Consolidating passenger and freight transportation in an urban–rural transit system

Highlights

• •The urban-rural transportation system is modeled with a mixed integer programming.
• •Some extensions of the mathematical programming is discussed.
• •The properties and benefits of the urban-rural transportation system are analyzed in case study.

Graphical abstract

Abstract

Buses are the most critical part of urban–rural transit systems. However, bus transit services in urban–rural areas face a trade-off between the need for better services and the low profitability resulting from low travel demand. In this study, we show that we can improve the utilization and profitability of urban–rural buses by merging freight transportation with passenger transportation. We developed a mixed-integer program to model and analyze the coordination between freight and passenger transportation in an urban–rural transit system. We then conducted a case study to evaluate the effectiveness of the proposed approach. The numerical results indicate that the consolidation of passenger and freight transportation significantly reduces the operation cost of logistics companies and improves the profit of bus companies. We finally discuss the consolidation’s positive impacts on logistics companies, bus service providers, and society.

1. Introduction

1.1. Background

Buses are the most critical part of urban–rural transit systems due to the low demand for trips and the geographical barriers between urban and rural areas [1]. In comparison with trains, subways, and airplanes, buses are more energy efficient and inexpensive [2], especially for short-distance trips [3]. With urban–rural transit systems based on public buses, rural residents can easily access services such as medical consultations, medical treatment [4], education, entertainment, and grocery stores.

Nonetheless, bus transit services in urban–rural areas suffer from the trade-off between the need for better services (e.g., higher frequency of bus departures) and the low demand for trips. Bus services for urban–rural areas also face longer distances and a more inadequate infrastructure than similar services for intra-urban areas. These facts make providing urban–rural bus services more costly and less profitable. Such inefficiency can quickly drive a bus transit service into a downward spiral of even lower demand and worse service, which makes the system unsustainable [4]. Researchers have been trying to break this vicious cycle by coupling the service with new means of transportation (e.g., flying cars [5]) and emerging technologies (e.g., demand-responsive transport [6]). While these methods may eventually solve the problems, they still suffer from immaturity and high costs. Notably, small coach buses may be suitable for improving the service level of urban–rural buses, but they generate extra operation costs. The extra costs mainly include the cost of updating new buses, employing more drivers, and management. Using small coach buses is not as beneficial to society as the consolidation approach examined in this study because the energy consumption in small coach buses per passenger is higher than the counterpart of a large bus.

This study explores the possibility of solving this dilemma by consolidating existing transportation resources. Specifically, we show that we can improve the utilization of urban–rural buses by merging freight transportation with passenger transportation (e.g., carrying packages by using the available space of buses). Intuitively, such a configuration has several advantages: (i) It requires neither technological innovation nor heavy investments, but only coordination between bus service providers (bus carriers and bus companies) and shipping carriers (logistics companies). (ii) It decreases the travel miles and the shipping costs of shipping trucks by leveraging scheduled bus lines between urban and rural areas. (iii) It converts empty spaces on buses into revenue by carrying goods and packages between urban and rural areas. (iv) It improves the profitability of bus providers, which can give them more opportunities to provide better services. These advantages make the consolidation approach an attractive alternative to existing means of transportation.

It is worth noting that using bus services for freight delivery was adopted in Sweden and some developed countries in the 1960s or 1970s. However, this mode of delivering freight subsequently disappeared. Several factors may account for this: (i) As staff costs increased and freight rates decreased, companies revenues from freight transport were not sufficient to cover the additional costs of handling parcels. (ii) The bus driver loaded and unloaded parcels along the line during the trip. This increased travel times for passengers, and as the value of travel time and competition from other modes grew, keeping travel times down became increasingly important. (iii) Bus services became a public responsibility and subsidized. For legal reasons, bus companies were prohibited from offering freight services since their subsidized services would compete with commercial logistics services. After modeling and analyzing the consolidation of passenger and freight transportation with well-designed operation and management in this study, Section 5 will discuss why the proposed consolidation method can overcome these three hurdles.

1.2. Related literature

Operation and Planning of Intercity Buses: Our study is related to a stream of research that attempted to improve the service of intercity buses. Scholars have developed models to help intercity bus service providers plan bus routes and schedules considering variable market share [7], stochastic travel time [8], dynamic demand [9], and the electrification of buses [10], [11]. For example, ref. [7] utilized passengers’ mode choices to formulate the market share of intercity buses. They developed a nonlinear mixed-integer program to describe the bus scheduling problem with a variable market share. Ref. [8] proposed a framework to solve the bus routing and scheduling problem with a stochastic travel time, including scheduling planning and adjustment. Their study did not consider multi-stop bus trips, and bus schedules were usually fixed. Researchers have integrated the dynamic demand of passengers into the planning of intercity bus lines [9]. Potential locations of stations and ideal service times were solved from a mixed-integer program. El-Taweel and Farag [10] incorporated electric buses into intercity bus service and derived the electric bus schedule considering the worst case when the average energy consumption of congested traffic was used. Therefore, the study presented a conservative solution. Uslu and Kaya [11] developed a novel mathematical model to determine the locations and capacities of charging stations for intercity electric coach buses to minimize the establishment cost, operation costs of charging stations, and the number of stops of coach buses on the routes.

While the urban–rural transit buses studied in this paper can be viewed as intercity transit buses with shorter traveling distances, the demand for urban–rural travel is usually much lower than that for intercity travel. Studies on the operation and planning of intercity buses focused on reducing operation costs, energy consumption, and the discomfort of passengers. However, with travel demand spreading across time and space, the demand for each specific bus line will be low, making the operation of urban–rural transit buses less profitable. Thus, it is hard for providers of urban–rural transit buses to provide high-quality services. The actual question, in our case, is different from how good the services provided should be, but how to make it possible to offer good services. This is especially important because there are very few alternative modes of public transportation between urban and rural areas.

