# The Truck Platooning Routing Optimization Model Based on Multicommodity Network Flow Theory

Authors: Zexi Zhang
Journal: Journal of Advanced Transportation
 (2023)

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## Abstract

Truck platooning has been identified as an emerging and promising operational technology with the advantages of fuel consumption savings and carbon emissions reductions. We formulate the truck platooning routing optimization problem as a multi-commodity network flow problem from a transportation optimization and scheduling perspective. Based on fuel consumption savings generated through the reduction of aerodynamic drag by the formation of truck platooning, the route of each truck is also set to be a decision variable needing settlement to facilitate the formation of truck platooning to maximize fuel consumption savings. Considering fuel consumption and detour costs, we construct a truck platooning routing optimization model with minimum overall system fuel consumption as the optimization objective. The output of the routing optimization model could both reflect the composition of each truck platooning on each link and directly show the routings of each truck. To explore the impact of the restrictions on the number of trucks in truck platooning on overall fuel consumption savings, road networks are constructed and the truck platooning routing optimization model is solved by the commercial solver CPLEX. Compared to individual trucks, 8% or 12% fuel consumption savings are achieved, respectively, with the number of trucks being restricted or not restricted in truck platooning. Considering the different fuel reduction rates of the following trucks in platooning on the system performance in terms of the total fuel cost, a sensitivity analysis is also conducted. The results also show that the ideal truck platooning routing plan can be obtained by the proposed model, and the study provides a theoretical reference for the promotion and application of truck platooning.


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## Body

## 1. Introduction

Transportation has a driving role in the development of the regional economy. According to the survey (International Transport Forum), about 60% of surface freight transportation (including road and rail transport) is done by road. Therefore, road freight transportation is essential for economic development. However, road freight transportation is the main area of energy consumption. According to the reports of the International Energy Agency, the transportation sector consumes about 32% of the global energy consumed, while consumption by road transport accounts for about 75% of the transportation sector. Faced with the transportation problems of energy scarcity, air pollution, and road congestion, the adoption of new technologies such as ITS (Intelligent Transport Systems) is one of the important ways. Meanwhile, the development of these technologies will also reshape future freight transport services to make traffic networks sustainable.Generally, cooperative adaptive cruise control (CACC) can be regarded as the first step of the introduction of automated vehicles and an important step towards a longer-term vision of trucks operating in closely-coupled automated platoons (Tsugawa [1], Nowakowski et al. [2]). Given the limited market penetration of connected and automated trucks, we chose trucks equipped with the CACC control system as the technical basis for the truck platooning routing optimization study. The concept of platooning was proposed by Levine and Athans [3]. This area has attracted attention from scholars and researchers due to the benefits of truck platooning in terms of lowering fuel consumption, reducing emissions, and increasing the effective capacity of roads.A group of trucks with cooperative adaptive cruise control is virtually linked closely with short intertruck distance through wireless communication technology in the same lane. That is, although there is no physical connection, one or more following trucks on a flat road could automatically brake, steer, accelerate, and decelerate based on the driving actions of the leading truck (the first truck of platooning). Similar to a train, this operational technology is also called a “road train.” Due to the close intertruck distances between trucks in truck platooning, truck platooning gains fuel cost savings and emissions reductions by reducing the overall aerodynamic drag compared to trucks traveling individually.Environmental pollution has constrained economic development, so many countries agreed to reduce their greenhouse gas emissions under the Kyoto Protocol. The European Union has set more ambitious targets, aiming to reduce emissions by 80–90% by 2050 compared to 1990. This requires a 60% reduction in greenhouse gas emissions from the transportation sector (or a 70% reduction compared to the 2008 level). In this case, truck platooning has been touted as one of the most promising operational technologies to offer significant fuel savings andemission reductions. Studies have shown that the following trucks will experience a significant reduction of aerodynamic drag due to the formation of an airflow vacuum belt. Hence, the overall aerodynamic drag is reduced, which in turn lowers greenhouse gas emissions and fuel consumption. As early as 1995, Zabat et al. [4] stated that truck platooning could reap the benefits of fuel consumption savings, studied the aerodynamic drag of individual trucks compared with truck platooning, and quantitatively estimated the aerodynamic drag generated by different headways. Alam et al. [5] measured the different fuel consumption generated by truck platooning of different sizes. The experiments showed that when two identical trucks travel at a speed of 70 km/h with a 25 m headway, 30% of air resistance can be reduced, and this reduction increases to 40% with truck platooning of three trucks. In 2021, Noruzoliaee et al. [6] calculated that truck platooning could lead to 7.9% fuel savings by 2025 with the U.S. national road network as the application context. Obviously, fuel cost savings and emissions reductions from truck platooning have also been the primary motivation for the study.In addition to fuel cost savings and emissions reductions, truck platooning takes up less road space, thus significantly increasing road capacity. Shladover et al. [7] showed that the use of cooperative adaptive cruise control enables vehicles within platooning to follow the leading vehicle with higher accuracy, faster response, and shorter gaps, greatly enhancing the stability of traffic flow, improving road safety, and reducing traffic congestion. Lioris et al. [8] demonstrate the potential mobility benefits of platooning for passingthrough an urban road system with 73 links and 16 intersections as an example, and the result showed that the passing capacity of the intersection can be increased to twice the original capacity by platooning.Furthermore, truck platooning can also enhance road traffic safety with the following trucks following the leading truck with significantly lower reaction times and less room for human error than traveling individually. Namely, human drivers are generally not capable of safely maintaining the close inter-truck distances as required by platooning. However, automatic systems can usually react more quickly to dangerous situations and can exploit additional information resulting from the communication and cooperation between vehicles (Alam et al. [9]; Peloton Technology [10]).Truck platooning brings various benefits for individual truck drivers and society as a whole and has thus recently received heightened interest from many research institutions and researchers. A large volume of the literature focuses on the formation of truck platooning from a technological perspective, including sensor control, wireless communication, radar positioning, and other technologies. However, the research on operational management and scheduling technology is slightly insufficient. Generally, the performance of this operational technology is largely determined by the actual level of operation management, so research on optimizing truck platooning with the goal of improving operational management would be beneficial to further exploit the advantages of truck platooning and improve performance in logistics operations. As Russo et al. [11–13] mentioned, a good plan contributes to converging theories, rules, and implementation. To fully reap these benefits in the initial phases of truck platooning deployment, systematic and appropriate planning is necessary in order to place trucks in platoons.This study mainly focuses on truck platooning routing optimization and attempts to make several contributions to the still scarce literature on transportation optimization of truck platooning. For the first contribution, we quantify the fuel consumption savings generated due to the reduction of aerodynamic drag by the formation of truck platooning. Second, we develop a truck platooning routing optimization model considering the reasonable detour. Unlike the previous literature, in which the route of each truck is fixed, the route of each truck in this study is a decision variable needing settlement. The output of the optimization model could reflect the composition of truck platooning on each link and directly show the routings of each truck by setting decision variables, which represented whether the transportation task passed through a link or not. Finally, we explore the impact of the restrictions on the number of trucks in truck platooning on overall fuel consumption savings and analyze the different optimization results for each scenario. The numerical experiments demonstrate the validity and rationality of the proposed model.The remainder of this paper is organized as follows. Section2 presents a brief literature survey on the driving technologies of truck platooning, the control theory of truck platooning, and the operational planning of truck platooning. In Section 3, we quantify the fuel consumption savings and propose the conditions for the formation of truck platooning. A truck platooning routing optimization model considering the reasonable detour is developed in Section 4. With the numerical experiments as the context, Section 5 measures fuel consumption savings generated by the formation of truck platooning with different influencing factors. Section 6 concludes the paper and draws directions for future research.


