A congestion-aware vehicle routing optimization model for sustainable urban supply: An AnyLogic simulation approach
JingGu1
XuefeiLiu1
MohammadKamrulHasan2
MaoweiChen3,4✉Emailmuwi@kangwon.ac.kr
1Department of Economics and ManagementHebei University of Environmental Engineering066102QinhuangdaoChina
2School of Business AdministrationTongling University244061TonglingChina
3Department of Business AdministrationKangwon National University24341ChuncheonKangwon-doRepublic of Korea
4
A
Room 307Building5Natural Sciences)Kangwon National University1 Kangwondaehak-gilChuncheon-siKangwon ProvinceRepublic of Korea
Jing Gu1, Xuefei Liu1, Mohammad Kamrul Hasan2 & Maowei Chen3*
1 Department of Economics and Management, Hebei University of Environmental Engineering, Qinhuangdao 066102, China
2 School of Business Administration, Tongling University, Tongling 244061, China
3 Department of Business Administration, Kangwon National University, Chuncheon, 24341, Kangwon-do, Republic of Korea
* Correspondence concerning this article should be addressed to Maowei Chen, Room 307, Building 5 (Natural Sciences), Kangwon National University, 1 Kangwondaehak-gil, Chuncheon-si, Kangwon Province, Republic of Korea, muwi@kangwon.ac.kr
A congestion-aware vehicle routing optimization model for sustainable urban supply: An AnyLogic simulation approach
Abstract
Urban traffic congestion significantly affects the efficiency, cost, and environmental performance of logistics operations. In particular, the selection of distribution routes plays a crucial role in ensuring timely delivery, reducing carbon emissions, and supporting sustainable urban mobility. This study proposes a congestion-aware supply path selection model that integrates congestion probabilities into the classical Dijkstra algorithm. By incorporating dynamic traffic conditions and assigning congestion probabilities to road segments, the model provides a more realistic representation of urban transportation networks. The AnyLogic simulation platform is employed to develop and validate the model, using the supply network of Wu-Mart supermarkets in Beijing as a case study. Simulation results demonstrate that the enhanced model effectively avoids congested areas, shortens transportation time, improves service efficiency, and reduces environmental impacts compared with traditional approaches. The findings highlight the feasibility and practicality of introducing congestion probabilities into urban vehicle routing problems, offering methodological support for logistics enterprises to optimize path planning. Moreover, this study contributes to the growing field of green logistics by demonstrating how congestion-aware routing can reduce fuel consumption and carbon emissions while maintaining delivery quality and efficiency. Future research should extend the model to multi-vehicle and multi-distribution center contexts, incorporating economic and environmental costs to further enhance sustainable logistics practices.
Keywords:
AnyLogic simulation
Congestion probability
Enhanced Dijkstra algorithm
Supply path optimization
Sustainable urban transportation
1. Introduction
As the economy develops and people's living standards improve, the use of motor vehicles is increasing. Even in cities with a developed economy and well-connected urban roads, the growth in the number of automobiles has exceeded the carrying capacity of the cities1. This has led to increasing traffic congestion and carbon emissions, which are not only contradictory to low-carbon policies but also seriously hinder the efficiency of suppliers' distribution2. Delivering goods to stores at the end of the supply chain is a key part of logistics operations. And the choice of supply routes is crucial in actual transportation3. The choice of supply routes directly affects the quality, efficiency, cost, and environmental impact of the transportation process. Choosing a timely avoidance of congestion points and the most efficient transportation paths can improve service efficiency to meet more customers’ demand and reduce environmental pollution2. Subsequently, the selection of a reasonable distribution route that avoids road congestion and ensures the timely delivery of products to the store is a crucial problem to be solved.
Since its introduction in 1945, the Vehicle Routing Problem (VRP) has been extensively studied, resulting in numerous research findings4. Desrochers and Verhoog5 proposed a hybrid vehicle route model, while Solomon and Desrosiers6 incorporated the concept of time windows into the vehicle path problem. Jabali et al.7 addressed the time window constraint by penalizing the cost, introducing the concepts of soft and hard time windows. Some scholars focused on the VRP with soft time windows8,9, while others explored the VRP problem under uncertainty10. In the context of urban distribution, researchers have conducted targeted studies. Guedria et al.11 integrated vehicle path planning and vehicle loading plan decision problems and proposed a hybrid algorithm for optimization. Franceschetti et al.12 transformed the vehicle path problem into an urban zoning problem, assigning each vehicle a separate service area. Ye et al.13 studied a freight vehicle path-planning model in the context of dynamic time-varying networks with the spatial and temporal distribution of carbon dioxide emission trajectories. Zhao et al.14 considered traffic congestion, vehicle speed, and load in distribution cost calculation, aiming to minimize total distribution cost and carbon emissions. Zhou et al.15 used a time-dependent function based on vehicle speed to reflect time-varying characteristics. Fu and Liu16 constructed an optimization model for the open vehicle path problem considering time-varying road networks, freshness constraints, and flexible vehicle departure time. These studies contribute to the advancement of knowledge and provide various approaches to address different aspects of vehicle routing and urban distribution path problems.
