combination of loaded and empty.³¹ Specially, the energy consumption for BEDT models has reported energy consumption rates ranging from 1.6 to 2.6 kWh/mile after 2020.⁶² Given these reference values, this study will apply a sensitivity analysis within this range to test performance for different energy consumption rates.

In addition to regular on-road movements, we note that the dataset does not capture the details of truck movement activities within the POLA and POLB terminals, as all movements inside the port terminal were considered by the data vendor to be part of the port stop and are not represented. Trucks inside the port terminal operate for extended periods of time in low-speed and creep transient operating modes associated with on-dock movements or queuing. Therefore, we estimate the energy consumption during port dwell periods based upon the assumed distance traveled in the port. For on-dock movements, previous test results show that drayage trucks travel between 2 to 6 miles near-dock.^20,63,64 To confidently explore the feasibility of BEDTs, the extra energy demand for 6 miles of on-dock movement is added when the trip destination is within port boundaries.

The total energy consumption for a truck in the dataset is therefore the combination of the on-road movement and the in-port consumption. We don’t put an explicit restriction on the necessary battery size in our analysis, but we analyze the implications of the necessary battery size to satisfy the energy demand of identified tours. In this case, we assume the characteristics of tours are definitively known before departure, and each BEDT will commence the first tour with a fully charged battery and the truck operator can choose to charge or not at the end-of-tour to achieve optimal charger management with the restriction of ensuring that the battery has enough energy stored to complete the following tour.

Given these assumptions, each BEDT chooses to be charged or not at the end-of-tour, which means the energy required for the charging session at each end-of-tour is determined by the energy consumption and charging event by preceding tours. Table S2 shows a sample of processed data. Our dataset has been processed into a collection of energy demands for each of 1,051 trucks associated with the time window, truck tours, and fleets. In this paper, energy demand is represented as the energy required for a tour. This allows us to analyze performance without having to pre-specify the battery size. The required battery sizes for each truck are determined by the highest absolute value of energy demand observed for each truck over the course of the month.

Simplification of charging behaviors

Given these energy demands, we can now investigate whether the use of a BEDT will affect the existing drayage operations. With the depots identified for the trucks in the sample, we turn to the problem of defining available charging times to plan for the necessary charging infrastructure. Understanding battery behavior is crucial for charging infrastructure planning. While it might seem logical to assume electric trucks charge at a constant rate when they are connected to charging stations, that is not actually the case.^65,66 Pelletier et al. explained that charging behavior is typically achieved using a Constant-Current Constant-Voltage system (CCCV). Initially, the battery charge increases linearly (constant current charge) but the charging speed gets progressively slower after the charge in the battery reaches a certain charge threshold (constant voltage charge).⁶⁷ Although the charging behavior functions are nonlinear, they are nearly linear under reasonable operating policies. Since the charging behavior is time inefficient when the battery nears fully charged, it makes sense to implement a policy that limits BEDTs to charging up to a level below 100%, instead of fully charging them. The logical charging behavior is to extend BEDT charging slightly beyond the constant-voltage phase. This charging behavior can be approximated as a linear function over time with a specific charging rate. As a result, this paper assumes that trucks will be operated under such a policy so that charging behaviors are linear functions when the BEDT state of charge is less than fully charged. Furthermore, California has several drayage truck models,⁶⁸ including Volvo,⁶⁹ Nikola,⁷⁰ Peterbilt,⁷¹ Freightliner,⁷² Tern,⁷³ all of which recommend 80% of battery capacity as usable battery capacity for health protection. Additionally, existing literature on charging infrastructure optimization for drayage trucks supports this 80% SOC range, which emphasizes the importance of long-term planning and operational efficiency.^44,45,74,75 In this paper, we assume that fleets will operate trucks to charge up to 80% of capacity until the end of the constant current stage. The implication of this assumption is that when we discuss the battery size later, that is 80% of manufacturer designed battery capacity.