## 2. Literature Review

### 2.1. Driving Technology of Truck Platooning

Tsugawa [1] stated that ITS-related systems encompass many components and can be divided into ATMS (Advanced Traffic Management Systems), ATIS (Advanced Traveler Information Systems), and AVCSS (Advanced Vehicle Control and Safety Systems), and some systems have been deployed nationwide and have shown their effectiveness on energy savings and carbon emission reduction to some extent. According to the different technologies of transportation control, truck platooning can be classified into three different types, such as human-driven, autonomous, and semiautonomous platooning (Hybrid platooning). Human-driven platooning means that all trucks in truck platooning are driven by human drivers and the following truck drivers manually complete the task of following. Autonomous platooning involves completely autonomous trucks which can complete all dynamic driving tasks at any time and on any path. In confined spaces such as port terminals and warehouses, autonomous platooning may be easier to be achieved. However, it is difficult to achieve autonomous platooning with the current level of technological development for complex real road networks. At the same time, Bhoopalam et al. [14] stated that truck platooning can be seen as the first step towards automated driving in an open environment in the future.Therefore, many scholars such as Bhoopalam et al. [14] and You et al. [15] have utilized novel semiautonomous driving technologies (also referred to as cooperative adaptive cruise control (CACC)) to optimize truck platooning. According to microscopic traffic simulations, Lee et al. [16] also demonstrated the feasibility of the novel traffic operation strategy in platooning environments. Trucks equipped with cooperative adaptive cruise control systems are virtually linked and interconnected with each other to achieve autonomous followed by a leading truck through wireless communication technology. Although the leading truck is still manually driven at the first position of truck platooning, one or more following trucks in truck platooning will automatically handle all the driving tasks including braking, steering, acceleration, and deceleration based on the actions of the leading truck. Usually, the following trucks still need drivers to deal with some unexpected situations. Given the development of driving technology, it is likely that truck platooning equipped with cooperative adaptive cruise control systems can be formed with planning in advance.Truck platooning has been introduced as a promising operational technology of next generation transportation systems. Europe was the first region to implement truck platooning. In 2009, the EU-funded SARTRE project (Safe Road Trains for the Environment [17]) perfected truck platooning for operation on traditional highways. Other field tests are planned or are currently taking place in the U.S (Peloton Technology [10]), Singapore [18] Japan (Tsugawa [1]), and Australia [19].


### 2.2. Control Theory of Truck Platooning

Based on automated driving technology, some scholars have studied the optimal control of truck platooning. Zhang et al. [20] presented an overview of existing studies about fuel savings for truck platooning and summarized control strategies to generate fuel-efficient speed profiles for each vehicle driving in a platooning over different road grades.In the 1960s, Levine and Athans [3] described this operational technology as “a string of moving vehicles” and used optimal control theory to construct an optimal linear feedback system to realize the cooperative operation of multiple moving vehicles by regulating the position and velocity of each vehicle. The simulation results for a string of three vehicles were given at the end of the paper. The paper solved the problem of controlling the position and velocity of each vehicle in platooning after the formation of platooning and did not involve how to coordinate vehicles to form platooning.Larson et al. [21] proposed control methods to maximize fuel savings by facilitating platoon formation. By knowing the current position, travel speed, and destination of the vehicles, the local controller can quickly adjust the travel speed of the vehicles to form platooning. The simulation results showed fuel savings of up to 9%. Similar to the velocity control mentioned above, Liang et al. [22] also focused on the change of velocity during the formation of truck platooning and calculated the optimal velocity of two trucks on the same travel route during the formation of truck platooning with the objective of achieving maximum fuel savings. Then they proposed a coordination algorithm for the task of coordinating neighboring trucks pairwise to form truck platooning. Torabi and Wahde [23] constructed a speed profile optimization (P-SPO) approach and applied the simple vehicle controller to a set of road profiles of 10 km length to achieve fuel reduction.


### 2.3. Operational Planning of Truck Platooning

A few experts and research teams have studied truck platooning from a transportation optimization and scheduling perspective. First, Bhoopalam et al. [14] reviewed and analyzed the existing literature related to the planning of truck platooning and then summarized the relevant operation research models from different perspectives. Finally, they proposed that an interesting direction for future research is the development of specialized solution methods to handle the various restrictions such as those relating to platoon size. However, this is also one of the research focuses of this study.In the existing literature, according to whether the path is determined or not, truck platooning planning problems can be divided into two categories: fixed path and flexible path. Usually, due to the fuel consumption savings generated through the reduction of aerodynamic drag generated by the formation of truck platooning, a large body of literature such as Hoef [24], Zhang et al. [25], and Boysen et al. [26] has optimized truck platooning planning under fixed routing with the goal of minimizing fuel consumption. In such cases, the route of each truck is not part of truck platooning planning decisions.Specifically, Hoef [24] assumed the existence of a truck platooning coordinator that enables trucks with an overlapping route and time to form truck platooning to save significant amounts of fuel. According to transport assignments information, a list of potential platoon pairs was identified efficiently. An adapted plan considering routes and speed profiles was computed by a truck platooning coordinator. However, the optimization objective was to maximize fuel cost savings by the formation of truck platooning due to reducing air drag, without setting the route as the decision variable to be solved, and thus did not fully exploit the advantages of truck platooning.Zhang et al. [25] developed a model comprehensively considering travel time costs, fuel consumption costs, and schedule miss penalties under travel time uncertainty. The results meant that platooning on a common route and a network with diverging routes have the same functional form for independent vehicles. Boysen et al. [26] explored factors affecting the efficiency of truck platooning and derived an algorithm to test these influencing factors. Their results showed that the diffusion of platooning technology, platooning size, and the tightness of time windows could impact the formation of truck platooning.Unlike other studies of truck platooning optimization, Larsson et al. [27] were the first to define a routing problem called the platooning problem, proving that the truck platooning problem was an NP-hard problem. They constructed an integer linear programming model under a flexible route with unlimited platooning without time constraints with the objective of minimizing fuel consumption and solved it by using heuristic algorithms. However, they only solved the same-start unlimited truck platooning problem.You et al. [15] studied the local container drayage problem by using the truck platooning operation mode and treated the problem as a traveling salesman problem in which the truck departed from a specific warehouse and returned to the same warehouse after completing the transportation task. However, the model only solved the routing optimization problem of truck platooning and did not consider the fuel savings effect of truck platooning. The model still did not take full advantage of truck platooning.Xue et al. [28] further processed the optimization model on the basis of You et al. [15], and they still took the local container drayage problem as the background and divided the transportation process into two stages: picking up and delivering containers. The model considered the factors that might have an impact on the formation of truck platooning, such as the traveling time of truck platooning and truck platooning size, used a heuristic algorithm to solve the model and quantitatively estimated the advantages of truck platooning. However, the article still used the same warehouse as the starting and ending nodes of truck platooning, and trucks with different origins and destinations could not form truck platooning under this mode.Several other studies investigated truck platooning from a transportation optimization perspective, but they took a perspective significantly different from ours. Truck platooning was all in a fixed mode, i.e., once truck platooning was formed, other trucks could not merge into it at any time, and truck platooning could not be split. However, this study adopts a flexible truck platooning mode, i.e., truck platooning can be split and merged according to different transportation tasks to achieve maximum fuel savings. For any trucks from different origins and destinations, they can form different platoons with different trucks during the operation to fully demonstrate the advantages of truck platooning.


