Urban Sharing Logistics Strategies against Epidemic Outbreaks: Its Feasibility and Sustainability

Abstract

Epidemic (e.g., COVID-19) outbreaks can seriously disrupt logistics, and the coordination of intercity logistics and urban distribution plays an important role in goods distribution. In previous studies, some scholars analyzed different sharing logistics mechanisms for cost reduction and efficiency improvement, while others analyzed the disruption problems in both logistics and supply chain management. In this study, we combine these two operational management philosophies and first develop a two-echelon logistics benchmark model (BM), with two intercity logistics companies and two urban distribution companies, taking into consideration the load ratio and the disruption factor. This is the first time that the load ratio is considered in research on logistics, and it will make the supply and demand as well as the cost structure of logistics services much more practical. We then develop three urban sharing logistics models with two intercity logistics companies and one urban sharing logistics distribution company, with the sharing mechanisms SM1 (only sharing logistics), SM2 (sharing logistics with revenue sharing), and SM3 (sharing logistics with equity investment). We compare the pros and cons of the three sharing mechanisms and identify the optimal and suboptimal Pareto improvements for the BM. We identify different sharing decisions with respect to different load ratios and the disruption ratio. Finally, we analyze the sustainability of the three sharing mechanisms from the load ratio, low-carbon, and low-disruption dimensions. The managerial implications drawn from the model and case study provide a practice framework for sharing logistics operations: vertical integration, the standardization of logistics technology and equipment, and coordination and sharing.

1. Introduction

1.1. Background and Motivation

In December 2019, the COVID-19 pandemic swept through Wuhan, China. The entire city of Wuhan was locked down in 2020, and the people needed to obtain items allocated by the government [1]. As the high incidence of COVID-19 coincided with the traditional Spring Festival in China, a large number of urban laborers returned to their hometowns, and the number of laborers in Wuhan shrank dramatically, especially in the logistics industry. The regional control (e.g., the lockdown of the city) and shortages in the labor force put great pressure on the logistics supply chain during the COVID-19 pandemic [2]. For example, COVID-19 caused severe disruptions across the world in the healthcare supply chain [3]. Limiting the death toll caused by COVID-19 depended on the ability to allocate sufficient numbers of ventilators before infections peaked and ensuring that the inventory did not run out [4]. Further examples include how the COVID-19 lockdown caused widespread disruption of food supply chains in India and food retail logistics in Germany [5]. In December 2020, a new COVID-19 virus variant broke out in the UK, paralyzing the logistics system, and a large number of trucks were stranded (see Figure 1). Therefore, a flexible and efficient logistics system is needed to deal with pandemics [6].

Given the obvious rapid and large-scale human-to-human transmission ability of COVID-19, it spread widely across vast geographical regions in more than 200 countries [7]. In most countries, the logistics industry is still a labor-intensive industry, and the traditional logistics operation mode requires many front-line workers. In the face of such a major public health emergency, the coordination of intercity logistics and urban distribution may provide a relatively economical and efficient way to solve the problems of supplying items to urban residents, as well as healthcare systems. It can fix the range of activities of logistics workers and greatly reduce unnecessary travel by residents, which will reduce the probability of contact with infected individuals and, thus, virus transmission.

With the progress of intercity logistics, urban distribution has become a new bottleneck of logistics development. Traditional urban distribution is not only inefficient but also wastes more than 50% of various types of operating costs (site, personnel, energy consumption, communication, etc.) due to the repeated construction of terminal networks. With the increase in labor and land costs, the intensity and information level of urban distribution must be improved, and innovation of the sharing logistics modes must be carried out. However, due to the lack of mutual cooperation, trust, and benefit-sharing mechanisms, it is difficult for urban logistics to achieve effective sharing and docking. In the post-epidemic era, the urban distribution system shows the characteristics of small-batch, convenience, and continuity demands. Although some studies have investigated the sharing mechanism of urban sharing distribution [8], they have not fully considered those characteristic factors. In previous studies (e.g., Vanovermeire et al. [9], Guajardo and Rönnqvist [10], and Tinoco et al. [11]), the majority of scholars proposed different cost or profit-sharing mechanisms based on the Shapley value theory or even operations research theory, but they ignored the incentive compatibility and market efficiency problems. They answer the question of how to do it but ignore whether they are willing to do it. In recent years, some scholars (Niu et al. [12], He et al. [13] and Lai et al. [14]) analyzed the sharing logistics problem in e-commerce supply chains, such as Fulfilled by Amazon and JD Logistics. However, e-commerce logistics is the smallest segment of the market for the whole modern logistics industry. Therefore, it is necessary to find better solutions that can ensure both incentive compatibility and market efficiency for the other logistics market segments, such as less-than-truckload logistics and contract logistics, accounting for more than 75 percent of the whole modern logistics industry (https://www.sohu.com/a/787632161_121123887, accessed on 6 June 2024).

1.2. Research Questions and Key Findings

In this study, we attempt to solve the following problems:

(1)

When the cost (small batch), efficiency (convenience), and disruption risk (continuity) factors are considered together, what type of sharing mechanism is feasible and can achieve Pareto improvements?

(2)

How can the best sharing decision be made for intercity logistics companies under different conditions?

(3)

What type of sharing mechanism of urban distribution is sustainable (in terms of load ratio, low-carbon, and low-disruption dimensions), especially when fighting against epidemic outbreaks (e.g., COVID-19)?

In order to solve these problems, this study introduces the sharing economy into urban distribution and examines a two-echelon sharing logistics supply chain, which includes an urban sharing distribution company and two intercity logistics companies upstream. We develop a decision-making model that considers both the load ratio and the disruption factor. The load ratio mainly refers to the vehicle resource allocation of the urban distribution company for a specific quantity of goods. The larger the load ratio, the more vehicles will be allocated, which increases the operating costs while improving the operating efficiency. The disruption factor mainly refers to the probability of urban logistics disruption being affected by the epidemic situation. Obviously, the more vehicles are allocated, the more likely urban distribution will be disrupted. These two factors happen to be contradictory, and a scientific sharing mechanism needs to be designed in order to make the most scientific choice. In addition, the entire logistics operation system can be regarded as composed of the most subdivided delivery vehicle units; that is, each vehicle is the smallest logistics organization unit. We use the combination of the disruption of logistics vehicle units to indirectly describe the large-scale disruption of logistics, which is logical.

Here, we consider four different operational mechanisms and solve their equilibriums. Firstly, we analyze a benchmark model (BM) in which the two intercity logistics companies outsource the urban logistics distribution to different urban distribution companies. Secondly, we propose an only-sharing logistics mechanism (SM1) in which the two intercity logistics companies outsource their urban distribution orders to the same urban sharing logistics distribution company. Then, we further discuss the urban sharing logistics distribution with a revenue-sharing mechanism (SM2) and an equity investment mechanism (SM3).

The main findings are as follows:

(1)

When logistics sharing for cost reduction and efficiency improvement, the load ratio, and the disruption risk factor are considered together, the sharing logistics mechanisms based on revenue sharing and equity investment proposed in this paper are feasible and can achieve Pareto improvements for any given load ratio. In contrast, the first sharing logistics mechanism only based on the wholesale price contract is not optimal for some load ratios. In the majority of scenarios, the sharing logistics mechanism based on equity investment is better than that based on revenue-sharing contracts, but, sometimes, the opposite is the case.

(2)

Regarding practices, it is necessary to scientifically design the load ratio of trucks to delivery vehicles, as it plays an important role in the performance of the sharing logistics implementation.

(3)

For any given load ratio of trucks to delivery vehicles, compared with the BM, all of the sharing mechanisms generally increase the load ratio and significantly reduce the unit carbon emission rate, as well as the unit disruption risk.

1.3. Contribution Statements and Structure of This Paper

The contributions of this study are as follows. First, we introduce the concept of the sharing economy in operations management into the field of urban logistics distribution and design several mechanisms for cooperation and sharing. Second, we propose a type of research framework and a model that considers not only the characteristics (for example, revenue and cost structures) of the entire logistics chain but also the sustainability of the operations (in terms of the load ratio, low-carbon, and low-disruption dimensions). Third, we summarize and refine the business-based equity cooperation phenomenon that often occurs in the modern logistics industry after conducting field research on many logistics companies and e-commerce logistics companies. Therefore, we propose an urban sharing logistics distribution mechanism based on both supply chain coordination contracts and equity investment.

To sum up, the sharing economy is transforming traditional production and lifestyles from all aspects. This study attempts to introduce the sharing economy model into the field of delivery service in order to identify an optimized upgrading scheme that could effectively reduce its operating costs, improve operational efficiency, and fight against epidemic outbreaks.

The remainder of this paper is organized as follows: Section 2 summarizes related studies. Section 3 identifies the problems and the hypotheses of this study. Section 4 discusses the BM and the sharing mechanisms (SM1, SM2, SM3). Section 5 presents a comparative analysis composed of a feasibility analysis and a sustainability analysis (in terms of the load ratio, low-carbon, and low-disruption dimensions). Section 6 draws conclusions and identifies several future research directions.

2. Literature Review

This study focuses on supply chain disruptions during epidemic outbreaks, and it aims to alleviate such disruptions through urban sharing logistics mechanisms. Supply chain disruptions and resilience, logistics service supply chain and urban logistics, sharing mechanisms in operations management, emergency and humanitarian logistics, and epidemic (e.g., COVID-19) outbreaks are aspects related to this study.

2.1. Supply Chain Disruptions and Resilience

Industrial accidents, epidemics, and natural disasters cause supply chain disruptions [15,16], and companies are affected by supply chain disruptions [17,18]. Therefore, many studies have examined how to deal with the risk of supply chain disruptions, for example, by purchasing insurance, increasing flexibility or inventory, and diversifying purchasing strategies [19,20,21,22,23,24,25,26,27,28,29,30,31,32,33]. Some studies have also intervened from other perspectives. For example, Hu et al. [34] studied how buyers can incentivize reliable suppliers to resume investment after a supply chain disruption event. Cai and Zhou [35] revealed how to make decisions upstream of the supply chain to minimize losses when public transportation in foreign markets is interrupted. Yu et al. [36] showed that supply chain resilience determines the impact of supply chain disruption orientation on financial performance. Hendricks et al. [37] empirically demonstrated the performance of an affected company’s stock market through empirical evidence; supply chain disruption caused by an earthquake in Japan damaged shareholder value and had a negative impact on upstream and downstream companies. Habib et al. [38] discussed the differences between COVID-19 and previous supply chain disruption events in terms of the metal supply chain. On the basis of the above-mentioned literature, we employ urban sharing logistics services to deal with the disruption of the supply chain of emergency medical supplies or community residents’ living supplies caused by epidemics (such as COVID-19).

