Contract Design of Logistics Service Supply Chain Based on Smart Transformation

Abstract

A logistics service integrator (LSI) usually requires a logistics service provider (LSP) to carry out smart transformation in order to improve the level of logistics service. However, LSP’s smart transformation faces uncertainty in terms of investments and income, which seriously hinders LSP’s enthusiasm for logistics service innovation. In this paper, we construct a logistics service supply chain (LSSC) consisting of an LSI and an LSP to explore the incentive mechanism for LSPs to undergo smart transformation. As a benchmark for comparison, we first obtain the equilibrium results under centralized decision making and wholesale price (WP) contracts. Then, cost-sharing (CS), revenue-sharing (RS), and cost sharing–revenue sharing (CS-RS) hybrid contracts are proposed. It is found that when the CS coefficient is in a certain interval, the CS contract can increase the profit of LSI and the smart level of logistics service, but it will decrease the profit of LSP. With the exception that the wholesale price of logistics services will decrease, the equilibrium results under the RS contract and WP contract remain consistent. Only the CS-RS hybrid contract can achieve the perfect coordination of LSSC. In addition, by conducting numerical analysis, we find that the enhancement of the smart effect can encourage LSP to improve the smart level and increase the overall revenue of LSSC. To the best of our knowledge, this paper is the first study to explore the incentive mechanism between LSI and LSP in the context of logistics service smart transformation. Our findings guide the LSI in implementing an effective contract.

1. Introduction

With the increase in customer demand for specialized and customized logistics services, many logistics enterprises began to change their service model from large-scale logistics services to large-scale customized logistics services [1]. In the environment of mass customized logistics services, to meet the customization demands of customers, increase scale benefits, and reduce uncertainties in the service process, many logistics enterprises spontaneously formed a logistics service supply chain (LSSC) through alliances and integration [2,3]. LSSC consists of functional logistics service providers (LSPs), logistics service integrators (LSIs), and customers [4]. With the continuous differentiation of the capabilities and advantages of each member in LSSC, logistic enterprises with resources and information advantages have gradually transformed into the role of LSIs, while enterprises specializing in basic logistics services have become functional LSPs [5].

Smart logistics is based on modern Internet information technology and realizes the systematic perception of warehousing, packaging, circulation processing, transportation, and distribution in the logistics industry through technology empowerment [5]. For logistics enterprises, the smart logistics development mode helps reshape the enterprise supply chain management and increase enterprise profits. Relevant studies have shown that companies that carry out smart logistics modes have a higher added value of products, higher operating efficiency, and shorter supply cycles, which have stronger advantages compared to traditional logistics modes [5,6].

As the core strategy of many logistics companies, smart transformation is no longer a multiple-choice question, but a survival issue [4]. In the process of smart transformation of the entire LSSC, LSI often takes the lead in encouraging LSPs to participate in this work [5]. Through smart transformation, LSI can reduce costs and improve operational efficiency, while LSP can obtain more orders from LSI. For example, as an LSP of the Cainiao platform (the LSI), YTO Express provides customers with integrated warehousing and distribution services through the smart transformation of logistics service, such as introducing more advanced technologies and equipment, improving logistics service processes, and expanding logistics networks. As a result, YTO Express has obtained more orders from Cainiao.

However, for LSPs, participating in smart transformation is often a daunting task. First, smart transformation is a long-term process that cannot provide significant or immediate business benefits in a short period of time. Second, smart transformation typically requires significant capital investment. Therefore, LSP’s smart transformation faces the uncertainty of investment and income, which seriously hinders LSP’s enthusiasm for logistics service innovation [6]. Therefore, instead of imposing strict requirements on LSPs, how can LSIs motivate LSPs to innovate their logistics services while increasing their profits?

Motivated by the above issues, this paper proposes a cost-sharing (CS) contract in that LSI shares part of the smart transformation cost of LSP, a revenue-sharing (RS) contract in that LSI shares part of the profit with LSP, and a cost sharing-revenue sharing (CS-RS) hybrid contract. We mainly explore the following two questions.

(1)

What are the equilibrium results (the smart level of logistics service and LSSC member’s revenue, etc.) under the three contracts?

(2)

What kind of contract can motivate LSP to improve the smart level of logistics service and realize the coordination of LSSC?