Integration of Passenger and Freight Transportation with Buses: There is also an active body of research from the past decade that considered the integration of passenger and freight transportation to improve the efficiency of the traffic system. Previous papers [12], [13], [14] have investigated the potential of integrating passenger and freight transportation and have identified intracity buses as promising tools to realize this integration. Optimization models were also developed to model the concept of passenger–freight integration. Ghilas et al. [15,16] utilized scheduled bus lines to carry packages from one station hub to another to lower the travel miles of trucks. They used the pickup-and-delivery problem with time windows and scheduled lines (PDPTW-SL) to model such a traffic system and developed a branch-and-price algorithm to solve the problem efficiently. Cheng et al. [17] also investigated the package delivery problem with intracity public buses. They described the delivery problem as a multi-commodity flow problem modeled by a mixed-integer linear program. They showed that more than 60% packages could be delivered to their final destinations within 500 m of the bus stations. Mourad et al. [18] investigated integrating autonomous delivery service into a passenger transportation system based on the PDPTW-SL problem with time windows and scheduled lines. They modeled the PDPTW-SL problem as a two-stage stochastic problem with stochastic passenger demand. They proposed a sample average approximation method and an adaptive large neighborhood search algorithm to solve the problem. Peng et al. [19] utilized a two-stage model to integrate passenger and freight transportation at the railway station by a bus-pooling service. In the first stage, passengers were matched fairly; in the second stage, buses delivered parcels. They analyzed the influence of fairness, the waiting times of passengers, and the walking distances of recipients on the matching rate between scheduled bus lines and freight.

1.3. Contributions

In this study, we incorporate the properties of urban–rural bus lines into the consolidation of passenger and freight transportation. This makes our model different from existing models in several ways. For example, while the operation of intercity buses is “point-to-point”, urban–rural bus lines usually make several stops. However, compared with intracity buses, urban–rural bus lines usually depart from two or more passenger transport hubs (THs). The departure intervals of urban–rural bus lines are also longer than those of intracity buses, allowing us to pre-determine the feasible truck schedules between distribution centers (DCs) and THs. Each truck can visit more than one TH to deliver freights, and the freights on each bus can be delivered to the TH by more than one truck. In addition, the long departure intervals in THs also make it worth considering the storage of freights and their inventory management.

The contributions of this study are two-fold. First, to support the abovementioned concept, we developed a mixed-integer program to model the coordination between freight and passenger transportation in an urban–rural transit system. To the best of our knowledge, this is the first model integrating passenger and freight transport in urban–rural transit systems. Tractable approximation methods and extensions to the model are also discussed in this paper. Second, we conducted a case study in Hangzhou, China, to evaluate the effectiveness of the proposed approach. The numerical results indicate that the consolidation of passenger and freight transportation significantly reduces the operation costs of logistics companies and improves the profits of bus companies.

1.4. Organization

The remainder of this paper is organized as follows. In Section 2, we present the formulation and analysis of the model of the traffic system. In Section 3, we discuss extensions to our transportation model. In Section 4, we conduct numerical tests in a case study. We conclude the paper in Section 5.

2. Formulation

Consider a logistics carrier who delivers packages from warehouses near a densely populated urban area to towns (or to locations such as satellite cities and suburban areas) around the metropolitan area of the urban core (See Fig. 1). Let $\mathcal{I}$ be the set of DCs near the urban core, $\mathcal{K}$ be the set of towns, and $\mathcal{S}$ be the set of THs. We take each day as a separate planning horizon. For each $i\in \mathcal{I}$ and $k\in \mathcal{K}$, we let $D_{ik}$ denote the total quantity (e.g., weight, volume, or value) of packages that need to be delivered from warehouse $i$ to town $k$, and let ${\psi }_{ik}$ be the cost of each unit quantity of such a delivery. Consider also a bus operator who operates bus lines from the urban core to nearby towns. Let $\mathcal{J}$ denote the set of bus lines leaving the urban core. For each $j\in \mathcal{J}$, let ${\mathcal{K}}_j\subset \mathcal{K}$ denote the set of towns that bus line $j$ visits.

Fig. 1.

Schematic of the studied scene.

The bus operator offers to deliver packages for the logistics carrier (at a competitive price) when there is space on the buses. Each bus’s schedule and available space are known at the beginning of the day. Let $B_j$ denote the volume of packages that can be carried by bus $j$, and let ${\varphi }_j$ denote the corresponding price per unit quantity of packages (note that we do not differentiate the cost by destination; this is because buses only take packages from their departing stations, and emptying a bus earlier does not make the operator more profitable). To deliver packages by bus, the packages need to be sent to bus stations by trucks before the bus’ departure. Trucks leave from DCs and can carry at most $\theta$ units of packages.

2.1. Model

The logistics carrier considers a set $\mathcal{R}$ of pre-determined routes. Each route $r\in \mathcal{R}$ is designed such that all stations on the route are visited on time (it is meaningless to visit a station after the bus’s departure). For each $r\in \mathcal{R}$, let ${\phi }_r$ denote the cost to send a truck on the route, and let ${\mathcal{J}}_r\subseteq \mathcal{J}$ denote bus lines whose stations can be visited before bus line $j$ departs by trucks on route $r$. In addition, for each $i\in \mathcal{I}$, let ${\mathcal{R}}_i\subseteq \mathcal{R}$ denote truck routes that start from DC $i$. Here, we assume that $\mathcal{R}={\cup }_{i\in \mathcal{I}}{\mathcal{R}}_i$ and ${\mathcal{R}}_{i^{\prime }}\cap {\mathcal{R}}_{i^{″}}=⌀$ for any distinct $i^{\prime },i^{″}\in \mathcal{I}$.

Remark 2.1

In the basic model, there are no appropriable warehouses in THs for storing the freights from DCs. The freights from DCs should be immediately taken away by the bus line after the truck visits the THs. Even if appropriable warehouses are built, their capacities are limited.

To reduce the complexity and increase the flexibility of the model, we assume that route $r$ is not a simple combination of the links between the DC and THs; it is also related to the departure time of the bus lines. That is to say, route $r$ visits a TH before one bus line $j$ departs if $j\in {\mathcal{J}}_r$, and the departure time of bus line $j$ is the closest to the arrival time of the truck at the TH. We will provide a detailed explanation of the set of routes in the following subsection.

