Open AccessArticle

Research on Logistics Service Supply Chain Coordination in the Context of Green Innovation

Business School, Jiangnan University, Wuxi 214122, China

Author to whom correspondence should be addressed.

Sustainability 2025, 17(2), 646; https://doi.org/10.3390/su17020646

Submission received: 4 December 2024 / Revised: 7 January 2025 / Accepted: 10 January 2025 / Published: 15 January 2025

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Abstract

With the global advancement of sustainable development concepts, the logistics industry is confronting significant environmental challenges, making green innovation a critical driver for industrial transformation and upgrading. However, during the green innovation process in logistics service supply chains, the differing roles of logistics service integrators and logistics service providers, combined with high costs and uncertain returns, hinder coordination efficiency. Therefore, it is imperative to enhance the coordination of supply chain contracts. Nevertheless, existing literature provides limited insights into the coordination capacities and impacts of different contracts on green innovation in logistics service supply chains. This study develops a Stackelberg game model where the logistics service integrator acts as the leader and logistics service providers serve as followers, examining the effects of cost-sharing contracts, revenue-sharing contracts, and hybrid cost-sharing and revenue-sharing contracts on supply chain coordination. Numerical simulations are employed to validate the findings. The results indicate that hybrid contracts provide the strongest incentives for green innovation among supply chain participants, whereas cost-sharing contracts offer relatively weaker incentives for integrators’ green design innovation. In addition, revenue-sharing contracts and hybrid contracts were effective in reducing the wholesale price of green logistics services, although all three contract types resulted in higher market prices. Finally, all three contract types achieve Pareto improvements in the supply chain, with hybrid contracts maximizing the total profit of the supply chain. This study not only elucidates the incentive mechanisms and relative advantages of different contracts in supply chain collaboration, but also offers critical theoretical and practical insights for designing contracts to foster green innovation in the logistics sector.

Keywords:

logistics service supply chain; green innovation; Stackelberg game; cost-sharing contract; revenue-sharing contract

1. Introduction

As a crucial sector of the global economy, the logistics industry faces significant environmental challenges in its operations. According to statistics from the International Transport Forum, 20% of global resource consumption in recent years has been attributed to logistics and transportation [1]. Additionally, practices such as empty backhauls and the use of disposable packaging materials contribute to resource wastage and environmental pollution. Therefore, while driving economic growth, the logistics industry faces the significant challenge of reducing its environmental impact [2].

Against this backdrop, green innovation has become critical to addressing these issues [3]. Green innovation in logistics enterprises encompasses several aspects, including the use of environmentally friendly materials, improving energy efficiency, optimizing logistics routes, developing clean energy, and recycling waste. These innovative measures not only reduce environmental pollution and resource consumption, but also enhance the overall operational efficiency and market competitiveness of enterprises [4].

With the development of the logistics industry, logistics services now exhibit characteristics of a supply chain. The core members of the logistics service supply chain (LSSC) are logistics service integrators (LSIs) and logistics service providers (LSPs).

In LSSC, LSIs, and LSPs bear different green innovation responsibilities, respectively. Specifically, LSIs are mainly responsible for planning green logistics solutions at the strategic level, coordinating upstream and downstream enterprises to operate together and share information, and promoting the full implementation of green logistics measures in the supply chain through optimizing the transportation network, integrating resources, and introducing green technologies to enhance the overall greening level of the supply chain [5]. LSPs, on the other hand, focus on green delivery at the operational level, such as adopting new energy vehicles to optimize loading rates and transportation routes in the transportation chain; applying energy-efficient equipment in warehouse management to improve inventory turnover, and using biodegradable materials in the packaging stage or through recycled packaging to reduce resource consumption. Overall, LSIs and LSPs need to form an efficient and close cooperation to realize the win–win situation of economic and environmental benefits of a logistics service supply chain through information technology, system planning, and efficient implementation. This paper refers to the distinct green innovation behaviors of LSPs and LSIs such as green delivery innovation and green design innovation, respectively, to distinguish between the two.

