Pricing of the Bus-Truck Co-Delivery Mode of Last Mile Delivery Considering Social Welfare Maximization

Abstract

In order to solve the problems of low delivery efficiency and high cost at the end of express delivery, and the impact of express trucks on urban road traffic, the co-delivery mode of trucks and buses is proposed. In this mode, without affecting the normal operation of the bus, it uses the idle resources of the bus to cooperate with the trucks to complete the delivery. The express company pays the bus delivery service fee to the bus operator, so as to improve the revenue of the bus operator. At the same time, the delivery efficiency can be improved, the express delivery cost can be reduced, and the impact of express trucks on urban traffic can be lower. A two-layer optimization model is constructed to solve the bus delivery service pricing and express space-time path selection scheme under the co-delivery mode. An example analysis is carried out through the actual bus routes and express delivery demand in Dalian. The results show that the co-delivery mode can provide consumers with more efficient services, reduce costs for express companies, provide additional revenue for bus operators, and improve social welfare. Unless the timeliness of delivery is extremely considered, the measure of using the co-delivery mode is better than the measure of relaxing restrictions on express delivery vehicles.

1. Introduction

In 2021, the national express delivery business volume reached 108.30 billion pieces [1], a year-on-year increase of 29.9%. The express delivery industry has already reached a considerable scale and has become an important industry that is practically related to the quality of life of citizens, supports the manufacturing industry, and drives product sales. The state has also incorporated the development of the express delivery industry into the plan [2,3] and regards improving the quality of express delivery services as one of the main goals of express delivery development. The government proposes that “by 2035, it will reach the delivery time limit of 1 day in major domestic cities, 3 days in major cities in neighboring countries, and 5 days in major cities around the world.” Terminal express delivery takes 1–2 days, which has become a bottleneck restricting the improvement of express delivery efficiency. Urban road restrictions are an important factor restricting the efficiency of terminal delivery [4], which leads to detours of delivery trucks and the night work of delivery personnel. To this end, the government has especially relaxed the restrictions on the passage of delivery trucks for express delivery and adopted the policy of issuing passes for express delivery trucks to drive in restricted areas/sections. However, the passage of express delivery trucks will undoubtedly cause a negative impact on urban road traffic, which is reflected in increased road congestion, increased traffic environmental load, reduced road traffic safety, and driving burdens for car drivers. How to achieve both timeliness in express delivery and a good urban road traffic environment are important issues that need to be solved urgently for the healthy and sustainable development of the express industry and urban traffic.

In fact, the problems of low express delivery efficiency and the impact of express delivery trucks on urban road traffic can be solved at the same time [5,6] by carrying express delivery boxes in the free space of ground buses. Public transit is not affected by the traffic restriction policy, and it has the advantages of a high frequency of departure and full coverage of the city. With the high-frequency and small-batch delivery of existing public transit, the timely, efficient, green, and low-carbon distribution of express delivery can be realized [7], and the mileage of trucks can be reduced [8,9]. In addition, the operation of public transit has been losing money all year round, and it relies on government subsidies to maintain operations. The express transportation business can generate revenue for public transit and reduce the financial pressure on the government caused by its perennial deficit. Under the bus-truck co-delivery model, the government is the price setter of the bus transportation express business. Its primary goal is to maximize social welfare. Secondly, to make up for the bus operation deficit, its second goal is to maximize bus revenue. Express delivery companies are the decision-makers of express delivery. Their purpose is to complete the delivery of all parcels with the lowest cost and the highest efficiency [10]. The fee for public transit transportation is a part of its cost. Therefore, the pricing of public transit transportation is the key to the bus-truck co-delivery model.

The research on passenger and cargo integrated transportation was first proposed by Trentini and Mahléné in 2010 [11], and then it was explored in air, sea [12], railway [13,14], and intercity transportation [15], but rarely in urban express delivery. Sampaio et al. [16] analyzed a case of passenger and cargo integrated transportation in urban express delivery. Schlenther et al. [17] studied the potential of private vehicles in express delivery. Zhou et al. [18] studied the route optimization problem using the co-delivery of subways and trucks. Nocera et al. [19] analyzed how to evaluate and plan the last-mile integrated transportation of passenger and cargo. Galkin et al. [20] studied the mode of parcel delivery by public transit. Zhao and Zhu [21] compared the “bus” mode and “taxi” mode for same-day delivery. Marcucci et al. [22] investigated under which conditions passengers would be willing to act as crowd shippers and found out under which conditions people would be willing to receive their goods via a crowd-shipping service. Di et al. [23] investigated the joint optimization problem of carriage arrangement and flow control in a metro-based underground logistics system, in which passengers and freights share each service train. Peng et al. [24] integrated the passenger and freight transportation at the railway station by a bus-pooling service. Most of the above studies consider the overall optimality of the passenger and freight system and rarely consider the interest relationship between bus operators and express delivery companies or the impact of the freight vehicle restriction policy. However, the pricing of the bus delivery service directly affects the realization and scale of the bus-truck co-delivery mode, and the freight vehicle restriction policy directly affects the price of the bus delivery service.