The logistics carrier thus faces the following optimization problem:

$$\begin{array}{cc}\hfill \underset{x,y}{\min }& \sum _{r\in \mathcal{R}}{\phi }_r{y}_r+\sum _{i\in \mathcal{I}}\sum _{i\in \mathcal{K}}{\psi }_{ik}(D_{ik}-\sum _{r\in {\mathcal{R}}_i}\sum _{j\in {\mathcal{J}}_r}{x}_{rijk})+\sum _{j\in \mathcal{J}}\sum _{x\in \mathcal{I}}\sum _{k\in \mathcal{K}}\sum _{r\in {\mathcal{R}}_i}{\varphi }_j{x}_{rijk}\hfill \end{array}$$ ({IP})

$$\begin{array}{ccc}\hfill \text{s.t.}& \sum _{r\in {\mathcal{R}}_i}\sum _{j\in {\mathcal{J}}_r}{x}_{rijk}\le D_{ik}\hfill & \hfill i\in \mathcal{I}k\in \mathcal{K}\end{array}$$ (1a)

$$\begin{array}{ccc}& \sum _{r\in {\mathcal{R}}_i}\sum _{i\in \mathcal{I}}\sum _{k\in \mathcal{K}}{x}_{rijk}\le B_j\hfill & \hfill j\in \mathcal{J},\end{array}$$ (1b)

$$\begin{array}{ccc}& \sum _{i\in \mathcal{I}}\sum _{j\in {\mathcal{J}}_r}\sum _{k\in {\mathcal{K}}_j}{x}_{rijk}\le \theta y_r\hfill & \hfill r\in \mathcal{R}\end{array}$$ (1c)

$$\begin{array}{cc}& y\in {\mathbb{Z}}_{+}\hfill \end{array}$$ (1d)

$$\begin{array}{cc}& x\ge 0\hfill \end{array}$$ (1e)

In Eq. IP, decision variable $x_{rijk}$ denotes the volume of packages to be sent from warehouse $i$ to town $k$ through truck route $r$ and bus line $j$, while decision variable $y_r$ denotes the (integer) number of trucks to be sent on route $r$. The objective function of Eq. IP is the total delivery cost, with its first term being the cost of truck–bus delivery, its second term being the cost of dedicated delivery, and its third term being the extra operation cost of a bus caused by carrying freights. Constraint (1a) states that total delivery on each “DC–town” pair should not exceed the demand (this is to avoid unboundedness when the problem is ill-conditioned, e.g., the costs of bus delivery are higher than the costs of dedicated delivery). Constraint (1b) states that the total quantity of packages on each bus should not exceed its space capacity. Constraint (1c) states that the number of trucks on each route should be sufficient to deliver the planned packages. Constraint (1d) states that the number of trucks on each route should be integral.

Remark 2.2

The consolidation between urban freight transportation and an urban–rural transit system should consider the freight truck routing, truck–bus consolidation, and freight allocation. We generate a general route set for the model Eq. IP to describe the complex process. We also propose the feasible and limited number of routes in Section 2.2 to ensure that the problem is effective for practical applications.

2.2. Route generation

In Eq. IP, the sets $\mathcal{I}$, $\mathcal{J}$, $\mathcal{K}$, and ${\mathcal{K}}_j$ are readily available from a specific urban–rural transit system, but the route-related sets ($\mathcal{R}$, ${\mathcal{R}}_i$, and ${\mathcal{J}}_r$) need to be delicately constructed. ${\mathcal{J}}^s$ is the set of bus lines that depart from TH $s$, and ${\cup }_{s\in \mathcal{S}}{\mathcal{J}}^s=\mathcal{J}$. As stated in Remark 2.1, the routes in $\mathcal{R}$ depart from DCs and visit some bus lines. Then, we define the set of all possible routes as

$$\begin{array}{ccc}\hfill \tilde{\mathcal{R}}& :=& \left\{\right(i,j_1,\cdots ,j_n):i\in \mathcal{I};1\le n\le |\mathcal{S}|\hfill \\ & & j_n\in \mathcal{J};\text{if}{j}_{n_1}\in {\mathcal{J}}^s,j_{n_2}\notin {\mathcal{J}}^s,\forall n_1\ne n_2;s\in \mathcal{S}\}\hfill \end{array}$$

The total number of the routes linearly increases with $\left|\mathcal{I}\right|$ and sharply increases with $\left|\mathcal{S}\right|$. We should delete infeasible routes and inefficient routes. To select feasible routes, new notation is defined as follows:

• •${\mathcal{J}}_r:=\{j_1,j_2,\cdots ,j_{|{\mathcal{J}}_r|}\}$ denotes the set of bus lines that route $r$ visits. Note that all bus lines in ${\mathcal{J}}_r$ depart from different THs. ${\mathcal{J}}_r$ can be easily obtained by the definition of $\bar{\mathcal{R}}$.
• •$t_j$ denotes the departure time of bus line $j$.
• •$s_j$ denotes the TH from which bus line $j$ departs.
• •$j^{-}$ denotes the bus line before bus line $j$ that departs at the same TH.
• •${\mathcal{T}}_{m{m}^{\prime }}\left(j\right)$ records the travel time between $m$ and $m^{\prime }$, where $m\in \mathcal{M}$ and $\mathcal{M}=\mathcal{I}\cup \mathcal{S}$. ${\mathcal{T}}_{m{m}^{\prime }}$ varies with the clock time, but for simplicity, we use ${\mathcal{T}}_{m{m}^{\prime }}\left(j\right)$ to represent the value of ${\mathcal{T}}_{m{m}^{\prime }}$ at time $t_j$.

Regarding this notation, we provide additional remarks.

Remark 2.3

For ${\mathcal{J}}_r$, we set an imaginary bus line $j_0$ that departs from an imaginary TH (denoted as $s=-1$), and we set $s_{j_0}=-1$ and ${\mathcal{T}}_{-1,s}=0$ ($s\in \mathcal{S}$). As for $j^{-}$, if $j^{-}\notin \mathcal{J}$, i.e., bus line $j$ is the first line in TH in one day, we set $t_{j^{-}}=-M$, where $M$ is a large number.

According to the above notation and remarks, the route $r$ is feasible when the following inequalities hold:

$$\begin{array}{cc}& t_{j_m^{-}}+\frac{1}{2}\sum _{o=n}^{m-1}[{\mathcal{T}}_{s_{j_o},s_{j_{o+1}}}\left(j_o\right)+{\mathcal{T}}_{s_{j_o},s_{j_{o+1}}}\left(j_{o+1}\right)]+ϵ\left(j_m\right)\le t_{j_n}\hfill \end{array}$$ (2a)

$$\begin{array}{cc}& t_{j_m}+\frac{1}{2}\sum _{o=m}^{n-1}[{\mathcal{T}}_{s_{j_o},s_{j_{o+1}}}\left(j_o\right)+{\mathcal{T}}_{s_{j_o},s_{j_{o+1}}}\left(j_{o+1}\right)]-ϵ\left(j_m\right)\ge t_{j_n^{-}}\hfill \end{array}$$ (2b)

In (2a), (2b), $j_m,j_n\in {\mathcal{J}}_r;m,n\in \{1,2,\dots ,|{\mathcal{J}}_r\left|\right\}m<n$. Thus, (2a), (2b) reveals that some routes in $\bar{\mathcal{R}}$ cannot be visited by freights since the sum of the travel time and unloading time between two bus departure lines is higher than the interval of these departure lines. The bounded conditions are illustrated in Fig. 2.