To answer the above questions, we construct an LSSC including an LSP and an LSI, in which the LSP is undergoing a smart transformation. As a benchmark to judge whether the contract is effective, we first solved the equilibrium results under centralized decision making and WP contracts; then, the equilibrium results under the three coordination contracts are solved. Relevant conclusions are obtained by performing mathematical derivation and numerical analysis.

The main contributions of this paper are the following three points. First, to the best of our knowledge, this paper is the first study to explore the incentive mechanism of LSSC under the background of smart transformation. We propose three coordination contracts and analyze which contract can improve the smart level of logistics service and realize the coordination of LSSC. Second, we compare the coordination effects of CS and RS contracts and propose the CS-RS hybrid contract to realize the perfect coordination of LSSC. Third, this study provides theoretical guidance for the smart transformation of LSSC and provides a reference for LSI to select an appropriate incentive mechanism.

The rest of this paper is organized as follows. Section 2 reviews the relevant literature on smart logistics and supply chain contracts. In Section 3, relevant models are constructed and solved, including the basic model of centralized decision making and WP contract, as well as the coordination model under the three contracts. Section 4 provides numerical analysis, and Section 5 summarizes this paper. All proofs are presented in the Appendix A.

2. Literature Review

The literature related to this paper includes the following three streams: smart logistics, CS and RS contracts, and LSSC.

2.1. Smart Logistics

The existing research on smart logistics is mainly discussed from three aspects. The first aspect is the operation level of smart logistics, emphasizing the application of smart technology, such as the application of big data technology [7]. The second aspect is the design level of the smart logistics system, emphasizing the overall improvement of the smart level [8,9]. The third aspect is the theoretical analysis of smart logistics, studying the current situation and future trends of smart logistics [10,11]. In general, smart logistics is a logistics system that uses smart technology and smart facilities to comprehensively perceive and identify all links of logistics and make decisions to optimize logistics services [12]. Kirch et al. [13] believed that smart logistics is the key means to developing cross-company or cross-industry transportation network logistics and information-based and efficient organization, and it is the inevitable trend of modern logistics development. Liu and Zhang [14] put forward the construction scheme of supply chain smart logistics mode based on logistics information service platform from the perspective of supply chain and provide a specific strategy of supply chain smart logistics mode transformation in combination with the actual situation of China’s logistics industry. Liu et al. [15] used the social network analysis method to build a research framework to analyze the relationship between risk factors of smart logistics ecological chain. In addition, Liu et al. [6] used a case study approach and selected four cases to explore the factors affecting the implementation of circular supply chains in the smart logistics eco-chain. Pan et al. [16] studied the main factors affecting the construction of smart logistics in Chinese cities and whether carbon emission is the reason for the construction of smart logistics. Different from the above research, this paper focuses on the smart transformation of LSP and proposes three contracts. We mainly explore the incentive mechanism effects of three contracts.

2.2. CS and RS Contracts

Scholars have extensively studied the supply chain collaboration problem, and most of the studies design supply chain contracts to solve the coordination problem. Typical contracts include CS and RS, etc. The CS contract motivates supply chain members to improve their innovation efforts by sharing costs to improve the quality of service. For example, Ghosh et al. [17] discussed the impact of CS contracts on key decisions of enterprises implementing green initiatives. Zhao et al. [18] confirm that the CS contract is an effective coordination mechanism in LSSC. The RS contract is an effective supply chain coordination mechanism, which is first applied to the video rental industry [19]. At present, the RS contract has been applied to different industries such as e-commerce platforms [20,21], LSSC [22], product R & D [23]. In addition, some scholars have compared CS contracts and RS contracts. For example, Ma et al. [24] explored the impact of government subsidies and cooperation contracts on enterprises’ green innovation efforts and benefits. The authors observed that, under the premise of government subsidies, the RS contract is more effective than the CS contract. Considering the reference emission and cost learning effects, Yu et al. [25] studied emission reduction and pricing strategies of the supply chain under the CS contract and RS contract. They observed that the manufacturer and the entire supply chain prefers CS contracts. Liu et al. [26] investigated which contracts are more effective in promoting enterprises to improve product greenness and increase revenue under different power structures. Liu et al. [27] construct a Stackelberg game model based on the mutual influence and restriction in the relationship between a manufacturer and an LSP. The authors explored whether CS and RS contracts can coordinate supply chains and proposed a CS-RS hybrid contract to achieve the perfect coordination of supply chains.