## 2.1. Driving Technology of Truck Platooning

Tsugawa [1] stated that ITS-related systems encompass many components and can be divided into ATMS (Advanced Traffic Management Systems), ATIS (Advanced Traveler Information Systems), and AVCSS (Advanced Vehicle Control and Safety Systems), and some systems have been deployed nationwide and have shown their effectiveness on energy savings and carbon emission reduction to some extent. According to the different technologies of transportation control, truck platooning can be classified into three different types, such as human-driven, autonomous, and semiautonomous platooning (Hybrid platooning). Human-driven platooning means that all trucks in truck platooning are driven by human drivers and the following truck drivers manually complete the task of following. Autonomous platooning involves completely autonomous trucks which can complete all dynamic driving tasks at any time and on any path. In confined spaces such as port terminals and warehouses, autonomous platooning may be easier to be achieved. However, it is difficult to achieve autonomous platooning with the current level of technological development for complex real road networks. At the same time, Bhoopalam et al. [14] stated that truck platooning can be seen as the first step towards automated driving in an open environment in the future.Therefore, many scholars such as Bhoopalam et al. [14] and You et al. [15] have utilized novel semiautonomous driving technologies (also referred to as cooperative adaptive cruise control (CACC)) to optimize truck platooning. According to microscopic traffic simulations, Lee et al. [16] also demonstrated the feasibility of the novel traffic operation strategy in platooning environments. Trucks equipped with cooperative adaptive cruise control systems are virtually linked and interconnected with each other to achieve autonomous followed by a leading truck through wireless communication technology. Although the leading truck is still manually driven at the first position of truck platooning, one or more following trucks in truck platooning will automatically handle all the driving tasks including braking, steering, acceleration, and deceleration based on the actions of the leading truck. Usually, the following trucks still need drivers to deal with some unexpected situations. Given the development of driving technology, it is likely that truck platooning equipped with cooperative adaptive cruise control systems can be formed with planning in advance.Truck platooning has been introduced as a promising operational technology of next generation transportation systems. Europe was the first region to implement truck platooning. In 2009, the EU-funded SARTRE project (Safe Road Trains for the Environment [17]) perfected truck platooning for operation on traditional highways. Other field tests are planned or are currently taking place in the U.S (Peloton Technology [10]), Singapore [18] Japan (Tsugawa [1]), and Australia [19].


## 2.2. Control Theory of Truck Platooning

Based on automated driving technology, some scholars have studied the optimal control of truck platooning. Zhang et al. [20] presented an overview of existing studies about fuel savings for truck platooning and summarized control strategies to generate fuel-efficient speed profiles for each vehicle driving in a platooning over different road grades.In the 1960s, Levine and Athans [3] described this operational technology as “a string of moving vehicles” and used optimal control theory to construct an optimal linear feedback system to realize the cooperative operation of multiple moving vehicles by regulating the position and velocity of each vehicle. The simulation results for a string of three vehicles were given at the end of the paper. The paper solved the problem of controlling the position and velocity of each vehicle in platooning after the formation of platooning and did not involve how to coordinate vehicles to form platooning.Larson et al. [21] proposed control methods to maximize fuel savings by facilitating platoon formation. By knowing the current position, travel speed, and destination of the vehicles, the local controller can quickly adjust the travel speed of the vehicles to form platooning. The simulation results showed fuel savings of up to 9%. Similar to the velocity control mentioned above, Liang et al. [22] also focused on the change of velocity during the formation of truck platooning and calculated the optimal velocity of two trucks on the same travel route during the formation of truck platooning with the objective of achieving maximum fuel savings. Then they proposed a coordination algorithm for the task of coordinating neighboring trucks pairwise to form truck platooning. Torabi and Wahde [23] constructed a speed profile optimization (P-SPO) approach and applied the simple vehicle controller to a set of road profiles of 10 km length to achieve fuel reduction.


## 2.3. Operational Planning of Truck Platooning

A few experts and research teams have studied truck platooning from a transportation optimization and scheduling perspective. First, Bhoopalam et al. [14] reviewed and analyzed the existing literature related to the planning of truck platooning and then summarized the relevant operation research models from different perspectives. Finally, they proposed that an interesting direction for future research is the development of specialized solution methods to handle the various restrictions such as those relating to platoon size. However, this is also one of the research focuses of this study.In the existing literature, according to whether the path is determined or not, truck platooning planning problems can be divided into two categories: fixed path and flexible path. Usually, due to the fuel consumption savings generated through the reduction of aerodynamic drag generated by the formation of truck platooning, a large body of literature such as Hoef [24], Zhang et al. [25], and Boysen et al. [26] has optimized truck platooning planning under fixed routing with the goal of minimizing fuel consumption. In such cases, the route of each truck is not part of truck platooning planning decisions.Specifically, Hoef [24] assumed the existence of a truck platooning coordinator that enables trucks with an overlapping route and time to form truck platooning to save significant amounts of fuel. According to transport assignments information, a list of potential platoon pairs was identified efficiently. An adapted plan considering routes and speed profiles was computed by a truck platooning coordinator. However, the optimization objective was to maximize fuel cost savings by the formation of truck platooning due to reducing air drag, without setting the route as the decision variable to be solved, and thus did not fully exploit the advantages of truck platooning.Zhang et al. [25] developed a model comprehensively considering travel time costs, fuel consumption costs, and schedule miss penalties under travel time uncertainty. The results meant that platooning on a common route and a network with diverging routes have the same functional form for independent vehicles. Boysen et al. [26] explored factors affecting the efficiency of truck platooning and derived an algorithm to test these influencing factors. Their results showed that the diffusion of platooning technology, platooning size, and the tightness of time windows could impact the formation of truck platooning.Unlike other studies of truck platooning optimization, Larsson et al. [27] were the first to define a routing problem called the platooning problem, proving that the truck platooning problem was an NP-hard problem. They constructed an integer linear programming model under a flexible route with unlimited platooning without time constraints with the objective of minimizing fuel consumption and solved it by using heuristic algorithms. However, they only solved the same-start unlimited truck platooning problem.You et al. [15] studied the local container drayage problem by using the truck platooning operation mode and treated the problem as a traveling salesman problem in which the truck departed from a specific warehouse and returned to the same warehouse after completing the transportation task. However, the model only solved the routing optimization problem of truck platooning and did not consider the fuel savings effect of truck platooning. The model still did not take full advantage of truck platooning.Xue et al. [28] further processed the optimization model on the basis of You et al. [15], and they still took the local container drayage problem as the background and divided the transportation process into two stages: picking up and delivering containers. The model considered the factors that might have an impact on the formation of truck platooning, such as the traveling time of truck platooning and truck platooning size, used a heuristic algorithm to solve the model and quantitatively estimated the advantages of truck platooning. However, the article still used the same warehouse as the starting and ending nodes of truck platooning, and trucks with different origins and destinations could not form truck platooning under this mode.Several other studies investigated truck platooning from a transportation optimization perspective, but they took a perspective significantly different from ours. Truck platooning was all in a fixed mode, i.e., once truck platooning was formed, other trucks could not merge into it at any time, and truck platooning could not be split. However, this study adopts a flexible truck platooning mode, i.e., truck platooning can be split and merged according to different transportation tasks to achieve maximum fuel savings. For any trucks from different origins and destinations, they can form different platoons with different trucks during the operation to fully demonstrate the advantages of truck platooning.