Fig. 2.

Two bounded conditions for feasible routes.$j_m,j_n\in {\mathcal{J}}_r$ and $m<n$. (a) The bounded condition in Eq. 2a. (b) The bounded condition in Eq. 2b.

In (2), we use the average value of the travel time between two stations when bus $j_o$ departs and bus $j_{o+1}$ departs to represent the real-time travel time between two THs. An error term $ϵ\left(j_p\right)$ dependent on the bus line is also introduced to improve the feasible routes’ robustness in practice. The term is related to the time of unloading and the variance of the travel time. Calculating the optimal value of $ϵ\left(j_p\right)$ is outside the scope of this study, and we set it as a constant in the case study.

Let ${\mathcal{R}}^f$ denote the set of feasible routes and

$${\mathcal{R}}^f\subseteq \tilde{\mathcal{R}}$$

In addition, to ensure that the route is cost efficient, the following inequality also should be satisfied:

$${\phi }_r+{\varphi }_j\theta <\underset{k\in {\mathcal{K}}_j}{\max }{\psi }_{ik}\theta r\in {\mathcal{R}}^f,i\in {\mathcal{I}}_r,j\in {\mathcal{J}}_r$$ (3)

Inequality Eq. 3 indicates that route $r$ is cost efficient when carrying freights with bus line $j$ ($\forall j\in {\mathcal{J}}_r$) and can reduce the total trip cost of carrying freight from one DC to town $k$. The formulations of ${\phi }_r$, ${\varphi }_j$, and ${\psi }_{ik}$ are constructed by the travel time and distance between DCs, THs, and towns. Finally, we can obtain the feasible and cost-efficient route set $\mathcal{R}\subseteq {\mathcal{R}}_f\subseteq \bar{\mathcal{R}}$ according to Eqs. 2 and 3.

3. Extensions

In Section 2, the urban–rural transit system with the consolidation of passenger and freight transportation was described by a mixed-integer program (MIP) with a simple form and high extensibility. The MIP can be extended with consideration of the existence of factors such as warehouses in the THs, the adoption of electric urban–rural buses, and the adoption of different delivery vehicles with different capacities. Two possible extensions are discussed as follows.

3.1. Appropriable warehouses in transport hubs (THs)

In Eq. IP, it is assumed that the freight is put in the clearing of a TH before being loaded onto a bus, i.e., there is no warehouse built in the TH for storing the freight from the truck. However, when bus companies have long-standing corporation with logistics companies, dedicated warehouses should be built to store the freights temporarily. The existence of warehouses can allow the space of most trucks and buses to be fully utilized. To describe the warehouse’s influence on the basic model, we introduce a new set ${\mathcal{J}}^{sk}$. ${\mathcal{J}}^{sk}$ denotes the set of bus lines that depart from TH $s$ and stop at town $k$.

When warehouses in THs are considered, the constraints of warehouses are formulated as follows:

$$\begin{array}{ccc}& \sum _{j\in {\mathcal{J}}_u^{sk}}\sum _{i\in \mathcal{I}}{x}_{rijk}\le {\theta }^{sk}+\sum _{j\in {\mathcal{J}}_{u-1}^{sk}}{B}_j\hfill & \hfill s\in \mathcal{S},k\in \mathcal{K},u\in \{1,2,\dots ,|{\mathcal{J}}^{sk}\left|\right\}\end{array}$$ (4a)

$$\begin{array}{ccc}& \sum _{j\in {\mathcal{J}}_u^{sk}}\sum _{i\in \mathcal{I}}{x}_{rijk}\ge \sum _{j\in {\mathcal{J}}_u^{sk}}{B}_j\hfill & \hfill s\in \mathcal{S},k\in \mathcal{K},u\in \{1,2,\dots ,|{\mathcal{J}}^{sk}\left|\right\}\end{array}$$ (4b)

$$\begin{array}{ccc}& \sum _{j\in {\mathcal{J}}^{sk}}\sum _{i\in \mathcal{I}}{x}_{rijk}\le \sum _{j\in {\mathcal{J}}^{sk}}{B}_j\hfill & \hfill s\in \mathcal{S},k\in \mathcal{K}\end{array}$$ (4c)

When the warehouse is considered, constraints Eq. 1b should be replaced by constraints (4a), (4c). In constraint Eq. 4a, ${\theta }^{sk}$ is the capacity of the warehouse in TH $s$ for storing the freights in town $k$, where ${\mathcal{J}}_u^{sk}\subseteq {\mathcal{J}}^{sk},\left|{\mathcal{J}}_u^{sk}\right|=u$, ${\mathcal{J}}_0^{sk}=⌀$, and $j>j^{\prime }$ ($\forall j\in {\mathcal{J}}_u^{sk},\forall j^{\prime }\in {\mathcal{J}}^{sk}\setminus {\mathcal{J}}_u^{sk}$). Constraint Eq. 4a indicates that the volume of the freights in the warehouse does not exceed the warehouse’s capacity. Constraint Eq. 4b indicates that the freights can fill the available space of the bus. Constraint Eq. 4c indicates the last bus line can take away all freight in the warehouse.

3.2. Upgrading the delivery vehicle

The truck is the most common means for delivering freights in urban and rural areas. However, it may not be the most suitable means in our urban–rural system. Truck drivers always visit more than one TH to unload all cargo from the truck, since the available spaces in buses are not fixed and are always lower than the capacity of the truck. As such, the weight of the carried goods per time in a truck is less than ideal. In recent years, minivans and electric tricycles are widely used to solve the last-mile problem for goods delivery. In addition, some emerging shipping tools, i.e., autonomous delivery services, including NURO [20], modular autonomous vehicles [21], and flying delivery vehicles [22], have been developed for freight delivery, whose capacities are small or flexible.

