Abstract
This paper proposes a mixed decision strategy for freight and passenger transportation in metro systems during offpeak hours (MTSOPH). The definition of the mixed decision strategy is proposed, and fixed and flexible loading modes are considered for different passenger flow volumes. A mathematical model of the MTSOPH is proposed and solved using an improved variable neighborhood search algorithm. Case studies demonstrate the performance and applicability of the proposed model and algorithm, and the MTSOPH is discussed for different delivery distances, passenger flows, and metro network types. The proposed strategy is suitable for longdistance delivery, and the proposed model framework can be applied to different types of metro networks with different levels of complexity. The mixed decision strategy provides a decision support tool for metro and freight companies and can propose corresponding solutions according to different passenger flows.
1. Introduction
With the continuous development of ecommerce and home deliveries, urban freight transport has emerged as a key link in urban economic and social development [1, 2]. Road transportation is the primary mode for urban freight transportation [3], and 85–90% of freight is transported by road in France [4]. However, the freight transportation by vehicles poses a series of problems pertaining to urban traffic congestion, greenhouse gas emissions, and noise. Urban freight accounts for 10% of total transportation, but it accounts for 40% of urban pollutant emissions [5]. Therefore, optimizing the transportation structure, strengthening the cooperation of different transportation modes, promoting the organic connection between intercity trunk transportation and cityend distribution [6], and encouraging the development of intensive distribution models are of great significance for creating a green and efficient logistics system.
As mentioned above, the freight transportation needs to change towards more efficient and sustainable transportation systems to cope with increasing demand for freight transportation in urban areas. The metro has the advantages of high efficiency, large capacity, and sustainability, but most metro networks suffer from insufficient utilization of metro trains due to the low passenger flow during offpeak hours [7]. Therefore, introducing goods into the metro network during offpeak hours is a very potential way of freight [8]. The present mixed transport strategy for freight and passenger transportation in metro systems is usually by subjective experience [9], lacking reasonable theoretical framework and mathematical formulation. Furthermore, the entire metro network should be considered to deal with the freight, rather than a single metro line [10]. Therefore, a general theoretical framework and model for constructing the mixed passenger and freight transportation strategy on the metro network during offpeak hours are indispensable.
The purpose of this study is to combine the existing metro network with the first and lastmile delivery services operated by logistics companies and propose a feasible passenger and freight flow mixed transport strategy for metros during offpeak hours (MTSOPH). The paper considers fixed and flexible loading modes under different passenger flows and analyzes different cargo characteristics and delivery time requirements. A model for quantitatively evaluating the mixed transportation strategy is established, and an improved variable neighborhood search (VNS) algorithm is designed. They are then applied to the cargo transportation of Ningbo and Beijing metro networks, respectively, and the mixed transportation strategy under different delivery distances, passenger flows, and metro network types is analyzed. The model and method can also be applied to the metro network of other rail transit cities.
The remainder of this paper is organized as follows: Section 2 reviews related research on metro mixed transportation. Section 3 formulates a nonlinear programing model of the MTSOPH, and then, an improved VNS algorithm is designed to solve the proposed model in Section 4. Subsequently, two case studies are implemented to verify the proposed model in Section 5. In Section 6, the conclusions of the study and scope for future research are presented.
2. Literature Review
2.1. Urban Freight and Passenger Transportation
Nash [11] first proposed the use of urban public transportation for freight transportation. Later, based on the concept of sharing, Trentini et al. [12] proposed to introduce urban freight transportation into passenger transportation to achieve the purpose of sharing transportation resources and transportation infrastructure. On this basis, the flow of urban freight and passenger transport was quantified, and a new urban transport system for passenger and freight was constructed and implemented in La Rochelle, France [13]. GonzalezFeliu [14] used a socioeconomic costbenefit analysis to assess the applicability of tram freight transport in the Paris region. The study showed the potential of the tram freight transport mode. Fatnassi et al. [15] integrated personal rapid transportation and freight rapid transportation modes and used electric vehicles to achieve mixed passenger and freight transportation on automatic rails. Masson et al. [16] proposed a hybrid freight method based on the integration of passenger and freight systems to solve mixed urban traffic problems. This method used buses to transport goods from the central distribution center to the transfer point and then used a tricycle to transport the goods from the transfer point to the destination.
There are some successful cases of urban passenger and freight transportation. In Dresden, the tram line from the Volkswagen warehouse to the city center can transport 300,000 tons of goods a year, 10 times a day, which significantly reduces carbon dioxide emissions [17]. In Paris, the commuter line D transports household goods, leisure products, and other goods from the MONOPRIX warehouse (CombslaVille and Lieusaint) on the outskirts of Paris to the Bercy station [18]. These goods are then transported to stores through trucks that use natural gas vehicle fuel to satisfy the emission reduction principles along the logistics line. In New York, subway waste is collected through stations using modified metro trains [19]. However, most of the existing research on mixed transportation modes is based on road and railway transportation. These above studies can be applied into the mixed freight and passenger transportation in the metro system. Since the operation mode, transportation efficiency, and transportation timeliness of metro are different from railways, the mixed transportation of freight and passenger transportation in the metro systems needs further research.