## 3. Motivation and Conditions

In this section, we quantify the fuel consumption savings generated due to the reduction of aerodynamic drag by the formation of truck platooning and explore the formation process of truck platooning based on a flexible truck platooning mode.


### 3.1. Fuel Consumption Savings

Compared with traveling individually, one of the primary benefits of truck platooning is fuel consumption savings through the reduction of aerodynamic drag. Aerodynamic drag in different operational technology is shown in Figure1. Specifically, Alam et al. [5] found that the follower truck will experience a significant reduction of aerodynamic drag compared to leading trucks due to a relatively large reduced pressure at the front. Hence, fuel consumption savings will be generated for the following trucks due to the reduction of aerodynamic drag. However, the reduction of aerodynamic drag for the leading truck could be neglected. In general, from an overall perspective, we take the minimum overall fuel consumption of all trucks in the system as the optimization objective.Figure 1
Diagram of aerodynamic drag.In real-world traffic scenarios, fuel consumption is mainly determined by the road condition, the driver’s driving habits, wind force et al. There are a wide variety of influencing factors. Therefore, it is very difficult to accurately quantify the fuel consumption of a truck. In this study, we develop an intuitive fuel consumption formula based on simulation experiments and previous research, such as Alam et al. [5], Noruzoliaee et al. [6], Hoef [24], and Xue et al. [28].Specifically, the fuel consumption for nonplatooning trucks could not generate fuel consumption savings, and the fuel consumption for nonplatooning trucks on a link can be expressed as follows:(1)CijFuel1=ζφdij100∀i,j∈L,where Cijfuel1 denotes the fuel consumption of a truck traversing from node i to adjacent node j (Yuan). ζ and φ are unit fuel price (Yuan/L) and unit fuel consumption (L/100 km) of a truck, respectively. dij is the distance from node i to adjacent node j (km). The set of road links is denoted by L.The overall fuel consumption for truck platooning on a link can be expressed as follows:(2)CijFuelω=ζφdij100+ω−11−βζφdij100∀i,j∈L,where ω is the number of trucks in truck platooning. Cijfuelω denotes the fuel consumption of truck platooning from node i to adjacent node j (Yuan). Taking a truck that drives on its own and experiences no fuel savings as the benchmark, β is the fuel reduction rate of the following trucks due to the formation of truck platooning. This is because truck platooning reduces aerodynamic drag and lowers their fuel consumption (McAuliffe et al. [29]). The parameter β is derived from the previous relevant tests and experiments [6].As shown in Figure1, the formation of truck platooning has a negligible effect on the aerodynamic drag for the leading truck. Therefore, the fuel consumption for the leading truck could be neglected. From formula (2), it can also be derived that fuel consumption savings only consider the following truck and do not include the leading truck. Similarly, each following truck in truck platooning has approximately the same reduction of aerodynamic drag, thus can save fuel consumption by the same ratio of β.Thus, the average fuel consumption per truck in truck platooning compared to traveling without truck platooning is given by:(3)ΔCijFuelω=βω−1ζφdij100ω∀i,j∈L,where ΔCijfuelω is the average fuel consumption per truck that can be generated within truck platooning formed by ω trucks from node i to adjacent node j (Yuan).The average fuel consumption per truckΔCijfuelω is proportional to the factor of truck platoon consumption savings β and the size of trucks in truck platooning ω. Obviously, the higher the factor of truck platoon consumption savings β, the higher the average fuel consumption savings per truck will generate.


### 3.2. Formation of Truck Platooning

The efficiency of truck platooning is not only dependent on the aerodynamic drag but is also influenced by the truck platooning formation process. Unlike the fixed truck platooning mode that only calculates fuel consumption savings from the reduction of aerodynamic drag, a truck equipped with cooperative adaptive cruise control (CACC) may determine its own route and choose to join and leave truck platooning at any point and time. Each truck can either travel the shortest route individually or form truck platooning together to their destination. To form truck platooning, a truck may adjust its route and even make a reasonable detour to join truck platooning. Figure2 depicts a simple example of such a scenario with three trucks.Figure 2
Formation of truck platooning.As we show in Figure2, one truck needs to travel from A to H and two trucks from D to H. The blue, orange, and purple dashed lines represent the respective shortest routes. To fully reap the benefits of truck platooning, truck 1 could make a reasonable detour to form truck platooning with truck 2 and truck 3; that is, the green solid line indicates the formed truck platooning. Although this needs to be judged based on specific parameters, it provides a new way of thinking about the formation of truck platooning. In summary, fuel cost savings and emissions reductions from truck platooning have been the primary motivation for the study. To fully reap these benefits in the initial phases of truck platooning deployment, an appropriate truck platooning plan is required. Thus, we construct a truck platooning routing optimization model as follows. The traveling routes of each transportation task are determined in accordance with each spatially distributed delivery request in a road network.


## 3.1. Fuel Consumption Savings

Compared with traveling individually, one of the primary benefits of truck platooning is fuel consumption savings through the reduction of aerodynamic drag. Aerodynamic drag in different operational technology is shown in Figure1. Specifically, Alam et al. [5] found that the follower truck will experience a significant reduction of aerodynamic drag compared to leading trucks due to a relatively large reduced pressure at the front. Hence, fuel consumption savings will be generated for the following trucks due to the reduction of aerodynamic drag. However, the reduction of aerodynamic drag for the leading truck could be neglected. In general, from an overall perspective, we take the minimum overall fuel consumption of all trucks in the system as the optimization objective.Figure 1
Diagram of aerodynamic drag.In real-world traffic scenarios, fuel consumption is mainly determined by the road condition, the driver’s driving habits, wind force et al. There are a wide variety of influencing factors. Therefore, it is very difficult to accurately quantify the fuel consumption of a truck. In this study, we develop an intuitive fuel consumption formula based on simulation experiments and previous research, such as Alam et al. [5], Noruzoliaee et al. [6], Hoef [24], and Xue et al. [28].Specifically, the fuel consumption for nonplatooning trucks could not generate fuel consumption savings, and the fuel consumption for nonplatooning trucks on a link can be expressed as follows:(1)CijFuel1=ζφdij100∀i,j∈L,where Cijfuel1 denotes the fuel consumption of a truck traversing from node i to adjacent node j (Yuan). ζ and φ are unit fuel price (Yuan/L) and unit fuel consumption (L/100 km) of a truck, respectively. dij is the distance from node i to adjacent node j (km). The set of road links is denoted by L.The overall fuel consumption for truck platooning on a link can be expressed as follows:(2)CijFuelω=ζφdij100+ω−11−βζφdij100∀i,j∈L,where ω is the number of trucks in truck platooning. Cijfuelω denotes the fuel consumption of truck platooning from node i to adjacent node j (Yuan). Taking a truck that drives on its own and experiences no fuel savings as the benchmark, β is the fuel reduction rate of the following trucks due to the formation of truck platooning. This is because truck platooning reduces aerodynamic drag and lowers their fuel consumption (McAuliffe et al. [29]). The parameter β is derived from the previous relevant tests and experiments [6].As shown in Figure1, the formation of truck platooning has a negligible effect on the aerodynamic drag for the leading truck. Therefore, the fuel consumption for the leading truck could be neglected. From formula (2), it can also be derived that fuel consumption savings only consider the following truck and do not include the leading truck. Similarly, each following truck in truck platooning has approximately the same reduction of aerodynamic drag, thus can save fuel consumption by the same ratio of β.Thus, the average fuel consumption per truck in truck platooning compared to traveling without truck platooning is given by:(3)ΔCijFuelω=βω−1ζφdij100ω∀i,j∈L,where ΔCijfuelω is the average fuel consumption per truck that can be generated within truck platooning formed by ω trucks from node i to adjacent node j (Yuan).The average fuel consumption per truckΔCijfuelω is proportional to the factor of truck platoon consumption savings β and the size of trucks in truck platooning ω. Obviously, the higher the factor of truck platoon consumption savings β, the higher the average fuel consumption savings per truck will generate.