When the trucks are replaced by these delivery tools, problem Eq. IP should be modified to adapt to the new urban–rural traffic system. It is a general consideration that we assume that some trucks are replaced. With this consideration, we present the modification for problem Eq. IP as follows.

• •Route generation. If trucks are replaced by flying delivery vehicles, the routes for the new delivery vehicle should be reconstructed by a similar method to that in Section 2.2 since flying cars and trucks do not share common routes. Otherwise, the new delivery vehicle and the truck share the same routes.
• •Problem statement. We should add new variables and constraint conditions to describe the new delivery vehicle’s impact on the traffic system. We do not present the modified model since it is a simple extension of the problem Eq. IP.

The introduction of multiple delivery vehicles may improve the efficiency of the urban–rural transportation system due to the capacity/route flexibility of multiple delivery vehicles. It is easy to extend the proposed model with this consideration, and therefore, this is omitted in this study.

4. Case study

In this section, we consider Hangzhou, China as an example to evaluate the efficiency of the consolidation of passenger and freight transportation with an urban–rural (satellite cities) transit system. As shown in Fig. 3, five THs (“Hangzhou Transport Center,” “Hangzhou East Station,” “Hangzhou South Station,” “Hangzhou West Station,” and “Hangzhou North Station”), three DCs (“Integrated logistics area of SF,” “Transit center of Yuantong,” “Warehouses in Hangzhou of Alibaba”), and six towns (“Tonglu,” “Linan,” “Anji,” “Deqing,” “Tongxiang,” and “Haining”) were selected in this case study. The bus lines in this urban–rural transit system were always point-to-point, i.e., there was one town (county) visited by each bus line. The bus lines between Hangzhou and the surrounding prefecture-level city (e.g., Shaoxing and Huzhou) were not considered in this case study since the bus lines/train routes between Hangzhou and these cities operate with a high and steady frequency, and there is no need to provide extra transportation service to break the geographical barriers. The parameters in the urban–rural transit system are investigated and determined in Appendix A.

Fig. 3.

Urban–rural transit system in Hangzhou. Map approval number GS(2023)-G677.

The problem was solved by Gurobi (10.0.1) with Python (3.10) in Mac OS 12.6 with an M1 Pro Chip (10-core CPU and 16 GB of unified memory). Since some parameters are random, the solving time varied with the range $[55\mathrm{s},72\mathrm{s}]$. The problem should be solved at the beginning of the planning horizon, and the solving efficiency is sufficient for practical applications. In this case study, we analyzed the monetary benefit of the consolidation of passenger and freight transportation by an urban–rural transit system considering warehouses in THs, the adoption of electric coach buses, and different capacities of the trucks. We first investigated the properties of freight flow in the transportation system, considering the use of warehouses in THs. Then, we analyzed the monetary benefits of the consolidation in different cases (with or without warehouses, minivans, electric buses, and different densities of freights). Finally, the benefit of this consolidation of passenger and freight transportation on the operation of bus companies was analyzed.

4.1. Assignment of freights

We first present the result of the properties of the selected routes, as shown in Fig. 4, which illustrates that most trucks will visit only one TH to deliver freights to the buses that depart from the THs. The result proves that the urban–rural transit system is robust, since most trucks only need to visit one TH in the interval between the departure times of the two bus lines. It is a simple task for truck drivers. Few trucks will visit two or three THs, and the freights on these trucks always be carried to Town 1 and Town 3. The reason for the result is intuitively that the distances from DCs to Town 1 and Town 3 are relatively longer than the distances between DCs to other towns (see Table A.1).

Fig. 4.

Number of trucks on the selected routes.(a) When trucks only visit one TH; (b) when trucks visit more THs.

Fig. 4a also shows that the warehouses in the THs for storing freights could reduce the number of trucks leaving from DCs since the warehouses could improve the load rate of the trucks. The warehouses could therefore reduce the total operation cost of the urban–rural transit system. Fig. 5 further shows the distribution of the flow of the freights in the urban–rural transit. Warehouses can reduce the number of DC–town pairs, and most trucks depart from DCs and visit the nearest TH. Fig. 5 also illustrates the ratio of the transport costs by bus and truck for the freights from one DC to one town. When warehouses are used in the THs, the ratio between the transport costs of buses and trucks will increase since the load ratio of the trucks increases.

Fig. 5.

Cargo from distribution centers (DCs) to towns by bus and transport costs with and without warehouses.(a) The cargo flow from DCs to Ts without warehouse; (b) The cost for carrying the cargo in (a) with and without urban-rural transit; (c) The cargo flow from DCs to Ts with warehouse; (d) The cost for carrying the cargo in (c) with and without urban-rural transit.

To further demonstrate the benefit of warehouses, Fig. 6 illustrates the distribution of the load rate of trucks with the influence of warehouses in the THs.1 From Fig. 6a, we found that the warehouses in the THs dramatically improved the mean value of the truck’s load ratio from 0.44 to 0.95. Most of the trucks ran with a high load ratio when warehouses were used in the THs to temporarily store freights. Fig. 6b also illustrates the benefit of warehouses in THs that the warehouses can reduce the frequency of the trucks departing from DCs.

Remark 4.1

The influence of trucks with different capacities on the freight assignment was similar to the influence of warehouses, and repetitions have been removed.

Fig. 6.

Influence of warehouses in transport hubs (THs) on the load ratio of trucks. (a) Probability of the trucks with or without warehouses. (b) Change of freight volume in the warehouse in TH2 (to town 2).

4.2. Monetary benefit of consolidation

In this section, we first present the total reduced cost caused by the consolidation of the urban–rural transit system with different considerations in Fig. 7.2 The introduction of minivans, warehouses, and electric buses can reduce the total operation cost of the traffic system. The ratio between the prices of minivans and trucks when carrying freights with the same volume on the same route was always greater than 1, since the driver’s salary could not be substantially decreased by introducing the minivan. It is possible for the ratio to drop as low as 1 (or a smaller value) when autonomous delivery vehicles are introduced. The benefit from minivans was less than the benefit from warehouses, even though the ratio was equal to 1. The reason for this result was that the load ratio of minivans was also always less than 1 due to the stochasticity of the available space of buses. It is another important finding that the introduction of minivans and warehouses can stabilize the value of the reduced cost, based on the error bars in Fig. 7. The total reduced cost was sensitive to the density of freights and the adoption of electric buses because the cost of storing and handling work for freights in THs and the energy consumption cost of buses increase with the freight’s density. Therefore, freights with low densities are suggested to be carried by urban–rural buses.