Take the leading company in China’s e-commerce logistics industry, Cainiao Group (Cainiao), as an example. Cainiao, as an LSI, relies on smart technologies such as big data, the Internet of Things, and cloud computing as the pillars of intelligent logistics. It continuously optimizes its operational efficiency while offering differentiated product services and providing cost-effective technical solutions to its partner logistics enterprises [6]. Currently, Cainiao collaborates with more than 30 logistics enterprises, including domestic LSPs such as STO Express, ZTO Express, and Yunda Express, which provide logistics services for Cainiao. Cainiao and these LSPs form an upstream and downstream relationship within an LSSC. To achieve the greening of logistics services, Cainiao launched a series of green logistics service products, such as introducing electronic waybills, using reusable packaging boxes, and deploying photovoltaic logistics parks. Cainiao also committed to reducing its Scope 3 greenhouse gas emissions intensity by 50% compared to 2021 levels by 2030, achieving carbon neutrality in its operations and reaching net-zero greenhouse gas emissions by 2050. Cainiao outsources these functional GLSPs to various LSPs. For instance, in 2023, ZTO Express installed approximately 370,000 square meters of photovoltaic panels, generating 40,150 megawatts of electricity, which is a year-on-year increase of 34%. Meanwhile, in 2023, Yunda Express achieved an 89.48% usage rate for reusable transfer bags and over 99.9% usage rate for electronic waybills, significantly reducing packaging material waste.

For the logistics industry, green innovation remains an ambiguous domain, primarily because existing research on green innovation is largely focused on manufacturing, with limited theoretical studies dedicated to the logistics sector [4]. However, the green innovation capabilities of different industries exhibit unique characteristics [7]. Specifically, green innovation in traditional manufacturing supply chains is primarily driven by manufacturing enterprises, focusing on procurement, production, and transportation, while retailers at the downstream end of the supply chain have minimal engagement with green innovation. In contrast, green innovation in logistics service supply chains requires not only providers to optimize the execution of logistics activities, enhance operational efficiency, and reduce environmental impacts, but also requires integrators to ensure overall coordination and strategic planning. This involves designing green logistics service solutions, optimizing logistics networks, monitoring environmental performance, and promoting green technology research and development to achieve sustainable development goals. Collaboration between providers and integrators is essential to jointly drive green innovation and sustainable development within logistics service supply chains. Thus, research on green innovation in other industries offers limited practical reference for the logistics sector [8]. Secondly, as an emerging service aligned with contemporary trends, green logistics services face significant market demand volatility due to a lack of historical data [1]. Consequently, decision makers have only a vague understanding of the market demand environment for green logistics services, making it challenging to accurately assess the returns from green innovation. Finally, green innovation is a long-term process requiring substantial financial investment from logistics enterprises [5]. It does not yield immediate benefits, particularly for providers, for whom green innovation entails significant updates to infrastructure and hardware. This results in investment pressures and uncertainties in returns, severely hindering their motivation to pursue green innovation.

The Stackelberg game, originating in the 1930s, is an asymmetric dynamic game model widely applied in fields such as economics, management, and operations research [9]. The core feature of this game model lies in the sequential decision-making order of participants. One party, referred to as the leader, makes its decision first, while the other party, referred to as the follower, responds after observing the leader’s decision. This sequence allows the leader to anticipate the follower’s response, optimize its own decision, and thereby gain an advantage in the game. In the logistics service supply chain, LSIs, as the core coordinator of the supply chain, are responsible for resource integration, formulating comprehensive logistics service plans, and leveraging its market information and strategic decision-making capabilities to exert a dominant influence on the overall operation of the supply chain [10]. LSPs, on the other hand, focus on executing specific logistics activities, such as transportation, warehousing, and distribution, with its decisions guided by the integrator’s directives [11]. Therefore, the game process between LSI and LSP is well suited to be modeled using the Stackelberg game framework.