2.2. Urban Freight and Passenger Transportation in Metro Systems
The feasibility and application prospects of urban metro freight have been studied in a few research papers. Rijsenbrij and Pielage [20] discussed the feasibility of using the metro for mixed passenger and freight transportation, which gained the attention of national and international scholars on metro freight transportation. Kikuta et al. [9] conducted a test study on the combination of the public metro service and conventional truck operation to prove the feasibility of this mode of transportation. For the metro distribution service, Motraghi and Marinov [21] collaborated with the Newcastle metro network to theoretically analyze urban freight transportation. However, further research is required before actual implementation of their findings. The above research made some explorations on the mixed transportation of freight and passengers in metro systems but did not establish an implementation ability and systematism theory framework. Therefore, a general mixed transportation theoretical framework in the metro systems should be designed to realize the freight and passenger mixed transportation strategy.
In addition, a few studies focused on metro freight. Brice et al. [22] reported a baggage transfer system to facilitate passengers transporting luggage from Newcastle city center to Newcastle International Airport via the metro. They proved the feasibility of the new baggage transfer solution and reported that the corresponding cost is higher than that of the existing service. Ghilas et al. [23] found that integrated freight and scheduled line services can potentially reduce the operating costs of logistics service providers and the public transportation sector can obtain additional revenue. However, the existing mixed transportation models are established based on a single metro line. Considering the different directions of goods circulation, existing models cannot accurately describe the mixed transport strategy in metro systems. Therefore, a mixed transportation model on the metro network should be established to realize the circulation of goods.
2.3. Optimization Method of Urban Freight and Passenger Transportation
Location and route selection have long been the significant issues in the freight and passenger transportation domain. Fatnassi et al. [15] proposed two mathematical formulas to solve the vehicle route between stations and used dynamic optimization methods and developed algorithms to solve the shared transportation of goods and passengers. Zhao et al. [24] proposed a segmentation method of urban metro network, using complex network theory and the TOPSIS model to determine the candidate metro distribution hubs for the location model. Dong et al. [25] analyzed the characteristics of underground cargo capacity and established a mixed integer programing model to select the location of metro distribution hubs. However, the limitation of the frequency of goods transfer in the metro network is barely considered in these studies.
Likewise, time window constraint is a critical issue along with the rapid increase in freight demand during recent years. Behiri et al. [8] studied an environmentfriendly urban freight transportation alternative using a passenger railway network and proposed a heuristic based on dispatching rules and a singletrainbased decomposition heuristic to solve the FreightRailTransportScheduling Problem. Yang et al. [26] studied the vehicle routing problem with mixed backhauls and time windows for city logistics, and the timedependent pickups and deliveries can be depicted by extending the state dimensions. However, freight transportation in the passenger transportation system focuses on the study of the cargo time window, ignoring the impact on the normal operation time window of the passenger transportation system.
In addition, the development of solving algorithms has attracted the attention of researchers and practitioners. Bräysy [27] introduced the internal design of variable neighborhood descent and variable neighborhood search algorithms in detail, analyzed the vehicle routing problem with time windows problem, and pointed out that the variable neighborhood search algorithm is one of the most effective methods to solve the vehicle routing problem with time windows problem. de Armas and MeliánBatista [28] studied a dynamic rich vehicle routing problem with time windows and proposed a metaheuristic algorithm based on variable neighborhood search to solve this problem. However, the stability and reliability of the calculation results need to be strengthened. Therefore, we design two types of neighborhood structures to obtain highquality solutions.
2.4. Contribution
The main contributions of this study are summarized as follows:(i)We propose a general theoretical framework of MTSOPH. This framework includes new concept and transportation standards of MTSOPH. This definition clarifies the process and applicable time of mixed transportation. Relative to previous study on the types of mixed transportation goods [13, 29], MTSOPH further explored the types of goods suitable for mixed transportation on the basis of transporting small goods. The mixed transportation standard of separate loading of passengers and cargo and priority transportation of passenger flow is established. Furthermore, fixed and flexible cargo loading modes are proposed according to different offpeak passenger flows.(ii)We formulate a nonlinear programing model for the MTSOPH. Based on the research of Fatnassi et al. [15] and Zhao et al. [30], our model improves the mixed transportation strategy research to a mixed transportation strategy research under load rates of passenger flow during offpeak hours. To the best of our knowledge, this is the first time that the problem of mixed passenger and freight transportation under different passenger flows has been addressed in the context of metro transportation during offpeak hours. Moreover, an improved VNS algorithm is designed to solve the model, which provides a decision support tool for logistics companies.(iii)We presented the real case study of the Ningbo and Beijing metro network to verify the practicality and efficiency of the proposed model. The applicability of the model is discussed from the distribution distance, offpeak passenger flow, and metro network type. Our results show that the proposed model can be applied to different metro networks. Furthermore, the mixed transportation mode in the metro systems has the advantages of high speed, high punctuality, low economic investment, low environmental impact, and low energy consumption [31–33].