In recent years, there has been a growing academic interest in the green vehicle path problem, which focuses on promoting sustainable development and reducing energy consumption, and carbon emissions. Researchers17–21 have established Green Vehicle Routing Problem (GVRP) models with different optimization objectives. These objectives include minimizing fuel consumption, minimizing driving distance, minimizing rental car costs, and ensuring on-time delivery. They have utilized various algorithms such as improved particle swarm algorithms, two-stage methods based on simulated annealing and contraindicated search, and path division-based contraindicated search algorithms to solve these models. To emphasize the impact of vehicle energy consumption and carbon emissions on the environment, several studies have analyzed the relationship between vehicle departure time and speed22–25. Those studies have constructed single-objective pollution path models based on time dependence. Various algorithms, including Taboo search algorithms, departure time and speed optimization algorithms, Heuristic algorithms, hybrid algorithms based on iterative neighborhood search and local MIP, and improved particle swarm algorithms, have been employed to solve these models. Other research works have focused on analyzing fuel consumption conditions generated by transport vehicles under different road network conditions and identifying the main influencing factors26. Some studies have constructed Vehicle Routing Problem with Time Windows (VRPTW) models considering low-carbon factors and carbon tax policies, aiming to minimize the total distribution cost while taking distribution time into account27–30. Additionally, there are studies on the construction of a multi-objective optimization model aiming to minimize fuel consumption costs and the number of vehicles, while considering the diversity of driving routes between two distribution points3. These research efforts contribute to the advancement of the green vehicle path problem field by addressing various aspects of energy consumption, carbon emissions, and optimization objectives in transportation and distribution.
Previous research on logistics vehicle route problems considering traffic conditions has yielded significant results. In real traffic road networks, vehicle travel is influenced by various unpredictable factors, with traffic conditions being the most significant. Road congestion, for example, can cause fluctuations in vehicle travel speed, travel time, and travel costs, introducing uncertainty31. In previous research, most scholars have primarily focused on known static path information, such as path distance and economic costs. Only a few researchers have considered the time aspect by incorporating changing dynamic information. However, even among these studies, the consideration of road conditions and speed variations during different driving periods is often oversimplified, leading to the possibility of overlooking more optimal paths during actual operations.
This paper recognizes that the selection of delivery paths has a direct impact on the quality, efficiency, cost, and environmental impact of transportation. To address this, the research focuses on the congestion probability threshold and conducts simulation studies on supplier city delivery path selection. By integrating the model with practical examples, its feasibility is validated. The simulation results are then analyzed quantitatively to offer well-founded recommendations for supplier path selection. This approach facilitates a comprehensive evaluation of the model's effectiveness and supports the development of informed strategies to optimize supplier path selection.
The remainder of this paper is structured as follows. Section 2 presents the problem description and underlying assumptions. Section 3 outlines the methodology, focusing on Dijkstra’s algorithm with consideration of congestion probability, and describes how the improved algorithm is applied to the simulation modeling process of a multi-agent system. Section 4 uses the supply route selection for the supplier of Beijing Wu-Mart Supermarket as a case study, presenting simulation results that compare the model’s performance before and after the algorithm’s improvement. Section 5 discusses the practical implications of the study and evaluates the rationality of the improved method. The overall structure of this paper is illustrated in Fig. 1.
Fig. 1
Research structure.
2. Problem description
This study addresses the problem of urban supply routing for suppliers under conditions of traffic congestion and considers a logistics distribution center that dispatches multiple vehicles to deliver goods to customers located in various areas of the city. Each customer has specific demand requirements and designated time windows for delivery. The locations of all customer points are known, as are the areas prone to traffic congestion. These congestion conditions directly influence vehicle speed and travel time. The objective of this study is to determine an optimal vehicle scheduling and routing solution that fulfills customer demand and time window constraints while minimizing transportation costs. For more convenience, the most important variables are summarized in Table 1.
Variables | Description |
|---|---|
N | a set of nodes, , where 0 denotes the distribution center and the remaining nodes are demand points |
a set of arcs connecting the nodes, | |
a set of distances from any node i to j | |
a set of distribution networks | |
and | indicates a congested area and is a non-congested area. |
Number of vehicles, | |
Speed of vehicle on section , there are two speeds and, , is the speed of the vehicle on the congested road section, and is the speed of the vehicle traveling in a clear condition in the non-congested area. | |
The load of the vehicle on the road section | |
The amount of goods demanded at the demand point  | |
The time window requirement at the demand point | |
The time when the vehicle arrives at the demand point |
To simplify the study, the relevant assumptions are made as follows:
(1)
The locations of the distribution center and the customer point are known. The vehicle starts from the distribution center and returns to the distribution center after completing the distribution task;
(2)
The same type and specifications of the distribution center's transportation vehicles;
(3)
Vehicles traveling in congested urban areas and non-congested roadways travel at different speeds;
(4)
Each customer's cargo requirements are determined to be less than the maximum load capacity of the vehicle with the service window requirement;
(5)
The weight of the cargo carried by each vehicle must not exceed its maximum load capacity;
(6)
Transportation vehicles are loaded and transported from the supplier to the customer's location and back to the supplier's location;
(7)
The relevant parameters, such as suppliers, customers, and customer demand, are known;
(8)
The goal of optimization is to reduce transportation time and improve transportation efficiency.