2.2. Urban Sharing Logistics in the Logistics Supply Chain

The cooperation and integration among logistics supply chain members, such as intercity logistics companies and urban distribution companies, has become a research hotspot in logistics studies [39,40,41,42,43]. For example, Wang et al. [44] discussed the selection of logistics service providers and the distribution of orders under the mass customization logistics service mode. Revenue sharing or logistics cost sharing contracts help to coordinate logistics supply chain members and achieve a win–win situation [45]. The rapid development of e-commerce has led to a rapid increase in express delivery parcels, and the urban population and the number of vehicles continue to increase, which highlights the contradictions in the last-mile delivery in cities and puts huge pressure on social and environmental well-being. To solve this problem, Deng et al. [46] proposed a method in which the Urban Integration Center is operated by an aggregator and bundles goods from multiple carriers before the last-mile delivery, or carriers share delivery capacity. This echoes the urban sharing logistics strategy in our study. In epidemic situations, urban distribution presents new characteristics and challenges, such as small-batch, convenience, and continuity demands. Appropriate sharing mechanisms need to be developed to improve the efficiency and continuity of logistics and reduce its costs.

2.3. Sharing Mechanisms in Operations Management

2.3.1. Sharing Economics in Operations Management

Technological progress makes it possible to share products or services on a large scale, thereby improving resource utilization efficiency and promoting sustainable economic development [47]. In recent years, shared accommodation, shared travel, and common delivery platforms have flourished, such as Airbnb, Uber, Didi, and Cainiao. Gibbs et al. [48] discussed pricing issues in the sharing economy. Narasimhan et al. [49] summarized several issues in the sharing economy from different perspectives of experience and behavior. Kim et al. [50] examined the factors affecting the willingness of shared services and proposed corresponding marketing strategies. Many studies start with shared bicycles because of the increased development of this mode of shared transportation [51,52,53,54,55,56,57]. Jiang et al. [58] investigated the issue of information sharing in the supply chain under retailers’ different risk preferences.

2.3.2. Sharing Contracts

The cooperation content of a sharing contract includes information sharing, capacity sharing, revenue sharing, risk sharing, and cost sharing. The interruption and bullwhip effect in the supply chain can be reduced by strengthening cooperation and sharing [59,60,61,62,63,64,65,66,67,68]. Free-riding can easily occur in the development of green and sustainable supply chains, and revenue sharing and cost sharing contracts have been widely introduced [69,70,71,72]. Sharing mechanisms can be applied to the research of logistics service supply chain management [73]. Wei et al. [8] discussed a two-echelon supply chain consisting of a shared distribution platform and N express companies, and they investigated two revenue-sharing strategies with different sharing factors based on the order flow ratio and the revenue-sharing factor.

2.4. Emergency and Humanitarian Logistics

Due to the impact of the COVID-19 outbreak on the economy and society, many studies on COVID-19 and humanitarianism have emerged [74,75,76]. Previous studies on humanitarianism involved the preparation, response, and recovery phases of humanitarian relief [77,78,79,80,81]. Ben-Tal et al. [82] employed robust optimization to dynamically allocate emergency response and evacuation traffic flow problems with time-dependent demand uncertainty, and they generated reliable logistics plans, thereby reducing the risk of the humanitarian relief supply chain. Taniguchi et al. [83] first proposed the concept of humanitarian logistics and applied the road network emergency model to assist emergency preparedness and response decision-making. Ghorbani and Ramezanian [84] integrated the selection of carriers and suppliers through contractual agreements, established pre-designated contracts with suppliers in the preparation stage, and aimed to minimize costs. Liberatore et al. [85] proposed a restoration plan for damaged components in the distribution network and used the 2010 Haiti earthquake as a case study to demonstrate it. In addition, deprivation costs are introduced into humanitarian logistics, which are often used as a key economic indicator of human suffering related to emergency logistics [86].

Compared with previous studies, the contribution of this study is mainly to make up for the problem of previous research being either too macro- or too micro-oriented. One research stream studies the supply chain disruption by means of mathematical programming tools, which is too microscale, while another research stream studies the same problems using the empirical research method, which is too macroscale. This paper proposes a practical and feasible sharing operation mechanism, which is not only based on supply chain coordination and equity investment contracts but also takes into account the actual cost and profit structure of logistics operations.

3. Problem Descriptions and Hypotheses

Modern logistics consists of a very long industrial chain, comprising both intercity logistics transportation and urban logistics distribution from the perspective of its service area (see Figure 2). In real business practices, the majority of logistics companies in China receive logistics service orders that require completing the whole process of logistics transportation from the front-end customers to the end customers, as well as from the retailers to the customers. Most logistics companies operate intercity logistics transportation by themselves and outsource urban distribution (or last-mile delivery) to professional urban logistics distribution companies. Only some logistics companies operate the whole logistics chain by themselves. Although modern logistics has experienced rapid development in the past ten years in China, the scale of the logistics industry is still relatively low, and the market concentration is insufficient. This decentralized operation has brought about the disadvantages of low efficiency and high costs of the operations.

When faced with major public safety emergencies such as COVID-19, the logistics transportation and distribution of anti-epidemic and living supplies will be very important in the battle for epidemic prevention and control. If efficiency and cost are important considerations for conventional logistics transportation and distribution, then efficiency and safety (non-disruption) during the epidemic prevention and control period will be the core of the supply of important materials. To solve the disadvantages of decentralized operation, we introduce a sharing operation mechanism into logistics distribution and analyze its feasibility and sustainability (with a high load ratio, low carbon, and low disruption).

As a benchmark, we analyze a two-echelon logistics service supply chain with two intercity logistics companies, which operate logistics transportation from different cities to the same city, and two urban logistics distribution companies in a benchmark model (BM). Then, we study a two-echelon logistics service supply chain with two intercity logistics companies and one urban sharing logistics distribution company using the sharing mechanisms SM1 (only sharing logistics mechanism), SM2 (sharing logistics with revenue-sharing mechanism), and SM3 (sharing logistics with equity investment mechanism). Finally, we compare the pros and cons of the three sharing mechanisms and the BM, and we determine whether there are Pareto improvements for the traditional intercity logistics transportation and urban logistics distribution.

According to Niu et al. [12] and He et al. [13], we assume that the two intercity logistics companies own one truck each; thus, their market demands can be represented by $q_1=1-p_1$ and $q_2=1-a{p}_2$, where $p_i, i=1,2$ is the unit logistics service price charged to the front-end customers by the two intercity logistics companies; $a (>0)$ is the influence coefficient of the price on demand for intercity logistics $i=2$; $a\ne 1$represents the heterogeneity between the two intercity logistics companies; $a=1$represents a homogeneous scenario; and the market demands satisfy $q_i\in \left(0,1\right),i=1,2$. In the BM, the two intercity logistics companies outsource urban logistics distribution to an urban logistics distribution company that charges a unit distribution price $w_i, i=1,2$ to the intercity logistics companies. In the three sharing mechanisms, the unit distribution price $w$ is charged by only one urban sharing logistics distribution company to the two intercity logistics companies. Furthermore, the relationships between $p_i$ and $w_i$($i=1,2$) and between $p_i$ ($i=1,2$) and $w$ are as shown in Figure 3.

As previously stated, the entire logistics chain includes two important logistics transportation processes: intercity logistics transportation and urban logistics distribution. Due to different transportation conditions and other external factors, the two logistics transportation processes require different vehicles to complete the logistics transportation tasks. In general, intercity logistics transportation needs to use trucks as a means of transportation, and urban logistics distribution needs to use delivery vehicles as a means of transportation. Obviously, trucks and delivery vehicles have different tonnages or volumes. In this study, we assume that the load ratio of trucks to delivery vehicles is $\lambda$; this means that a full truck of goods requires $\lambda$ urban delivery vehicles for delivery, which means that a full truck of goods can only fill $\lambda$ urban delivery vehicles (see Figure 4).

Therefore, if the intercity logistics companies need to fulfill a logistics service order, i.e., market demands $q_i,i=1,2$, and they outsource urban logistics to different urban logistics distribution companies in the BM, the urban logistics distribution companies need to dispatch $Q_i$ delivery vehicles. Furthermore, $Q_i$ satisfies $Q_i=\left|\lambda q_i\right|+1,i=1,2$. Similar to the BM, if the intercity logistics companies need to fulfill a logistics service order, i.e., market demands $q_i,i=1,2$, and they outsource urban logistics to only one urban logistics distribution company in the sharing mechanism SMi  ($i=1,2,3$), the urban logistics distribution company needs to dispatch $Q$ delivery vehicles. Moreover, this satisfies $Q=\left|\lambda \left(q_1+q_2\right)\right|+1=\left|\lambda {{\displaystyle \sum }}_{i=1}^2{q}_i\right|+1$. The operating cost of each delivery vehicle is relatively fixed, so we assume that the operating cost of each delivery vehicle is $c$.

Intuitively, after the implementation of sharing logistics, the probability of a delivery vehicle’s disruption risk should be significantly reduced because fewer delivery vehicles are needed. Efficiency and safety (non-disruption) during the epidemic prevention and control period are the core of the supply of important anti-epidemic and living supplies. Similar to the assumptions of risk aversion and risk preference in classic studies, we introduce the non-disruptive risk preference into the utility function of the urban logistics distribution company. It is represented in the BM as:

$$\kappa {\left(1-\sigma \right)}^{Q_i},\sigma \in \left[0,1\right],i=1,2$$

(1)

and in the sharing mechanism as:

$$\kappa {\left(1-\sigma \right)}^Q$$

(2)

where $\sigma$ is the disruption risk of one delivery vehicle, and $\kappa$ is the preference coefficient of the non-disruption risk. In this study, the two intercity logistics companies examined operate intercity logistics transportation services from different cities to the same destination. Therefore, the heterogeneity between the two intercity logistics companies is not the focus of this study. To facilitate a comparative analysis, we can assume that $a=1$; that is, we can assume that the two intercity logistics companies are homogeneous. According to the definition of the market demand function and the load ratio of trucks to delivery vehicles, we can further express some of the above-mentioned related variables and expressions as follows:

$$Q_i=\left|\lambda q_i\right|+1=\left\{\begin{array}{cc}\begin{array}{c}\lambda \\ \lambda -1\\ ⋮\end{array}& \begin{array}{c}{p}_i\in \left[0,\right.\left.{\displaystyle \frac{1}{\lambda }}\right)\\ p_i\in \left[{\displaystyle \frac{1}{\lambda }},\right.\left.{\displaystyle \frac{2}{\lambda }}\right)\\ ⋮\end{array}\\ 2& p_i\in \left[1-{\displaystyle \frac{2}{\lambda }},\right.1-\left.{\displaystyle \frac{1}{\lambda }}\right)\\ 1& p_i\in \left[1-{\displaystyle \frac{1}{\lambda }},\right.\left.1\right)\end{array}\right.$$

(3)

$$\kappa {\left(1-\sigma \right)}^{Q_i}=\kappa {\left(1-\sigma \right)}^{\left|\lambda q_i\right|+1}=\left\{\begin{array}{cc}\begin{array}{c}\kappa {\left(1-\sigma \right)}^{\lambda }\\ \kappa {\left(1-\sigma \right)}^{\lambda -1}\\ ⋮\end{array}& \begin{array}{c}{p}_i\in \left[0,\right.\left.{\displaystyle \frac{1}{\lambda }}\right)\\ p_i\in \left[{\displaystyle \frac{1}{\lambda }},\right.\left.{\displaystyle \frac{2}{\lambda }}\right)\\ ⋮\end{array}\\ \kappa {\left(1-\sigma \right)}^2& p_i\in \left[1-{\displaystyle \frac{2}{\lambda }},\right.1-\left.{\displaystyle \frac{1}{\lambda }}\right)\\ \kappa \left(1-\sigma \right)& p_i\in \left[1-{\displaystyle \frac{1}{\lambda }},\right.\left.1\right)\end{array}\right.$$