3. Mathematical Formulation
This section provides a detailed description of the MTSOPH, analyzes the types of goods suitable for mixed transportation, and provides different mixed transportation methods based on different load rates of passenger flow during offpeak hours. Finally, a nonlinear programing model of a mixed transportation strategy is constructed.
3.1. Description of MTSOPH
MTSOPH integrates the existing urban metro network with the first and lastmile delivery services operated by logistics firms. The key aspect of this strategy is to transport goods and passengers together without affecting the metro passenger flow. Thus, the transportation standard of separate loading of passengers and cargo and priority transportation of passenger flow should be considered. First, metro train carriages are divided into passenger carriages and freight carriages, similar to the passenger carriages and female carriages set in the Shenzhen metro trains in China [34]. Different types of carriages are set with boundary lines and dedicated passages to divide the passenger and freight flows, as shown in Figure 1. To minimize the impact of cargo flow on passengers, we introduce relevant constraints on the types of cargo used for mixed transportation. For ease of operation, all goods are placed in a samesize freight box as freight parcels. Concurrently, small cargo packages should be selected for metro mixed transportation. A similar conclusion has been reported in related studies on bus freight [13] and metro freight [9, 29]. Thus, goods in the freight parcel should be small goods, such as documents, books, clothing, and small mechanical parts, rather than fresh goods that need to be frozen and kept fresh, which are not affected by time and the environment, in order to maintain the metro carriage environment tidy.
Second, to satisfy the passenger flow priority transportation standard without changing the headway and stop time of metro trains during offpeak hours, this study proposes different mixed transportation methods based on different load rates of passenger flow during offpeak hours. When the number of passengers and freight demand is greater than the metro capacity, each train adopts a mixed passenger and cargo transportation mode during offpeak hours, as shown in Method 1 (i.e., fixed loading mode) in Figure 2. When the number of passengers and freight demand is less than the metro capacity, one of every two trains is selected to employ the mixed transportation mode while the other train is used for passenger transportation, as shown in Method 2 (i.e., flexibility loading mode) in Figure 2. In Figure 2, represents the headway of metro trains during offpeak hours.
In summary, MTSOPH is a transportation strategy based on the aforementioned mixed transportation standard, which satisfies the optimal distribution cost of the cargo flow under the condition of determining the origin and terminal stations of the goods. The transportation strategy is to use the metro passenger transportation network, which is composed of cargo distribution centers, metro stations, terminal cargo stations, metro trains, and freight vehicles, as shown in Figure 3.
In Figure 3, the operation process of MTSOPH is divided into five stages. The first and fifth stages are vehicle delivery, second and fourth stages are manual transshipments, which transfer cargo from the vehicle to metro carriage, and third stage is metro delivery. The transfer of goods between each stage is completed by trolley.
In the first stage, the cargo is packed in freight parcels, placed in freight boxes, loaded onto transportation vehicles, and delivered to the departure metro station via freight vehicles. Then, the freight boxes are unloaded from the vehicle and loaded on the trolley. In the second stage, the freight boxes are transported to the metro platform via trolleys and transported to the metro freight carriage when the train enters the platform. In the third stage, freight boxes are transported on the metro network (transfers are performed via trolleys). Here, the train operation mode is from the first station to the last station regardless of the train service route. The freight boxes enter the fourth stage after being transported via the metro train. The freight boxes are unloaded from the metro freight carriage and transported via trolleys to the arrival metro station. In the last stage, the freight boxes are loaded onto the freight vehicle and transported to the corresponding terminal cargo station. All the aforementioned stages constitute the MTSOPH operation process, while the third stage of the operation period in MTSOPH is the offpeak hours of metro operation.
3.2. Assumptions and Notations
The MTSOPH model can be described as the process of delivering multiple freight stations from a cargo distribution center with the optimal delivery cost as the goal. The number of terminal cargo stations is determined, but the freight stations are located in different geographical locations. All transportation paths are based on the actual shortest distance of the road network or metro network. Thus, certain assumptions have been considered as follows:(i)The freight is placed in a standardized unit parcel to measure the arrival demand of the terminal cargo stations.(ii)There is no storage function at the metro exit station, and freight vehicles are arranged for delivery immediately after the cargo arrives at the metro exit station.(iii)The freight vehicles used for transportation are of the same model with the same fuel consumption and load capacity.(iv)The freight vehicles run at a uniform velocity without consideration of the road conditions. Furthermore, after the freight is transported, the vehicles are not required to return to the cargo distribution center or arrival metro stations.(v)Up to two freight transfers occur in the urban metro network.
Table 1 summarizes the notations used throughout the paper.
3.3. System Constraints
3.3.1. Number of Freight Carriages Constraints
Equation (1) determines the number of freight carriages ((x) represents the smallest integer greater than x).
3.3.2. Freight Loading Mode Constraints
The freight loading mode is selected by Equation (2). Among them, is a fixed loading mode; that is, each train uses a mixed passenger and freight transportation mode during offpeak hours; is a flexible loading mode; that is, one of every two trains chooses to use a mixed transportation mode and the other for passenger transportation.