CS and RS contracts are widely used in supply chain co-innovation problems. However, currently, there is no research on LSSC to explore the incentive mechanism of contract for the smart transformation of LSP. This study aims to fill this gap by exploring how to design a suitable supply chain contract to achieve LSSC coordination based on improving the smart level of logistics service.

2.3. LSSC

The supporting role of the logistics industry in economic development has prompted many scholars to study LSSC. For example, Yunmiao et al. [28] studied the coordination problem of LSSC under uncertain demand. Liu et al. [29] explored the impact of different risk attitudes on the LSSC quality control game. Liu et al. [30] studied the impact of demand disruption on LSSC coordination. Considering the fairness concern behavior of LSI, Wang et al. [31] studied the coordination problem of LSSC. Liu et al. [6] investigated the impact of LSP’s fairness concern behavior on LSI order allocation decisions. Liu et al. [32] studied the impact of CS contracts on key decisions of mass customization LSSC. Wang et al. [33] explored the impact of logistics enterprise risk preference on LSSC decision making in a fuzzy environment. Niu et al. [34] explored the role of IoT in building a traceable and sustainable LSSC. Different from the above literature, this paper focuses on the smart transformation of LSSC, explores the corresponding incentive mechanism, and compares the coordination effects of different mechanisms.

2.4. Literature Summary

By conducting a literature review, we find that although smart logistics has attracted the attention of many scholars, there is no literature to explore the smart transformation of LSSC. The most similar study to ours is the literature [27], but the literature [27] studies the smart transformation between the LSP and the manufacturer, while we focus on the smart transformation between the LSP and the LSI. From the above three sections, we conclude that the existing literature has not adequately addressed our research questions presented in the Introduction. As far as we know, this paper is the first study to explore the incentive mechanism between LSI and LSP in the context of logistics service smart transformation.

3. Model

The LSSC we study contains an LSI and a functional LSP. The LSI provides integrated logistics services to customers at a price $p$, while purchasing functional logistics service capabilities from providers at a wholesale price $w$. In practice, LSP will improve service quality and customer satisfaction through smart transformation, such as introducing more advanced technology and equipment, improving the logistics service process, expanding the logistics network, etc., which in turn leads to an increase in the demand for logistics services. The demand is related to the logistics service price and the smart level of logistics service $e$ of the LSP. Referring to [27,35,36,37,38], we suppose the demand function is $D=a-p+ke$, where $a$ is the potential market demand for logistics service, and $k$ is the sensitivity coefficient of demand with respect to smart transformation level (that is, the smart effect).

LSP needs to pay a corresponding cost to carry out smart transformation, and with reference to the literature [27,35,37,39,40,41], it is assumed that the smart transformation cost is $C\left(e\right)=g{e}^2/2$, where $g$ is the cost coefficient of smart transformation. The notations used in this paper are shown in

Table 1. Notations.

Notations	Meanings
$a$	Potential market demand for logistics service
$c$	Unit logistics service cost of LSP
$w$	Unit logistics service wholesale price
$p$	Unit logistics service price
$e$	The smart level of logistics service
$k$	The effect of smart transformation
$g$	The cost coefficient of smart transformation
$u$	CS coefficient of CS contract
$v$	RS coefficient of RS contract
$D$	Market demand function
${\pi }_F$	Profit function of LSP
${\pi }_I$	Profit function of LSI

.

Similar to the literature [27,35,37,42,43,44,45,46], we assume $g>k^2$ and $a>c$ ensure that there are optimal solutions to models and that the optimal solutions are non-negative. Usually, smart transformation requires huge costs; in addition, the logistics service market size is usually large; otherwise, LSSC cannot operate normally. Therefore, this assumption is reasonable. The model structure is shown in Figure 1.

3.1. Basic Model

3.1.1. Centralized Decision Making (Indicated by Superscript C)

The purpose of supply chain coordination is to bring the revenue under decentralized decision making to the level under centralized decision making. Therefore, we first solve the decision of LSSC in the integration case. The overall profit function of LSSC is as follows.

$${\pi }_{SC}^C=\left(p-c\right)D-C\left(e\right)$$

(1)

In this case, LSI and LSP as a whole make decisions to maximize total profit. Thus, Lemma 1 is obtained.

Lemma 1.