(4)

$$Q=\left|\lambda \left(q_1+q_2\right)\right|+1=\left\{\begin{array}{cc}\begin{array}{c}2\lambda \\ 2\lambda -1\\ ⋮\end{array}& \begin{array}{c}{p}_1+p_2\in \left[0,\right.\left.{\displaystyle \frac{1}{\lambda }}\right)\\ p_1+p_2\in \left[{\displaystyle \frac{1}{\lambda }},\right.\left.{\displaystyle \frac{2}{\lambda }}\right)\\ ⋮\end{array}\\ 2& p_1+p_2\in \left[2-{\displaystyle \frac{2}{\lambda }},\right.2-\left.{\displaystyle \frac{1}{\lambda }}\right)\\ 1& p_1+p_2\in \left[2-{\displaystyle \frac{1}{\lambda }},\right.\left.2\right)\end{array}\right.$$

(5)

$$\kappa {\left(1-\sigma \right)}^Q=\kappa {\left(1-\sigma \right)}^{\left|\lambda \left(q_1+q_2\right)\right|+1}=\left\{\begin{array}{cc}\begin{array}{c}\kappa {\left(1-\sigma \right)}^{2\lambda }\\ \kappa {\left(1-\sigma \right)}^{2\lambda -1}\\ ⋮\end{array}& \begin{array}{c}{p}_1+p_2\in \left[0,\right.\left.{\displaystyle \frac{1}{\lambda }}\right)\\ p_1+p_2\in \left[{\displaystyle \frac{1}{\lambda }},\right.\left.{\displaystyle \frac{2}{\lambda }}\right)\\ ⋮\end{array}\\ \kappa {\left(1-\sigma \right)}^2& p_1+p_2\in \left[2-{\displaystyle \frac{2}{\lambda }},\right.2-\left.{\displaystyle \frac{1}{\lambda }}\right)\\ \kappa \left(1-\sigma \right)& p_1+p_2\in \left[2-{\displaystyle \frac{1}{\lambda }},\right.\left.2\right)\end{array}\right.$$

(6)

All of the terms and notations used in this paper are shown in

Table 1. Terms and notations used in this paper.

Notation	Description
Parameters
$\lambda$	load ratio of trucks to delivery vehicles
$\sigma$	disruption risk per delivery vehicle
$\kappa$	non-disruption risk preference coefficient
$\kappa {\left(1-\sigma \right)}^{Q_i}$	non-disruption risk preference in the benchmark model (BM)
$\kappa {\left(1-\sigma \right)}^Q$	non-disruption risk preference in sharing mechanism (SMi; $i=1,2,3$)
$Q_i$	number of dispatched delivery vehicles for urban logistics company $i$ in BM
$Q$	number of dispatched delivery vehicles in SMi  ($i=1,2,3$)
$c$	operational cost of one delivery vehicle
$\mathbb{F}\mathrm{𝕣}\left(.\right)$	feasible regions of the lemmas
$\mathbb{L}ℝ$	increase rate of load ratio
$\mathbb{L}ℂ$	reduction rate of carbon emissions per unit product
$\mathbb{L}\mathbb{D}$	reduction rate of the risk of disruption per unit product
Decision variables
$p_i$	logistics service price
$q_i$	market demands
$w_i$	distribution service price in BM
$w$	distribution service price in SMi  ($i=1,2,3$)
$r$	revenue-sharing factor in SM2
Utility functions
$U_i^{NS}$	utility function of the intercity logistics companies in BM
$U_i^D$	utility function of the urban logistics distribution companies in BM
$U_i^{S1}$	utility function of the intercity logistics companies in SM1
$U^{D1}$	utility function of the urban sharing logistics distribution company in SM1
$U_i^{S2}$	utility function of the intercity logistics companies in SM2
$U^{D2}$	utility function of the urban sharing logistics distribution company in SM2
$U_i^{S3}$	utility function of the intercity logistics companies in SM3
$U^{D3}$	utility function of the urban sharing logistics distribution company in SM3

.

Definition 1.

Pareto improvements of SMj for the BM: The SMj  is a type of sharing logistics mechanism, and the BM is a type of non-sharing logistics mechanism. The Pareto improvements of sharing mechanism SMj  for the BM can be defined as follows ($j=1,2,3$): 

(1) 

Optimal Pareto improvement: 

i.  $U_i^{Sj}\ge U_i^{NS}, \forall i=1,2,$ ii.  $U^{Dj}\ge {{\displaystyle \sum }}_{i=1}^2{U}_i^D$.

(2) 

Suboptimal Pareto improvement: 

i.  $U_i^{Sj}\ge U_i^{NS}, \forall i=1,2,$ii.  $U^{Dj}\ge U_i^D, \forall i=1,2$.

Definition 1 provides the core connotations of both the optimal and suboptimal Pareto improvements of the sharing mechanism SMj  for the BM, and we use them to obtain the solutions of the Pareto improvements for any given load ratio in Section 5 and its proof.

4. Equilibrium Analysis

In this section, we study four different operational mechanisms (BM, SM1, SM2, and SM3) and solve their equilibrium. Firstly, we analyze the BM in which the two intercity logistics companies outsource urban logistics distribution to different urban logistics distribution companies.

4.1. The Benchmark Model (BM)

In the BM, the utility function $U_i^{NS}$ of the two intercity logistics companies is:

$$U_i^{NS}=\left(p_i-w_i\right)q_i=\left(p_i-w_i\right)\left(1-p_i\right),i=1,2$$

(7)

The utility function of the two urban logistics distribution companies is:

$$U_i^D=w_i{q}_i-c{Q}_i+\kappa {\left(1-\sigma \right)}^{Q_i},i=1,2$$

(8)

This includes not only the revenue and costs of logistics distribution but also the utility of the non-disruption risk preference. We solved the BM mode by using backward induction, and the equilibrium results are shown in Proposition 1. The structure of the revenue model reflects the particularity of the revenue and cost function structure of logistics transportation. Urban logistics distribution companies charge distribution fees according to the order volume (tonnage or square volume), but their cost expenditures are determined by the fixed distribution vehicle cost structure. Each vehicle has a relatively fixed cost structure, such as gas, tolls, labor, and insurance.

Proposition 1.

For any given load ratio of trucks to delivery vehicles $\left(\lambda \right)$, the optimal equilibrium in the benchmark model (BM) exists and satisfies the following: 

(1) 

While $\lambda \in \left\{2,3,4\right\}$, the optimal decisions are ${p_i}^{*}={\displaystyle \frac{3}{4}},{q_i}^{*}={\displaystyle \frac{1}{4}},{w_i}^{*}={\displaystyle \frac{1}{2}}$, and the optimal utilities are  ${U_i^{NS}}^{*}={\displaystyle \frac{1}{16}}$,  ${U_i^D}^{*}={\displaystyle \frac{1}{8}}-c+\kappa \left(1-\sigma \right)$; 

(2) 

While  $\lambda \in \left\{5+4N,6+4N,7+4N,8+4N\right\}$, where  $N=0,1,2,3,\dots$, the optimal decisions and utilities are 

(i) 

if $c+\kappa {\left(1-\sigma \right)}^{1+N}-\kappa {\left(1-\sigma \right)}^{2+N}\ge {\displaystyle \frac{1}{8}}-\left[1-{\displaystyle \frac{2\left(1+N\right)}{\lambda }}\right]{\displaystyle \frac{1+N}{\lambda }}$, then ${p_i}^{*}=1-{\displaystyle \frac{1+N}{\lambda }},{q_i}^{*}={\displaystyle \frac{1+N}{\lambda }}$,  ${w_i}^{*}=1-{\displaystyle \frac{2\left(1+N\right)}{\lambda }}$,  ${U_i^{NS}}^{*}={\left({\displaystyle \frac{1+N}{\lambda }}\right)}^2$, ${U_i^D}^{*}=\left[1-{\displaystyle \frac{2\left(1+N\right)}{\lambda }}\right]{\displaystyle \frac{1+N}{\lambda }}-\left(1+N\right)c+\kappa {\left(1-\sigma \right)}^{1+N}$; 

(ii) 

If  $c+\kappa {\left(1-\sigma \right)}^{1+N}-\kappa {\left(1-\sigma \right)}^{2+N}<{\displaystyle \frac{1}{8}}-\left[1-{\displaystyle \frac{2\left(1+N\right)}{\lambda }}\right]{\displaystyle \frac{1+N}{\lambda }}$ , then  ${p_i}^{*}={\displaystyle \frac{3}{4}},{q_i}^{*}={\displaystyle \frac{1}{4}},{w_i}^{*}={\displaystyle \frac{1}{2}},{U_i^{NS}}^{*}={\displaystyle \frac{1}{16}}$,  ${U_i^D}^{*}={\displaystyle \frac{1}{8}}-\left(2+N\right)c+\kappa {\left(1-\sigma \right)}^{2+N}$.

For the proof, see the Supplementary Materials.

Proposition 1 provides all optimal decisions and utilities for any given $\lambda$. We can see that the utility of intercity logistics companies, as well as the decision variables $p_i$, are only determined by the load ratio of trucks to delivery vehicles $\lambda$, while the urban logistics distribution companies’ utility is determined by $\lambda$, operational cost $c$, and the non-disruption risk preference $\kappa \left(1-\sigma \right)$. We present a much more detailed analysis in Section 5, including a comparative analysis.

4.2. Sharing Mechanism 1: SM1

In the sharing logistics mechanism SM1, the utility function $U_i^{S1}$ of the two intercity logistics companies is:

$$U_i^{S1}=\left(p_i-w\right)q_i=\left(p_i-w\right)\left(1-p_i\right),i=1,2$$

(9)

Because the two intercity logistics companies outsource their urban logistics distribution orders to the same urban logistics distribution company in SM1, the utility function of the urban sharing logistics distribution company is:

$$U^{D1}=w\left(q_1+q_2\right)-cQ+\kappa {\left(1-\sigma \right)}^Q$$

(10)

This includes not only the revenue and costs of the logistics distribution but also the utility of the non-disruption risk preference. We solved the SM1 mode by using backward induction, and the equilibrium results are shown in Proposition 2.

Proposition 2.