## 3.2. Formation of Truck Platooning

The efficiency of truck platooning is not only dependent on the aerodynamic drag but is also influenced by the truck platooning formation process. Unlike the fixed truck platooning mode that only calculates fuel consumption savings from the reduction of aerodynamic drag, a truck equipped with cooperative adaptive cruise control (CACC) may determine its own route and choose to join and leave truck platooning at any point and time. Each truck can either travel the shortest route individually or form truck platooning together to their destination. To form truck platooning, a truck may adjust its route and even make a reasonable detour to join truck platooning. Figure2 depicts a simple example of such a scenario with three trucks.Figure 2
Formation of truck platooning.As we show in Figure2, one truck needs to travel from A to H and two trucks from D to H. The blue, orange, and purple dashed lines represent the respective shortest routes. To fully reap the benefits of truck platooning, truck 1 could make a reasonable detour to form truck platooning with truck 2 and truck 3; that is, the green solid line indicates the formed truck platooning. Although this needs to be judged based on specific parameters, it provides a new way of thinking about the formation of truck platooning. In summary, fuel cost savings and emissions reductions from truck platooning have been the primary motivation for the study. To fully reap these benefits in the initial phases of truck platooning deployment, an appropriate truck platooning plan is required. Thus, we construct a truck platooning routing optimization model as follows. The traveling routes of each transportation task are determined in accordance with each spatially distributed delivery request in a road network.


## 4. Model

According to the existing studies, there is a consensus that truck platooning can bring fuel and emission savings. Generally, their truck platooning optimization goal is to maximize fuel cost savings generated through the reduction of aerodynamic drag generated by the formation of truck platooning along a fixed path. However, the efficiency of truck platooning is not only dependent on the aerodynamic drag. In practice, a truck sometimes deviates from the shortest route, but a proper detour route could help trucks form truck platooning with other trucks and generate more fuel savings while reaching the destination. Therefore, considering the routes for each truck as a decision variable can be helpful for better optimizing truck platooning and saving fuel consumption to the maximum extent. In the initial phases of truck platooning deployment, we assume that trucks belong to the same freight transportation enterprises in which the truckers are willing to generate detours to form truck platooning to achieve the lowest overall system fuel consumption. Based on the multi-commodity network flow model, we construct a truck platooning routing optimization model considering the route for each truck.In a road networkG=N,L, let N and L represent the set of all nodes and links, respectively. Moreover, K represents the set of all trucks. Due to the freight being transported in units of trucks, each transportation task includes only one truck. Therefore, those two have the same meaning containing the same origin and destination. However, for different trucks (or transportation tasks), they travel separately from their origins to destinations. How to maximize fuel savings by optimizing routes to form truck platooning is the key of the study.The decision variablexijk is constructed to represent the passage of trucks on the link i,j. Due to each truck moving on one route only at the same time, xijk is a binary decision variable. The variable xijk is 1 if truck k traverses from node i to adjacent node j, and is 0 otherwise. In addition, the decision variable yijkm is constructed to determine whether truck platooning is formed or not. The variable yijkm is 1 if truck m following truck k traverses from node i to adjacent node j, and is 0 otherwise.Based on the multi-commodity network flow theory, the truck platooning routing operation model is developed to minimize the overall fuel consumption cost of all trucks in the system. The objective function is stated as follows:(4)min∑i,j∈LCijFuel∑k∈Kxijk−β∑k∈K∑m∈Kyijkm,where Cijfuel represents the fuel consumption costs by a truck to traverse from node i to adjacent node j, and it is assumed that the fuel consumption of each truck is only related to the number of miles traveled. According to the abovementioned quantification of the fuel consumption savings, we use the simple and intuitive principle. That is, each of the following trucks in truck platooning can save fuel by the same ratio β, while the leading truck is neglected due to small fuel consumption savings.It is necessary to ensure that each truck is delivered from the origin to the destination in the truck platooning routing optimization model. Therefore, the node flow conservation constraint for each node and each demand is expressed as follows:(5)∑j∈Nxijk−∑j∈Nxjik=1i=ok0i≠ok−1i=dk,i≠dk∀k∈K,where ok is the origin of truck k and dk is the destination of truck k, respectively.Within truck platooning, the truck is also defined as the immediate predecessor truck and the immediate successor truck. This concept is different from the leading truck and the following truck. The truck that closely follows the closest distance before a certain truck is defined as the immediate predecessor truck, and the truck that closely follows the closest distance after a certain truck is defined as the immediate successor truck. The description of the immediate predecessor truck is unrelated to the truck platooning size, and the immediate predecessor truck may be either the leading truck or the following truck of truck platooning.Taking truck platooning of four trucks as an example, truck platooning contains four trucks with the labels No. 1, No. 2, No. 3, and No. 4, respectively, according to the order. For truck No. 2, the immediate predecessor truck is truck No. 1 and the immediate successor truck is truck No. 3. Similarly, for truck No. 3, the immediate predecessor truck is truck No. 2 and the immediate successor truck is truck No. 4. Thus, for each truck within truck platooning, it can only follow the immediate predecessor truck and cannot have more than one immediate predecessor truck at the same time. Only one truck can follow, and this constraint that ensures the formation of truck platooning can be expressed as follows:(6)∑k∈Kyijkm≤1∀m∈K,i,j∈L.Other logical constraints can be written as follows:(7)∑m∈Kyijkm≤xijk∀k∈K,i,j∈L,(8)∑k∈Kyijkm≤xijm∀m∈K,i,j∈L.Truck platooning size constraints can be expressed as follows:(9)∑k∈Kxijk≤θ∀i,j∈L,where θ is the maximum size of truck platooning.The following equation is the detour rate constraint. To avoid excessive detours by individual trucks in order to form truck platooning with other trucks, a certain detour rate constraint is needed to constrain the detour costs.(10)∑i,j∈Lxijkdij≤ρDk∀k∈K,where Dk is the shortest route for truck k to travel from its origin to destination. ρ denotes the rate of reasonable detour, usually ρ≥1.Moreover, constraints (7) and (8) define the decision variables as binary ones.(11)xijk∈0,1∀k∈K,i,j∈L,yijkm∈0,1∀k,m∈K,i,j∈L.


## 5. Numerical Experiments

In this section, we first test small-scale numerical instances with upto 16 nodes and 24 links (a 4 × 4 grid) to demonstrate the generated fuel consumption savings by truck platooning and explore the impact of the restrictions on the number of trucks in truck platooning on overall fuel consumption savings. Then, we design a simulated road network to analyze the changes of a certain truck traveling route during the formation of truck platooning.Next, we conduct the sensitivity analysis considering the different fuel reduction rates of the following trucks in platooning on the system performance in terms of the total fuel cost. Finally, we believe that both networks confirm the accuracy of the truck platooning routing optimization model.