Description of charging strategies

In this section, we introduce several charging strategies to decide how and when to charge a set of vehicles with a smaller number of chargers to meet their temporally distributed power demand. Researchers have studied four different charging strategies. The maximum duration charging strategy assumes that each BEDT is assigned its own dedicated charger. The immediate and delayed charging strategies have been applied in earlier research^30,31,76 and are included here for comparison. In the immediate charging strategy, a drayage truck begins charging at maximum power immediately after arriving at the depot. This type of strategy maximizes fleet flexibility since it will maximize the amount of time that trucks are available with 100% State of Charger (SOC). In the delayed charging strategy, a drayage truck starts charging at maximum power such that SOC reaches 100% exactly when the truck needs to depart from the depot. There is no direct logic for why this would be a preferred strategy for fleet operations, but if the fleet’s trucks tend to start their day in the morning it may indirectly lead to most charging happening during off-peak hours, which are likely associated with lower electricity costs. In the smart charging strategy, a drayage truck can start charging at any time slot during its dwell period to ensure a full recharge before departure. This strategy also allows for charging interruption during the charging period for optimal usage of chargers.

In this study, we adopt the smart charging strategy for the optimal requirements of chargers and examine the capability of existing charger technologies to meet the charging rate requirements. CARB proposes the utilization of 50 kW and 350 kW chargers for charging heavy-duty vehicles, allowing for an initial assessment of charger demand at the county level.⁷⁷ This study focuses on current and near-term charging capabilities, considering 350 kW as the maximum power level for a single charger. As larger charging infrastructure continues to develop, the feasibility of battery electric drayage trucks (BEDTs) is expected to improve by reducing charging time.

Simple feasibility analysis by sensitivity test of energy consumption rate

The current and planned heavy-duty electric truck models feature battery sizes ranging from 120 to 1000 kWh, as documented by various studies.^{30,78,79,80,81} For the feasibility analysis presented in this paper, we have assumed the most optimistic battery capacity of 800 kWh, considering the CCCV threshold (80% of the manufacturer designed battery capacity).

As noted above, to examine the relationship between the fraction of satisfied tours by BEDTs and battery sizes, as well as the energy consumption rates for BEDTs, we conducted a sensitivity analysis using a range of energy consumption rates from 1.6 to 2.6 kWh/mile.

In Figure S8, the upper to lower vertical pearl points displayed the fraction of satisfied tours per BEDT with the order from 1.6 to 2.6 kWh/mile. The maximum difference between the upper and lower points occurred at 300 kWh battery size, indicating that the energy consumption rate plays a crucial role in this battery size. Battery size over 400 kWh led to a smaller standard deviation in fraction of satisfied tours, which reduced the variability of the fraction of satisfied tours. Furthermore, CARB also reported an average consumption rate is 2.1 kWh/mile for BEDTs according to real-world operational data.^82,83 When examining the distribution of the fraction of satisfied tours per BEDT, a nearly symmetrical pattern centered around the fraction by 2.1 kWh/mile is evident, particularly when the battery size exceeds 600 kWh. When battery size surpasses 700 kWh, the fraction of satisfied tours was found to be almost identical to the fraction of satisfied tours observed at 2.1 kWh/mile consumption rate, which is more than 95% and reaches 98% for 800 kWh battery size.

In the following analysis, we chose a conservative energy consumption value of random choice range from 1.6 to 2.6 kWh/mile in order to capture variations in truck operations, including acceleration, deceleration, and diverse load conditions such as empty containers, half-load containers, and fully loaded containers.⁶² This choice ensures that the assessment of BEDTs’ performance takes into consideration real-world conditions and provides a robust basis for further analysis.

Formulation for requirements of chargers

Depot charging

Charging infrastructure is critical to the large scale of electrification, yet significant challenges remain related to ZEV operations, and specifically related to the charging infrastructure necessary to support wide-scale deployment of BEDTs. Decisions about electric vehicle charging systems are categorized into three levels: strategic decisions focus on the number and location of chargers, tactical decisions concentrate on fleet sizing, and operational decisions address vehicle-level charging schedules.⁸⁴ Ultimately, these decisions are intertwined—the charging schedule depends on the fleet size and charger configurations and vice versa. Because the State of California has mandated 100% ZEVs in drayage operation in 2035, planning for charging infrastructure is a long-term problem that should focus on meeting the worst case of energy demand.^18,85 To conservatively support the operation of BEDTs, end-of-tour charging is considered for charging infrastructure planning. The detailed formulation for depot charging is presented below.