For any given load ratio of trucks to delivery vehicles  $\lambda$, the optimal equilibrium in the sharing mechanism SM1 exists and satisfies the following: 

(1) 

While  $\lambda =2$, the optimal decisions are  $p^{*}={\displaystyle \frac{3}{2}},{p_i}^{*}={\displaystyle \frac{3}{4}},{q_i}^{*}={\displaystyle \frac{1}{4}},w^{*}={\displaystyle \frac{1}{2}}$, and the optimal utility are  ${U_i^{S1}}^{*}={\displaystyle \frac{1}{16}}$,  $U^{D1*}={\displaystyle \frac{1}{4}}-c+\kappa \left(1-\sigma \right)$; 

(2) 

While  $\lambda \in \left\{3+2M,4+2M\right\}$, where  $M=0,1,2,3,\dots$, the optimal decisions and utility are 

(i) 

if  $c+\kappa {\left(1-\sigma \right)}^{1+M}-\kappa {\left(1-\sigma \right)}^{2+M}\ge {\displaystyle \frac{1}{4}}-\left(1-{\displaystyle \frac{1+M}{\lambda }}\right){\displaystyle \frac{1+M}{\lambda }}$, then  $p^{*}=2-{\displaystyle \frac{1+M}{\lambda }},{p_i}^{*}=1-{\displaystyle \frac{1+M}{2\lambda }},{q_i}^{*}={\displaystyle \frac{1+M}{2\lambda }},w^{*}=1-{\displaystyle \frac{1+M}{\lambda }},{U_i^{S1}}^{*}={\left({\displaystyle \frac{1+M}{2\lambda }}\right)}^2$,  $U^{D1*}=\left(1-{\displaystyle \frac{1+M}{\lambda }}\right){\displaystyle \frac{1+M}{\lambda }}-\left(1+M\right)c+\kappa {\left(1-\sigma \right)}^{1+M}$; 

(ii) 

if  $c+\kappa {\left(1-\sigma \right)}^{1+M}-\kappa {\left(1-\sigma \right)}^{2+M}<{\displaystyle \frac{1}{4}}-\left(1-{\displaystyle \frac{1+M}{\lambda }}\right){\displaystyle \frac{1+M}{\lambda }}$, then  $p^{*}={\displaystyle \frac{3}{2}},{p_i}^{*}={\displaystyle \frac{3}{4}},{q_i}^{*}={\displaystyle \frac{1}{4}},w^{*}={\displaystyle \frac{1}{2}},{U_i^{S1}}^{*}={\displaystyle \frac{1}{16}}$,  $U^{D1*}={\displaystyle \frac{1}{4}}-\left(2+M\right)c+\kappa {\left(1-\sigma \right)}^{2+M}$.

For the proof, see the Supplementary Materials.

Proposition 2 gives all the optimal decisions and utility for any given $\lambda$. We can see that the utility of the intercity logistics companies, as well as the decision variables $p_i$, is only determined by the load ratio of trucks to delivery vehicles $\lambda$, while the utility of urban logistics distribution companies is determined by $\lambda$, operational cost $c$, and the non-disruption risk preference $\kappa \left(1-\sigma \right)$. We present a much more detailed analysis in Section 5, including a comparative analysis.

4.3. Sharing Mechanism 2: SM2

In SM2, we further introduce the revenue-sharing mechanism. As the two intercity logistics companies outsource all orders to the same urban sharing logistics distribution company and not to two different ones, they have much more market power than before. We assume that each of the intercity logistics companies shares $rw\left(q_1+q_2\right)$ from the revenue of the urban sharing logistics distribution company. In addition, the revenue-sharing factor is $r\in \left[0,{\displaystyle \frac{1}{2}}\right]$. Therefore, the utility function $U_i^{S2}$ of the intercity logistics companies is:

$$U_i^{S2}=\left(p_i-w\right)q_i+rw\left(q_1+q_2\right) i=1,2$$

(11)

The utility function of the urban sharing logistics distribution company is:

$$U^{D2}=\left(1-2r\right)w\left(q_1+q_2\right)-cQ+\kappa {\left(1-\sigma \right)}^Q$$

(12)

We solved the SM2 mode by using backward induction, and the equilibrium results are shown in Proposition 3.

Proposition 3.

For any given load ratio of trucks to delivery vehicles  $\lambda$, the optimal equilibrium in the sharing mechanism SM2 exists and satisfies the following:

(1) 

While  $\lambda =2$, the optimal decisions are  $p^{*}={\displaystyle \frac{3}{2}},{p_i}^{*}={\displaystyle \frac{3}{4}},{q_i}^{*}={\displaystyle \frac{1}{4}},w^{*}={\displaystyle \frac{1}{2\left(1-r\right)}},i=1,2$, and the optimal utility are  ${U_i^{S2}}^{*}={\displaystyle \frac{3}{16}}-{\displaystyle \frac{1}{8}}\left({\displaystyle \frac{1-2r}{1-r}}\right)$,  $U^{D2*}={\displaystyle \frac{1}{4}}\left({\displaystyle \frac{1-2r}{1-r}}\right)-c+\kappa \left(1-\sigma \right)$; 

(2) 

While  $\lambda \in \left\{3+2M,4+2M\right\}$, where  $M=0,1,2,3,\dots$, the optimal decisions and utility are 

(i) 

if  $c+\kappa {\left(1-\sigma \right)}^{1+M}-\kappa {\left(1-\sigma \right)}^{2+M}\ge \left({\displaystyle \frac{1-2r}{1-r}}\right)\left[{\displaystyle \frac{1}{4}}-\left(1-{\displaystyle \frac{1+M}{\lambda }}\right){\displaystyle \frac{1+M}{\lambda }}\right]$, then  $p^{*}=2-{\displaystyle \frac{1+M}{\lambda }},{p_i}^{*}=1-{\displaystyle \frac{1+M}{2\lambda }},{q_i}^{*}={\displaystyle \frac{1+M}{2\lambda }}$,  $w^{*}=\left(1-{\displaystyle \frac{1+M}{\lambda }}\right){\displaystyle \frac{1}{1-r}}$,  ${U_i^{S2}}^{*}=\left(1-{\displaystyle \frac{1+M}{2\lambda }}\right){\displaystyle \frac{1+M}{2\lambda }}-{\displaystyle \frac{1}{2}}\left({\displaystyle \frac{1-2r}{1-r}}\right)\left(1-{\displaystyle \frac{1+M}{\lambda }}\right){\displaystyle \frac{1+M}{\lambda }}$,  $U^{D2*}=\left({\displaystyle \frac{1-2r}{1-r}}\right)\left(1-{\displaystyle \frac{1+M}{\lambda }}\right){\displaystyle \frac{1+M}{\lambda }}-\left(1+M\right)c+\kappa {\left(1-\sigma \right)}^{1+M}$; 

(ii) 

if  $c+\kappa {\left(1-\sigma \right)}^{1+M}-\kappa {\left(1-\sigma \right)}^{2+M}<\left({\displaystyle \frac{1-2r}{1-r}}\right)\left[{\displaystyle \frac{1}{4}}-\left(1-{\displaystyle \frac{1+M}{\lambda }}\right){\displaystyle \frac{1+M}{\lambda }}\right]$, then $p^{*}={\displaystyle \frac{3}{2}},{p_i}^{*}={\displaystyle \frac{3}{4}},{q_i}^{*}={\displaystyle \frac{1}{4}},w^{*}={\displaystyle \frac{1}{2\left(1-r\right)}},i=1,2$,  ${U_i^{S2}}^{*}={\displaystyle \frac{3}{16}}-{\displaystyle \frac{1}{8}}\left({\displaystyle \frac{1-2r}{1-r}}\right)$,  $U^{D2*}={\displaystyle \frac{1}{4}}\left({\displaystyle \frac{1-2r}{1-r}}\right)-\left(2+M\right)c+\kappa {\left(1-\sigma \right)}^{2+M}$.

For the proof, see the Supplementary Materials.

Proposition 3 gives all the optimal decisions and utility for any given $\lambda$. We can see that the intercity logistics companies’ utility, as well as the decision variables $p_i$, is determined by the load ratio of trucks to delivery vehicles $\lambda$ and the revenue-sharing factor $r$, while the urban logistics distribution companies’ utility is determined by $\lambda$, operational cost $c$, the non-disruption risk preference $\kappa \left(1-\sigma \right)$, and the revenue-sharing factor $r$. We present a much more detailed analysis in Section 5, including a comparative analysis.

4.4. Sharing Mechanism 3: SM3

SM3 is a type of sharing logistics mechanism based on an equity investment contract, whereby the two intercity logistics companies jointly establish an urban sharing logistics distribution company by themselves through an equity investment contract. Therefore, they share the revenue of this urban sharing logistics distribution company based on their equity. Consider the homogeneity of the two intercity logistics companies; each of their equities will be same, that is, $r={\displaystyle \frac{1}{2}}$. In addition, their logistics service prices will be the same, that is, $p_1=p_2$. Let $p=p_1+p_2=2p_1=2p_2$. The utility function of the two intercity logistics companies is:

$$U_i^{S3}=\left(p_i-w\right)q_i+{\displaystyle \frac{1}{2}}{U}^{D3} i=1,2$$

(13)

The utility function of the jointly established urban sharing logistics distribution company is:

$$U^{D3}=w\left(q_1+q_2\right)-cQ+\kappa {\left(1-\sigma \right)}^Q$$

(14)

We solved the SM3 mode by using backward induction, and the equilibrium results are shown in Proposition 4.

Proposition 4.

For any given load ratio of trucks to delivery vehicles $\lambda =2,3,4,\dots$, the optimal equilibrium in the sharing mechanism SM3 exists and satisfies the following: 

(1) 

if $c+\kappa {\left(1-\sigma \right)}^{\lambda -1}-\kappa {\left(1-\sigma \right)}^{\lambda }\ge {\displaystyle \frac{1}{2{\lambda }^2}}$, the optimal decisions and utility are  $p^{*}=1+{\displaystyle \frac{1}{\lambda }},{p_i}^{*}={\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2\lambda }},{q_i}^{*}={\displaystyle \frac{1}{2}}-{\displaystyle \frac{1}{2\lambda }}$,  ${U_i^{S3}}^{*}={\displaystyle \frac{1}{4}}\left(1-{\displaystyle \frac{1}{{\lambda }^2}}\right)-{\displaystyle \frac{1}{2}}\left(\lambda -1\right)c+{\displaystyle \frac{1}{2}}\kappa {\left(1-\sigma \right)}^{2\left(\lambda -1\right)}$; 

(2) 

if  $c+\kappa {\left(1-\sigma \right)}^{\lambda -1}-\kappa {\left(1-\sigma \right)}^{\lambda }<{\displaystyle \frac{1}{2{\lambda }^2}}$, the optimal decisions and utility are  $p^{*}=1,{p_i}^{*}={\displaystyle \frac{1}{2}},{q_i}^{*}={\displaystyle \frac{1}{2}}$,  ${U_i^{S3}}^{*}={\displaystyle \frac{1}{4}}-{\displaystyle \frac{1}{2}}\lambda c+{\displaystyle \frac{1}{2}}\kappa {\left(1-\sigma \right)}^{\lambda }$.

For the proof, see the Supplementary Materials.

Proposition 4 gives all the optimal decisions and utility for any given $\lambda$. We can see that the utility of intercity logistics companies is determined by the load ratio of trucks to delivery vehicles $\lambda$, operational cost $c$, and the non-disruption risk preference $\kappa \left(1-\sigma \right)$. We present a much more detailed analysis in Section 5, including a comparative analysis.

5. Comparative Analyses

According to the equilibrium analysis in Section 4, in this section, we conduct detailed comparative analyses composed of a feasibility analysis and a sustainability analysis, which provide very powerful support for the managerial implications that we detail later. In the feasibility analysis, we study the sharing mechanisms’ optimal and suboptimal Pareto improvements for the BM and analyze the pros and cons among the sharing mechanisms. In the sustainability analysis, we mainly analyze the changes in the load ratio, low-carbon, and low-disruption dimensions of the sharing mechanisms compared with those of the BM.