3.3.3. Vehicle Line Capacity Constraints
Vehicles in the “first mile and lastmile” distribution network should meet vehicle capacity constraints, vehicle number constraints, and line capacity constraints.
Equation (3) assigns a unique route for each vehicle from the cargo distribution center to the departure metro station. Equation (4) imposes the restriction that each vehicle can have one unique route from one arrival metro station to one terminal cargo station in the third stage. Equation (5) constrains the capacity on the route. The total number of vehicles in the complete distribution process should be restrained, as shown in Equation (6).
3.3.4. Metro Line Capacity Constraints
The goods in the metro network by train should meet the train capacity constraint and the number of transfer constraints.
Equation (7) expresses the capacity limit of the metro. Equation (8) stipulates the number of transfers in the metro network.
3.3.5. Delivery Time Constraint
The mixed transportation is based on the offpeak hours of urban rail transit, and the departure time of mixed transportation trains shall not be earlier than the start time of offpeak hours.
Equation (9) determines the earliest time when the freight to cargo station is loaded into the train at a station. In this equation, represents the running time between S and S − 1 when the train is at station S, and when , . Equation (10) ensures the time to start delivery for the terminal cargo station. Equation (11) is the time window constraint of the terminal cargo station.
The delivery time of the train in the whole mixed transportation process meets the sum of the delivery time of the “first mile and lastmile” and the metro delivery time.
Equation (12) addresses the relationship between the start time and end time of delivery from the cargo distribution center to the terminal cargo station.
The delay cost coefficient is affected by the delivery time window of the goods. Failure to complete the delivery within the time window needs to calculate the delay cost based on the delay cost coefficient.
Equation (13) addresses the delay cost due to the failure to complete the delivery within the time window; the delay cost is related to the time of completion of the delivery.
3.3.6. Decision Variable Constraints
The relevant decision variables are constrained as follows. Equation (14) expresses the constraint on the initial number of vehicles.
3.4. Composition of the Objective Function
The objective function of MTSOPH is composed of vehicle transportation cost, transfer cost, and delay cost. Each cost parameter is described in the following.
3.4.1. Vehicle Transportation Cost
The transportation cost of vehicles is mainly composed of the transportation distance, number of vehicles, number of freight parcels, and fixed operating cost of vehicles. Therefore, the transportation cost in route () is as shown in
To express clearly, Equation (19) is simplified as
Therefore, the vehicle transportation cost in the route () can be obtained similarly.
In summary, Equation (23) represents the vehicle transportation cost.
3.4.2. Transfer Cost
The number of freight parcels and frequency of transfer constitute the transit cost. The number of transfers is mainly determined by the number of times the cargo is loaded and unloaded; the completion of one loading and unloading of cargo is regarded as one transfer. Equation (24) shows the calculation method for the node transfer cost .
3.4.3. Delay Cost
The delay cost is caused by the freight arriving at the terminal cargo station in an unexpected time window. The delivery time window of MTSOPH is based on the offpeak start time, so the delay cost will only be calculated if the delivery time window is exceeded. This is expressed with , as in
Because only part of the metro carriages is used for freight, the weight of the cargo is much smaller than that of the metro. Therefore, the delivery cost of MTSOPH is not affected by metro fixed operating cost and metro transportation distance.
In summary, the delivery cost is the sum of the vehicle transportation cost , node transit cost , and delay cost , i.e., . Hence, the mathematical formulation of the MTSOPH model is built as follows:
Equation (26) denotes the smallest delivery cost, and the calculation process is, respectively, performed using Equations (19)–(25).
In the MTSOPH model, the pickup and delivery constraints of the time window and transshipment value are considered [8, 35, 36] and the mode selection constraints are added according to the two loading modes of the proposed mixed transport strategy. This model is developed based on the generalized assignment problem, which belongs to a NPhard problem [37–39] and is usually solved by heuristic algorithms.
4. Solution Approaches
The heuristic algorithm for solving the MTSOPH is based on the VNS [40, 41]. VNS provides a flexible framework for constructing heuristics for approximately solving combinatorial optimization problems and nonlinear optimization problems. The main idea is to dynamically change the neighborhood structure set during the search process to expand the search range and obtain local optimal solutions. Using such a variable neighborhood strategy, it is possible to move away from the optimum and finally reach convergence after multiple iterations. In the VNS algorithm used in this study, the objective function (indicated by ) in Equation (8) is used as an evaluation index for evaluating the quality of the generated solution, as shown in the following:
In this study, the VNS algorithm includes the following three parts: initial solution, shaking process, and variable neighborhood descent (VND) process. We use to denote the solutions generated in the algorithm. represents the neighborhood structure set included in the shaking process, where , and represents the neighborhood structure set included in the VND process, where . The detailed structure of the improved VNS algorithm is shown in Algorithm 1.

The shaking process is a perturbation operator in the VNS. The process is used to generate different neighborhood solutions. The remaining initial solution and VND process are described in detail in the next section.