When$k^2/g<2$, there is an optimal solution for centralized decision making. The equilibrium results are as follows.

$$p^{C*}=c+\frac{\left(-a+c\right)g}{-2g+k^2},e^{C*}=\frac{\left(-a+c\right)k}{-2g+k^2},D^{C*}=\frac{g\left(a-c\right)}{2g-k^2},{\pi }_{SC}^{C*}=\frac{g{\left(a-c\right)}^2}{2(2g-k^2)}.$$

3.1.2. WP Contract

Due to the existence of the double marginal effect, the WP contract cannot coordinate the supply chain. However, it can usually be used to judge whether other contracts are valid. Under the WP contract, the profit functions of LSI and LSP are as follows.

$${\pi }_L^{WP}=\left(p-w\right)D$$

(2)

$${\pi }_F^{WP}=\left(w-c\right)D-C\left(e\right)$$

(3)

The decision-making order of this model is as follows. Generally, LSI is in the dominant position, and it determines the unit logistics service price first; then, LSP determines the unit logistics service wholesale price and the smart level of logistics service according to the decision of LSI. Thus, we obtain Lemma 2.

Lemma 2.

When$k^2/g<2$, there is an optimal solution under the WP contract. The equilibrium results are as follows.

$$\begin{gathered} w^{WP*}=c+\frac{\left(a-c\right)g}{4g-2k^2},e^{WP*}=\frac{\left(a-c\right)k}{4g-2k^2},p^{WP*}=\frac{\left(3a+c\right)g-\left(a+c\right)k^2}{4g-2k^2}, \\ {D}^{WP*}=\frac{\left(a-c\right)g}{2\left(2g-k^2\right)},{\pi }_L^{WP*}=\frac{{\left(a-c\right)}^{2}g}{8g-4k^2},{\pi }_F^{WP*}=\frac{{\left(a-c\right)}^{2}g}{8\left(2g-k^2\right)}. \end{gathered}$$

Proposition 1.

The equilibrium results under centralized decision making and WP contracts satisfy the following relationship:$e^{C*}>e^{WP*}$,$p^{C*}<p^{WP*}$, and${\pi }_{SC}^{C*}>{\pi }_{SC}^{WP*}$.

Proposition 1 shows that the total profit and the smart level under centralized decision making are greater than those under the WP contract, but the logistics service price under centralized decision making is lower than that under the WP contract. This shows that there is room for coordination between centralized decision making and the WP contract. By designing corresponding contracts, it is possible to improve the smart level of logistics service and increase the revenue of LSSC members.

3.2. Coordination Contract

3.2.1. CS Contract

As an effective method of interest coordination, the CS contract is widely used in equipment manufacturing [38,40] and technology R & D [39,46,47]. In this section, we use CS contracts to coordinate LSSC; that is, LSI shares part of the cost of logistics smart transformation to encourage LSP to carry out logistics innovation. It is assumed that the CS coefficient is $u$. Therefore, the profit functions of LSI and LSP are as follows.

$${\pi }_L^{CS}=\left(p-w\right)D-uC\left(e\right)$$

(4)

$${\pi }_F^{CS}=\left(w-c\right)D-\left(1-u\right)C\left(e\right)$$

(5)

The decision-making order of this model is as follows. Firstly, LSI determines the CS coefficient, and then it determines the unit logistics service price. Finally, LSP determines the unit logistics service wholesale price and the smart level of logistics service. Thus, Lemma 3 is obtained.

Lemma 3.

When$k^2/g<2\left(1-u\right)$, there is an optimal solution under the CS contract. The equilibrium results are as follows.

$$\begin{gathered} w^{CS*}=\frac{ag{\left(-1+u\right)}^2+3cg{\left(-1+u\right)}^2+c{k}^2\left(-2+3u\right)}{4g{\left(-1+u\right)}^2+k^2\left(-2+3u\right)}, \\ {e}^{CS*}=\frac{\left(a-c\right)k\left(1-u\right)}{4g{\left(-1+u\right)}^2+k^2\left(-2+3u\right)}, \\ {p}^{CS*}=\frac{c\left(k^2+g\left(-1+u\right)\right)\left(-1+u\right)+a\left(3g{\left(-1+u\right)}^2+k^2\left(-1+2u\right)\right)}{4g{\left(-1+u\right)}^2+k^2\left(-2+3u\right)}, \\ {D}^{CS*}=\frac{\left(a-c\right)g{\left(-1+u\right)}^2}{4g{\left(-1+u\right)}^2+k^2\left(-2+3u\right)},{\pi }_L^{CS*}=\frac{{\left(a-c\right)}^{2}g{\left(-1+u\right)}^2}{8g{\left(-1+u\right)}^2+2k^2\left(-2+3u\right)}, \\ {\pi }_F^{CS*}=\frac{{\left(a-c\right)}^{2}g\left(k^2+2g\left(-1+u\right)\right){\left(-1+u\right)}^3}{2{\left(4g{\left(-1+u\right)}^2+k^2\left(-2+3u\right)\right)}^2}. \end{gathered}$$

Proposition 2.