The delivery vehicles in China can be classified into the following categories according to their load: micro-trucks (total weight < 1.8 tons), light trucks (1.8 tons < total weight ≤ 6 tons), medium trucks (6.0 tons < total weight ≤ 14 tons), and heavy trucks (total weight > 14 tons). In addition, the load of the trucks used by the intercity logistics companies is generally 32 tons. Therefore, the load ratio of trucks to delivery vehicles$\lambda$ is generally $\left[2,18\right]$, which means that the value of $\lambda$ cannot be infinite. Therefore, due to space limitations, in the following feasibility analysis, we only analyze some of the $\lambda$ values in detail, and we provide a general solution process for the remaining $\lambda$ values.

5.1. Feasibility Analysis

In the feasibility analysis, we study the sharing mechanisms’ optimal and suboptimal Pareto improvements for the BM in turn and analyze the pros and cons among the sharing mechanisms. Furthermore, we present the comparison results through Propositions 5–8.

Proposition 5 (SM1 vs. BM).

For different load ratios of trucks to delivery vehicles  $\lambda$, optimal or suboptimal Pareto improvements exist for the sharing mechanism SM1 to the BM. Examples are given in

Table 2. Optimal or suboptimal Pareto improvements for any given $\lambda$.

$$\mathit{\lambda }$$	Optimal or Suboptimal	Pros and Cons	Related Parameter Conditions
2	Optimal	$$\begin{gathered} U_i^{S1}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D1}\ge {{\displaystyle \sum }}_{i=1}^2{U}_i^D \end{gathered}$$	$c-\kappa \left(1-\sigma \right)\ge 0$
3	Suboptimal	$$\begin{gathered} U_i^{S1}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D1}\ge U_i^D, \forall i=1,2 \end{gathered}$$	$c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\le {\displaystyle \frac{1}{8}}$
4	Suboptimal	$$\begin{gathered} U_i^{S1}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D1}\ge U_i^D, \forall i=1,2 \end{gathered}$$	$c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\le {\displaystyle \frac{1}{8}}$
5	Optimal	$$\begin{gathered} U_i^{S1}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D1}\ge {{\displaystyle \sum }}_{i=1}^2{U}_i^D \end{gathered}$$	$\sigma <{\displaystyle \frac{1}{2}}$
	Optimal		$$\begin{gathered} c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\ge {\displaystyle \frac{1}{200}} \\ c+\kappa {\left(1-\sigma \right)}^2-\kappa {\left(1-\sigma \right)}^3<{\displaystyle \frac{1}{100}} \\ c+2\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^3\le {\displaystyle \frac{1}{100}} \end{gathered}$$
	Suboptimal	$$\begin{gathered} U_i^{S1}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D1}\ge U_i^D, \forall i=1,2 \end{gathered}$$	$c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\le {\displaystyle \frac{3}{25}}$
6	Optimal	$$\begin{gathered} U_i^{S1}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D1}\ge {{\displaystyle \sum }}_{i=1}^2{U}_i^D \end{gathered}$$	$\sigma <{\displaystyle \frac{1}{2}}$
	Optimal		$$\begin{gathered} c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\ge {\displaystyle \frac{1}{72}} \\ c+\kappa {\left(1-\sigma \right)}^2-\kappa {\left(1-\sigma \right)}^3<{\displaystyle \frac{1}{36}} \\ c+2\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^3\le {\displaystyle \frac{1}{36}} \end{gathered}$$
	Suboptimal	$$\begin{gathered} U_i^{S1}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D1}\ge U_i^D, \forall i=1,2 \end{gathered}$$	$c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\le {\displaystyle \frac{1}{9}}$
7	Optimal	$$\begin{gathered} U_i^{S1}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D1}\ge {{\displaystyle \sum }}_{i=1}^2{U}_i^D \end{gathered}$$	$$\begin{gathered} c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\ge {\displaystyle \frac{9}{392}} \\ c+\kappa {\left(1-\sigma \right)}^3-\kappa {\left(1-\sigma \right)}^4\ge {\displaystyle \frac{1}{196}} \\ c+2\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^3\le {\displaystyle \frac{2}{49}} \end{gathered}$$
	Optimal		$$\begin{gathered} c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\ge {\displaystyle \frac{9}{392}} \\ c+\kappa {\left(1-\sigma \right)}^3-\kappa {\left(1-\sigma \right)}^4<{\displaystyle \frac{2}{392}} \\ 2c+2\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^4\le {\displaystyle \frac{9}{196}} \end{gathered}$$
	Suboptimal	$$\begin{gathered} U_i^{S1}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D1}\ge U_i^D, \forall i=1,2 \end{gathered}$$	$$\begin{gathered} c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2<{\displaystyle \frac{9}{392}} \\ c+\kappa {\left(1-\sigma \right)}^3-\kappa {\left(1-\sigma \right)}^4<{\displaystyle \frac{2}{392}} \\ 2c+\kappa {\left(1-\sigma \right)}^2-\kappa {\left(1-\sigma \right)}^4\ge {\displaystyle \frac{1}{8}} \end{gathered}$$

.

For the proof, see the Supplementary Materials.

Different from the other values of $\lambda$, for $\lambda =3,4$, the sharing mechanism SM1 only achieves suboptimal Pareto improvements for the BM. This may be because the max value of $q_i$ is one. When the load ratio of trucks to delivery vehicles is $\lambda =3,4$, urban sharing logistics distribution is not a much better operation strategy. If the max value of $q_i$ is not one but any other number, the suboptimal Pareto improvement may exist for $\lambda$ values other than 3 or 4. When $\lambda =2$, the optimal Pareto improvement only exists under the conditions $c-\kappa \left(1-\sigma \right)\ge 0$, which means that the operational cost for one delivery vehicle $c$ is higher than the non-disruption risk preference for one delivery vehicle $\kappa \left(1-\sigma \right)$. Obviously, this can hold and must be held. For other $\lambda$ values, either optimal or suboptimal Pareto improvements exist for SM1 to BM, but, overall, the number of optimal Pareto improvements is larger than that of suboptimal Pareto improvements. When the overall market size is relatively stable, the use of sharing operations to increase the level of scale and intensive operation and, to a certain extent, increase the market concentration will inevitably lead to the survival of the fittest. In the process of operational improvement from the BM to SM1, the number of intercity logistics companies does not change, but the number of urban logistics distribution companies reduces from two to one. Therefore, regardless of whether the Pareto improvements are optimal or suboptimal, the three enterprises achieve improvements in utility.

Proposition 6 (SM2 vs. BM).

For different load ratios of trucks to delivery vehicles  $\lambda$, optimal or suboptimal Pareto improvements exist for the sharing mechanism SM2 to the BM. Examples are given in

Table 3. Optimal or suboptimal Pareto improvements for any given $\lambda$.

$$\mathit{\lambda }$$	Optimal or Suboptimal	Pros and Cons	Related Parameter Conditions
2	Optimal	$$\begin{gathered} U_i^{S2}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D2}\ge {{\displaystyle \sum }}_{i=1}^2{U}_i^D \end{gathered}$$	${\displaystyle \frac{1}{4}}-\left[c-\kappa \left(1-\sigma \right)\right]\le {\displaystyle \frac{1}{4}} · {\displaystyle \frac{1-2r}{1-r}}$
3	Optimal	$$\begin{gathered} U_i^{S2}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D2}\ge {{\displaystyle \sum }}_{i=1}^2{U}_i^D \end{gathered}$$	$$\begin{gathered} {\displaystyle \frac{1}{4}}-\left[c-\kappa \left(1-\sigma \right)\right]\le {\displaystyle \frac{2}{9}} · {\displaystyle \frac{1-2r}{1-r}} \\ c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\ge {\displaystyle \frac{1}{36}} · {\displaystyle \frac{1-2r}{1-r}} \\ r\in \left[{\displaystyle \frac{5}{21}},{\displaystyle \frac{1}{2}}\right] \end{gathered}$$
	Suboptimal	$$\begin{gathered} U_i^{S2}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D2}\ge U_i^D, \forall i=1,2 \end{gathered}$$	$c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2<{\displaystyle \frac{1}{36}} · {\displaystyle \frac{1-2r}{1-r}}$
4	Optimal	$$\begin{gathered} U_i^{S2}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D2}\ge {{\displaystyle \sum }}_{i=1}^2{U}_i^D \end{gathered}$$	$$\begin{gathered} {\displaystyle \frac{1}{4}}-\left[c-\kappa \left(1-\sigma \right)\right]\le {\displaystyle \frac{3}{16}} · {\displaystyle \frac{1-2r}{1-r}} \\ c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\ge {\displaystyle \frac{1}{16}} · {\displaystyle \frac{1-2r}{1-r}} \\ r\in \left[{\displaystyle \frac{1}{3}},{\displaystyle \frac{1}{2}}\right] \end{gathered}$$
	Suboptimal	$$\begin{gathered} U_i^{S2}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D2}\ge U_i^D, \forall i=1,2 \end{gathered}$$	$$\begin{gathered} r\in \left(0,{\displaystyle \frac{1}{4}}\right),c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2<{\displaystyle \frac{1}{16}} · {\displaystyle \frac{1-2r}{1-r}} \\ r\in \left[{\displaystyle \frac{1}{4}}\right.,\left.1\right),c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\le {\displaystyle \frac{1}{4}} · {\displaystyle \frac{1-2r}{1-r}}-{\displaystyle \frac{1}{8}} \end{gathered}$$
5	Optimal	$$\begin{gathered} U_i^{S2}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D2}\ge {{\displaystyle \sum }}_{i=1}^2{U}_i^D \end{gathered}$$	$$\begin{gathered} c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\ge {\displaystyle \frac{1}{200}} \\ c+\kappa {\left(1-\sigma \right)}^2-\kappa {\left(1-\sigma \right)}^3<{\displaystyle \frac{1}{100}} · {\displaystyle \frac{1-2r}{1-r}} \\ c+2\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^3\le {\displaystyle \frac{1}{4}} · {\displaystyle \frac{1-2r}{1-r}}-{\displaystyle \frac{6}{25}} \end{gathered}$$
	Optimal		$$\begin{gathered} c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2<{\displaystyle \frac{1}{200}} \\ c+\kappa {\left(1-\sigma \right)}^2-\kappa {\left(1-\sigma \right)}^3\ge {\displaystyle \frac{1}{100}} · {\displaystyle \frac{1-2r}{1-r}} \\ 2c-\kappa {\left(1-\sigma \right)}^2\ge {\displaystyle \frac{1}{4}}-{\displaystyle \frac{6}{25}} · {\displaystyle \frac{1-2r}{1-r}} \\ r\in \left[{\displaystyle \frac{9}{57}},{\displaystyle \frac{1}{2}}\right] \end{gathered}$$
	Optimal		$$\begin{gathered} c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2<{\displaystyle \frac{1}{200}} \\ c+\kappa {\left(1-\sigma \right)}^2-\kappa {\left(1-\sigma \right)}^3<{\displaystyle \frac{1}{100}} · {\displaystyle \frac{1-2r}{1-r}} \\ c-2\kappa {\left(1-\sigma \right)}^2+\kappa {\left(1-\sigma \right)}^3\ge {\displaystyle \frac{1}{4}}-{\displaystyle \frac{1}{4}} · {\displaystyle \frac{1-2r}{1-r}} \end{gathered}$$
	Suboptimal	$$\begin{gathered} U_i^{S2}\ge U_i^{NS}, \forall i=1,2 \\ {U}^{D2}\ge U_i^D, \forall i=1,2 \end{gathered}$$	$$\begin{gathered} c+\kappa {\left(1-\sigma \right)}^2-\kappa {\left(1-\sigma \right)}^3\ge {\displaystyle \frac{1}{100}} · {\displaystyle \frac{1-2r}{1-r}} \\ {\displaystyle \frac{1}{200}}\le c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2\le {\displaystyle \frac{6}{25}} · {\displaystyle \frac{1-2r}{1-r}}-{\displaystyle \frac{3}{25}} \\ r\in \left[0,{\displaystyle \frac{23}{71}}\right] \end{gathered}$$

.