The spatiotemporal path optimization problem of express delivery in the bus-truck co-delivery mode is essentially the route optimization problem of the heterogeneous vehicle with soft time windows. Its soft time window shows in the requirements of the delivery time of express delivery. The heterogeneity is reflected in the differences in the rated cargo capacity, transportation speed, and transportation flexibility between buses and trucks. The soft time window heterogeneous vehicle routing problem is a derivative of the vehicle routing problem [25], which is a combination of the soft time window vehicle routing problem [26] and the heterogeneous vehicle routing problem [27,28,29]. There is a lot of research on these problems. They are mature in both model construction and solution algorithms. However, there are few studies considering the restriction of trucks. Xiao et al. [30] studied the route optimization problem of multi-energy and multi-vehicle types under the travel restriction scenario. Du et al. [31] studied the problem of reasonably allocating the proportion and quantity of traditional energy and new energy vehicles in the logistics distribution fleet when the number of vehicles and the delivery time is uncertain under the travel restriction scenario.

In this paper, a two-layer optimization model analyzing the relationship between the government and express delivery companies is built. In the upper-layer model, a public transportation distribution pricing model is constructed to solve the optimal pricing of the bus delivery service with the objective function of the maximization of social welfare and public transportation operation revenue. In the lower-layer model, an optimization model of the express delivery time-space route is constructed to solve the spatiotemporal path of express delivery based on the known bus delivery pricing, with the objective function of minimizing the cost to express companies. Then, based on the actual data of Dalian City, the results of the bus-truck co-delivery mode under the truck restriction policy and the results of the truck direct delivery mode under the non-restriction policy are solved. The two strategies of the co-delivery mode and the cancellation of the express delivery truck restriction are compared and analyzed.

2. Problem Description

The minimum research scenario for the bus-truck co-delivery mode is one bus route, multiple express companies, and one courier station scenario, as shown in Figure 1.

The distribution centers of these express companies are all in a same area. The parcels are standardized through Cargo Carrying Units (CCUs). Since parcels arrive at the distribution center in batches, an express delivery company may have multiple delivery needs in one day. Delivery demand i of express company m has a delivery demand $d_i$ and its delivery time window $(t_i^s,t_i^e$). Each delivery demand has two modes of delivery from which to choose. The first is direct delivery by truck; that is, the truck at express delivery station D drives to distribution center O to pick up the parcels, then drives back to D. The second is the bus-truck co-delivery mode; that is, the minivans in the distribution center O transport the parcels to bus stop A, the bus transports them to bus stop B, and then another minivan drives from station D pick up the parcels and deliver them to station D. In order to minimize the impact on bus passengers, buses can only load and unload parcels at the first and last stations, not at intermediate stations, and the frequency of bus departures and bus travel routes also can’t be changed.

3. Model Construction

In this section, a two-layer model is built. The upper layer is a bus delivery service pricing model, with the goal of maximizing social welfare and bus revenue. The price of the bus delivery service and the bus transformation plan are calculated. The lower layer is the delivery mode and space-time route selection model, aiming at minimizing the cost of express delivery and solving the express delivery plan, including the delivery mode, the departure time of vehicles, the delivery routes, and so on.

3.1. Pricing Model of the Co-Delivery Mode

This model aims at maximizing social welfare and bus revenue. It is assumed that the operation route and departure time of the buses won’t be changed, only a place on the bus will be transformed for express delivery boxes; therefore, the transforming cost is only the cost of the bus retrofitting. Social welfare, $W$, is determined by the revenue of the bus operator, $R^B$; the cost to the express companies, $C$; and the consumer surplus, $S$. Since the customer surplus is mainly determined by the delivery delay, and the delivery delay is also considered in the cost to the express company, it is not repeated here (see Equation (1)).

$$W=R^B-C$$

(1)

$R^B$ is expressed as the difference between the income obtained by the express delivery of the bus, $P^B$, and the cost of the bus renovation, $C^B$, as shown in Equation (2).

$$R^B=P^B-C^B$$

(2)

$P^B$ is determined by the pricing function $P\left(q_{m_i}\right)$ and the number of parcels transported by buses (see Equation (3)). $x_{m_i}$ is a 0–1 variable. When $x_{m_i}$ = 1, it means that express delivery batch i of express company m is transported by bus; otherwise, it means that this batch of express delivery is not transported by bus. Referring to the air cargo transportation pricing rules [32], the pricing function $P\left(q_{m_i}\right)$ is designed as Equation (4). $q_{m_i}$ is the number of parcels in batch i of express company m. $\alpha$ and $\beta$ are parameters; see Equations (5) and (6).