### 5.1. Fuel Consumption Savings for Various Operational Technology

It is well known that as the number of trucks in truck platooning increases, more fuel consumption savings are generated. However, long truck platooning could lead to traffic congestion due to the disruption of the previous traffic flow. Additionally, this will cause wear and tear on infrastructure as a result of higher truck density. Meanwhile, from the optimization and calculation perspective, the introduction of restrictions may also complicate matters as they make it more difficult for planners to find feasible solutions. Nevertheless, we investigate the effect of the number of trucks being restricted in truck platooning on fuel consumption savings and the formation of truck platooning by numerical experiments.Figure3 shows the diagram of the road network (a 4 × 4 grid). The link weight that has been marked equals the Euclidean distance between the nodes. Let A and B be the origins of the transportation task, and let C and D be the destinations of the transportation task. By continuously increasing the number of trucks in the road network, we compare the fuel consumption in different situations in which the number of trucks being restricted or not in truck platooning under a flexible route. Although the regularity of the grid network may appear to be simple, we find that the opposite is the case. This is because there are many different routes of the same length between most pairs of origin and destination nodes.Figure 3
Diagram of the road network (a 4 × 4 grid).The parameters used in the proposed truck platooning routing optimization model are as follows: the maximum size of truck platooningθ is set to 3. According to the relevant literature (Noruzoliaee et al. [6]; Larsson et al. [27]) and practical situations, the unit fuel price ζ and unit fuel consumption φ are set to be 7 Yuan/L and 15 L/100 km, respectively. The fuel reduction rate β can be set to 20%. We test the proposed model on a set of instances. All numerical experiments are coded in C# on a windows PC with an Intel (R) Core (™) i5-10210U CPU@ 1.60 GHz 2.11 GHz, 16 GB RAM. The linear restraints are solved by branch and bound algorithm in CPLEX 12.8. In all numerical experiments, the maximum CPU time used is 81.67 s.We change the number of trucks in the road network from 2 to 12. As shown in Figure4, the orange dashed line is presented as a reference showing the fuel consumption savings generated by the number of trucks not being restricted in truck platooning. The blue solid line shows the fuel consumption savings generated by the number of trucks being restricted in truck platooning. The middle bars represent the difference between the fuel consumption savings generated in the two cases. The results show that the fuel consumption savings generated increase with the number of trucks in the road network, regardless of the number of trucks being restricted or not in truck platooning. On the other hand, when the number of trucks is restricted in truck platooning, the increase in fuel consumption savings is much smaller. This is because the number of trucks being restricted may discourage the formation of larger truck platooning. The effect of the number of trucks in platooning on fuel savings is also demonstrated by equation (3). Obviously, the larger the size of the truck platooning, the greater the fuel savings generated.Figure 4
Fuel consumption savings with the number of trucks being restricted or not in truck platooning.


### 5.2. Truck Platooning Routing Optimization Experiments

If there is a need for truck platooning to be formed, the routes of the trucks may differ slightly from the obvious shortest routes to maximize fuel consumption savings. To explore this change, we designed a simulated road network. As shown in Figure5, there are 13 nodes and 20 links in the road network. Similarly, the number marked next to each link is the Euclidean distance between the nodes. Other parameters remain the same as mentioned above.Figure 5
Diagram of the simulated road network.To test the truck platooning routing optimization model, we generate random transportation tasks on a road network. The OD matrix for each transportation task is shown in Table1.Table 1
OD matrix for each transportation task.
IDOriginDestination1AC2AE3AF4AK5AM6BM7CK8CM9DA10DI11DK12DM13EC14EI15FA16FI17FJ18FM19IM20LIThis truck platooning routing optimization model with the number of trucks being not restricted is solved by commercial software CPLEX 12.8, and the CPU time used is 180 s. 20 transportation tasks are divided into 16 truck platoons. Compared to individual trucks, 12% fuel consumption savings are achieved for truck platooning, amounting to over 1000-yuan fuel consumption savings. The traveling route of each truck and the formation of the truck platooning on each link are shown in Table2.Table 2
Optimization results with the number of trucks not being restricted in truck platooning.
IDLinkTransportation taskFuel consumption (yuan)Fuel consumption savings (yuan)1A⟶B(1)(2)(3)518.779.82A⟶H(4)(5)234.3626.043B⟶A(9)(15)359.139.94B⟶C(1)(2)(3)464.171.45B⟶G(6)199.506C⟶B(9)(15)321.335.77C⟶F(2)(3)(7)(8)596.19105.218D⟶C(9)170.109D⟶E(10)(11)(12)600.692.410E⟶F(13)147011E⟶L(10)(11)(12)(14)535.594.512F⟶C(13)(15)315.6335.0713F⟶E(2)147014F⟶G(16)(17)326.9736.3315F⟶L(7)(8)(18)333.0651.2416G⟶J(6)(16)(17)289.3844.5217H⟶J(4)(5)285.3931.7118I⟶J(19)148.05019J⟶I(10)(14)(16)(20)503.3788.8320J⟶K(4)(5)(6)(19)3576321K⟶J(10)(14)(20)2734222K⟶M(5)(6)(19)371.2857.1223L⟶K(7)(10)(11)(14)(20)529.2100.824L⟶M(8)(12)(18)354.954.6In Table2, each link is set as a unit of measurement. For example, the link A⟶B includes transportation tasks (1), (2), and (3), and the fuel consumption cost of truck platooning on the link is 518.7 yuan. Compared to three trucks traveling individually, the fuel consumption savings is 79.8 yuan due to truck platooning. Meanwhile, the traveling route of the transportation task (1) is A⟶B⟶C. In addition, there are two transportation tasks that make a small detour in this experiment with the number of trucks being not restricted, namely, transportation tasks (2) and (12) (3).As discussed above, the number of trucks in the link exceeds 5, and the number of other links also exceeds 4. Generally, we set the maximum size of truck platooning to 3 in order not to affect the existing traffic flow. Based on the optimization results mentioned above, we conduct experiments to study the effect of the number of trucks being restricted in truck platooning. The results show that the transportation tasks are more evenly distributed over each link. And Table 3 displays the optimization results with the number of trucks being restricted in truck platooning.Table 3
Optimization results with the number of trucks being restricted in truck platooning.
IDLinkTransportation taskFuel consumption (yuan)Fuel consumption savings (yuan)1A⟶B(1)(2)(3)518.779.82A⟶H(4)(5)(10)338.5252.083B⟶A(9)(10)(15)518.779.84B⟶C(1)(3)321.335.75B⟶G(2)(6)359.139.96C⟶B(9)(10)(15)464.171.47C⟶F(3)(7)(8)455.9170.148D⟶C(9)(10)306.1834.029D⟶E(11)(12)415.846.210E⟶F(13)(14)264.629.411E⟶L(11)157.5012E⟶M(8)(12)472.552.513F⟶C(13)(15)315.6335.0714F⟶E(2)(8)264.629.415F⟶G(14)(16)(17)472.2972.6616F⟶L(6)(7)(18)333.0651.2417G⟶F(2)(6)326.9736.3318G⟶J(14)(16)(17)289.3844.5219H⟶I(10)110.25020H⟶J(4)(5)285.3931.7121I⟶J(19)148.05022J⟶I(14)(16)(20)384.9359.2223J⟶K(4)(5)(19)2734224K⟶J(20)105025K⟶M(5)(19)257.0428.5626L⟶K(7)(11)(20)327.650.427L⟶M(6)(18)245.727.3L⟶KDue to the number of trucks being restricted in truck platooning, one of the trucks may make a small detour to form truck platooning and stay within the truck platooning size limit. In truck platooning, the fuel consumption savings with the number of trucks being restricted is about 700 yuan. Fuel consumption savings generated are slightly lower than those for unrestricted truck platooning. In addition, there are four transportation tasks that make a small detour in this experiment with the number of trucks being restricted, namely, transportation tasks (2), (6), (10), and (14).Unlike the traditional route optimization model in which the shortest route between the origin and destination was selected, trucks in our truck platooning routing optimization model could make a small detour to minimize overall fuel consumption. Figure6 shows 2 simple examples of such a situation.Figure 6
Traveling route of the truck. (a) Traveling route of transportation task (12) with the number of trucks not being restricted in truck platooning. (b) Traveling route of transportation task (10) with the number of trucks being restricted in truck platooning.
(a)(b)As shown in Figure6, the orange dashed line indicates the shortest route from the origin to the destination, and the blue solid line represents the actual traveling route of a certain truck to form truck platooning. As the optimization objective is to minimize the total fuel consumption of the overall transportation task in the system, we have taken detour costs into account. To derive more fuel consumption savings from truck platooning, some reasonable detours should be considered by drivers.