4.1. Initial Solution
The initial delivery route of the MTSOPH is formed by constructing a line of length according to the number of a terminal cargo station. The initial route is mainly composed of departure metro stations and arrival metro stations shown in Figure 4. Herein, each in corresponds to each in individually, and a group constitutes a metro distribution route. The following conditions should be met: .
4.2. Neighborhood Structure
Two types of neighborhood structures are applied. The first consists of neighbors which exchange strategies on existing delivery routes. The second consists of neighbors obtained by updating the distribution strategy on the existing route. The methods for generating neighbors for the first type of neighborhood structure are Swap2 and Insertingt [42]. For the second type of neighborhood structure, Altert method of producing neighbors is designed in our study.
Swap2 refers to the random exchange of two adjacent or nonadjacent rows in the initial solution, as shown in Figure 5(a). Insertiont is formed by repeating t times on the basis of Insertion1. As shown in Figure 5(b), Insertion1 randomly deletes a row from the initial solution and randomly inserts it into other positions. In Figure 5(c), Alter1 randomly selects a position in the initial solution and selects a new number from the set to replace . Altert is to repeat the Alter1 operation t times. In addition, to prevent the value of t from being too large and destroying the stability of the obtained solution structure, the value of t is controlled to be in the range of [0, 5] in the insertion operation and change operation of this study. The iterations of repeated deletions, changes, and insertions let the algorithm search in a larger solution space, thereby enhancing the ability of the neighborhood search algorithm to move away from the local optimal region.
(a)
(b)
(c)
4.3. Shaking Procedure
We use G = {Alter−3, Alter−4} as the set of neighborhood structures in the shaking procedure. For each structure , it maps a given solution r to a series of neighborhoods . When the shaking procedure is applied, a solution will be randomly chosen from the neighborhoods. Accordingly, the detailed procedure is given in Algorithm 2.

4.4. Variable Neighborhood Descent
During a local search in VND, when a better solution than the current solution cannot be found in this neighborhood, the search is continued by moving to the next neighborhood solution. Contrarily, if a better solution than the current solution is found in this neighborhood, the first neighborhood solution will be returned to restart the search. For a better solution, the first neighborhood solution should be returned and the search should be started again. The local optimal solution obtained through such a search process is likely to be the global optimal solution. A detailed operation of the VND process is provided in Algorithm 3.

5. Numerical Experiments
Case studies of the Ningbo metro network and Beijing metro network were conducted to evaluate the accuracy and efficiency of the proposed model and method. Examples of the application in different delivery distances, different passenger flows, and different types of metro networks were illustrated. The proposed algorithm framework was coded in MATLAB 10.0 on a Window 10 personal computer with 4.0 GB processor. The MTSOPH problem is solved by IBM CPLEX 12.5 Academic Version on the same platform.
5.1. SmallScale Case Study
In this section, based on the logistics information of a certain express company in Ningbo, we considered a distribution situation between the express delivery distribution center and six terminal express delivery stations. For convenience, the cargo distribution center is represented by I and the six cargo stations are named A, B, C, D, E, and F, respectively, i.e., . The geographical location of freight stations is evenly distributed, and the receipt volume of each cargo station obeys the uniform distribution of [40, 60]. The metro network of the Ningbo Urban Rapid Rail Transit Construction Plan (2013−2020) [43] was considered as an example, as shown in Figure 6.
The airport logistics park near the metro line was selected as the express delivery distribution center, which is represented by a red star in Figure 6. L1−L5 indicate each metro line. Considering the actual situation and model solution, each metro line station was uniformly numbered according to positive integers from left to right, with the letter “I” representing the departure metro station and “O” representing the arrival metro station.
The average speed of freight vehicles was 20 km/h [30], and the delivery cost of unit express delivery per unit distance of freight vehicles was assumed to be 2 yuan [44]. The values of the other parameters are listed in Table 2. In the experiment, the distribution data and time window are shown in Table 3.
In the algorithm parameter setting process, this study sets the number of neighborhood solutions in one iteration to 100 and the total number of iterations to 50 [27]. The neighborhood structures of VND and shaking are as follows: VND, {Alter_3, Alter_5, Insertion_2, Insertion_1, Opt_2}; Shaking, {Alter_3, Alter_5}.
For related problems in route planning and distribution, the genetic algorithm (GA) is widely used [45–47]. Therefore, the GA and the improved VNS algorithm are used to solve the problem. The population size of the GA is 100, the number of iterations is 50, the crossover probability is 0.6, and the mutation probability is 0.1 [48]. The optimization results of the two algorithms were obtained by running 20 times, as shown in Table 4. Although GA has a shorter calculating time, VNS can obtain the best delivery cost of higher quality, and after many repeated trials, the results show that the stability of the optimal solution obtained by VNS is better than that of GA, which verifies the effectiveness of the algorithm.
In order to further prove the effectiveness of the improved VNS algorithm, we first give the actual maximum crosssection passenger flow to Equation (12), making MTSOPH an integer linear programing model. Secondly, the ILOG CPLEX solver is used to solve it. After implementations, we finally obtained the returned solution with a calculation time of 328 s, where the relative gap turns out to be 5.00%. The approximate optimal objective value is 5861.0 yuan, which is consistent with the solution result of the improved VNS algorithm. Therefore, the proposed algorithm is effective.