With the development of globalization, supply chains have become increasingly complex, and any additional costs or individual behaviors can influence the decision making of supply chain node enterprises. However, the objectives of supply chain members often conflict with the overall goals of the supply chain. For individual enterprises, the decision-making objective is to maximize their own profits, whereas the optimal decision for the supply chain rarely aligns with individual optimal decisions. This phenomenon is known as the double marginalization effect. To align the differing objectives of supply chain members and enhance supply chain performance, supply chain contracts have been extensively studied by scholars. Supply chain contracts are agreements through which supply chain members provide appropriate information and incentive mechanisms to one another, thereby constraining the decision-making behaviors of supply chain participants. In general, an effective supply chain contract can not only improve the overall performance of the supply chain and its members, but also enable risk sharing among node enterprises. This ensures that the risks borne by enterprises are proportional to the benefits they receive, ultimately achieving a “win–win” outcome. Based on the above theoretical background, during the green innovation process of logistics service supply chains, integrators and providers not only incur additional green innovation costs, but also face uncertainties in returns. This significantly reduces the cooperation efficiency among members of the logistics service supply chain. Therefore, it is crucial to study the application of supply chain contracts in the context of green innovation within logistics service supply chains.

From the perspective of logistics enterprises’ practices, green innovation in logistics service supply chains is essential. However, its implementation faces challenges that require the coordination of supply chain contracts. To the best of our knowledge, research on green innovation in logistics service supply chains is limited, and no studies specifically conducted a comparative analysis of the coordination effects of different supply chain contracts. Therefore, based on the practical context and theoretical background, and addressing the research gap in the existing literature, this study establishes a two-level logistics service supply chain consisting of an LSI and an LSP. The two entities form a Stackelberg leader–follower game, with specific consideration given to the green design innovation cost of the integrator and the green delivery innovation cost of the provider. This study designs cost-sharing contracts, revenue-sharing contracts, and hybrid cost-sharing-revenue-sharing contracts to coordinate the logistics service supply chain. Numerical analyses are conducted to compare the coordination effects of these three contracts and examine their respective coordination advantages. This paper focuses on the following three research questions:

(1): How do the three contracts differ in their incentive effects on the green innovation levels of the LSI and LSP?
(2): How do the three contracts impact the wholesale price and market price of logistics services?
(3): From the perspective of the profits of the LSI and LSP, which contract achieves Pareto improvement for the supply chain? Which contract maximizes the total profit of the supply chain?

The main contributions of this paper are twofold: First, although the importance of green innovation in the development of logistics enterprises is widely recognized, research on green innovation in logistics service companies remains scarce. Moreover, no scholars specifically studied or compared the coordination effects of different contracts on green innovation in logistics services. Therefore, this paper establishes a Stackelberg game model to comparatively analyze the impacts of three contracts on the wholesale price, market price, and the design and delivery innovation levels of the LSI and LSP. We address a research gap and enrich the literature on logistics service supply chain management. Second, this paper also contributes to managerial practice. Through numerical simulations of the model, we analyze the coordination advantages of different contracts and determine the optimal contract parameter design, providing theoretical support for practitioners in supply chain management.

The remainder of this paper is organized as follows: Section 2 provides a literature review of related research. Section 3 describes the research methodology and establishes the basic profit function. Section 4 constructs the game model under centralized and decentralized decision making. Section 5 constructs models under the coordination of three types of contracts. Section 6 conducts numerical analysis. Section 7 is a discussion of the conclusions of the study. Section 8 concludes the paper by summarizing the findings, discussing the limitations of the study, and suggesting directions for future research.

2. Literature Review

Research related to this paper falls into four main areas: logistics service supply chains, green innovation in logistics services, Stackelberg game in the supply chain and logistics industry, and supply chain contract coordination.