Fig. 7.

Total reduced cost in one day with different considerations. The baseline represents the system without warehouses, electric buses, or trucks with different capacities. Three alterations (the introduction of minivans, warehouses, and both electric buses and warehouses) were analyzed. ‘P#1.5’ represents that the ratio between the prices of minivans and trucks when carrying freights on the same route was 1.5. ‘D#1.5’ represents that the average density of the freights was 1.5 times the water’s density.

In China, the bus services between core and satellite cities and the bus services between the city and rural areas are always designed to meet the passenger demand during rush hour and holidays. Providing bus service is hardly profitable for bus companies, so these companies enjoy a surplus with extensive subsidies from the government.

In the following content, we show that bus companies can reap the rewards by charging logistics companies for carrying freights. The cost of operating bus lines between urban and rural areas includes impairment losses, salaries for the drivers and conductors, energy consumption costs, road tolls, highway maintenance fees, bus insurance, and management costs from the TH. In addition, the management cost from the TH was charged from the passenger’s fare at a flat rate of 10% when the consolidation of passenger and freight transportation is not introduced. When the consolidation is considered, the extra cost of freight storage and cartage will increase the charge rate. The specific calculation for the operation costs of bus companies and data collection can be found in Appendix A. The reduced costs of logistics companies from the consolidation is equal to the difference in the costs before and after utilizing the urban–rural transit system.

Fig. 8 illustrates the profit of the bus companies when operating bus lines in the urban–rural transit system. The bus lines from TH1 to Town 5 were analyzed. The figure reveals that passenger and freight transportation consolidation can benefit both logistics and bus companies. When the average value of the passenger number was 13 (the number of seats was 43), the bus company could be self-financing if $\gamma =0.7$ delivering freights to Town 5 with urban–rural bus lines (the definition of $\gamma$ can be found in the caption of Fig. 8), while the number was 16 when the consolidation was not adopted. The logistics company could reduce its cost to 600 CNY. $\gamma$ must be greater than 0.32 for the parameter values in Appendix A due to the extra management cost, extra energy cost, and the cost of bus depreciation caused by carrying freights. Fig. 8 reveals another result that the benefit of the consolidation for logistics companies was steady with the variation of the passenger demand, but the profit of bus companies had a large variation range.

Fig. 8.

Profit of the bus line from TH1 to town 5 and the reduced costs of logistics companies for delivering freights to town 5.$\gamma$ represents the charge ratio, which is equal to the ratio between the charge to the logistics companies for utilizing bus lines and the cost reduction of logistics companies from the bus lines (without charge). The purple line represents the minimum value of the passenger number when providing bus line service is profitable without subsidies and consolidation.

Unfortunately, even if $\gamma =0.7$, providing bus line services could not be profitable without subsidies when the passenger’s demand was less than 13. At present, the mean value of the passenger’s demand from TH1 to town 5 was about 11 (see Fig. A.1). The low demand was possibly caused by COVID-19, and it is predicted that the consolidation can provide a bus service profit when the influence of COVID-19 on the travel demand is reduced. In addition, the space of the seats was not used to carry freight. The utilization of empty seats can sharply reduce the minimum number of passengers on one bus line to ensure the bus service provider is profitable (the bus should be modified to utilize the empty space in the seats to carry freights).

Fig. A.1.

Probability distribution of the number of passengers on the bus lines from TH1 to town 5, where the mean value was 11.08 and the standard deviation was 5.11. The data was collected in the ticket booking application on weekdays (from 2022-03-02 to 2022-04-15).

5. Discussion

5.1. Policy impact

Based on the results and analyses in the above sections, we suggest that the passenger and freight consolidation in urban–rural transit has the following policy effects:

Cost Savings in Freight Delivery: By utilizing the empty space on buses, the logistics carrier is able to reduce the total mileage of trucks and thus lower transportation costs. The logistics carrier can also potentially improve the utilization of its truck space because it can now focus more on deliveries within the urban core. Both changes can help reduce the total operation cost of the logistics carrier.

Improving Service Level of Bus Transit: The operation of bus transit is constrained by profitability. Due to the low travel demand between urban and rural areas, the departure frequency of urban–rural bus lines is usually low. However, with the extra profitability offered by the logistics carrier, bus companies are able to provide bus lines at a better service level. Passengers can thus have access to bus lines more frequently. Better bus services can also attract more travelers, bringing more profits to bus companies and creating a self-reinforcing feedback loop. This may help break the geographical barrier and better connect urban and rural areas.

Long-Term Social Benefit: In addition to the short-term monetary benefit to logistics carriers and bus operators, the consolidation of passenger and freight delivery has the following long-term social benefits: (1) By reducing the mileage of trucks, the overall energy consumption of the system is reduced. This contributes to the sustainability of the transportation sector. (2) As fewer trucks need to perform long-distance travel between urban and rural areas, the adoption of electric trucks becomes more feasible for the logistics carrier (considering that the current range of electric trucks is quite limited). This also promotes environmental sustainability. (3) As our simulation results have shown, bus operators can more easily fund themselves when freight delivery is integrated. Thus, the consolidation improves the ability of bus operators to survive the low travel demand, and thus benefits residents in rural areas, especially those who do not have access to other travel methods. (4) The passenger and freight consolidation with an urban–rural transit system can avoid mass layoffs caused by the reduced frequency of bus lines. In addition, the consolidation can provide extra opportunities for work in loading and unloading freights and managing the warehouses. Therefore, consolidation can alleviate unemployment to some extent.

To sum up, the consolidation of passenger and freight transportation can bring a monetary benefit to both the logistics carrier and bus operators. It can also bring long-term social benefits by promoting the sustainability of the transportation sector and improving the access of rural residents to public transportation.

5.2. Present versus previous consolidation

As mentioned in the Introduction, the configuration with freights carried by bus services from an urban area to a rural area was adopted in the last century, but it disappeared for various reasons (see the last paragraph in Section 1.1). To the author’s knowledge, the main obstacle that stopped the implementation and promotion of the configuration was that the operation and management were not well-designed for consolidating freight and passenger transportation.