This study assumes that trucks can take advantage of any end-of-tour stops at their depot to recharge. The goal of this methodology is to minimize the number of chargers to support drayage operations. This formulation determines the number of chargers required, the specific charging times, and the power for all trucks in the fleet over a given time horizon as dictated by charging requirements and windows provided. Table S3 outlines the notation used in this section for clarity and reference.

The optimization model is mathematically formulated as follows. In addition to the feasible charger levels defined in the literature, the formulation adds a single charger with effectively super large power to ensure a feasible solution is found and a constraint is applied to decrease its utilization. This charger is not a realistic charging option but serves as a soft constraint to ensure that a solution is always found. The cases in which the virtual charger is utilized for a specific truck indicate that its tour could not be completed under realistic charging constraints. The objective Equation 3 formulates the optimization number of the chargers. The Equation 4 is the minimum utilization of feasible chargers, excluding the super large charger.

$$\text{Minimize}=\sum _j\sum _l{q}_j^l$$ (Equation 3)

$$C=\sum _j{q}_j^1$$ (Equation 4)

The formulation of the constraints are as follows:

• (1)Dwell time constraint: the charging activities of the individual tour i for truck k must occur within the dwell period. This is captured by Equation 5 as follows:

$$\begin{array}{cc}{x}_{k,l}^{i,j,t}=0& \forall t<a_k^{i}ort>d_k^i\end{array}$$ (Equation 5)

• (2)Remaining energy constraint: Equation 6 provides the formulation for total power charged for individual tour i by truck k. Equation 7 specifies that the remaining energy of truck k for tour i should be the battery size minus the total energy consumption and the amount of power charged before tour i. Equation 8 establishes the constraint that the remained energy should be higher than the energy demand for tour i. Considering the prolonging of charging efficiency, the remaining battery power should be less than $\varphi B$.

$$\begin{array}{cc}{c}_k^i=\sum _j\sum _t{x}_{k,l}^{i,j,t}\times p_j^l& \forall a_i\le t\le d_i\end{array}$$ (Equation 6)

$$\begin{array}{cc}{r}_k^i=B-\sum _{i=1}^{i-1}{e}_k^i+\sum _{i=1}^{i-1}{c}_k^i& \forall i\in I,\forall k\in K\end{array}$$ (Equation 7)

$$\begin{array}{cc}{e}_k^i{\le r}_k^i\le \varphi B& \forall i\in I,\forall k\in K\end{array}$$ (Equation 8)

• (3)Installments and assignments constraint: enforce any assigned charger j for individual tour i of truck k at time t should be installed in Equation 9. In addition, in Equation 10, the size of solution space by limiting the number of times of using chargers to M for each charger j. Equation 11, the same level of charger assigned at any time should less than the total installed same level of chargers. Equation 12, the number of installed chargers is constrained by the maximum allowable number for each level of chargers. Equation 13 aims to avoid utilization of super large charger unless necessary.

$$\begin{array}{cc}{x}_{k,l}^{i,j,t}\le q_j^l& \forall j\in J,\forall i\in I,\forall k\in K,\forall t\in T\end{array}$$ (Equation 9)

$$\begin{array}{cc}\sum _k\sum _i\sum _t{x}_{k,l}^{i,j,t}\le M{q}_j^l& \forall i\in I,\forall k\in K,\forall t\in T\end{array}$$ (Equation 10)

$$\begin{array}{cc}\sum _i\sum _j{x}_l^{i.j,t}\le \sum _l{q}_j^l& \forall j\in J,\forall i\in I\end{array}$$ (Equation 11)

$$\begin{array}{cc}\sum _l{q}_j^l\le L^l& \forall l\in L^l\end{array}$$ (Equation 12)

$$\begin{array}{cc}\sum _i\sum _j\sum _t{x}_{k,l}^{i,j,t}\times p_j^l\le N& \forall i\in I,\forall I\in J,\forall t\in T\end{array}$$ (Equation 13)

• (4)Served charger constraint: each charger j is assigned to at most one individual tour i in each time slot.