### 5.3. Sensitivity Analysis

To explore the impact of considering different fuel reduction rates of the following trucks in platooning on the system performance in terms of the total fuel cost, we compare the solutions to the truck platooning routing optimization model with the restricted and unrestricted number of trucks. Five groups of instances are respectively included withβ=0%, β=5%, β=10%, β=15%, and β=20%. In general, the distance between trucks in a platoon is related to the fuel reduction rates of the following trucks in platooning β and this data is mainly obtained experimentally according to the previous relevant literature. When β=0%, it means that truck platooning has not been formed. The fuel reduction rates of the following trucks increase as the distance between trucks in platooning decreases. The results are summarized in Table 4.Table 4
Comparison of the truck platooning routing optimization model with the number of trucks not being restricted and restricted.
Optimization model of the number of trucks being not restrictedOptimization model of the number of trucks being restrictedβ (%)0510152005101520Total fuel cost (yuan)9476.39211.48946.58668.28380.79476.39356.39281.59006.68731.8Saving proportion (%)02.75.68.511.601.32.15.07.9It shows that the total fuel cost considering the reduced fuel reduction rates of the following trucks in platooning will increase. Similar to the abovementioned conclusion, the restricted trucks in platooning save fewer fuels than the trucks that are not restricted in platooning. In addition, we also find that the consideration of different fuel reduction rates for the following trucks may also affect the routing of transportation tasks and truck platooning plans. Specifically, this may be attributed to the fact that some transportation tasks may lose opportunities to form truck platooning by making a small detour due to the lower fuel reduction rate of the following truck in platooning.


## 5.1. Fuel Consumption Savings for Various Operational Technology

It is well known that as the number of trucks in truck platooning increases, more fuel consumption savings are generated. However, long truck platooning could lead to traffic congestion due to the disruption of the previous traffic flow. Additionally, this will cause wear and tear on infrastructure as a result of higher truck density. Meanwhile, from the optimization and calculation perspective, the introduction of restrictions may also complicate matters as they make it more difficult for planners to find feasible solutions. Nevertheless, we investigate the effect of the number of trucks being restricted in truck platooning on fuel consumption savings and the formation of truck platooning by numerical experiments.Figure3 shows the diagram of the road network (a 4 × 4 grid). The link weight that has been marked equals the Euclidean distance between the nodes. Let A and B be the origins of the transportation task, and let C and D be the destinations of the transportation task. By continuously increasing the number of trucks in the road network, we compare the fuel consumption in different situations in which the number of trucks being restricted or not in truck platooning under a flexible route. Although the regularity of the grid network may appear to be simple, we find that the opposite is the case. This is because there are many different routes of the same length between most pairs of origin and destination nodes.Figure 3
Diagram of the road network (a 4 × 4 grid).The parameters used in the proposed truck platooning routing optimization model are as follows: the maximum size of truck platooningθ is set to 3. According to the relevant literature (Noruzoliaee et al. [6]; Larsson et al. [27]) and practical situations, the unit fuel price ζ and unit fuel consumption φ are set to be 7 Yuan/L and 15 L/100 km, respectively. The fuel reduction rate β can be set to 20%. We test the proposed model on a set of instances. All numerical experiments are coded in C# on a windows PC with an Intel (R) Core (™) i5-10210U CPU@ 1.60 GHz 2.11 GHz, 16 GB RAM. The linear restraints are solved by branch and bound algorithm in CPLEX 12.8. In all numerical experiments, the maximum CPU time used is 81.67 s.We change the number of trucks in the road network from 2 to 12. As shown in Figure4, the orange dashed line is presented as a reference showing the fuel consumption savings generated by the number of trucks not being restricted in truck platooning. The blue solid line shows the fuel consumption savings generated by the number of trucks being restricted in truck platooning. The middle bars represent the difference between the fuel consumption savings generated in the two cases. The results show that the fuel consumption savings generated increase with the number of trucks in the road network, regardless of the number of trucks being restricted or not in truck platooning. On the other hand, when the number of trucks is restricted in truck platooning, the increase in fuel consumption savings is much smaller. This is because the number of trucks being restricted may discourage the formation of larger truck platooning. The effect of the number of trucks in platooning on fuel savings is also demonstrated by equation (3). Obviously, the larger the size of the truck platooning, the greater the fuel savings generated.Figure 4
Fuel consumption savings with the number of trucks being restricted or not in truck platooning.