Without well-designed operation and management, people deliver their packages by bus, and drivers handle the packages with their own feet and hands. The charge for delivering packages with this mode would be expensive. For example, a driver charges an amount of 20 CNY as a fee for delivering a small package from a town to a surrounding city (a distance of less than 50 km). With the development of the logistics industry, sending a small package by couriers within a short distance is cheap, especially in China (5 CNY for a small parcel), and the price for sending packages by couriers is only a quarter of the price by a bus driver.

The consolidation with well-designed operation and management in this study can avoid the above problems, which is explained as follows.

• In this study, the parcel carrier is still the logistics company. With the benefits from consolidation, the courier charges will be reduced, thereby creating more demand.

• The consolidation in this study builds cooperation between the logistics and bus transit companies. There exists no competition between bus and logistics companies in this consolidation. Instead, the logistics and bus companies can reach a mutually beneficial solution to the current situation.

• The interval of the departure time of bus lines with the same origin and destination is over 30 min in practice. The time is sufficient to load the parcels to the buses’ baggage compartments. When buses are upgraded to carry more freights with empty space for passengers, a new entrance for uploading parcels should be built. In addition, with intricate planning of the departure time and the number of trucks from DCs, the parcels can be immediately sent to the nearest area of the arrival bus in the THs. Therefore, the consolidation in this study has no influence on the running time of the bus line services with a high probability. Moreover, the bus service providers can provide steadier and more frequent services since they are profitable, even though the number of passengers is not high, which can alleviate long passenger travel times caused by uncertain departure times of bus lines.

• In this case study, we took the salaries for extra staff into consideration: (i) We used a coefficient $\eta$ to represent the extra cost for employing staff, which was related to the parcel’s mass. (ii) We assumed that THs charge the bus service providers a management fee, and THs will charge bus service providers an extra fee for storing and handling freights, which includes the salary for extra staff. With the two considerations, the consolidation of freight and passenger transportation in this study is also beneficial to the logistics and bus companies, which proves that the benefits generated from well-designed consolidation can cover extra costs to realize the consolidation.

The above discussion indicates that the well-designed consolidation method of freight and passenger transportation in the urban–rural transit system proposed in this study can address the problems caused by using bus services to carry freights.

6. Conclusion

In this study, we investigated the possibility of consolidating passenger and freight transportation in urban–rural transit systems, in which buses can carry both passengers and freights for better travel demand. Mixed-integer programming was proposed to describe such a traffic system. The model is flexible and can describe different cases (e.g., the adoption of warehouses and multi-class trucks). The model can also describe the consolidation of passenger and freight transportation in different traffic networks (e.g., different road networks in an urban area and different TH–town pairs) by predesigning truck routes and some related sets.

A case study of the consolidation with the urban–rural transit system in Hangzhou, China was then analyzed. In the case study, the mixed-integer program determined the assignments of freight flow from DCs to THs with the information from urban–rural transit systems (e.g., the departure time and available space of buses). The numerical results indicated that the trucks departing from a DC always visit the nearest TH to deliver the freights. The warehouses in THs can improve the efficiency of the urban–rural transit system with the consolidation of passenger and freight transportation, as can the adoption of mini-vans and electric buses. The consolidation can benefit both logistics and bus companies if bus companies charge logistics companies reasonable fees. The bus companies can also have the opportunity to provide buses with higher frequency and improve the transit service between urban and rural areas. In addition, the consolidation is also beneficial to society by promoting the sustainability of the transportation sector and breaking the geographical barrier between urban and rural areas.

In practice, we must first calibrate the travel time between DCs to THs and the travel time between THs from the data. We can then construct a feasible set of routes for trucks. In future studies, we will investigate how to use historical traffic data to predesign a route set with both flexibility and robustness. In addition, we are also interested in the transportation mode choices of the passengers from an urban area to a rural area, and then we can quantitatively investigate the benefit of the urban–rural transit system to society (recall that intercity buses are energy efficient and thus eco-friendly).

Declaration of competing interest

The authors declare that they have no conflicts of interest in this work.

Biographies

Tao Wang received the B.Eng. degree and Ph.D. degree from Beihang University, in 2016 and in 2021. He was a postdoctoral fellow in School of Vehicle and Mobility, Tsinghua University, Beijing, China from 2021 to 2023. He is currently an associate professor in Hefei University of Technology, Hefei, Anhui. His research interests include transportation system modeling and optimization, autonomous vehicle’s operation, and travel behavior analyses.

Hongzhang Shao is a PhD candidate in operations research at the Georgia Institute of Technology. His research interests lie at the intersection of mathematical optimization, revenue management and transportation systems.

Xiaobo Qu received the BEng degree from Jilin University, Changchun, China, the M.Eng. degree from Tsinghua University, Beijing, China, and the PhD degree from the National University of Singapore, Singapore. He is currently a Changjiang Chair Professor of intelligent transportation with Tsinghua University, Beijing, China. His research interests include integrating emerging technologies into urban transport system. He is an Elected Member of Academia Europaea—the Academy of Europe.

Jonas Eliasson received his Ph.D. degree in transport and location analysis from KTH Royal Institute of Technology, Sweden in 2000. He is currently the director of Transport Accessibility at the Swedish National Transportation Administration, Fellow of the Royal Swedish Academy of Engineering Sciences (IVA), and visiting professor at Linköping University, Sweden. His research interests focus on transport policy design and evaluation, including areas such as cost-benefit analysis, transport pricing, railway capacity allocation, transport demand modeling, congestion charges, decision making in the transport sector, public and political acceptability of transport policies, and valuations of travel time and reliability.

Appendix A. Parameters in urban–rural transit system

This appendix presents the parameters of the case study.

• Data of the urban–rural transit in Hangzhou

We first present the travel time and distance data on weekdays at 17:00 between the TH and DC, TH and TH, and TH and towns in Table A.1. We also collect the travel time data in another period on weekdays to evaluate the feasibility of the routes in the case study, but we do not list it for brevity and to avoid redundancy. Then, the departure times of bus lines between THs and towns (counties) are summarized in Table A.2. According to the freight standard in China, the freight charge is about 0.42 CNY/km/${\mathrm{m}}^3$ if the transport distance is within 100 km.

Table A.1.

Distance and travel time on weekday at 17:00, 2022-03-17 between transport hubs (THs), distribution centers (DCs), and Ts (km/min).