Finally, the optimal solution for the delivery of vehicles is calculated. Meanwhile, the optimal transportation strategy during offpeak hours for the individual distribution of freight vehicles is calculated; this transportation strategy is called VTSOPH. Table 5 shows the comparison between the MTSOPH and VTSOPH. The delivery time of VTS is mainly composed of two parts: loading and unloading time and transportation time. Among them, the loading and unloading time is determined according to the quantity of goods and the transportation time is determined by the transportation distance and the transportation speed. If the delivery time is less than 1 min, it is approximated to 1 min.
As evident from Table 5, the MTSOPH and VTSOPH complete deliveries within the time window. The average time to complete a delivery in the VTSOPH is 69 min, and in the MTSOPH, the average time is 73 min. However, the MTSOPH spends approximately onethird of the delivery cost of the VTSOPH to complete a delivery. According to this smallscale case analysis results, the MTSOPH has certain advantages when compared with the VTSOPH.
The delivery route is shown in Table 6, and the result shows that for the express station “F” delivery, the MTSOPH requires less time than the VTSOPH, and for the delivery of the other express stations, the VTSOPH requires less time than the MTSOPH. Therefore, further investigation is required regarding the applicability of the MTSOPH for different distances.
5.2. Applicability of MTSOPH considering Different Delivery Distances
To study the applicability of the MTSOPH for different delivery distances, we divide the actual express delivery information provided by the airport logistics park into three different distribution range data tables. The metro network of Ningbo is shown in Figure 7.
According to the metro network and express delivery information data, Ningbo is divided into three areas with different distribution scopes as S1, S2, and S3. Twenty delivery destinations (terminal express delivery stations) are selected with uniform locations in each area, as shown in Figure 8. Each delivery area is separated by a blue dotted line, where S1 is a shortdistance delivery area, S2 is a mediumdistance delivery area, and S3 is a longdistance delivery area. According to different distribution ranges, different time window requirements are allotted [44], as shown in Table 7.
In the experiment, the time horizon is considered to be 9:00−12:00, which is the offpeak period of metro operation. In addition, the metro model in Ningbo is type B composed of six carriages with a total capacity of 1,460 people. According to statistics from the Ningbo Rail Transit Group, the maximum load rate during offpeak hours in the Ningbo metro network is 90%. Hence, at least five metro carriages are required for passenger transportation during offpeak hours, and the remaining one carriage is used for goods transportation. The remaining parameter values and algorithm parameter settings are consistent with the smallscale case study presented in Section 5.1.
5.2.1. Analysis of the ShortDistance Delivery Area
The demand and time window of the terminal express station in S1 are listed in Table 8.
The data in Table 8 are used in the VNS algorithm for 20 calculations to obtain the optimal solution for the MTSOPH and VTSOPH, as shown in Table 9, and the optimal delivery routes of the two strategies are given in Table 10.
In Table 9, the delivery cost of the MTSOPH is approximately 66.4% higher than that of the VTSOPH. In addition, 12 of the 20 terminal express delivery stations in the MTSOPH failed to deliver on time, while the VTSOPH completed all deliveries with the set time window. In the shortdistance distribution area, the success rate of the MTSOPH to complete the delivery within the time window was 40%. However, the MTSOPH reduces the vehicle delivery distance by 56.7% when compared with that of the VTSOPH. Although the vehicle transportation distance is reduced, the delivery time is increased, as shown in Table 10. According to the above analysis, in the shortdistance delivery area, the MTSOPH is not suitable for multitarget delivery and the overall operation of express delivery companies, but the singletarget delivery remains to be studied. This corresponds well with the study of highspeed railway freight distribution by Pazour et al. [49].
5.2.2. Analysis of the MediumDistance Delivery Area
The demand and time window of the terminal express station in S2 are listed in Table 11.
Similarly, the data in Table 11 are used in the VNS algorithm for 20 calculations, and the optimal solution is listed in Table 12.
As shown in Table 12, the delivery cost of the VTSOPH is 8.0% higher than that of the MTSOPH, but the average delivery time of the VTSOPH is 33.7% less than that of the MTSOPH. In addition, the specific delivery time, delivery route, transfer times, and train number of each express station under the two modes are shown in Table 13. Concurrently, VTSOPH completed all deliveries within the time window. There were two express delivery stations in the MTSOPH that failed to deliver on time. The vehicle delivery distance in MTSOPH is 24.7% of that in VTSOPH.
Combining the results listed in Tables 9 and 12, the number of express stations that did not deliver on time significantly improved when the MTSOPH was selected in the mediumdistance delivery area, when compared with the MTSOPH in the shortdistance delivery area. From the original 12 express stations that failed to deliver on time, two express delivery stations failed to deliver on time. Therefore, although the VTSOPH requires less time to complete 100% ontime distribution, the MTSOPH delivery cost is slightly lower and the MTSOPH significantly reduces the vehicle transportation distance. This means that when choosing the MTSOPH for delivery, the transportation distance of vehicles can be reduced and pressure on urban roads can be reduced. According to the above analysis, the MTSOPH is more suitable for the mediumdistance distribution area than for the shortdistance distribution area. The MTSOPH and VTSOPH exhibit varied advantages in mediumdistance delivery areas; however, considering the urban system, the MTSOPH is better than the VTSOPH.