$$P^B={\displaystyle {\displaystyle \sum }_{m,i}}P\left(q_{m_i}\right)x_{m_i}$$

(3)

$$P\left(q_{m_i}\right)=\alpha +\beta q_{m_i}$$

(4)

$$\alpha \ge 0$$

(5)

$$\beta \ge 0$$

(6)

$x_{m_i}$ is determined by $x_{m_i,b_j}$; see Equation (7). $x_{m_i,b_j}$ is a 0–1 variable. When parcels in batch i of express company m are transported by bus b in departure j, $x_{m_i,b_j}$ = 1. Otherwise, $x_{m_i,b_j}$ = 0.

$$x_{m_i}=\{\begin{array}{ll}1,& {\displaystyle {\displaystyle \sum }_{b,j}}{x}_{m_i,b_j}\ge 1\\ 0,& {\displaystyle {\displaystyle \sum }_{b,j}}{x}_{m_i,b_j}=0\end{array},\forall m,i$$

(7)

$C^B$ is determined by depreciation cost of retrofitting a single bus, $c^B$, and the number of buses retrofitted, ${\displaystyle {{\displaystyle \sum }}_b}{x}_b$, as shown in Equation (8). $x_b$ is a 0–1 variable. When bus b is retrofitted, $x_b$ = 1. Otherwise, $x_b$ = 0.

$$C^B=c^B{\displaystyle {\displaystyle \sum }_b}{x}_b$$

(8)

The cost to the express companies, $C$, includes the depreciation cost of trucks, $C^K$; the co-delivery cost, $C^C$; the direct delivery cost, $C^V$; and the penalty cost of delivery delay, $C^T$, as shown in Equation (9).

$$C=C^K+C^C+C^V+C^T$$

(9)

$C^K$ is determined by the depreciation cost per truck, $c_k$, and number of trucks, as shown in Equation (10). $y_k$ is a 0–1 variable. When truck k is used to deliver the parcels, $y_k$ = 1. Otherwise, $y_k$ = 0. k is the truck serial number, $k\in K^1{{\displaystyle \cup }}^{}{K}^2$. $K^1$ is the set of trucks departing from the distribution centers of various express companies. $K^2$ is the set of trucks departing from the express delivery station.

$$C^K={\displaystyle {\displaystyle \sum }_{k\in K^1{{\displaystyle \cup }}^{}{K}^2}}{c}_k{y}_k$$

(10)

$y_k$ is an intermediate variable, which is determined by $y_{m_i,k_{j^{\prime }}}$ through the functional relationship of Equations (11) and (12). $y_{m_i,k_{j^{\prime }}}$ is a 0–1 variable. When parcels in batch i of express company m are transported by truck k in departure $j^{\prime }$, $y_{m_i,k_{j^{\prime }}}$ = 1. Otherwise, $y_{m_i,k_{j^{\prime }}}$ = 0. $y_{k_{j^{\prime }}}$ is a 0–1 variable. When truck k is used for express delivery in departure $j^{\prime }$, $y_{k_{j^{\prime }}}$ = 1. Otherwise, $y_{k_{j^{\prime }}}$ = 0.

$$y_k=\{\begin{array}{ll}1,& {\displaystyle {\displaystyle \sum }_{j^{\prime }}}{y}_{k_{j^{\prime }}}\ge 1\\ 0,& {\displaystyle {\displaystyle \sum }_{j^{\prime }}}{y}_{k_{j^{\prime }}}=0\end{array},\forall k,j^{\prime }$$

(11)

$$y_{k_{j^{\prime }}}=\{\begin{array}{ll}1,& {\displaystyle {\displaystyle \sum }_{m,i}}{y}_{m_i,k_{j^{\prime }}}\ge 1\\ 0,& {\displaystyle {\displaystyle \sum }_{m,i}}{y}_{m_i,k_{j^{\prime }}}=0\end{array},\forall k,j^{\prime }$$

(12)

In the co-delivery mode, parcels are transported from the distribution center of each express company by truck to the first bus stop, then by bus to the last bus stop, and finally by truck from the last bus stop to the express delivery station. The cost of co-delivery, $C^C$, includes the delivery cost of trucks at both ends, $C^{CV}$; the cost of bus delivery, $C^{CB}$; the cost of loading, $C^{CL}$; and the cost of unloading, $C^{CUL}$, as shown in Equation (13).

$$C^C=C^{CV}+C^{CB}+C^{CL}+C^{CUL}$$

(13)

$C^{CV}$ is determined by the per kilometer fuel cost, $c^f$; the travel distance of the trucks at the two ends ($d_m^{OF}$ and $d^{ED}$); and the number of deliveries, as shown in Equation (14). The cost of bus delivery, $C^{CB}$, is the freight paid to the bus operator, as shown in Equation (15).