Vehicles are set to travel at the congested speed
in congested sections and
in non-congested sections. The congested road section and the congested speed will change as time changes. If there is traffic congestion on the
section (i.e.
), the vehicle travels at the congested speed
with a slower speed, and its travel time is
; if there is no congestion on the
section (i.e.
), the vehicle travels at the normal speed
with a faster speed, and its travel time is
; if the travel crosses the congested and non-congested sections, its travel time consists of the time spent on the congested section
and the time spent on the non-congested section
, and is
. The vehicle travel time on
is calculated as shown in Eq. (1).
(1) |
Where
is the congested area and
is the non-congested area.
3. Methodology
3.1. Dijkstra's algorithm
Dijkstra’s algorithm is one of the most well-established algorithms for solving the shortest path problem in weighted graphs and is widely used in transportation, telecommunications, and robotics32. It operates based on a greedy strategy, iteratively selecting the vertex with the minimum tentative distance and updating the distances of its adjacent vertices. The algorithm guarantees the shortest path in static, non-negative weight graphs, and has been widely adopted in logistics and transportation systems33,34.
However, a key limitation of the traditional Dijkstra’s algorithm lies in its assumption of static edge weights. In real-world urban transportation networks, road conditions are highly dynamic, with travel times varying significantly across different time periods due to traffic congestion. Several studies have attempted to address this limitation by integrating time-dependent or stochastic factors into the shortest path algorithms35,36. Yet, few have explicitly modeled congestion probability as a variable influencing travel time.
To address this gap, this study proposes an enhanced version of Dijkstra’s algorithm that incorporates time-varying congestion probabilities for each road segment. Instead of using static travel times, this improved model estimates expected travel durations based on historical traffic data and assigns congestion probabilities to dynamically adjust the edge weights. This approach allows the algorithm to more accurately reflect the temporal variability of urban road networks and supports more informed route decision-making in urban logistics.
To validate the proposed method, a simulation model is developed using AnyLogic, focusing on the delivery routes to the Wu-Mart Supermarket in Beijing. The simulation results demonstrate that the enhanced Dijkstra’s algorithm significantly improves route efficiency, reduces transportation costs, and minimizes environmental impact by avoiding congestion hotspots.
3.2. Multi-agent systems
A multi-agent system (MAS) refers to a means of solving complex problems by subdividing them into smaller tasks37. The individual tasks are allocated to autonomous entities, known as agents. Each agent acts proactively to achieve their goals through a set of rules to adapt to changes in the external environment. In terms of operation control, there are three main architectures for MAS: centralized, distributed, and hybrid38. In a centralized MAS, agents are organized into groups, and each group has a global management agent responsible for centralized control, task assignment, and planning based on the overall goals. The agents within each group operate under the guidance of the central management agent, following a hierarchical structure. In a distributed MAS, agents operate in a parallel and interconnected manner. Each agent is independent and equal in status to the others. The agents collaborate and work together to accomplish tasks without a central control mechanism. They make decisions and coordinate with each other through communication and negotiation. A hybrid MAS combines elements of both centralized and distributed structures39. It involves a mixture of centralized and distributed components. Some agents may be managed in a centralized manner, while others operate in a distributed fashion. This hybrid structure allows for partial task decomposition and coordination, with the advantages of both centralized and distributed architectures. It provides flexibility and scalability while avoiding the limitations of each structure. Among the three architectures, the hybrid MAS structure is the most commonly used due to its ability to combine the benefits of centralized and distributed architectures. It offers effective coordination, management, and collaboration among agents while maintaining scalability and adaptability.
This work conducted research using simulation methods based on a hybrid MAS. The AnyLogic simulation system allows us to create a hybrid MAS model that simulates the selection of supply routes in urban areas, considering the likelihood of congestion. The hybrid MAS model consists of three main agents: The Main Agent, the retailer Agent, and the truck Agent. Each agent has specific roles and responsibilities, and they are interconnected to form a comprehensive simulation system. The retailer Agent generates demand information and provides location coordinates, while the truck Agent receives order information, calculates the optimal route, and carries out the transportation. All relevant information is then recorded and stored in Excel for future data analysis.
3.2.1. Main agent
The primary agent assumes a prominent position within the entire simulation model, serving as the foundation for supplying data throughout the model's operation. Additionally, it serves as the repository for storing data during the model's operation and offers support for subsequent data analysis. The Main Agent simulation fulfills three primary functions.
Data Support: The Main Agent incorporates essential information, such as the locations of suppliers and customers, customer demands, road congestion probabilities, and congestion duration, into the database. This data provides technical support for the subsequent operation of the model.