For the proof, see the Supplementary Materials.

Different from the only sharing logistics mechanism SM1, revenue-sharing contracts are included in the sharing logistics mechanism SM2. In SM2, the two intercity logistics companies can share some revenue from the urban sharing logistics distribution company based on a revenue-sharing contract. For each value of $\lambda$, the sharing mechanism SM2 achieves at least one optimal Pareto improvement for the BM. We can see that, when $\lambda =5$, optimal Pareto improvements exist under three different parameter conditions. Different from SM1, when the load ratio of trucks to delivery vehicles is $\lambda =3,4$, both optimal and suboptimal Pareto improvements exist for the BM. The majority of the related parameter conditions are related to the revenue-sharing factor $r$ in SM2, which means that the related parameter conditions change as $r$ changes from 0 to ${\displaystyle \frac{1}{2}}$. Obviously, for any given operation cost$c$ and non-disruption risk preference $\kappa \left(1-\sigma \right)$, we can adjust the value of $r\in \left[0,\right.\left.{\displaystyle \frac{1}{2}}\right)$ to motivate and drive all the intercity logistics companies and the urban sharing logistics distribution company to achieve a balanced and much better sharing cooperation under the parameter conditions being satisfied. In summary, the sharing mechanism SM2 is much more flexible and extensive than SM1. In the process of operational improvement from BM to SM2, the number of intercity logistics companies does not change, but the number of urban logistics distribution companies reduces from two to one. Therefore, regardless of whether the Pareto improvements are optimal or suboptimal, the three enterprises achieve improvements in utility.

Proposition 7 (SM3 vs. BM).

For different load ratios of trucks to delivery vehicles  $\lambda$, only optimal Pareto improvements exist for the sharing mechanism SM3 to the BM. Moreover, this type of optimal Pareto improvement is not only for any one company in this two-echelon sharing logistics service supply chain but also for the entire supply chain. Examples are given in

Table 4. Optimal or suboptimal Pareto improvements for any given $\lambda$.

$$\mathit{\lambda }$$	Optimal or Suboptimal	Pros and Cons	Related Parameter Conditions
2,3,4	Optimal	$$\begin{gathered} U_i^{S3}\ge U_i^{NS}, \forall i=1,2 \\ {{\displaystyle \sum }}_{i=1}^2{U}_i^{S3}\ge {{\displaystyle \sum }}_{i=1}^2\left(U_i^{NS}+U_i^D\right) \end{gathered}$$	$\left(\lambda -2\right)c+2\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^{\lambda }\le {\displaystyle \frac{1}{8}}$
$$\begin{gathered} 5+4N, \\ 6+4N, \\ 7+4N, \\ 8+4N \end{gathered}$$, $N=0,1,2,3\dots$	Optimal	$$\begin{gathered} U_i^{S3}\ge U_i^{NS}, \forall i=1,2 \\ {{\displaystyle \sum }}_{i=1}^2{U}_i^{S3}\ge {{\displaystyle \sum }}_{i=1}^2\left(U_i^{NS}+U_i^D\right) \end{gathered}$$	$$\begin{gathered} c+\kappa {\left(1-\sigma \right)}^{1+N}-\kappa {\left(1-\sigma \right)}^{2+N}<{\displaystyle \frac{1}{8}}-\left[1-{\displaystyle \frac{2\left(1+N\right)}{\lambda }}\right]{\displaystyle \frac{1+N}{\lambda }} \\ \left[\lambda -2\left(2+N\right)\right]c+2\kappa {\left(1-\sigma \right)}^{2+N}-\kappa {\left(1-\sigma \right)}^{\lambda }\le {\displaystyle \frac{1}{8}} \\ {\displaystyle \frac{1}{4}}-{\displaystyle \frac{1}{2}}\lambda c+{\displaystyle \frac{1}{2}}\kappa {\left(1-\sigma \right)}^{\lambda }\ge {\left({\displaystyle \frac{1+N}{\lambda }}\right)}^2 \end{gathered}$$
	Optimal		$$\begin{gathered} c+\kappa {\left(1-\sigma \right)}^{1+N}-\kappa {\left(1-\sigma \right)}^{2+N}\ge {\displaystyle \frac{1}{8}}-\left[1-{\displaystyle \frac{2\left(1+N\right)}{\lambda }}\right]{\displaystyle \frac{1+N}{\lambda }} \\ \left[\lambda -2\left(1+N\right)\right]c+2\kappa {\left(1-\sigma \right)}^{1+N}-\kappa {\left(1-\sigma \right)}^{\lambda }\le {\displaystyle \frac{1}{2}}+2{\left({\displaystyle \frac{1+N}{\lambda }}\right)}^2-2\left({\displaystyle \frac{1+N}{\lambda }}\right) \\ {\displaystyle \frac{1}{4}}-{\displaystyle \frac{1}{2}}\lambda c+{\displaystyle \frac{1}{2}}\kappa {\left(1-\sigma \right)}^{\lambda }\ge {\displaystyle \frac{1}{16}} \end{gathered}$$

. 

For the proof, see the Supplementary Materials.

Different from the only sharing logistics mechanism SM1 and the sharing logistics with revenue-sharing contracts mechanism SM2, the two intercity logistics companies invest in and establish one urban sharing logistics distribution company and outsource all their urban logistics distribution orders to this company. This means that the two intercity logistics companies achieve vertical integration based on the sharing logistics operation and equity investment cooperation. Therefore, we can see that, for any value of$\lambda$, the sharing mechanism SM3 only achieves the optimal Pareto improvement for the BM. Furthermore, this type of optimal Pareto improvement is not only for any one company in this two-echelon sharing logistics service supply chain but also for the entire supply chain, that is, $U_i^{S3}\ge U_i^{NS},\forall i=1,2$, and ${{\displaystyle \sum }}_{i=1}^2{U}_i^{S3}\ge {{\displaystyle \sum }}_{i=1}^2\left(U_i^{NS}+U_i^D\right)$. Obviously, from this perspective, the sharing mechanism SM3 is much better than SM1 and SM2.

According to the comparison of Propositions 5–7, some meaningful conclusions can be summed up in Corollary 1:

Corollary 1.

For any given load ratio of trucks to delivery vehicles  $\lambda$, there will be at least one optimal Pareto improvement for the sharing mechanisms SM2 and SM3. In addition, the mechanism SM1 can only achieve the suboptimal Pareto improvement for  $\lambda =3,4$  while there will be at least one optimal Pareto improvement for any   $\lambda \ne 3,4$. The mechanism SM3 can always achieve the optimal Pareto improvement for any given  $\lambda$. The pros and cons between any SMi ($i=1,2,3$) and BM have no obvious monotonic increasing or monotonic decreasing relationship with the value of  $\lambda$. However, the scientific design of the load ratio of trucks to delivery vehicles  $\lambda$ is very important for the sharing logistics mechanism. 

Due to the length limitations of this paper and the complexity of the related solution process, we only present some of the analysis results for $\lambda$ in Propositions 5, 6, and 7 and their proof processes. In order to facilitate understanding, we show the specific solution process in

Table 5. Solution process of Pareto improvement for any given $\lambda$ in the SMi.

For any given $\lambda =2,3,4\dots$ and SMi  $\left(i=1,2,3\right)$ =>BM: N($\lambda$)    =>SMi : M($\lambda$)      =>Lemma 0, Lemma i, min {$\mathbb{F}\mathrm{𝕣}\left(\mathrm{Lemma}0\right)$, $\mathbb{F}\mathrm{𝕣}\left(\mathrm{Lemma}i\right)$} => Feasible region   =>BM($\lambda$, N ):$U_j^{NS}$,$U_j^D$ $j=1,2$     =>SMi ($\lambda$, M ):$U_j^{Si}$,$U^{Di}$ $j=1,2;i=1,2,3$       =>Compare the $U_j^{Si}$ $U_j^{NS}$ and the $U^{Di}$ ${{\displaystyle \sum }}_{j=1}^2{U}_j^D$ $U_j^D$ $i=1,2,3$;$j=1,2$       =>According to Definition i, decide the optimal or suboptimal Pareto improvement       End

.

According to Propositions 5–7, when the load ratio of trucks to delivery vehicles is $\lambda =2,3,4,5$, the relationships among the sharing mechanisms SM1, SM2, and SM3 are as follows:

(1)

$\lambda =2$. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into region I in Figure 5a, the relationship among the sharing mechanisms satisfies SM3 > SM2 > SM1. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into region II in Figure 5a, the relationship among the sharing mechanisms satisfies SM2 > SM3 > SM1. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into region III in Figure 5a, the relationship among the sharing mechanisms satisfies SM2 > SM1, and SM3 is not better than the BM. See Figure 5a and

Table 6. Expression of the conditions in (a) Figure 5a, (b) Figure 5b, (c) Figure 5c, and (d) Figure 5d.

(a)
Conditions	Mathematical Expression of the Conditions
Condition (1)	${\displaystyle \frac{1-2r}{1-r}}=-{\displaystyle \frac{1}{2}}+8c-4\kappa {\left(1-\sigma \right)}^2$
Condition (2)	$\left(\lambda -2\right)c+2\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^{\lambda }={\displaystyle \frac{1}{8}}$
(b)
Conditions	Mathematical Expression of the Conditions
Condition (1)	${\displaystyle \frac{1}{4}}-\left[c-\kappa \left(1-\sigma \right)\right]={\displaystyle \frac{2}{9}} · {\displaystyle \frac{1-2r}{1-r}}$
Condition (2)	$c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2={\displaystyle \frac{1}{8}}$
Condition (3)	$c+2\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^3={\displaystyle \frac{1}{8}}$
(c)
Conditions	Mathematical Expression of the Conditions
Condition (1)	${\displaystyle \frac{1}{4}}-\left[c-\kappa \left(1-\sigma \right)\right]={\displaystyle \frac{3}{16}} · {\displaystyle \frac{1-2r}{1-r}}$
Condition (2)	$c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2={\displaystyle \frac{1}{8}}$
Condition (3)	$2c+2\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^4={\displaystyle \frac{1}{8}}$
(d)
Conditions	Mathematical Expression of the Conditions
Condition (1)	$c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2={\displaystyle \frac{6}{25}} · {\displaystyle \frac{1-2r}{1-r}}-{\displaystyle \frac{3}{25}}$
Condition (2)	$2c-\kappa {\left(1-\sigma \right)}^2={\displaystyle \frac{1}{4}}-{\displaystyle \frac{6}{25}} · {\displaystyle \frac{1-2r}{1-r}}$
Condition (3)	$c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2={\displaystyle \frac{1}{200}}$
Condition (4)	$3c+2\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^5={\displaystyle \frac{9}{50}}$
Condition (5)	$\sigma ={\displaystyle \frac{1}{2}}$
Condition (6)	$c+\kappa \left(1-\sigma \right)-\kappa {\left(1-\sigma \right)}^2={\displaystyle \frac{3}{25}}$

a below for details.