$$C^{CV}={\displaystyle {\displaystyle \sum }_m}[2c^f\left(d_m^{OF}+d^{ED}\right){\displaystyle {\displaystyle \sum }_{j^{\prime },k\in K^2}}{y}_{k_{j^{\prime }}}]$$

(14)

$$C^{CB}={\displaystyle {\displaystyle \sum }_{m,i}}\left(\alpha +\beta q_{m_i}\right)x_{m_i}$$

(15)

$C^{CL}$ and $C^{CUL}$ are determined by the unit loading cost, $c^L$; unit unloading cost, $c^{UL}$; and volume of parcels delivered, ${\displaystyle {{\displaystyle \sum }}_{b,j}}{q}_{b_j}$. In the co-delivery mode, one parcel should be loaded and unloaded three times, so the total cost of loading and unloading is as Equation (16) shows.

$$C^{CL}+C^{CUL}={\displaystyle \sum }_{b,j}3\left(c^L+c^{UL}\right)q_{b_j}$$

(16)

$C^V$ includes the truck delivery cost, $C^{VV}$; loading cost, $C^{VL}$; and unloading cost, $C^{VUL}$, as shown in Equation (17).

$$C^V=C^{VV}+C^{VL}+C^{VUL}$$

(17)

$C^{VV}$ is determined by the per-kilometer fuel cost, $c^f$; the travel distance, $d_{m,k_{j^{\prime }}}^{OD}$; and the number of deliveries, as shown in Equation (18). Due to the Urban Truck Restriction Policy, for the same OD, the travel distance of trucks in different time periods is different, as shown in Equation (19). When the departure time of the truck, $t_{k_{j^{\prime }}}^{O1}$ or the completion time of the delivery, $t_{k_{j^{\prime }}}^{O1}+2d_m^{OD,UTC}/v_k$, is within the restricted time window $\left(t^{W1},t^{W2}\right)$, the travel distance of the truck, $d_{m,k_{j^{\prime }}}^{OD}$ is taken as the travel distance when the truck is restricted: $d_m^{OD,TC}$. Otherwise, it’s taken as the travel distance when the truck is unrestricted: $d_m^{OD,UTC}$. The number of deliveries for the direct delivery mode is the difference between the total number of truck deliveries at the head end, ${{\displaystyle \sum }}_{j^{\prime },k\in K^{m1}}{y}_{k_{j^{\prime }}}$, and the number of truck deliveries at the head end for the co-delivery mode, ${{\displaystyle \sum }}_{j^{\prime },k\in K^{m2}}{y}_{k_{j^{\prime }}}$. Among them, $K^{m1}$ represents the set of vehicles placed by express company m at the head end, and $K^{m2}$ represents the set of vehicles placed by express company m at the end.

$$C^{VV}={\displaystyle \sum }_{m}2c^f{d}_{m,k_{j^{\prime }}}^{OD}\left({\displaystyle \sum }_{j^{\prime },k\in K^{m1}}{y}_{k_{j^{\prime }}}-{\displaystyle \sum }_{j^{\prime },k\in K^{m2}}{y}_{k_{j^{\prime }}}\right)$$

(18)

$$d_{m,k_{j^{\prime }}}^{OD}=\{\begin{array}{c}{d}_m^{OD,TC},t^{W1}\le t_{k_{j^{\prime }}}^{O1}\le t^{W2}\mathrm{or}{t}^{W1}\le t_{k_{j^{\prime }}}^{O1}+2d_m^{OD,UTC}/v_k\le t^{W2}\\ d_m^{OD,UTC},otherwise\end{array},\forall k,j^{\prime },m$$

(19)

In the direct delivery mode, parcels are loaded and unloaded once. The loading cost, $C^{VL}$, and unloading cost, $C^{VUL}$, are calculated by Equation (20).

$$C^{VL}+C^{VUL}=\left(c^L+c^{UL}\right)\left({\displaystyle \sum }_{m,i}{q}_{m_i}-{\displaystyle \sum }_{b,j}{q}_{b_j}\right)$$

(20)

The penalty cost of delivery delay, $C^T$, is related to the delay penalty coefficient, $\tau$, and the delay time, as shown in Equation (21).

$$C^T=\tau {\displaystyle \sum }_{m,i,j^{\prime },k}max[\left(t_{k_{j^{\prime }}}^{D2}-t_{m_i}^e\right),0]y_{m_i,k_{j^{\prime }}}$$

(21)

3.2. The Optimization Model of Express Delivery Space-Time Path

The model aims at the lowest cost, C, of express companies, as shown in Equation (22).

$$Min C$$

(22)

S.T.