2.1. Logistics Service Supply Chain

Regarding logistics service supply chains, existing studies mainly focused on outsourcing, service procurement, information sharing, and service quality, with limited research on green innovation and sustainable development. For example, Luo et al. [12] constructed a retailer-led game model to study outsourcing decisions in a retailer-dominated logistics service supply chain and coordinated these decisions through cost-sharing contracts. Liu et al. [13] investigated service capability procurement in logistics service supply chains, focusing on the effects of loss aversion and demand updates on supply chain members’ decision making. To explore the coordination of profit distribution and demand information sharing in the context of the Internet of Things, Niu et al. [14] developed a supply chain model in which short-distance and long-distance LSPs jointly provide differentiated logistics services, concluding that long-distance LSPs always benefit from short-distance LSPs. Chen et al. [15] studied shipping logistics service supply chains, examining vertical competition between shipping companies and freight forwarders as well as the impact of blockchain applications on market structure changes.

2.2. Green Innovation in Logistics Services

Green innovation in logistics enterprises spans core aspects of the entire supply chain, including ordering, packaging, transportation, warehousing, and recycling. Table 1 lists definitions of green innovation from recent papers on logistics or supply chains. Through measures such as adjusting energy structures, applying carbon reduction technologies, and upgrading business models, green development is achieved by reducing resource waste and improving operational efficiency.

Current academic research on green innovation in logistics services can be broadly divided into three categories. The first focuses on drivers and influencing factors. For instance, Chu et al. [8] studied the impact of customer pressure on green innovation using third-party logistics service providers as the research subject, with particular attention to the moderating role of organizational culture. Zhang et al. [16], based on an empirical survey of Chinese express companies, investigated the influence of technological characteristics, social impact, and stakeholder pressure on green innovation. Shou et al. [17] specifically examined the impact of green technological innovation on the market value of logistics enterprises, emphasizing stakeholder engagement and public attention. The second category focuses on green logistics solutions. Jiang et al. explored the design of intermodal green logistics networks for urban clusters with stochastic demand using a logit-based stochastic equilibrium model. Chen et al. [18] addressed the collection of recycling boxes in green logistics by developing a Stackelberg game model to formulate pricing strategies for dual-channel recyclers and optimized reverse logistics networks using genetic algorithms. The third category pertains to game theoretical studies of green logistics enterprises. Wang et al. [19] investigated the impact of risk preferences on collaborative games in green logistics service supply chains under fuzzy environments. He et al. [20] proposed a tripartite evolutionary game among logistics enterprises, governments, and communities in the context of green transformation, analyzing the strategic choices for green transformation development under different conditions. Wang et al. [1] constructed a Stackelberg game model to study the impact of different power structures on the green levels of logistics service integrators and providers.

Summarizing the definitions of green innovation in logistics services from the studies above and integrating the focus of this paper, this research defines green innovation in the logistics service supply chain, based on different decision-making entities, as green design innovation and green delivery innovation. Green design innovation refers to strategic innovation activities led by LSIs, aimed at reducing the environmental impact of logistics activities and achieving sustainable supply chain development through integrating logistics resources, optimizing logistics networks, introducing environmentally friendly technologies, and promoting enterprise collaboration. LSIs must make significant efforts to achieve green design innovation, such as leveraging IoT and big data technologies to optimize logistics transportation networks, reduce empty vehicle mileage, and monitor energy consumption and warehouse utilization in real time, ensuring control over the entire logistics process. Additionally, LSIs invest in green fundamental research, develop recyclable and biodegradable materials, design reusable transport containers, and collaborate with governments or industry associations to establish operational standards for green logistics services. To realize green design innovation, LSIs incur substantial costs, including research and development costs, organizational coordination costs, and employee training costs. In contrast, green delivery innovation is led by LSPs and focuses on specific improvements at the logistics execution level, including transportation, warehousing, loading and unloading, packaging, and distribution. Examples include using new energy vehicles, implementing smart warehousing and wearable devices, adopting biodegradable packaging materials, and establishing circular logistics systems. The costs of green delivery innovation for LSPs are primarily reflected in equipment procurement, infrastructure upgrades, and operational maintenance. Although green design innovation and green delivery innovation have different focuses, they complement each other to form a comprehensive framework for green innovation in the logistics service supply chain. Design innovation provides strategic guidance for delivery innovation, while delivery innovation implements the goals of design innovation through practical applications.