Command Control: Upon receiving relevant demand information, the Main Agent issues commands to deploy vehicles for transportation simulation based on the prevailing traffic conditions.
Data Storage: As there is no guarantee of vehicle availability at all times after receiving order information, the Main Agent stores the orders and responds affirmatively to shipping requests when a vehicle becomes available.
3.2.2. Retailer agent
The primary role of the Retailer Agent is to generate demand information and provide location coordinates. The operation principle of this Agent is as follows. When the simulation model receives instructions from the Main Agent, the Customer Demand Agent generates customer demand randomly based on predefined principles. The generated demand is initially stored in the order collection and will be matched for delivery based on the first-order-first-delivery principle. The customer's location serves as the destination for vehicle transportation, and once the demand is generated, the vehicle will deliver the goods to the corresponding location.
3.2.3. Truck agent
The Truck Agent operates with a supplier-oriented approach. Upon receiving a demand order, it determines the destination and calculates the route with the shortest travel time. If a vehicle is available at the distribution center, it will directly transport the goods. However, if there is no vehicle present at the distribution center, the order will be temporarily stored. Once a vehicle becomes available, the principle of first-order first delivery is applied, and the transportation is implemented accordingly.
3.3. Simulation model run steps
The simulation model of the supplier city supply path selection under congestion probability, implemented in the AnyLogic software (version 8.8.6), operates in the following manner:
Generation of distribution demand: The Retailer Agent within the simulation model stores the demand information and demand points in the distribution information queue, based on the data obtained from a survey.
Reading of distribution information: Once the demand point coordinates are generated, this information is passed to the Vehicle Agent, following the "First-In-First-Out" (FIFO) principle. The demand point coordinates are determined after the information is read.
Calculation of the shortest path: The model utilizes an optimized Dijkstra algorithm, taking into consideration the time and speed factors, to determine the shortest path.
Vehicle distribution: The Truck Agent follows the calculated shortest path and proceeds with the transportation, distributing the goods accordingly.
3.4. Coordinates of the starting and ending points of supply
The starting point of the supply is the supplier's location. Since the supplier's location generally covers a large area and is close to the main road, the location close to the main road is used as the coordinates of the supplier's location for the convenience of calculating the simulation results.
to the demand customer M point
,
,
,
, the specific formula is as follow Eq. (2).
2
A
Figure 2. Schematic diagram of how transportation demand points are generated.4. Case study and simulation
This work selected Wu-Mart (a supermarket chain in China), and its suppliers as a case study to analyze the supplier supply route selection to Wu-Mart considering the congestion probability.
4.1. Data description
4.1.1. Distribution of Wu-Mart and suppliers
In this work, the main ring roads and the main roads connecting the ring roads are selected to establish the road network in Beijing. According to the survey, most of the road congestion in Beijing occurs within the fifth ring road. To enhance the accuracy of the study, Wu-Mart stores located within the Fifth Ring Road of Beijing are selected as the research subject. The spatial distribution of these Wu-Mart supermarket locations is illustrated in Fig. 3, where the red dots represent the selected stores, totaling 59 in number.
Fig. 3
Distribution of the Wu-Mart supermarket stores on the Fifth Ring Road of Beijing. (AnyLogic software (version 8.8.6) is used for plotting this figure; URL: The AnyLogic Company, https://www.anylogic.com)
The two suppliers of Wu-Mart are "Majuqiao DC warehouse" located in Tongzhou District, Beijing, and "Fresh Food Logistics Sub-center" (Xinfadi Logistics Center) in Fengtai District, Beijing, with the specific layout shown in Fig. 4.
Fig. 4
Distribution of suppliers of Wu-Mart. (AnyLogic software (version 8.8.6) is used for plotting this figure; URL: The AnyLogic Company, https://www.anylogic.com)
4.1.2. Supply and demand of Wu-Mart
Through interviews with the warehouse manager of Wu-Mart, it is discovered that the demand information of Wu-Mart stores is not manually generated by the stores and reported to the suppliers. Instead, Wu-Mart Supermarket employs a warehouse management system that conducts daily inventory checks. The system records the consumption of items in a book and automatically sends demand information to the suppliers when it detects that the inventory has dropped to the safety stock level. Each arrival quantity is maintained at a relatively low inventory level. Consequently, the supermarket's demand is primarily influenced by the inventory quantity and is not significantly affected by other factors. In this paper, the supermarket's demand is assumed to be uniformly distributed due to the consistent inventory management practices.
4.1.3. Beijing road traffic condition information
By observing the road traffic conditions in Beijing from 2022-01-10 to 2022-04-07, real-time road conditions were observed, and the data were obtained as shown in Table 2.