(1)

Constraints on the choice of express delivery modes

The same batch of parcels can only be delivered in one mode, as shown in Equation (23).

$$\left({\displaystyle \sum }_{m,i}{x}_{m_i}{y}_{m_i,k_{j^{\prime }}}-{\displaystyle \sum }_{m,i}{y}_{m_i,k_{j^{\prime }}}\right){\displaystyle \sum }_{m,i}{x}_{m_i}{y}_{m_i,k_{j^{\prime }}}=0,\forall k\in K^1,j^{\prime }$$

(23)

(2)

Vehicle Loading Constraints

The actual loading capacity of the bus, $q_{b_j}$, cannot exceed the rated loading capacity of the bus, $q_{b_j}^0$, as shown in Equation (24). The retrofitted buses should be the buses that have been selected for express delivery; that is, the actual loading capacity, $q_{b_j}$ is greater than 0. The other buses cannot be used for express delivery; that is, the actual load, $q_{b_j}$ needs to be 0 (see Equations (25) and (26)).

$$q_{b_j}\le q_{b_j}^0,\forall b,j$$

(24)

$$q_{b_j}-x_{m_i,b_j}\ge 0,\forall b,j,m,i$$

(25)

$$q_{b_j}\left(x_{m_i,b_j}-1\right)\ge 0,\forall b,j,m,i$$

(26)

$$q_{b_j}\in N,\forall b,j$$

(27)

The actual loading of the truck cannot exceed the rated loading of the truck, $q_k^0$, as shown in Equation (28). Among them, $q_{m_i,k_{j^{\prime }}}$ represents the volume of batch i of express delivery of express company m through the j′th departure of truck k.

$${\displaystyle \sum }_i{y}_{m_i,k_{j^{\prime }}}{q}_{m_i,k_{j^{\prime }}}\le q_k^0,\forall m,k,j^{\prime }$$

(28)

In order to avoid the confusion caused by different express delivery companies, it is assumed that a bus can only carry parcels of one express delivery company at a time, as shown in Equation (29). The trucks belong to different express companies, so it is assumed that express companies can only use their own trucks to deliver parcels, as shown in Equation (30).

$${\displaystyle \sum }_{m,i}{x}_{m_i,b_j}\le 1,\forall b,j$$

(29)

$$y_{m_i,k_{j^{\prime }}}=0,k\in \left(K-K^m\right),\forall m,i,j^{\prime }$$

(30)

(3)

Flow Conservation Constraint

Equation (31) guarantees that all parcels are delivered. Equation (32) ensures that all parcels delivered to the first bus stop are transported by bus. Equation (33) ensures that all parcels delivered to the last bus stop are delivered to the express delivery station.

$${\displaystyle \sum }_{j^{\prime },k\in K^1}{y}_{m_i,k_{j^{\prime }}}{q}_{m_i,k_{j^{\prime }}}=q_{m_i},\forall m,i$$

(31)

$${\displaystyle \sum }_{m,i,k\in K^1,j^{\prime }}{x}_{m_i}{q}_{m_i,k_{j^{\prime }}}={\displaystyle \sum }_{b,j}{q}_{b_j}$$

(32)

$$x_{m_i}{q}_{m_i}={\displaystyle \sum }_{j^{\prime },k\in K^2}{y}_{m_i,k_{j^{\prime }}}{q}_{m_i,k_{j^{\prime }}},\forall m,i$$

(33)

(4)

Time coherence constraints

Due to the short loading and unloading time of express delivery boxes, these are not included in the scope of consideration. At the distribution center, parcels should be loaded before the truck departs, as shown in Equation (34). $t_{m_i}^s$ represents the time when the ith batch parcels of express delivery company m arrived at the distribution center, and $t_{k_{j^{\prime }}}^{O1}$ represents the departure time of the $j^{\prime }$th departure of truck k.

$$t_{m_i}^s{y}_{m_i,k_{j^{\prime }}}\le t_{k_{j^{\prime }}}^{O1}{y}_{m_i,k_{j^{\prime }}},\forall k\in K^1,m,i,j^{\prime }$$

(34)

Parcels delivered by buses should be loaded before the bus departs, as shown in Equation (35). $d_m^{OF}$ is the shortest travel distance between the distribution center of express company m and the first bus stop, $v_k$ is the travel speed of the truck, and $t_{b_j}^{F1}$ is the departure time of the jth departure of bus b.

$$\stackrel{maxk\in K^1,j^{\prime }}{\to }\left\{y_{m_i,k_{j^{\prime }}}\left[t_{k_{j^{\prime }}}^{O1}+d_m^{OF}/v_k\right]\right\}{x}_{m_i,b_j}\le t_{b_j}^{F1}{x}_{m_i,b_j},\forall m,i,b,j$$

(35)

Since there is no storage space at the last bus stop, the truck should be already waiting when the bus arrives, as shown in Equation (36). $t_{k_{j^{\prime }}}^{D1}$ is the departure time of truck k in $j^{\prime }$th departure from the express delivery station.$d^{ED}$ is the shortest travel distance between the last bus stop and the express delivery station.$t_{b_j}^{E2}$ is the arrival time of bus b at the jth departure. Congestion and unexpected situations on the road are not considered, so $t_{b_j}^{E2}$ is a known variable.