5.2.3. Analysis of the LongDistance Delivery Area
The demand and time window of the terminal express station in S3 are shown in Table 14.
According to the above experimental data, the VNS algorithm is used to solve the two transportation strategies of MTSOPH and VTSOPH 20 times and the optimal solution obtained is shown in Table 15. The delivery route information is shown in Table 16.
As shown in Tables 15 and 16, we obtained a different delivery result when compared with results of previous analyses. In the longdistance delivery area, all indicators of the MTSOPH are better than those of the VTSOPH, except for the average delivery time. The delivery cost of MTSOPH is 52.2% of VTSOPH, the vehicle delivery distance is 17.6% of VTSOPH, and the average delivery time is slightly worse than that of VTSOPH. A significant change is observed in the number of express delivery stations that failed to deliver on time. In the MTSOPH, all express delivery stations completed the delivery within the time window, while in the VED mode, there were four express stations that failed to complete the delivery within the time window. Thus, the MTSOPH is suitable for longdistance distribution areas. A similar result was reported in a highspeed rail express delivery study conducted in [50].
Concurrently, by comparing the calculation results in Tables 9, 12, and 15, it is further verified that the MTSOPH is suitable for longdistance delivery. On the one hand, as the distribution distance increased, the distribution cost of the MTSOPH changed slightly and the vehicle delivery distance increased at an average growth rate of 18%, which was much smaller than that of the VTSOPH and increased with an average growth rate of 86%. The above analysis proves the feasibility and stability of the MTSOPH. On the other hand, from shortdistance delivery to mediumdistance delivery to longdistance delivery, the number of express stations that failed to complete the delivery within the time window under the MTSOPH changed from twelve to zero and that of the VTSOPH changed from zero to four.
5.2.4. Relationship between MTSOPH and VTSOPH under Different Delivery Distances
To further explore the relationship between the MTSOPH and VTSOPH under different delivery distances, we assumed that there was one terminal express station, did not consider the time window constraints, and quantitatively analyzed the delivery costs of the two transportation strategies.where represents the delivery cost of MTSOPH, represents the delivery cost of VTSOPH, is the number of express parcels, is the fixed operating cost of the vehicle, is the capacity of freight vehicles, is the vehicle transportation distance between two points, is per unit cargo transfer cost after one transfer, and is the number of transfers between two stations.
The delivery costs of the two transportation strategies are shown in Equations (28) and (29). Assuming that the number of express deliveries for delivery is 60 parcels that reach the upper limit of vehicle loading and the number of transfers is 2, the relationship between the two transportation strategies is
Equation (30) shows that when the vehicle delivery distance of VTSOPH is greater than the sum of 1.45 and the vehicle delivery distance of MTSOPH, the MTSOPH should be adopted; otherwise, the VTSOPH should be selected. The above conclusions further prove that the MTSOPH is more suitable for longdistance delivery.
5.3. Impact on MTSOPH under Different Load Rates of Passenger Flow during OffPeak Hours
In this section, we analyze the impact of different load rates of passenger flow on MTSOPH. We selected case data in S3 for analysis, the total number of express deliveries is 975 packages, and three train carriages are required as freight carriages. This determines the 50% fullload rate during offpeak hours as the boundary. Concurrently, following the principle of passenger and cargo diversion, according to the statistics of Ningbo Rail Transit Group, the maximum passenger flow load rate of the Ningbo metro network during offpeak hours is 90% and 5 train carriages are required as passenger carriages. Therefore, 90% of the passenger flow load rate is determined as upper limit. When the fullload rate of passenger flow during the offpeak hours is greater than 90%, the MTSOPH is not selected, as shown in Figure 9. When the interval for the fullload rate of passenger flow is [0%, 50%] and the total number of goods and passengers is less than the capacity of the metro train, the flexibility loading mode should be selected, the fullload rate of passenger flow should be (50%, 90%], the total number of goods and passengers is greater than the capacity of the metro train, and the fixed loading mode should be selected. When the fullload rate of passenger flow is greater than 90%, the metro is used for transporting passengers.
To further compare the two transportation methods in the MTSOPH, with the load rates of passenger flow of 50% and 90% as the boundary, the VNS algorithm was run 20 times to obtain the optimal results, as shown in Table 17.
In Table 17, the delivery cost and the vehicle delivery distance are equal in Methods 1 and 2, but considering the average delivery time, Method 2 is shorter than Method 1. When the load rate of passenger flow satisfies the boundary conditions, the delivery efficiency of Method 2 is better than that of Method 1 for the same delivery time. Considering longterm transportation, MTSOPH has the potential and has huge positive effects; for example, it can alleviate traffic congestion, has huge economies of scale [51, 52], and has much lower fuel consumption than the VTSOPH. The MTSOPH is adopted during offpeak hours, which can fulfill the use of the idle resources of the metro and does not require excessive initial investment.