Road section | Date | Time | Congestion |
|---|---|---|---|
Caiduying bridge-Guanganmen bridge | Jan 12 | 8:00 | 1 |
Caiduying bridge - Yuquanying bridge | Jan 12 | 18:00 | 1 |
Lize bridge - Caiduying bridge | January 23 | 8:00 | 0 |
Youanmen bridge - Caihuying bridge | January 23 | 12:00 | 0 |
Liuli bridge-Guanganmen bridge | Feb 9 | 18:00 | 1 |
Deshengmen-Xizhimen | Feb 11 | 8:00 | 1 |
Xizhimen - Baishi xinqiao | Feb 20 | 18:00 | 0 |
Xizhimen-Wenhuiqiao | Feb 20 | 18:00 | 0 |
Deshengmen-Gulou bridge | March 5 | 8:00 | 0 |
The road conditions in Beijing are represented by a binary scale, where 1 indicates congestion and 0 indicates smoothness. Based on observation data, it is evident that roads are generally smoother on weekends compared to weekdays when major traffic arteries experience higher congestion levels. However, since the supermarket follows a "daily fresh" strategy for vegetables and transports them early in the morning when the roads are typically less congested, this specific scenario is not currently taken into account. On the other hand, most deliveries of other supermarket commodities occur during the day, often resulting in late-night arrivals due to road congestion. To analyze the observed data, two peak congestion time periods (8:00 am and 6:00 pm) and two off-peak time periods (12:00 noon and 8:00 pm) were selected for observation and analysis.
A
The observed data reveal that during peak hours, the road network in Beijing experiences significant congestion, primarily concentrated in the sections of the Second Ring Road and Third Ring Road with high congestion probabilities. The southern part of Beijing generally has lower congestion probabilities compared to the northern region. Specifically, the West 3rd Ring Road, West 2nd Ring Road, East 2nd Ring Road, East 3rd Ring Road, and East 4th Ring Road exhibit more severe congestion. Figure 5 provides a visual representation of the road conditions in Beijing during peak hours, illustrating the areas of congestion. During off-peak hours, the likelihood of road congestion in Beijing decreases. However, there is still some congestion in the eastern part of the city, particularly on the East 2nd Ring Road and East 3rd Ring Road, which experience more severe congestion compared to other areas. Figure 6 depicts the road conditions in Beijing during off-peak hours, with red indicating severe congestion, yellow indicating general congestion, and green indicating smooth traffic flow.Fig. 5
Road conditions in Beijing during peak hours. (AnyLogic software (version 8.8.6) is used for plotting this figure; URL: The AnyLogic Company, https://www.anylogic.com)
Figure 6. Road conditions in Beijing during off-peak hours. (AnyLogic software (version 8.8.6) is used for plotting this figure; URL: The AnyLogic Company, https://www.anylogic.com)
Based on the obtained data, the road sections were classified into eight categories, such as the second ring, the third ring, and the fourth ring. The locations were selected from Baidu Map, and the passing times were recorded under congestion and smooth traffic conditions, respectively, and then the distance between two points was divided by the passing time (in hours) to obtain a comparison table of road speed under different traffic patterns, as shown in Table 3.
Road section | Open (km/h) | Congestion (km/h) |
|---|---|---|
Second ring | 55 | 20 |
Three rings | 85 | 25 |
Four rings | 90 | 35 |
Five rings | 95 | 45 |
Within the second ring | 38.16 | 13.88 |
Second to third ring | 40.11 | 19.34 |
Third ring to fourth ring | 45.19 | 21.30 |
Fourth ring to fifth ring | 44.97 | 25.85 |
4.2. Simulation results
After inputting the case data into the simulation system, the feasibility of the model was validated by comparing the number of transportation vehicles passing through major road sections during peak hours, both before and after applying the improved model. Additionally, the rationality of the simulation model was further confirmed. The results indicate a significant difference in transportation outcomes depending on whether road sections with high congestion probabilities are bypassed during peak hours.
4.2.1. Comparative results of the number of transportation vehicle passes on congested roadways
After running the model 150 times (i.e., generating 150 orders), major road sections during peak hours were selected to compare the number of passing transport vehicles before and after considering the congestion probability (Table 4).
Road segment classification | Specific road sections | Before | After | Difference |
|---|---|---|---|---|
Second ring | Guangqumen bridge - Dongbimen bridge | 6 | 2 | -4 |
Yuetan south bridge – Fuchengmen bridge | 22 | 6 | -16 | |
Bell tower north bridge - Gulou bridge | 12 | 1 | -11 | |
Three rings | Madian-Sun palace bridge | 15 | 0 | -15 |
Guomao-Shuangjingqiao | 30 | 1 | -29 | |
Four rings | Siyuan Bridge - Wanghe bridge | 3 | 8 | 5 |
Sifang Bridge - Dajiuting bridge | 1 | 17 | 16 | |
Five rings | Yangshan Bridge - Shangqing bridge | 8 | 22 | 14 |
Within the second ring | Dongsijiao - Chaoyangmen | 5 | 0 | 0 |
Second to third ring | Caeduoying-Yuzhanying | 20 | 2 | -18 |
Third ring to fourth ring | Aero-bridge-Dinghui bridge | 3 | 0 | -3 |
As shown in Table 4, the number of uses decreases for road sections with high congestion probability after considering road congestion. When vehicles are transported during peak hours, avoiding the road sections with higher congestion probability can improve transportation time efficiency.