$$\stackrel{maxk\in K^2,j^{\prime }}{\to }\left[y_{m_i,k_{j^{\prime }}}\left(t_{k_{j^{\prime }}}^{D1}+d^{ED}/v_k\right)\right]x_{m_i}\le \stackrel{minb,j}{\to }\left(t_{b_j}^{E2}{x}_{m_i,b_j}\right),\forall m,i$$

(36)

In addition, the time interval between two departures of the same truck should be sufficient for the truck to complete the express delivery, as shown in Equations (37) and (38). $t_{k_{j^{\prime }}}^{D2}$ is the time when truck k returns to the station on the $j^{\prime }$th departure, and $t_{k_{j^{\prime }}}^{O2}$ is the time when truck k returns to the distribution center on the $j^{\prime }$th departure, as shown in Equations (39) and (40).

$$t_{k_{j^{\prime }+1}}^{D1}\ge t_{k_{j^{\prime }}}^{D2},\forall k\in K^2,j^{\prime }$$

(37)

$$t_{k_{j^{\prime }+1}}^{O1}\ge t_{k_{j^{\prime }}}^{O2},\forall k\in K^1,j^{\prime }$$

(38)

$$t_{k_{j^{\prime }}}^{D2}=\stackrel{maxm,i}{\to }{t}_{b_j}^{E2}{y}_{m_i,k_{j^{\prime }}}+d^{ED}/v_k,\forall k\in K^2,j^{\prime }$$

(39)

$$t_{k_{j^{\prime }}}^{O2}=\{\begin{array}{c}{t}_{k_{j^{\prime }}}^{O1}+2d_m^{OF}/v_k,y_{m_i,k_{j^{\prime }}}{x}_{m_i}=1\\ t_{k_{j^{\prime }}}^{O1}+2d_m^{OD}/v_k,y_{m_i,k_{j^{\prime }}}\left(x_{m_i}+1\right)=1\end{array},\forall k\in K^1,j^{\prime }$$

(40)

4. Case Study

A small-scale example is formed by taking the actual bus line (Line 1) in Dalian, one courier station, and the one-day delivery demand of two express companies. Before solving the model, the solution scale is analyzed to determine which algorithm should be selected. The decision variables of the upper model are the parameters α and β of the pricing function and the bus transformation scheme. Since these parameters are used for pricing, they do not need to be taken as continuous values, so the solution scale is as follows: the number of optional values of parameter α × the number of optional values of parameter β × the number of optional bus transformation schemes. As the decision of pricing function parameters needs to consider the game relationship between bus operators and express companies, there are rules to follow, so branch and bound method can be used. The lower model decides the express delivery space-time path’s selection scheme. In this paper, it is assumed that the bus departure time is fixed, and the trucks’ departure time should cooperate with the buses’, so the truck departure time is discrete and determined according to the bus operation plan. Furthermore, as the minimum research scenario is selected, the feasible solution of the space-time delivery path is small in scale and can be solved by the exact solution algorithm. To sum up, based on the above optimization model, the results of the co-delivery mode and the direct delivery mode are calculated by the exact solution. Then, the results are compared and analyzed.

4.1. Data

The bus route, the distribution centers and the courier station are shown in Figure 2. Each of the two express companies has 4 batches of parcels arriving at the distribution center every day and waiting for delivery. The express delivery information is shown in

Table 1. The express delivery information.

Serial Number of Batches of Parcels	Volume of Parcels (CCU)	Arriving Time at Distribution Centers	Express Company
1	12	8:00	1
2	9	10:48	1
3	15	12:19	1
4	10	14:27	1
5	15	9:40	2
6	15	11:57	2
7	8	14:00	2
8	11	15:40	2

. The values of other parameters are shown in

Table 2. Value of parameters.

Symbol	Definition	Value
$c^B$	depreciation cost of bus retrofitting	0.8 yuan/vehicle 1
$c_k$	the depreciation cost per truck	34.2 yuan/vehicle, 2.4 yuan/vehicle 2
$c^f$	the per kilometer fuel cost	0.8 yuan
$c^L$	unit loading cost	0.1 yuan/CCU
$c^{UL}$	unit unloading cost	0.1 yuan/CCU
$\left(t^{W1},t^{W2}\right)$	the restricted time window	(6:00,17:00)
$q_{b_j}^0$	the rated loading capacity of the bus	16 CCU
$q_k^0$	the rated loading of the truck	84 CCU
$v_k$	the travel speed of the truck	30 km/h

¹ The cost of retrofitting a single bus is 3000 yuan. The depreciation time is 10 years. 3000/10/365 ≈ 0.8 yuan/vehicle. ² Vehicles serving between O and D are vans, with a value of 100,000 yuan/vehicle. The depreciation time is 8 years. 100,000/8/365 ≈ 34.2 yuan/vehicle. Vehicles serving in the two ends are electric tricycles, with a value of 4380 yuan/vehicle. The depreciation time is 5 years. 4380/5/365 ≈ 2.4 yuan/vehicle.