## 5.2. Truck Platooning Routing Optimization Experiments

If there is a need for truck platooning to be formed, the routes of the trucks may differ slightly from the obvious shortest routes to maximize fuel consumption savings. To explore this change, we designed a simulated road network. As shown in Figure5, there are 13 nodes and 20 links in the road network. Similarly, the number marked next to each link is the Euclidean distance between the nodes. Other parameters remain the same as mentioned above.Figure 5
Diagram of the simulated road network.To test the truck platooning routing optimization model, we generate random transportation tasks on a road network. The OD matrix for each transportation task is shown in Table1.Table 1
OD matrix for each transportation task.
IDOriginDestination1AC2AE3AF4AK5AM6BM7CK8CM9DA10DI11DK12DM13EC14EI15FA16FI17FJ18FM19IM20LIThis truck platooning routing optimization model with the number of trucks being not restricted is solved by commercial software CPLEX 12.8, and the CPU time used is 180 s. 20 transportation tasks are divided into 16 truck platoons. Compared to individual trucks, 12% fuel consumption savings are achieved for truck platooning, amounting to over 1000-yuan fuel consumption savings. The traveling route of each truck and the formation of the truck platooning on each link are shown in Table2.Table 2
Optimization results with the number of trucks not being restricted in truck platooning.
IDLinkTransportation taskFuel consumption (yuan)Fuel consumption savings (yuan)1A⟶B(1)(2)(3)518.779.82A⟶H(4)(5)234.3626.043B⟶A(9)(15)359.139.94B⟶C(1)(2)(3)464.171.45B⟶G(6)199.506C⟶B(9)(15)321.335.77C⟶F(2)(3)(7)(8)596.19105.218D⟶C(9)170.109D⟶E(10)(11)(12)600.692.410E⟶F(13)147011E⟶L(10)(11)(12)(14)535.594.512F⟶C(13)(15)315.6335.0713F⟶E(2)147014F⟶G(16)(17)326.9736.3315F⟶L(7)(8)(18)333.0651.2416G⟶J(6)(16)(17)289.3844.5217H⟶J(4)(5)285.3931.7118I⟶J(19)148.05019J⟶I(10)(14)(16)(20)503.3788.8320J⟶K(4)(5)(6)(19)3576321K⟶J(10)(14)(20)2734222K⟶M(5)(6)(19)371.2857.1223L⟶K(7)(10)(11)(14)(20)529.2100.824L⟶M(8)(12)(18)354.954.6In Table2, each link is set as a unit of measurement. For example, the link A⟶B includes transportation tasks (1), (2), and (3), and the fuel consumption cost of truck platooning on the link is 518.7 yuan. Compared to three trucks traveling individually, the fuel consumption savings is 79.8 yuan due to truck platooning. Meanwhile, the traveling route of the transportation task (1) is A⟶B⟶C. In addition, there are two transportation tasks that make a small detour in this experiment with the number of trucks being not restricted, namely, transportation tasks (2) and (12) (3).As discussed above, the number of trucks in the link exceeds 5, and the number of other links also exceeds 4. Generally, we set the maximum size of truck platooning to 3 in order not to affect the existing traffic flow. Based on the optimization results mentioned above, we conduct experiments to study the effect of the number of trucks being restricted in truck platooning. The results show that the transportation tasks are more evenly distributed over each link. And Table 3 displays the optimization results with the number of trucks being restricted in truck platooning.Table 3
Optimization results with the number of trucks being restricted in truck platooning.
IDLinkTransportation taskFuel consumption (yuan)Fuel consumption savings (yuan)1A⟶B(1)(2)(3)518.779.82A⟶H(4)(5)(10)338.5252.083B⟶A(9)(10)(15)518.779.84B⟶C(1)(3)321.335.75B⟶G(2)(6)359.139.96C⟶B(9)(10)(15)464.171.47C⟶F(3)(7)(8)455.9170.148D⟶C(9)(10)306.1834.029D⟶E(11)(12)415.846.210E⟶F(13)(14)264.629.411E⟶L(11)157.5012E⟶M(8)(12)472.552.513F⟶C(13)(15)315.6335.0714F⟶E(2)(8)264.629.415F⟶G(14)(16)(17)472.2972.6616F⟶L(6)(7)(18)333.0651.2417G⟶F(2)(6)326.9736.3318G⟶J(14)(16)(17)289.3844.5219H⟶I(10)110.25020H⟶J(4)(5)285.3931.7121I⟶J(19)148.05022J⟶I(14)(16)(20)384.9359.2223J⟶K(4)(5)(19)2734224K⟶J(20)105025K⟶M(5)(19)257.0428.5626L⟶K(7)(11)(20)327.650.427L⟶M(6)(18)245.727.3L⟶KDue to the number of trucks being restricted in truck platooning, one of the trucks may make a small detour to form truck platooning and stay within the truck platooning size limit. In truck platooning, the fuel consumption savings with the number of trucks being restricted is about 700 yuan. Fuel consumption savings generated are slightly lower than those for unrestricted truck platooning. In addition, there are four transportation tasks that make a small detour in this experiment with the number of trucks being restricted, namely, transportation tasks (2), (6), (10), and (14).Unlike the traditional route optimization model in which the shortest route between the origin and destination was selected, trucks in our truck platooning routing optimization model could make a small detour to minimize overall fuel consumption. Figure6 shows 2 simple examples of such a situation.Figure 6
Traveling route of the truck. (a) Traveling route of transportation task (12) with the number of trucks not being restricted in truck platooning. (b) Traveling route of transportation task (10) with the number of trucks being restricted in truck platooning.
(a)(b)As shown in Figure6, the orange dashed line indicates the shortest route from the origin to the destination, and the blue solid line represents the actual traveling route of a certain truck to form truck platooning. As the optimization objective is to minimize the total fuel consumption of the overall transportation task in the system, we have taken detour costs into account. To derive more fuel consumption savings from truck platooning, some reasonable detours should be considered by drivers.


## 5.3. Sensitivity Analysis

To explore the impact of considering different fuel reduction rates of the following trucks in platooning on the system performance in terms of the total fuel cost, we compare the solutions to the truck platooning routing optimization model with the restricted and unrestricted number of trucks. Five groups of instances are respectively included withβ=0%, β=5%, β=10%, β=15%, and β=20%. In general, the distance between trucks in a platoon is related to the fuel reduction rates of the following trucks in platooning β and this data is mainly obtained experimentally according to the previous relevant literature. When β=0%, it means that truck platooning has not been formed. The fuel reduction rates of the following trucks increase as the distance between trucks in platooning decreases. The results are summarized in Table 4.Table 4
Comparison of the truck platooning routing optimization model with the number of trucks not being restricted and restricted.
Optimization model of the number of trucks being not restrictedOptimization model of the number of trucks being restrictedβ (%)0510152005101520Total fuel cost (yuan)9476.39211.48946.58668.28380.79476.39356.39281.59006.68731.8Saving proportion (%)02.75.68.511.601.32.15.07.9It shows that the total fuel cost considering the reduced fuel reduction rates of the following trucks in platooning will increase. Similar to the abovementioned conclusion, the restricted trucks in platooning save fewer fuels than the trucks that are not restricted in platooning. In addition, we also find that the consideration of different fuel reduction rates for the following trucks may also affect the routing of transportation tasks and truck platooning plans. Specifically, this may be attributed to the fact that some transportation tasks may lose opportunities to form truck platooning by making a small detour due to the lower fuel reduction rate of the following truck in platooning.


## 6. Conclusion

Using truck platooning equipped with cooperative adaptive cruise control (CACC) as the technical basis of the study, we propose a truck platooning routing optimization model from the perspective of transportation optimization and scheduling for maximizing fuel consumption savings. Specifically, we set routing for each truck as a decision variable so that the optimization result can reflect both the composition of truck platooning on each link and the specific route of each truck. We formulate the truck platooning routing optimization problem as a multi-commodity network flow problem, in which we consider the truck platooning size and reasonable detour constraints to avoid excessive detours by individual trucks in order to form truck platooning with other trucks. For each scenario, we generate varying numbers of transportation tasks and explore the impact of the restrictions on the number of trucks in truck platooning on overall fuel consumption savings. Considering the different fuel reduction rates of the following trucks in platooning on the system performance in terms of the total fuel cost, a sensitivity analysis is also conducted. The results also verify the accuracy of the model.Due to the limitations of research objectives and space, we mainly focus on the construction of the truck platooning routing optimization model. Thus, the scale of the numerical experiments is small and can be solved by using commercial software, and the algorithm for solving large-scale real cases will be developed in future research. Furthermore, we assume that all the transportation information required for planning truck platooning is known in advance. In the future, we will study dynamic planning based on autonomous platooning that could change at any time according to the real-time situation.



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*Source: 6906655-2023-01-07.xml*