$$\begin{array}{cc}\sum _k\sum _i{x}_k^{i,j,t}\le 1& \forall i\in I,\forall k\in K\end{array}$$ (Equation 14)

• (5)Served charging tour constraint: each charging tour is assigned to at most one charger j in each time slot, which indicates that there is allowed at most one charger charging for the BEDT at each time slot.

$$\begin{array}{cc}\sum _j{x}_{k,l}^{i,j,t}\le 1& \forall j\in J\end{array}$$ (Equation 15)

• (6)Integrality constraints: binary constraints on the decision variables.

$$\begin{array}{cc}{x}_{k,l}^{i,j,t}\in \left\{0,1\right\}& \forall j\in J,\forall i\in I,\forall k\in K,\forall t\in T\end{array}$$ (Equation 16)

$$\begin{array}{cc}{q}_j^l\in \left\{0,1\right\}& \forall j\in J,\forall l\in L^l\end{array}$$ (Equation 17)

Offsite charging

When the energy demands of a tour exceed the maximum capacity of the battery or the charging requirements for depot charging surpass the power capacity of available chargers, the feasibility of BETDs may be compromised. In such cases, there may be an opportunity to enhance feasibility by charging the BEDTs as much as possible during offsite stops that extend beyond 30 minutes, except in remote areas (such as the California desert) where charger installation is not supported due to grid transmission issues. To identify the locations for charger installation, the Haversine Group algorithm is utilized to group offsite charging locations together. This algorithm assists in identifying potential locations for charger placement.

The rationale behind maximizing offsite charging is that certain cases involve multiple offsite charging locations before returning to the depot. The duration of idle time for offsite charging at the subsequent location is uncertain due to the shared utilization of offsite chargers by different fleets. However, collaborative charging between fleets and locations is not considered in this paper. Consequently, this study assumes that the BEDTs take advantage of every opportunity to charge as much as possible during each offsite charging stop, intending to enhance feasibility. The formulation with offsite charging is illustrated below.

Based on the discussions about the BEDTs can utilize offsite opportunity to charge, if the condition $r_k^i<0$ is met in depot charging, and a feasible offsite charging stop exists between tours i-1 and i, a dedicated offsite charging stop, denoted as o, is integrated into the optimization process. For offsite charging, the optimization of chargers is similar to depot charging, retaining the core constraints (1, 3-6) and changing i to o, while incorporating crucial modifications tailored to the unique dynamics of offsite charging. Notably, the remaining energy constraint, previously defined in Constraint (2), undergoes a revision, leading to Constraint (7):

• (7)Energy constraint: Equation 6 keeps the same. Equation 7 changes to Equation 18 specifies that the remaining energy of truck k for tour i should be the battery size minus the total energy consumption and the amount of power charged before tour i, further diminished by the energy consumption between tour i-1 and offsite stop o. Equation 8 modified to (18) establishes the constraint that the energy charged at stop o should be higher than the available left of battery size.

$$\begin{array}{cc}{r}_k^o=B-\sum _{i=1}^{i-1}{e}_k^i+\sum _{i=1}^{i-1}{c}_k^i-\sum _{i=i-1}^o{e}_k^i& \forall i\in I,\forall t\in T\end{array}$$ (Equation 18)

$$\begin{array}{cc}\varphi B-r_k^o\le c_k^o& \forall i\in I,\forall t\in T\end{array}$$ (Equation 19)

Subsequently, the depot charging results are updated according to the revised SOC at the end-of-tour i. Specifically, update Equation 7 with Equation 20 and apply depot charging formulation to reflect the updated results.

$$\begin{array}{cc}{r}_k^i=B-\sum _{i=1}^{i-1}{e}_k^i+\sum _{i=1}^{i-1}{c}_k^i-\sum _{i=i-1}^o{e}_k^i+\sum _{i=i-1}^o{c}_k^i& \forall i\in I,\forall t\in T\end{array}$$ (Equation 20)

Quantification and statistical analysis

The methods for characterizing drayage behavior and preparing the mathematical formulation are detailed in the preceding sections. The resulting model is a mixed-integer program, which was solved in Python 3.8.5 using Pyomo 6.2 and solved by Gurobi 9.5.0.

Published: May 11, 2025