4.2.2. Comparative results of transportation time for congested road sections
To assess the effectiveness of the simulation model in real transportation scenarios, let's take the example of "Xinfadi Logistics Center to Wu-Mart Supermarket (Zhengyi Road store)". We will calculate the time taken for both the original route and the optimized route during peak hours, and perform a comparative analysis.
Figure 7 displays the original route from Xinfadi Logistics Center to Wu-Mart Supermarket (Zhengyi Road Store). The original route comprises the following segments: Logistics Center - Xinfadi Bridge - Jingkai Expressway - Caihuying Bridge - West Second Ring Road - Tianning Temple - Xuanwumen West Street - Xuanwumen East Street - Qianmen West Street - Qianmen East Street - Wu-Mart Supermarket. However, this route encounters congestion probabilities at "Caiduying - West Second Ring Road" and "Tianning Temple to Xuanwumen West Street". The entire journey along the original route takes approximately 33 minutes.
Fig. 7
Original route from Xinfadi Logistics center to Wu-Mart supermarket (Zhengyi Road store). (AnyLogic software (version 8.8.6) is used for plotting this figure; URL: The AnyLogic Company, https://www.anylogic.com)
Figure 8 depicts the optimized route from Xinfadi Logistics Center to Wu-Mart Supermarket (Zhengyi Road Store). The optimized route is as follows: Logistics Center - Xinfadi Bridge - Jingkai Expressway - Jingkai Auxiliary Road - South Third Ring Road West Auxiliary Road - Majiapu East Road - Taiping Street - Beiwei Road - Wanming Road - Zhushikou West Street - Zhushikou East Street - Qianmen East Road - Qianmen East Street Auxiliary Road. This optimized route avoids the congested sections during rush hours, specifically bypassing the "Caiduoying - West Second Ring" and "Tianning Temple to Xuanwumen West Street" road sections. By taking the optimized route, the journey time is reduced to only 26 minutes. This indicates a significant improvement in transportation efficiency and time savings compared to the original route.
Fig. 8
Optimized route from Xinfadi Logistics center to Wu-Mart supermarket (Zhengyi Road store). (AnyLogic software (version 8.8.6) is used for plotting this figure; URL: The AnyLogic Company, https://www.anylogic.com)
The comparative analysis shows that using the simulation model that takes into account the probability of congestion, the supplier's supply route avoids congested roads, and the transportation time efficiency is improved. To better illustrate the time savings achieved by the optimized routes, Table 5 compares the original and optimized transportation times for key congested road sections during peak hours.
Route segment | Original time (min) | Optimized time (min) | Time saved (min) | Congestion avoided |
|---|---|---|---|---|
Caiduying - West Second Ring road | 12 | 5 | 7 | Yes (rerouted via Jingkai auxiliary road) |
Tianning Temple - Xuanwumen west street | 8 | 3 | 5 | Yes (rerouted via Taiping street) |
Xuanwumen East St. - Qianmen west street | 6 | 6 | 0 | No (no congestion detected) |
Total (Xinfadi → Zhengyi Road store) | 33 | 26 | 7 | 2 congested sections bypassed |
4.2.3. Statistical results of supply paths during peak hours
Figure 9 illustrates the supply path of transportation vehicles departing from Xinfadi Logistics Center during peak hours. The bubble diagram represents the frequency of vehicles passing through each node after departure. Analysis of the diagram reveals that during peak hours, the transport vehicles from Xinfadi Logistics Center frequently pass through nodes such as Fengke Road, Fengbei Bridge, and Yuezhuang. The chosen supply path involves entering the city via the fourth ring road, thereby avoiding the congested section of the third ring road, and reaching the designated demand points. This optimized route selection allows for smoother transportation and more efficient delivery during peak hours, enhancing overall logistics operations.
Figure 9. Vehicle transportation route map of Xinfadi logistics center in the peak section. (AnyLogic software (version 8.8.6) is used for plotting this figure; URL: The AnyLogic Company, https://www.anylogic.com)
Figure 10 presents the supply path of transport vehicles departing from Majuqiao DC depot during non-peak hours. Bubble diagrams are used to display the frequency of vehicles passing through each node after departure. The analysis of the diagram reveals that transport vehicles from Majuqiao DC depot predominantly pass through nodes such as Majuqiao, Dayangfang Road, and Dahongmen Bridge. The departure route involves leaving Majuqiao, traversing the Beijing-Shanghai Expressway, and eventually arriving at the fifth ring road. From there, the vehicles continue along the fifth ring road until reaching the designated demand point. This optimized supply path during non-peak hours ensures smoother transportation and efficient delivery, contributing to the overall effectiveness of the logistics operations.
Fig. 10
Vehicle transportation route map of Majuqiao DC depot in the peak section. (AnyLogic software (version 8.8.6) is used for plotting this figure; URL: The AnyLogic Company, https://www.anylogic.com)
To quantify vehicle distribution patterns, Table 6 summarizes the frequency of node passes during peak hours for routes originating from Xinfadi Logistics Center and Majuqiao DC Depot.