The equilibrium results under CS contracts and WP contracts satisfy the following relationship: $e^{CS*}>e^{WP*}$,$p^{CS*}>p^{WP*}$, and${\pi }_F^{CS*}<{\pi }_F^{WP*}$; when$0<u<0.5$,${\pi }_L^{CS*}>{\pi }_L^{WP*}$; when$0.5\le u<1$,${\pi }_L^{CS*}\le {\pi }_L^{WP*}$.

Proposition 2 shows that the CS contract can improve the smart level of logistics service of LSP, but it will increase the logistics service price and cannot increase the revenue of LSP. However, when the CS coefficient is small (i.e., $0<u<0.5$), it can increase the revenue of LSI. This shows that LSI sharing part of the cost of smart transformation can stimulate LSP to innovate logistics services and increase its revenue. Therefore, LSI is willing to share the cost of smart transformation. For LSP, CS reduces the pressure of logistics service innovation, but its profit cannot increase. This means that the CS contract cannot realize the coordination of the supply chain.

3.2.2. RS Contract

RS contract has practical industrial applications in e-commerce platforms and product development [48]. Therefore, this section uses the RS contract to coordinate LSSC. That is, LSI gives a part of its revenue to LSP to encourage LSP to carry out a smart transformation of logistics service. It is assumed that the RS coefficient is $v$. Therefore, the profit functions of LSI and LSP are as follows.

$${\pi }_L^{RS}=v\left(p-w\right)D$$

(6)

$${\pi }_F^{RS}=\left(w-c\right)D+\left(1-v\right)\left(p-w\right)D-C\left(e\right)$$

(7)

The decision-making order of the model is as follows. Firstly, LSI determines the RS coefficient, and then it determines the unit logistics service price. Finally, LSP determines the unit logistics service wholesale price and the smart level of logistics service. Therefore, Lemma 4 is obtained.

Lemma 4.

When$k^2/g<2$, there is an optimal solution under the RS contract. The equilibrium results are as follows.

$$\begin{gathered} w^{RS*}=\frac{-a{k}^2\left(-1+v\right)-c{k}^2\left(1+v\right)+cg\left(2+v\right)+ag\left(-2+3v\right)}{4gv-2k^{2}v},e^{RS*}=\frac{\left(a-c\right)k}{4g-2k^2}, \\ {p}^{RS*}=\frac{\left(3a+c\right)g-\left(a+c\right)k^2}{4g-2k^2}, \\ {D}^{RS*}=\frac{\left(a-c\right)g}{2\left(2g-k^2\right)},{\pi }_L^{RS*}=\frac{{\left(a-c\right)}^{2}g}{8g-4k^2},{\pi }_F^{RS*}=\frac{{\left(a-c\right)}^{2}g}{8\left(2g-k^2\right)}. \end{gathered}$$

Proposition 3.

The equilibrium results under RS contracts and WP contracts satisfy the following relationship:$e^{RS*}=e^{WP*}$,$p^{RS*}=p^{WP*}$,${\pi }_L^{RS*}={\pi }_L^{WP*}$, and${\pi }_F^{RS*}={\pi }_F^{WP*}$;$w^{RS*}<w^{WP*}$.

Proposition 3 shows that the RS contract reduces the wholesale price of LSP, but it does not improve the smart level of logistics service, nor does it increase the revenue of supply chain members. This shows that the RS contract does not play a corresponding incentive role and cannot realize the coordination of LSSC.

3.2.3. CS-RS Hybrid Contract (Indicated by Superscript CR)

The above research finds that the single CS and RS contract cannot achieve the coordination of LSSC. Therefore, in this subsection, CS-RS hybrid contract is proposed to coordinate LSSC. That is, LSI shares part of the cost of the smart transformation of logistics services and part of its revenue. Here, we still assume that the CS coefficient is $u$ and the RS coefficient is $v$. Therefore, the profit functions of LSI and LSP are as follows.

$${\pi }_L^{CR}=v\left(p-w\right)D-uC\left(e\right)$$

(8)

$${\pi }_F^{CR}=\left(w-c\right)D+\left(1-v\right)\left(p-v\right)D-\left(1-u\right)C\left(e\right)$$

(9)

The decision-making order of this model is as follows. Firstly, LSI determines the CS coefficient and RS coefficient, and then it determines the unit logistics service price; Finally, LSP determines the smart level of logistics service.