(2)

$\lambda =3$. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into region I in Figure 5b, the relationship among the sharing mechanisms satisfies SM3 > SM2 > SM1. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into region II in Figure 5b, the relationship among the sharing mechanisms satisfies SM3 > SM1, and SM2 is not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into regions III and IV in Figure 5b, the relationship among the sharing mechanisms satisfies SM3 > SM2, and SM1 is not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into regions V and VI in Figure 5b, the sharing mechanism SM2 is better, but SM1 and SM3 are not better than the benchmark model (BM). When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into regions VII and VIII in Figure 5b, the sharing mechanism SM3 is better, but SM1 and SM2 are not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into the other regions in $\left[0,1\right]\times \left[0,1\right]$ in Figure 5b, none of the sharing mechanisms—SM1, SM2, or SM3—is better than the BM. See Figure 5b and Table 6b below for details.

(3)

$\lambda =4$. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into region I in Figure 5c, the relationship among the sharing mechanisms satisfies SM3 > SM2 > SM1. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into region II in Figure 5c, the relationship among the sharing mechanisms satisfies SM3 > SM1, and SM2 is not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into regions III and IV in Figure 5c, the relationship among the sharing mechanisms satisfies SM3 > SM2, and SM1 is not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into regions V and VI in Figure 5c, the sharing mechanism SM2 is better, but SM1 and SM3 are not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into regions VII and VIII in Figure 5c, the sharing mechanism SM3 is better, but SM1 and SM2 are not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into the other regions in $\left[0,1\right]\times \left[0,1\right]$ in Figure 5c, none of the sharing mechanisms—SM1, SM2, or SM3—is better than the BM. See Figure 5c and Table 6c below for details.

(4)

$\lambda =5$. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into region I in Figure 5d, the relationship among the sharing mechanisms satisfies SM3 > SM2 > SM1. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into region II in Figure 5d, the relationship among the sharing mechanisms satisfies SM3 > SM1, and SM2 is not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into regions III and V in Figure 5d, the relationship among the sharing mechanisms satisfies SM2 > SM1, and SM3 is not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into region IV in Figure 5d, the sharing mechanism SM2 is better, but SM1 and SM3 are not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into regions VI and VII in Figure 5d, the sharing mechanism SM1 is better, but SM2 and SM3 are not better than the BM. When $\left({\displaystyle \frac{1-2r}{1-r}},1-\sigma \right)$ falls into the other regions in $\left[0,1\right]\times \left[0,1\right]$ in Figure 5d, none of the sharing mechanisms—SM1, SM2, or SM3—is better than the BM. See Figure 5d and Table 6d below for details.

Proposition 8 (SM1 vs. SM2 vs. SM3).

For different load ratios of trucks to delivery vehicles $\lambda$, as well as any value of  ${\displaystyle \frac{1-2r}{1-r}}$ and  $1-\sigma$, the sharing mechanism SM1 is never better than SM2 or SM3. When the value of  ${\displaystyle \frac{1-2r}{1-r}}$ is not larger than in some conditions, that is to say, when the value of the revenue-sharing factor $r$ is larger than in some conditions, SM2 is better than SM3. Otherwise, SM3 is always better than SM2. Of course, the conditions also differ for different load ratios $\lambda ,$ but we can determine those conditions through Propositions 5–7. 

5.2. Sustainability Analysis: Load Ratio, Low-Carbon, and Low-Disruption Dimensions

The three sharing logistics operation strategies, namely, SM1, SM2, and SM3, proposed in this article indeed achieve the goals of reducing operation costs and increasing efficiency. The feasibility analysis section studied the increase in utility and efficiency. In this section, we analyze the reduction in operation costs. Regarding urban logistics distribution, its cost mainly refers to the operating cost of delivery vehicles, which is related to the number of delivery vehicles required to transport goods, that is, the occupancy rate of delivery vehicles per unit of product. All of the delivery vehicle resources are shared in the three sharing logistics mechanisms, and this increases the load ratio. A decrease in the number of delivery vehicles used to distribute the same product from the BM to the SMi  ($i=1,2,3$) causes a decrease in the operation cost, which results in a reduction in carbon emissions. At the same time, the decrease in the number of delivery vehicles also reduces the disruption probability per unit product. In summary, we conduct a sustainability analysis composed of the load ratio, low-carbon, and low-disruption dimensions.

$\mathbb{L}ℝ$ represents the increase rate of the load ratio, $\mathbb{L}ℂ$ represents the reduction rate of carbon emissions per unit product, and $\mathbb{L}\mathbb{D}$ represents the reduction rate of the risk of disruption per unit product. Therefore, the sustainability analysis can be characterized from these three dimensions, that is, $\mathbb{L}ℝ$ (load ratio),$\mathbb{L}ℂ$ (low carbon), and $\mathbb{L}\mathbb{D}$ (low disruption). Their calculation formula is as follows:

$$\mathbb{L}ℝ={\displaystyle \frac{{\left.\frac{{{\displaystyle \sum }}_{i=1}^2{q}_i}{\frac{Q}{\lambda }}\right|}_{SMi}-{\left.\frac{{{\displaystyle \sum }}_{i=1}^2{q}_i}{\frac{{{\displaystyle \sum }}_{i=1}^2{Q}_i}{\lambda }}\right|}_{BM}}{{\left.\frac{{{\displaystyle \sum }}_{i=1}^2{q}_i}{\frac{{{\displaystyle \sum }}_{i=1}^2{Q}_i}{\lambda }}\right|}_{BM}}}\times 100\%$$

(15)

where ${\left.{\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^2{q}_i}{\frac{{{\displaystyle \sum }}_{i=1}^2{Q}_i}{\lambda }}}\right|}_{BM}$ represents the load ratio in the BM, and ${\left.{\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^2{q}_i}{\frac{Q}{\lambda }}}\right|}_{SMi}$ represents the load ratio in the sharing mechanism SMi. 

$$\mathbb{L}ℂ={\displaystyle \frac{{\left.\frac{Qc}{{{\displaystyle \sum }}_{i=1}^2{q}_i}\right|}_{SMi}-{\left.\frac{{{\displaystyle \sum }}_{i=1}^2{Q}_{i}c}{{{\displaystyle \sum }}_{i=1}^2{q}_i}\right|}_{BM}}{{\left.\frac{{{\displaystyle \sum }}_{i=1}^2{Q}_{i}c}{{{\displaystyle \sum }}_{i=1}^2{q}_i}\right|}_{BM}}}\times 100\%$$

(16)

where ${\left.{\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^2{Q}_{i}c}{{{\displaystyle \sum }}_{i=1}^2{q}_i}}\right|}_{BM}$ represents the carbon emission level per unit product in the BM, and ${\left.{\displaystyle \frac{Qc}{{{\displaystyle \sum }}_{i=1}^2{q}_i}}\right|}_{SMi}$ represents the carbon emission level per unit product in the sharing mechanism SMi. We use the operation cost per delivery vehicle to indirectly reflect its carbon emission level. As this operating cost is the operating cost of every vehicle, it corresponds to the carbon emission level per delivery vehicle:

$$\mathbb{L}\mathbb{D}={\displaystyle \frac{{\left.\frac{1-{\left(1-\sigma \right)}^Q}{{{\displaystyle \sum }}_{i=1}^2{q}_i}\right|}_{SMi}-{\left.\frac{1-{\left(1-\sigma \right)}^{{{\displaystyle \sum }}_{i=1}^2{Q}_i}}{{{\displaystyle \sum }}_{i=1}^2{q}_i}\right|}_{BM}}{{\left.\frac{1-{\left(1-\sigma \right)}^{{{\displaystyle \sum }}_{i=1}^2{Q}_i}}{{{\displaystyle \sum }}_{i=1}^2{q}_i}\right|}_{BM}}}\times 100\%$$

(17)

where ${\left.{\displaystyle \frac{1-{\left(1-\sigma \right)}^{{{\displaystyle \sum }}_{i=1}^2{Q}_i}}{{{\displaystyle \sum }}_{i=1}^2{q}_i}}\right|}_{BM}$ represents the probability of disruption risk per unit product in the BM, and ${\left.{\displaystyle \frac{1-{\left(1-\sigma \right)}^Q}{{{\displaystyle \sum }}_{i=1}^2{q}_i}}\right|}_{SMi}$ represents the probability of disruption risk per unit product in the sharing mechanism SMi. 

We calculated all values of $\mathbb{L}ℝ$ (load ratio), $\mathbb{L}ℂ$ (low carbon), and $\mathbb{L}\mathbb{D}$ (low disruption) for any given $\lambda$ in any sharing mechanism SMi  ($i=1,2,3$), and they are summarized in

Table 7. Values of load ratio ($\mathbb{L}\mathbb{R}$), low carbon ($\mathbb{L}\mathbb{C}$), and low disruption ($\mathbb{L}\mathbb{D}$) for any given $\lambda$.