Table 1. Definitions of green innovation.

Reference	Definition of Green Innovation
Zhang et al. [5]	The logistics industry introduced numerous green innovation products and integrated application practices, such as new energy delivery vehicles, electronic waybills, shared courier boxes, green warehousing, and online freight platforms, effectively reducing resource consumption and environmental impact.
Nan et al. [7]	Key strategies for green innovation in the logistics industry include enhancing the recruitment and training of specialized logistics professionals and encouraging the industry to leverage talent for green transformation and innovation in regional logistics technologies.
Silva et al. [3]	Green innovation refers to the creation of new products, processes, or systems that minimize environmental harm while maintaining economic value.
Takalo et al. [4]	“Green innovation” or “eco-innovation” can be defined as the process that contributes to the creation of new products and technologies aimed at reducing environmental risks, such as pollution and the negative consequences of resource exploitation.
Shou et al. [17]	Logistics companies can enhance efficiency by developing green technologies, such as optimizing logistics processes, reducing resource waste, and upgrading energy-efficient transportation equipment. Many logistics companies adopted advanced technologies to leverage real-time congestion information and the latest traffic data, optimizing transportation routes and significantly improving logistics efficiency.

2.3. Research on Stackelberg Game

The application of Stackelberg game theory in the fields of supply chain and logistics is both extensive and profound, encompassing contract design, pricing strategies, green innovation, competition analysis, risk management, and network optimization, among other areas. By modeling the dynamic decision-making relationships among supply chain members, the Stackelberg game provides a powerful analytical tool for both theoretical research and practical management [21]. Its value is particularly prominent in the context of complex market environments and multiple cost constraints. Barman et al. [22] applied the Stackelberg game to a dual-channel green supply chain, conducting a comparative analysis of the game outcomes under manufacturer leadership and retailer leadership. They used sales channels, carbon emission reduction rates, and online delivery times as decision variables to attract customers to purchase more products. Khan et al. [23] utilized game theory to establish a Stackelberg game model, introducing the information asymmetry between online recyclers and consumers in the online trading of second-hand products. This model was used to analyze the decision-making processes of online recyclers and consumers in such transactions. Cerqueti et al. [24] developed a Stackelberg differential game to analyze the economic impact of emission reduction schemes using two policy instruments: tradable permits and emission taxes. Ghalehkhondabi et al. [25] employed the Stackelberg game to examine the preferences of manufacturers and third-party logistics providers regarding green delivery strategies and marketing strategies.

2.4. Research on Supply Chain Coordination Contracts

Interfirm collaboration is one of the most effective methods for enhancing overall supply chain efficiency [26]. In the past, scholars proposed various contract models, such as revenue sharing, cost sharing, two-part pricing, transfer payments, and price discounts, to address coordination issues in supply chains and assist managers in making better decisions. Among these, cost-sharing and revenue-sharing contracts are widely applied and have been proven effective in coordinating profits when additional costs arise in the supply chain [27]. For example, Ghosh et al. [28] investigated the impact of cost-sharing contracts on the decision making of retailers and manufacturers in green supply chains. Their findings reveal that cost-sharing contracts effectively enhanced the profits of all parties and improved the green level of products. Guo et al. [27] proposed four cost-sharing strategies for strategic cooperation in supply chains to achieve triple-bottom-line sustainability. These strategies effectively reduced total costs and minimized environmental impacts. Chen et al. [29] derived and compared the optimal cost-sharing mechanisms for retailers under different power structures in closed-loop supply chains to maximize their economic benefits in each power structure. Rezayat et al. [30] applied revenue-sharing contracts to closed-loop supply chains for electronic products, specifically considering customer sensitivity to price and quality. Compared to decentralized decision making, the supply chain profits increased under revenue-sharing contracts.