Therefore, we obtain Proposition 4.

Proposition 4.

Under the CS-RS hybrid contract, when$w=c$,$u=v$and$0.5\le u\le 0.75$, LSSC can achieve perfect coordination.

Proposition 4 shows that, under CS-RS hybrid contract, when the parameters meet certain conditions, LSSC achieves perfect coordination; that is, the total profit reaches the level under centralized decision making, and the profits of LSI and LSP are Pareto improved. From Proposition 4, the condition for coordination is that the CS coefficient is equal to the RS coefficient, and LSI and LSP can accept this contract only when this coefficient meets certain conditions. Therefore, LSI can scientifically adjust the contract so that the contract parameters are in a reasonable interval, thus motivating LSP to improve the smart level of logistics service to achieve perfect coordination of LSSC.

4. Numerical Analysis

In this section, we use numerical simulation to analyze the influence of relevant parameters on equilibrium results.

4.1. Comparison between Centralized Decision Making and WP Contract

In this subsection, we first analyze the impact of the smart effect $k$ on equilibrium results of the centralized decision making and WP contract.

Referring to the literature [27,35,40] and setting $a=1000,c=2,g=2$, we obtain Figure 2, Figure 3, Figure 4 and Figure 5.

As observed from Figure 2, there is a positive correlation between $e^{C*},e^{WP*}$, and $k$. That is, a strong smart effect will lead to a higher smart level of logistics service. It is also found that $e^{C*}$ is always greater than $e^{WP*}$, which means that the smart level under centralized decision making is higher. Therefore, there is a huge coordination space between centralized decision making and the WP contract. By designing a reasonable contract, LSI can encourage LSP to improve the smart level of logistics service and bring consumers a better logistics experience.

As can be seen from Figure 3, there is a positive correlation between $p^{C*},p^{WP*}$, and $k$. That is, when the smart effect is strong, LSI has the motivation to set a higher logistics service price. In addition, when $k$ is low, $p^{C*}<p^{WP*}$. When $k$ is high, $p^{C*}>p^{WP*}$. This shows that compared with the logistics service price if consumers pay more attention to the logistics service experience, firms can formulate a higher logistics service price under centralized decision making to obtain more benefits.

As observed from Figure 4, there is a positive correlation between $D^{C*},D^{WP*}$, and $k$. This shows that a higher smart effect will lead to higher demand for logistics services. In addition, $D^{C*}$ is always greater than $D^{WP*}$, because the smart level of logistics service under centralized decision making is higher, which increases the demand for logistics service.

Figure 5 reflects the variation of total profit of the supply chain with $k$ under centralized decision making and WP contract, i.e., with the enhancement of the smart effect, the overall revenue of the supply chain gradually increases. In addition, the total profit under centralized decision making is always greater than that under the WP contract. Therefore, it is necessary to design corresponding contracts to increase the total revenue of the supply chain under decentralized decision making.

Next, we analyze the impact of the cost coefficient of smart transformation on equilibrium results of the centralized decision making and WP contract. Let $a=1000,c=2,k=1$, we obtain Figure 6, Figure 7, Figure 8 and Figure 9.

As observed in Figure 6, Figure 7, Figure 8 and Figure 9, the smart level, logistics service price, sales volume, and total supply chain profit decrease with respect to the cost of smart transformation. Specifically, higher transformation costs will force LSPs to reduce the smart level. When the smart level is low, LSIs can only attract consumers by reducing service prices. In short, the increase in the cost of smart transformation will be detrimental to the improvement of the overall revenue of the supply chain. Only when the cost of smart transformation is small, the economic effect of smart transformation is more prominent. However, no matter what, the smart level, sales volume, and total supply chain profit under centralized decision making are always greater than the corresponding values under the WP contract.

4.2. Comparison between CS Contract and RS Contract

The parameters are set as follows: $a=1000,c=2,k=0.5,g=2$. Considering the conditions for the existence of the optimal solution, we let the value range of $u$ and $v$ be $\left(0.1,0.8\right)$, and Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 are obtained.