Node | Xinfadi logistics center (pass count) | Majuqiao DC depot (pass count) | Role in route optimization |
|---|---|---|---|
Fengke road | 28 | - | Key bypass node for Fourth Ring road |
Fengbei bridge | 22 | - | Congestion-free alternative route |
Yuezhuang | 18 | - | Connects to demand points |
Majuqiao | - | 35 | Primary departure hub |
Dahongmen bridge | - | 27 | Links to Fifth Ring road |
4.2.4. Statistical Results of Supply Paths during Non-peak Hours
Figure 11 displays the supply path of transport vehicles departing from Xinfadi Logistics Center during non-peak hours. The bubble diagram illustrates the frequency of vehicles passing through each node after departure. Analysis of the diagram reveals that during off-peak hours, the transport vehicles from Xinfadi Logistics Center frequently pass through nodes such as Fengke Road, Fengbei Bridge, and Yuezhuang. The chosen supply path involves delivering along the fourth ring road and the third ring road. It can be observed that the number of times each node is passed by the vehicles is relatively more evenly distributed compared to other routes. This balanced distribution of vehicle frequency indicates efficient utilization of the road network during non-peak hours, allowing for smoother transportation and timely deliveries.
Fig. 11
Off-peak section of the Xinfadi logistics center vehicle transportation path map. (AnyLogic software (version 8.8.6) is used for plotting this figure; URL: The AnyLogic Company, https://www.anylogic.com)
Figure 12 illustrates the supply path of transportation vehicles departing from the Majuqiao DC depot during non-peak hours. The bubble diagram represents the frequency of vehicles passing through each node after departure. Analysis of the diagram reveals that when the vehicles are transported from the Majuqiao DC depot, they primarily pass through nodes such as the Majuqiao and the Dahongmen Bridge. The transportation vehicles depart from Majuqiao, proceed along the Beijing-Shanghai Expressway, and eventually arrive at the fifth ring road. The majority of the transportation and distribution activities occur along the fifth ring road, while other ring roads have comparatively less transportation volume. This supply path optimization allows for streamlined operations, ensuring efficient delivery and minimizing congestion during non-peak hours.
Fig. 12
Off-peak section Majuqiao DC depot vehicle transportation path map. (AnyLogic software (version 8.8.6) is used for plotting this figure; URL: The AnyLogic Company, https://www.anylogic.com)
Table 7 contrasts node usage between peak and off-peak hours to highlight the model’s adaptability.
Node | Peak hours (pass count) | Off-peak hours (pass count) | Change (%) | Reason for change |
|---|---|---|---|---|
Fengke road | 28 | 15 | -46.40% | Reduced need for bypass routes |
Yuezhuang | 18 | 22 | 22.20% | More direct paths are available |
Majuqiao | 35 | 40 | 14.30% | Increased use of shorter routes |
Dahongmen bridge | 27 | 20 | -25.90% | Less reliance on the Fifth Ring road |
4.2.5. Comparison of transport routes in two cases
To further evaluate the effectiveness of the proposed model, a detailed comparison of transport routes was conducted during both peak and off-peak hours. The key findings are summarized in Table 8, followed by a specific analysis.
Aspect | Peak hours | Off-peak hours |
|---|---|---|
Route selection | Avoids congested roads (e.g., Second and Third Ring roads); prefers Fourth and Fifth Ring roads. | Utilizes closer routes (e.g., East Third Ring, West Third Ring) due to smoother traffic. |
Congestion avoidance | Actively bypasses high-congestion sections (e.g., Guangqumen bridge, Yuetan south bridge). | Less emphasis on congestion avoidance; routes are more direct. |
Transport efficiency | Longer routes to avoid congestion, but significantly reduce travel time (e.g., 26 min vs. 33 min). | Shorter routes with minimal delays; balanced node distribution. |
Node frequency | Higher frequency at nodes like Fengke road, Fengbei bridge, and Yuezhuang. | More evenly distributed node usage (e.g., Majuqiao, Dahongmen bridge). |
Case example | Xinfadi logistics center to Wu-Mart (Zhengyi Road store): Optimized route saves 7 minutes. | Majuqiao DC depot: Efficient use of Fifth Ring road for faster deliveries. |
During both peak and off-peak hours, it is observed that transport routes tend to avoid the heavily congested second and third ring roads. Instead, the routes predominantly utilize the fourth, fifth, and sixth ring roads. This shift in route selection helps mitigate congestion issues and ensures smoother transportation operations. During off-peak hours, when the road network experiences smoother traffic flow, transport vehicles tend to choose routes from the East Third Ring, East Fifth Ring, and West Third Ring, which are closer and provide more efficient transportation. In summary, the utilization of the system simulation model, incorporating congestion probability, has successfully simulated and verified the supplier's supply path selection for Beijing Grocery Stores. Comparative analysis reveals that transportation vehicles adapt their routes based on prevailing road conditions, resulting in improved efficiency. These findings support the feasibility of the constructed system simulation model.