.

4.2. Results under the Two Measures

This section analyzes the original scenario and the effects of the two measures. In the original scenario, express delivery vans need to obey the urban truck restriction policy, and parcels are delivered by the direct delivery mode. In measure 1, the traffic policy for express vehicles is relaxed, and parcel delivery still adopts the direct delivery mode. In measure 2, express delivery vans need to obey the urban truck restriction policy, and parcels are delivered by the co-delivery mode.

According to the status quo of express delivery, the length of the express delivery time window is set as 180 min (3 h). The penalty coefficient for express delivery delay is set as 32.4 yuan/h (the average salary in Dalian is 95,442 yuan/year, VOT = 95,442/365/8 ≈ 32.4 yuan/h). The results for the three scenarios are shown in

Table 3. Results of three scenarios.

		Original Scenario	Measure 1	Measure 2
Express Delivery	The number of express batches by co-delivery mode	-	-	8
	The number of express batches by direct delivery mode	8	8	0
	Delayed delivery batches	7	0	0
	Average delay time (h/CCU)	3	0	0
Express Company	Total delivery cost (yuan)	9678	234	565
	Vehicle depreciation cost (yuan)	68	68	10
	Fees paid to bus operators (yuan)	-	-	425
	Delivery cost of express delivery vehicles (yuan)	59	147	73
	Handling cost (yuan)	19	19	57
	Delay penalty cost (yuan)	9531	0	0
Bus operator	Income of bus operator (yuan)	-	-	425
	α	-	-	46
	β	-	-	0.60
	Number of retrofitting buses (vehicle)	-	-	2
	Revenue of bus operator (yuan)	-	-	423
City	Social Welfare (yuan)	−9678	−234	−142

.

Firstly, from the perspective of the express delivery scheme, there are 7 batches of express delivery delays in the original scenario (8 batches in total), and there are no express delivery delays in measure 1 and measure 2. It can be seen that in terms of improving express delivery delays, the relaxation of the express truck traffic policy and the use of the co-delivery mode have both good results. Secondly, from the perspective of express company revenue, in the original scenario, the total express delivery cost is 9678 yuan, of which the delay penalty cost is the most, accounting for 98.5%. In measure 1, the total express delivery cost is 234 yuan, which is 97.6% lower than that in the original scenario. In measure 2, the total express delivery cost is 565 yuan, a 94.2% reduction compared to the original scenario. To sum up, both measures can greatly reduce the total cost of express delivery. The measure of the relaxation of the express truck traffic policy is slightly better than the measure of adopting the co-delivery mode. From the perspective of cost structure, in the original scenario and measure 1, the fixed cost input of express companies is relatively large, and in measure 2, the fixed cost input of express companies is only 14.7% of that in the original scenario and measure 1. Thirdly, from the perspective of the revenue of the bus operator, in measure 2, two buses are in service for express delivery to one station and two express companies, and an additional revenue of 425 yuan can be obtained in one day. In the current situation of thousands of courier stations, dozens of express companies, and more than 200 bus lines in the city, co-delivery can create considerable income for bus operators. Finally, from the perspective of the whole city, the social welfare value of the original scenario is the smallest, and the social welfare value of measure 2 is the largest.

To sum up, by the co-delivery mode, the costs to express delivery companies can be cut, and the fixed costs are lower, which is more conducive to the capital turnover and sustainable development; an additional revenue of the bus operator can be created; more on-time, high-quality service can be provided to consumers; and the biggest social welfare value can be obtained.

4.3. Sensitivity Analysis of Different Time Windows and Delay Penalty Coefficients

Considering the continuous improvement of the express delivery timeliness requirements, and the difference in the consignee’s perception of express delivery delays, the sensitivity analysis of the express delivery time window length and delay penalty coefficient is carried out. The time windows are set as 1–5 h and no time window (15 h). The delay penalty coefficients are set as 0, 1/2 VOT (16.2), VOT (32.4), 3/2 VOT (48.6), 2 VOT (65.4). The results of the above three scenarios are shown in Figure 3, Figure 4 and Figure 5.

In the original scenario, due to the urban truck restriction policy, no matter when parcels arrive at the distribution center, they can only be delivered during the non-restricted time; that is, after 17:00. Therefore, as shown in Figure 3, the delay of express delivery is directly related to the length of the time window. The shorter the time window, the more delayed batches and the longer the average delay time. The delay penalty coefficient has no effect on the delay situation, but only affects express companies’ costs and social welfare. The larger the delay penalty coefficient, the higher the cost to express delivery companies and the smaller the social welfare value.