As shown in Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14, the equilibrium results under the RS contract are independent of the RS coefficient $v$. Combining Lemma 2 and Lemma 4, the equilibrium results under the RS contract remains consistent with that under the WP contract except for the wholesale price. Therefore, the comparison between the CS contract and the RS contract is equivalent to the comparison with the WP contract.

Figure 10 shows that with the increase in CS coefficient $u$, $e^{CS*}$ gradually increases, and $e^{CS*}>e^{RS*}$ is always true. In addition, when $u$ is large enough, then $e^{CS*}>e^{C*}$. This shows that compared with the RS contract, the CS contract has a more obvious incentive effect on LSP, which can promote LSP to significantly improve the smart level of logistics service. When LSI bears more smart transformation costs, it can even exceed the smart level under centralized decision making.

Figure 11 shows that as $u$ increases, $p^{CS*}$ gradually increases and $p^{CS*}>p^{RS*}$ always holds. The potential reason is that LSI earns additional revenue by raising the price of logistics services to cover the expenses of sharing the cost of smart transformation. Figure 12 shows that as $u$ increases, $D^{CS*}$ gradually decreases; when $u$ is large enough, $D^{CS*}<D^{RS*}$. The main reason is that prices that are to high with respect to logistics services will lead to a reduction in demands for logistics services.

Figure 13 depicts the relationship between ${\pi }_I^{CS*},{\pi }_I^{RS*},{\pi }_F^{CS*},{\pi }_F^{RS*}$, and $u\left(v\right)$. As observed from Figure 13, with the increase in $u$, ${\pi }_I^{CS*}$ first increases and then decreases, while ${\pi }_F^{CS*}$ always decreases. In addition, when $u<0.5$, then ${\pi }_I^{CS*}>{\pi }_I^{RS*}$. When $u>0.5$, ${\pi }_I^{CS*}<{\pi }_I^{RS*}$. Moreover, ${\pi }_F^{CS*}<{\pi }_F^{RS*}$ is always true. Figure 14 shows that with the increase in $u$, ${\pi }_{SC}^{CS*}$ first increases and then decreases, and when $u$ is small, ${\pi }_{SC}^{CS*}>{\pi }_{SC}^{RS*}$. By conducting the above analysis, when the CS coefficient is in a reasonable range, the CS contract is better than the RS contract, but it cannot achieve the coordination of LSSC.

5. Conclusions

To explore whether the three contracts can motivate LSP to improve the smart level of logistics service and realize the coordination of the supply chain, this paper constructs an LSSC including an LSI and an LSP, in which LSP carries out smart transformations. As a benchmark for comparing whether the contract is effective or not, we first obtain the equilibrium results under the centralized decision and WP contract. Then, we propose a CS contract in which LSI bears part of the cost of smart transformation, an RS contract in which LSI shares part of the revenue, and a CS-RS hybrid contract in which LSP bears part of the cost of smart transformation and shares part of the revenue at the same time. By solving the game models under the three contracts and conducting a comparative analysis, we observed that the CS contract can increase the profit of LSI and the smart level of logistics service when the CS coefficient is in a certain interval, but it will reduce the profit of LSP. The equilibrium results under the RS contract and the WP contract remained consistent except that the wholesale price of logistics services will decrease. Only CS-RS hybrid contracts can achieve the perfect coordination of LSSC. In addition, by conducting numerical analyses, it was found that the enhancement of the smart effect can encourage LSP to improve the smart level of logistics service and increase the overall revenue of the supply chain.

From the above conclusions, we know that the single incentive mechanism of LSI cannot achieve the coordination of the supply chain, so the combination mechanism can be used to achieve the perfect coordination of LSSC. LSI can use its capital and technical advantages to help LSP carry out smart transformation and bear part of the transformation cost to motivate LSP to improve the level of smart transformation. On the other hand, when LSP provides logistics services at a cost price, the LSI should share part of the revenue to ensure that the revenue of both parties increases at the same time, to establish a long-term and stable cooperation relationship, and achieve a win–win situation.

Based on the research in this paper, there are some future research directions. First, the smart transformation of LSP faces the uncertainty of investments and income. It will be very interesting to design corresponding contracts under LSP risk aversion. Second, this paper only considers LSP for smart transformation. In the future, the contract for LSI and LSI to carry out smart transformation at the same time can be explored. Third, this paper assumes that the demand for logistics service is a linear function of price and smart level, future can explore the coordination decision under other forms of demand.