5. Discussion
The results confirm the feasibility of using AnyLogic software to establish a simulation model for a supplier's urban supply path selection based on congestion probability, which can avoid congestion points and select the optimal path at the right time. The results confirm the importance of introducing congestion probability in the model for optimizing supplier paths. The transportation paths selected after considering the congestion probability are more optimal, using shorter transportation time and improving the transportation efficiency, which is significant for reducing carbon emissions and improving the urban environment. With the government's increasing demand for environmental protection and sustainable development, people's awareness of saving energy and reducing carbon emissions continues to grow. It is feasible to consider the probability of congestion in the selection of supply paths for urban suppliers, with similar results obtained in previous studies. Fang et al.40 introduced energy saving and emission reduction into the cold chain logistics path optimization problem, and the total cost of distribution was reduced by 15.9% and 8% after the optimization compared to the pre-optimization. Zhao et al.14 proposed GVRP for multi-vehicle logistics and distribution vehicles considering traffic congested areas from a green perspective in order to address the problem of reducing carbon emissions generated in the logistics and distribution process. Through experimental simulation, to verified that the total cost of the green vehicle path considering the congested region of the multi-model vehicle is reduced by 1.5%, and the cost of fuel consumption and carbon emissions is reduced by 4.3%. This improves the economic efficiency of logistics enterprises and also promotes energy saving and emission reduction.
With the continuous promotion of the concept of sustainable development, green logistics has become a trend for the future development of the logistics industry. This work introduces the congestion probability into the model to find out the vehicle scheduling and path optimization model that satisfies the customer's cargo demand and time window requirements, with the consideration of transportation cost.
In order to verify the effectiveness of the model, this paper adopts examples to carry out simulation verification and quantitative analysis of the simulation results. The results show that our model is effective. The model can provide methodological support for logistics enterprises to scientifically plan a transportation path selection scheme. At the same time, it provides a good reference for enterprises to develop green logistics.
In this paper, we study the supplier's urban supply path selection problem considering the congestion probability, and the constructed model is closer to the actual distribution environment. However, many problems have not been well considered and need to be further improved. In terms of model construction, this paper only studies the distribution vehicle path optimization problem under a single distribution center, without considering the case of multiple distribution centers. However, enterprises always set up multiple distribution centers in order to improve distribution efficiency. Therefore, the problem of multi-vehicle co-distribution and multi-distribution centers should be fully considered in future research.
The objective function of this work considers the minimization of transportation time while ignoring the economic and environmental cost of replacement route selection. Fuel consumption is also an important factor that affects the transportation cost and leads to environmental pollution. In future research, the economic cost and environmental cost of suppliers' fuel consumption in distribution are considered to be introduced into the model, which is of practical significance.
6. Conclusion
With the growing emphasis on energy conservation and emission reduction in the transportation sector, the environmental impact of non-green factors, such as fuel consumption and carbon emissions, has become increasingly prominent. Urban road congestion not only prolongs transit times for transport vehicles but also reduces the quality of delivered goods and service efficiency, increases the risk of cargo damage, and leads to higher energy consumption. These challenges underscore the importance of incorporating road congestion considerations into the selection of urban supply routes for suppliers.
This study introduces a method for integrating congestion factors into the supplier city supply path selection process. The classical Dijkstra algorithm is enhanced by incorporating real-time traffic conditions across different time periods and assigning congestion probabilities to individual road segments. Utilizing the AnyLogic simulation platform, a congestion-aware supply path selection model is developed for urban logistics scenarios. The model is validated through simulations using the supply network of Wu-Mart supermarkets in Beijing as a case study.
Based on Beijing’s urban road network, congestion probabilities for key road segments are calculated for various time periods. These probabilities are then used to simulate and evaluate supply path selection for grocery store suppliers during both peak and off-peak hours. The simulation results confirm that the proposed model enables suppliers to identify optimal distribution routes that effectively circumvent congested areas. The enhanced Dijkstra algorithm, which incorporates congestion probabilities, produces superior optimization outcomes compared to traditional approaches.
The supplier urban supply path selection model, constructed using the AnyLogic simulation platform and incorporating congestion probabilities, enables transport vehicles to dynamically select optimal routes based on real-time road conditions. This contributes to improved service efficiency, fulfillment of customer demands, reduced transportation costs, and lower carbon emissions, thereby promoting environmental sustainability.
A
Data Availability
The data presented in this study are available on request from the corresponding author due to the data are not publicly available due to privacy or ethical restrictions.
The data presented in this study are available on request from the corresponding author due to the data are not publicly available due to privacy or ethical restrictions.
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Author Contribution
J. G.: Writing – original draft, Methodology, Formal analysis, Visualization; X. L.: Writing – review & editing, Investigation, Visualization; M. K. H.: Writing – review & editing, Data curation; M. C.: Writing – review & editing, Supervision, Resources. All authors reviewed the manuscript.
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Funding
This research was funded by the University-level Research Project of Hebei University of Environmental Engineering, grant number [XJXM-QN-2024006]; Bureau of Science and Technology of Qinhuangdao, grant number [202301A376].
Competing interests
The authors declare no competing interests.