In measure 1, when the delay penalty coefficient is not 0 and the time window is within 2 h, some batches of parcels are delayed, and when the time window length exceeds two hours, all parcels are delivered on time. When the delay penalty coefficient is 0, the number of delayed batches and the average delay time decrease with the increase of the time window length. Both the cost to express companies and social welfare decrease with the increase in the length of the time window and the decrease of the delay penalty coefficient. It can be seen that, in measure 1, the length of the time window has a phased effect on the improvement of the timeliness of express delivery. When the length of the time window is shortened to a certain extent, out of comprehensive consideration of cost and efficiency, express companies will not increase the number of departures to shorten the delivery time. And the setting of the delay penalty coefficient can improve the timeliness of express delivery.

In measure 2, when the delay penalty coefficient is not 0 and the time window length is 1 h, all parcels are delayed, and the average delay time is 0.47 h; when the time window length is greater than 1 h, all parcels arrive on time. This is because the average speed of buses is lower than that of express delivery vans, and the bus delivery section takes 58 min. The shortest time taken by the co-delivery mode exceeds one hour. It can be seen that co-delivery is not suitable for delivery services that require extremely fast delivery times. The cost to express delivery companies and the revenue of the bus operator are both the highest when the time window length is 1 h. When the time window length is greater than one hour, they are significantly reduced. In addition, they both increase with the increase of the delay penalty coefficient. When the time window length is 1 h, the social welfare value is the smallest and increases with the increase of the delay penalty coefficient. When the time window length is greater than 1 h, social welfare decreases with the increase of the time window length but does not change with the change of the delay penalty coefficient.

5. Discussion

Comparing the three scenarios, the two measures are analyzed from the perspectives of consumers, express delivery companies, the bus operator, and the government.

From the perspective of consumers, the delivery timeliness in the three scenarios is compared. Both measures can significantly improve delivery timeliness. Among them, when the length of the time window is 3 h and more, both measures can achieve on-time delivery of all parcels. When the length of the time window is 2 h, all parcels can still be delivered on time through measure 2, and some parcels delivered through measure 1 are delayed. When the length of the time window is 1 h, the parcels delivered through measure 1 are all delayed, and the parcels delivered through measure 2 are only partially delayed. It can be seen that when delivery timeliness is extremely considered, measure 1 performs better; when delivery timeliness is of moderate importance, measure 2 performs better; when the requirements for delivery timeliness are relatively loose, both measures perform well.

From the perspective of express delivery companies, the total delivery costs in the three scenarios are compared. Both measures can significantly reduce the total delivery costs. Measure 1 performs better than measure 2, and with the shortening of the time window length, the advantage of measure 1 is more prominent. This is mainly due to the fact that the bus delivery pricing in measure 2 is anchored in the original scenario. In the case of restricted express delivery vans, bus delivery can charge high delivery fees.

From the perspective of the bus operator, the revenue of the bus operator in measure 2 is analyzed. With different time window lengths and delay penalty coefficients, the bus operator’s revenue is between 226 yuan and 6340 yuan. This is only the revenue of a small-scale case of 2 buses, one courier station, and two express companies. In the current situation of thousands of courier stations, dozens of express companies, and more than 200 bus lines in the city, measure 2 can create considerable income for the bus operator.

From the perspective of the government, the impact of the two measures on the city and the government is analyzed. First, both measures can significantly improve social welfare. When the time window length is 1 h, measure 1 performs better; when the time window length is greater than one hour, measure 2 performs better. Second, compared with measure 2, measure 1 needs to relax the vehicle restriction policy, which may lead to problems such as increasing road congestion, aggravating the load on the traffic environment, impacting road traffic safety, and causing the driving burden of car drivers. Third, measure 2 can provide additional revenue for the bus operator. Under the status quo that urban public transportation has suffered losses for a long time and needs the government to provide financial subsidies to maintain normal operation, measure 2 can alleviate the degree of public transportation losses and reduce the financial burden of the government.

6. Conclusions

The bus-truck co-delivery mode and the pricing of the bus delivery service considering the maximization of social welfare are studied. A two-layer optimization model is constructed. The upper layer takes the maximization of social welfare and the revenue of the bus operator as the objective function to solve the optimal pricing of the bus delivery service; the lower layer takes the minimization of the cost to express companies as the objective function to solve the spatiotemporal routing problem of express delivery. Finally, a case analysis is carried out by taking the actual operation of bus lines and express delivery demand in Dalian as an example. Research shows that the co-delivery mode can provide consumers with more efficient services, reduce costs for express companies, provide additional revenue for bus operators, and improve social welfare. Unless the timeliness of delivery is extremely important, the measure of using the co-delivery mode is better than the measure of relaxing restrictions on express delivery vehicles.

Since a small-scale case is used, the scale effect of the co-delivery mode cannot be fully reflected. In addition, only the optimization at the route selection level is considered in this paper. In fact, however, urban public transport and express delivery can also be further integrated in terms of station location and route optimization, so as to achieve the overall optimization of urban public transport and express delivery systems.