	DC1	DC2	DC3	TH1	TH2	TH3	TH4	TH5
TH1	13/21	25/36	9/17	N/A	8.9/18	16/35	21/49	19/41
TH2	14/29	16/35	17/40	8.2/21	N/A	10/30	14/41	16/40
TH3	19/25	22/39	29/45	17/32	11/25	N/A	16/37	15/43
TH4	28/58	24/48	35/59	23/43	19/45	15/52	N/A	27/11
TH5	31/57	11/31	34/59	19/46	17/43	22/45	11/27	N/A
T1	91/104	110/109	109/112	105/100	93/103	104/92	82/79	99/90
T2	75/92	65/73	89/106	83/88	70/95	72/85	37/52	52/51
T3	95/105	75/72	96/105	84/86	80/95	121/102	67/82	64/62
T4	63/70	40/46	62/73	50/60	49/63	104/92	50/67	44/51
T5	61/105	64/63	49/56	53/56	57/66	69/73	71/94	79/97
T6	69/69	70/71	60/61	59/56	66/66	75/76	79/93	73/79

Table A.2.

Scheduled times of the bus lines in Hangzhou.

Shift No.	TH-Town Pairs
	TH1-T1	TH2-T1	TH3-T1	TH4-T1	TH2-T2	TH4-T2	TH2-T3	TH5-T3	TH1-T4	TH1-T5	TH1-T6
1	07:15	07:40	06:35	07:30	09:00	09:50	07:20	06:20	10:00	07:20	07:40
2	08:00	08:25	07:20	08:10	09:00	09:50	07:50	06:40	12:10	07:55	08:20
3	09:50	09:50	08:00	09:00	09:00	09:50	08:20	07:00	14:05	08:25	09:00
4	11:50	10:20	08:40	09:30	09:00	09:50	08:50	07:20	16:05	09:05	09:40
5	14:20	11:20	09:10	10:00	09:00	09:50	09:20	07:50		09:50	10:25
6	16:20	12:30	09:35	10:50	09:00	09:50	09:55	08:10		10:20	11:10
7	19:10	14:00	09:50	11:40	09:00	09:50	10:30	08:30		11:30	11:50
8		15:10	10:00	12:20			11:05	08:50		12:10	12:40
9		16:20	10:25	13:00			11:40	09:20		13:05	13:20
10		16:50	10:50	13:40			12:15	09:40		13:35	14:00
11		18:00	11:30	14:30			12:50	10:00		14:35	14:40
12		19:40	12:10	15:00			13:10	10:20		15:15	15:20
13			12:50				13:40	10:50		16:05	16:00
14			13:20				14:10	11:10		16:40	16:40
15			13:50				14:40	11:50		17:45	17:30
16			14:20				15:15	12:40		18:35	18:20
17			14:50				15:45	13:00
18			15:20				16:20	13:20
19			16:00				17:00	13:50
20			16:35				17:45	14:10
21			17:15				18:25	14:30
22			17:40				19:20	14:50
23			18:10					15:20
24			18:40					15:40
25			19:40					16:05
26								16:30
27								16:55
28								17:25
29								17:55
30								18:30

Note: TH1–TH5 represent “Hangzhou Transport Center”, “Hangzhou East Station”, “Hangzhou South Station”, “Hangzhou West Station”, and “Hangzhou North

Station”, respectively. T1–T6 represent the surrounding cities and countries “Tonglu”, “Linan”, “Anji”, “Deqing”, “Tongxiang”, and “Haining”, respectively.

The capacity of the frequently used truck in expressway delivery is 12 ${\mathrm{m}}^3$. The buses between the THs and towns are listed on the websites. We have surveyed more than 100 travelers and drivers in THs about the available spaces of buses, and 20% to 80% space of baggage compartments are empty in the workday based on the survey. We set the empty space as a stochastic variable that obeys a normal distribution. The standard baggage capacities are 0.15 ${\mathrm{m}}^3$ per passenger for a medium bus, 0.19 ${\mathrm{m}}^3$ per passenger for a “High II” large bus, and 0.22 ${\mathrm{m}}^3$ per passenger for a “High III” large bus in China. These were also considered in some of the numerical tests when the space for passengers was also utilized to carry freights by renovating the bus.

To estimate the extra cost caused by carrying freights, the energy consumption was calculated according to previous work [23]. The average fuel consumption per 100 kg per 100 km of the coach was 0.12 L, the average energy consumption per 100 kg per 100 km of the city bus was about 0.3 kWh, and the counterpart for a coach was lower than 0.3 kWh due to the steady speed in the highway. Thus, the cost of a bus for carrying freights per unit weight on a given bus line is calculated as

$${\varphi }_j=10·{\alpha }_{\text{energy}}·l_j·d_{\text{freight}}·(1+\eta )$$ (A.1)

where ${\alpha }_{\text{energy}}$ is the unit energy consumption ($\text{kWh}$ or $\mathrm{L}$) per 100 km per 100 kg of the bus for carrying freights, $l_j$ is the distance of the bus line, $d_{\text{freight}}$ is the average density $(\text{kg}/{\mathrm{m}}^3)$ of the freights, and $\eta$ is a parameter indicating the cost of extra service and bus depreciation caused by carrying freights. We set the value of $\eta$ to 0.4 in the case study.

• Operation cost of bus

We present the relevant data for evaluating the benefit of the consolidation of passengers and freights on the bus companies. The sum of the price of a large coach bus and the cost of repair and maintenance was about 0.7 million CNY, and the scrap cycle of the bus was 10 years, we calculated the depreciation expense over 8 years. The energy consumption was about 0.85 CNY per 100 km per 100 kg. The road toll was about 1 CNY per km with a discount card for a large coach bus. The insurance and road maintenance fee was about 160 CNY per day.

In addition, THs charged the bus service providers a management fee whose value was 10% of the total fares of the passengers. When the urban–rural transit carried the freight, the TH charged bus service providers an extra fee for storing and handling freights. For simplicity, we set the extra fee as a certain ratio of the passenger fares3, and the default ratio in the case study was 10%.

The available space of the bus was dependent on the number of passengers in the bus. $a_j$ represents the number of passengers on bus line $j$. The available space of the bus was $s_j$, and $s_j=0.2·a_j+0.22·(\bar{a}-a)$ according to the baggage capacity standard and the data of available space in the survey. The distribution of $a$ was obtained from the ticket booking data in mobile applications, which could be described by a normal distribution, as shown in Fig. A.1.