5.4. Applicability of MTSOPH considering Different Metro Networks
In order to further prove the applicability and feasibility of the model, we selected the Beijing metro network for numerical experiments. The Beijing metro network is one of the most complex metro networks in China, with 24 metro lines totaling 331 stations, including 62 transfer stations, as shown in Figure 10. In Figure 10, the green dots indicate the terminal express delivery stations, totaling 20. The red fivepointed star indicates the express delivery distribution center, which is the airport logistics park near the capital airport. Different from Ningbo’s radial metro network, Beijing’s metro network is a ringshaped radial network with more diversified route selections between lines. Therefore, we increased the maximum number of transfers in the model to 4 times.
In the experiment, the considered time horizon is set as 9:00–12:00, which is the offpeak period of metro operation. According to the data of Beijing Subway Operation Company, the maximum passenger load rates of passenger flow in the Beijing metro network during offpeak hours is 94.3%. The metro train is composed of 6 carriages, and it needs to occupy 5 carriages for passenger transportation. Thus, the loading mode of Method 1 for mixed transportation is selected. Some parameters in the experiments are set as follows. That is, the delivery time window is set to 2 hours or 3 hours, and the demand and time windows of each terminal express station are shown in Table 18. The remaining parameter values and algorithm parameter settings are consistent with the smallscale case study presented in Section 5.1.
The experimental data in Table 18 are used in the VNS algorithm for 20 calculations. The optimal solution and delivery route information are listed in Tables 19 and 20, respectively.
In Table 19, the delivery cost of MTSOPH is 59.5% of VTSOPH and the vehicle transportation distance is 34.1% of VTSOPH. The average delivery time of MTSOPH is slightly better than that of VTSOPH, and the delivery tasks are all completed within the time window. However, under the VTSOPH mode, there are 3 terminal express stations that failed to complete the delivery within the time window. In Table 20, terminal express stations closer to the express distribution center use VTSOPH for shorter delivery time, while terminal express stations farther away from the express distribution center use MTSOPH for shorter delivery time. In general, the MTSOPH mode can complete the delivery within the time window, and the average delivery time is shorter, which is better than the VTSOPH mode.
According to the case analysis results in Tables 19 and 20, MTSOPH is more suitable for longdistance multitarget delivery. Compared with VTSOPH, MTSOPH has lower total delivery cost, shorter vehicle transportation distance, and higher service level. The above analysis results are consistent with the Ningbo metro case analysis results, which prove that our proposed model can be applied to different types of metro networks with different levels of complexity.
6. Conclusion
This paper proposes a new mixed transport strategy based on the metro network during offpeak hours to determine the freight mode and its distribution cost under offpeak metro passenger flow. The mixed transportation standard of passenger flow priority and separate transportation of passenger and cargo flows of the same train are proposed. According to the aforementioned criteria, a nonlinear programing model of the mixed transport strategy is constructed. In addition, an improved VNS algorithm is designed to solve the model. Finally, considering the Ningbo and Beijing metro network as an example, it is verified that the proposed model and mixed transport strategy can provide decision support for logistics companies. The main contributions of the study are as follows.
A theoretical framework of the mixed transport strategy for different metro passenger flows during offpeak hours was developed via comparisons with related studies [9, 20, 29]. Thus, a mixed transportation standard with passenger flow priority and separate transportation of the same train passenger and cargo flows was established, which expanded the integrated transportation of urban freight and metro passenger transportation.
In practice, the model of the mixed transportation strategy proposed in this study can provide decision support for logistics companies based on different delivery distances, different offpeak passenger flows, and different types of metro networks. First, when the vehicle transportation distance under separate VTSOPH is greater than the sum of 1.45 and the vehicle transportation distance of MTSOPH, the MTSOPH should be adopted; otherwise, the VTSOPH should be selected. Second, when the number of passengers and freight transportation demand are greater than the metro capacity, the fixed loading mode of the MTSOPH should be selected for transportation; otherwise, the flexibility loading mode of the MTSOPH should be selected for transportation. Finally, the proposed model framework can be applied to different types of metro networks with different levels of complexity.
This study has some limitations to be further solved, such as freight vehicle scheduling and route planning and metro station and line performance evaluation [53, 54]. The study should mainly focus on the following aspects: (1) Freight vehicle routes should be planned to improve vehicle utilization, and train schedule issues should be analyzed from a datadriven perspective [55]. (2) Owing to the uneven distribution of passenger flow in the urban metro system during offpeak hours, the remaining loading capacity of other carriages can be considered in future studies. (3) To ensure the mixed strategy realizable, the metro turnover and rolling stock circulation and selecting the unloading stations should be considered.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was financially supported by the National Natural Science Foundation of China under Grants 71662011 and 71940009. This research was also jointly supported by Jiangxi Provincial Major Science and Technology Project5G Research Project (Grant no. 20212ABC03A07).