$\mathit{\lambda }$	$\mathbb{L}\mathbb{R}$			$\mathbb{L}\mathbb{C}$			$\mathbb{L}\mathbb{D}$
	SM1	SM2	SM3	SM1	SM2	SM3	SM1	SM2	SM3
2	100%	100%	100%	−50%	−50%	−50%	$$\begin{gathered} \mathrm{LD}1:-{\displaystyle \frac{1}{1+\frac{1}{1-\sigma }}} \\ \left[-50\%,\right.\left.0\right) \end{gathered}$$	$$\begin{gathered} \mathrm{LD}1:-{\displaystyle \frac{1}{1+\frac{1}{1-\sigma }}} \\ \left[-50\%,\right.\left.0\right) \end{gathered}$$	−50%
3	0	33.3% 0	33.3%	0	−25% 0	−25%	0	$$\begin{gathered} \mathrm{LD}2:{\displaystyle \frac{2{\left(1-\sigma \right)}^2-3\left(1-\sigma \right)+1}{2-2{\left(1-\sigma \right)}^2}} \\ 0\pm \end{gathered}$$ 0	$$\begin{gathered} \mathrm{LD}3:{\displaystyle \frac{2{\left(1-\sigma \right)}^2-{\left(1-\sigma \right)}^3-1}{2-2{\left(1-\sigma \right)}^2}} \\ <0 \end{gathered}$$
4	0	0	0	0	0	0	0	$$\begin{gathered} \mathrm{LD}4:{\displaystyle \frac{{\left(1-\sigma \right)}^2-2\left(1-\sigma \right)+1}{1-{\left(1-\sigma \right)}^2}} \\ >0 \end{gathered}$$ 0	$$\begin{gathered} \mathrm{LD}5:{\displaystyle \frac{2{\left(1-\sigma \right)}^2-{\left(1-\sigma \right)}^4-1}{2-{\left(1-\sigma \right)}^4}} \\ <0 \end{gathered}$$
5	33.3% −16.7%	−16.7% 60% 33.3% 0	0 60%	−25% 20%	20% −37.5% −25% 0	0 −37.5%	$$\begin{gathered} \mathrm{LD}6:-{\displaystyle \frac{{\left(1-\sigma \right)}^3}{\left(2-\sigma \right)\left[1+{\left(1-\sigma \right)}^2\right]}} \\ <0 \\ \mathrm{LD}9:{\displaystyle \frac{5{\left(1-\sigma \right)}^2-4{\left(1-\sigma \right)}^3-1}{5-5{\left(1-\sigma \right)}^2}} \\ 0\pm \end{gathered}$$	$$\begin{gathered} \mathrm{LD}7:{\displaystyle \frac{4{\left(1-\sigma \right)}^2-5{\left(1-\sigma \right)}^3+1}{4-4{\left(1-\sigma \right)}^2}} \\ >0 \\ \mathrm{LD}10: \\ {\displaystyle \frac{5{\left(1-\sigma \right)}^4-4{\left(1-\sigma \right)}^2-1}{5-5{\left(1-\sigma \right)}^4}} \\ <0 \\ \mathrm{LD}6:-{\displaystyle \frac{{\left(1-\sigma \right)}^3}{\left(2-\sigma \right)\left[1+{\left(1-\sigma \right)}^2\right]}} \\ <0 \end{gathered}$$ 0	$$\begin{gathered} \mathrm{LD}8: \\ {\displaystyle \frac{5{\left(1-\sigma \right)}^2-2{\left(1-\sigma \right)}^5-3}{5-5{\left(1-\sigma \right)}^2}} \\ <0 \\ \mathrm{LD}11: \\ {\displaystyle \frac{2{\left(1-\sigma \right)}^4-{\left(1-\sigma \right)}^5-1}{2-2{\left(1-\sigma \right)}^4}} \\ <0 \end{gathered}$$

In Table 7, LD1–LD11 represent different values of LD related to the disruption risk $\sigma$.

.

As shown in Table 7, all values of $\mathbb{L}ℝ$ (load ratio) and $\mathbb{L}ℂ$ (low carbon) are fixed for any given $\lambda$. However, the majority of $\mathbb{L}\mathbb{D}$ (low disruption) values for any given $\lambda$ are formulated depending on the disruption risk $\sigma$; as the disruption risk is $\sigma \in \left[0,1\right]$, we visualize these values in Figure 6 to facilitate our next analysis.

By comparing and analyzing all values, as well as the formulations in Table 7 and Figure 6, we can draw some meaningful conclusions, as shown in Observation 1:

Observation 1.

For any given load ratio of trucks to delivery vehicles  $\lambda$, almost all values of  $\mathbb{L}ℝ$are greater than zero for any sharing mechanism SMi ($i=1,2,3$), while almost all the values of  $\mathbb{L}ℂ$   and  $\mathbb{L}\mathbb{D}$are less than zero. This means that, compared with the BM, all the sharing mechanisms generally increase the load ratio and significantly reduce the unit carbon emission rate, as well as the unit disruption risk. 

Of course, some undesirable results exist, indicated by the values marked in bold in Table 7. However, this does not affect the main conclusions obtained from our analysis; in particular, it does not have a significant impact on the analysis results of the optimal or suboptimal Pareto improvements because there are generally alternatives in each strategy. In Table 7, there are non-bold alternatives next to each bold number, and they represent one sharing operation strategy.

6. Conclusions

6.1. Summary of Findings

This paper presents a study on the urban sharing logistics problem, taking into consideration the load ratio and the disruption factor. To our knowledge, this is the first study on the sharing mechanism of urban sharing logistics during an epidemic. We study four different operational mechanisms and solve their equilibrium. Firstly, we analyze a benchmark model (BM) in which two intercity logistics companies outsource urban logistics distribution to different urban distribution companies. Secondly, we propose an only sharing logistics mechanism (SM1) in which the two intercity logistics companies outsource their urban distribution orders to the same urban sharing logistics distribution company. Then, we further discuss urban sharing logistics distribution with a revenue-sharing mechanism (SM2) and an equity investment mechanism (SM3). The main findings are as follows. When logistics sharing for cost reduction and efficiency improvement, the load ratio, and the disruption risk factor are considered together, the sharing logistics mechanisms based on revenue sharing and equity investment proposed in this paper are feasible and can achieve Pareto improvements for any given load ratio. In contrast, the first sharing logistics mechanism only based on the wholesale price contract is not optimal for some load ratios. In the majority of scenarios, the sharing logistics mechanism based on equity investment is better than that based on revenue-sharing contracts, but, sometimes, the opposite is the case. Regarding practices, it is necessary to scientifically design the load ratio of trucks to delivery vehicles, as it plays an important role in the performance of sharing logistics implementation. For any given load ratio of trucks to delivery vehicles, compared with the BM, all the sharing mechanisms generally increase the load ratio and significantly reduce the unit carbon emission rate, as well as the unit disruption risk.

6.2. Managerial Implications

6.2.1. Vertical Integration Based on the Sharing Mechanism

In the structure of logistics costs, transportation costs account for the highest proportion, sometimes even more than half. To reduce the costs and increase the efficiency of the logistics industry, the transportation process is the most important link, especially urban distribution. As a new business model, the sharing economy is favored by the transportation industry for its empowerment. Urban sharing logistics, characterized by the integration and sharing of transport capacity resources, is an important innovation mode of sharing logistics.

According to our model conclusion, we found that three urban sharing logistics strategies, with the sharing mechanisms SM1 (only sharing logistics), SM2 (sharing logistics with revenue sharing), and SM3 (sharing logistics with equity investment), achieve optimal and suboptimal Pareto improvements for the BM. Therefore, urban sharing logistics can coordinate social transport resources, reduce the empty rate, and achieve good economic and social benefits.

The theory of vertical integration originated from Ronald Coase’s investigation and research on the boundaries of enterprises in 1937 [87]. In economics, a business layout that occupies several links in the industrial chain is called vertical integration. Vertical integration is a strategic plan, and it is a form of the expansion of an organization’s core capabilities within an enterprise. The advantage of vertical integration is that the internalization of external market activities introduces many aspects of economy, such as the economy of control and coordination, the economy of information, the economy of transaction cost savings, and the economy of stable relationships. Of course, it also brings various benefits, such as effectively ensuring supply and demand, increasing the level of differentiation, and increasing entry barriers.

Different from exogenous vertical integration, for example, extending from iron ore smelting to the production of finished steel products, intercity logistics companies obtain logistics orders from customers that need to be delivered to end customers; however, these companies only self-operate intercity logistics transportation, and they outsource urban logistics distribution to professional urban distribution companies. In this case, if the intercity logistics companies extend the development of the urban logistics distribution business based on the vertical integration strategy adopted by the logistics order already mastered, then this will result in an endogenous vertical integration strategy. Compared with exogenous vertical integration, the biggest advantage of endogeneity is that a new customer market does not need to be developed, and it can better provide existing customers with more value-added services. Obviously, the sharing logistics mechanisms that we propose in this paper belong to endogenous vertical integration. More importantly, in business practice, a few outstanding companies have attempted to adopt these mechanisms and have achieved good results, which is faster than the research progress in the academic field. We introduce two cases of sharing logistics vertical integration below.

Case 1 of sharing logistics vertical integration: Yimidida.com (see Figure 7).

Yimidida is the earliest well-known logistics company in China to practice the concept of urban sharing logistics distribution, starting in March 2015. Its scale, standardization, and brand were quickly achieved through the reorganization of equity based on business orders among similar types of LTL logistics companies. Yimidida has successfully won the favor of the capital market and received nearly CNY five billion in venture capital, quickly building a nationwide network covering 33 provinces (24 self-operated provinces and autonomous regions and 7 member provinces and autonomous regions), with access to Hong Kong, Macao, and Taiwan. Yimidida has more than 13,000 outlets; 1600 trunk lines; 200 distribution centers; 700,000 square meters of operation area; nearly 3000 vehicles; and a 100% coverage of first- and second-tier cities, districts, and counties. The degree of its coverage is 90%, and it had more than 16,000 employees across the country in July 2019. It is an LTL logistics network platform that leads its competitors in terms of the number of trunk lines and cargo volume in the country.

Case 2 of sharing logistics vertical integration: Panda Joint Distribution.

In recent years, China has begun exploring reforms and innovations in the field of logistics operations to improve the efficiency of logistics operations and reduce energy consumption in the logistics process. For example, Beijing, Chongqing, Chengdu, and Wuhan have launched pilot projects on joint distribution, leading to the emergence of more joint distribution platforms, such as Yimidida.com and Chengdu Green Panda Joint Distribution. Most production and living materials entering the core area of Chengdu need to be delivered to end customers through standardized and branded vehicles of the Green Panda Joint Distribution platform (see Figure 8).

6.2.2. Standardization of Logistics Technology and Equipment

According to the feasibility and sustainability analyses, the utility and sustainability of SMi  ($i=1,2,3$) are mainly affected by the load ratio $\lambda$. Therefore, the scientific design of the load ratio of trucks to delivery vehicles is very important for the sharing logistics mechanism, which puts forward requirements for the standardization of related logistics technology and equipment, for example, the load ratio, truck saddles, trays, and freight containers (see Figure 9).

In sharing logistics, the load ratio is a very important factor. It has a direct impact on various aspects of shared logistics, for example, maximizing the use of idle vehicles, operating costs, distribution flexibility, and distribution speed. Therefore, the reasonable setting of the load ratio affects not only the profits of logistics companies but also customer satisfaction. Logistics companies need to optimize the load ratio to reduce costs and improve distribution efficiency. There are many ways to optimize the load ratio, such as the reasonable allocation of goods resources to different vehicles, the mixed loading of goods, and the optimization of vehicle routing. However, there are still few logistics studies based on the load ratio.

6.2.3. Coordination and Sharing of the Handling Mechanisms during Emergencies

Public Incident

According to the values of $\mathbb{L}ℝ$ (load ratio), $\mathbb{L}ℂ$ (low carbon), and $\mathbb{L}\mathbb{D}$ (low disruption) for any given $\lambda$ in any sharing mechanism SMi  ($i=1,2,3$), compared with the BM, all of the sharing mechanisms generally increase the load ratio and significantly reduce the unit carbon emission rate, as well as the unit disruption risk. Therefore, in the event of an epidemic, the daily necessities of citizens can be jointly delivered to the community through the urban sharing logistics distribution system, which can minimize residents’ travel frequency and significantly reduce the probability of contact with potentially infected people (see Figure 10).

6.3. Limitations and Future Studies

This study has some limitations, which provide directions for future research. First, this study assumes that the two intercity logistics companies are completely homogeneous. In future research, we can analyze the situation of two non-homogeneous intercity logistics companies in urban sharing logistics cooperation. Second, the model of urban sharing logistics only considers the load ratio and the disruption factor. The epidemic posed many challenges to urban sharing logistics, such as timeliness, diversity, and uncertainty. These factors need to be effectively considered in the model so as to identify more effective sharing mechanisms. In addition, we can set the operating costs according to the load ratio of devices so as to analyze and optimize the load ratio decision according to the transportation volume.