In conclusion, most current research on green innovation focuses on manufacturing industries, and due to the late introduction of the concept of green innovation by LSI and LSP, few scholars studied green innovation in logistics service supply chains. Additionally, most scholars used a single contract model to coordinate supply chains, with limited research on the coordination ability of hybrid contracts to leverage the advantages of each contract. Moreover, some studies on logistics service supply chain coordination are not comprehensive. For example, in literature [31], the impact of various coordination contracts on logistics service supply chains in the context of smart transformation was examined, but it only considered the smart transformation costs for LSPs and did not account for the costs incurred by LSIs, which do not align with real-world situations. Based on the above analysis, this paper investigates the coordination issues in logistics service supply chains under the context of green innovation. A Stackelberg game model is developed for a two-tier logistics service supply chain consisting of one LSI and one LSP. The model focuses on the design innovation level of the LSI and the delivery innovation level of the LSP. It incorporates cost-sharing contracts, revenue-sharing contracts, and a cost-sharing-revenue-sharing hybrid contract to coordinate the supply chain’s benefits. Finally, a comparative analysis is conducted to examine the impact of the three contracts on the innovation levels, profits, wholesale prices, and market prices of green logistics services for the LSI and LSP, with the aim of providing managerial insights for logistics companies.

3. Research Methodology and Model Construction

This model is built upon the study of Wang [32], considering a two-tier logistics service supply chain consisting of one LSI and one LSP. The LSI, after receiving customer orders, procures logistics services from the LSP. The LSI acts as the leader in the Stackelberg game, determining the design delivery level and market price of the GLSP by analyzing the current state of green development in logistics services and the market environment. The LSP, as the follower, decides the delivery innovation level and wholesale price of the GLSP after observing the LSI’s decisions.

The model in this study first calculates the green design innovation level, green delivery innovation level, market price, wholesale price of logistics services, and supply chain profit for the LSI and LSP under centralized and decentralized decision making. These two decision-making modes primarily serve as a reference for comparing the results under the coordination of supply chain contracts. Existing research found that adding coordination parameters to supply chain contracts can improve collaboration efficiency but also increases the complexity of the contracts [33]. Therefore, using appropriate parameters to coordinate the supply chain to achieve higher efficiency is an important benchmark for supply chain management. Cost-sharing contracts and revenue-sharing contracts are considered effective mechanisms for supply chain coordination in many studies and are favored by scholars due to their simplicity in terms of parameter inclusion. Therefore, this paper selects cost-sharing and revenue-sharing contracts to coordinate the logistics service supply chain in the context of green innovation. To leverage the advantages of both contracts, hybrid contracts are also applied for supply chain coordination. Through model solving and numerical analysis, this study compares the coordination abilities and individual advantages of the three types of contracts, aiming to provide practical insights for managers.

With the growing awareness of sustainability among businesses and society, more consumers are willing to pay for green services and products [1]. Globally, consumer attention to green development reached unprecedented levels. According to a May 2024 report by BAIN & COMPANY on green consumption, approximately 64% of consumers expressed significant concern about this issue, and this proportion continues to grow. The 2023 China Consumer Trends Report also reveals that 73.8% of consumers prioritize green and environmentally friendly products or brands in their daily lives and are willing to pay a premium for green products. Based on reality and the research of Liu [34] and Wang [1,19], this paper considers a market with sustainability awareness, assuming that the design innovation level and delivery innovation level of the GLSP will positively influence total demand. Specifically, market demand decreases as the price of logistics services rises, while it rises as the level of green design innovation and green delivery innovation rises. The demand function is expressed as follows:

D = a - b p + μ v + φ e

, where

a

represents the basic market demand,

p

represents the market price of green logistics services,

b

represents the sensitivity of demand to market price, and

μ

and

φ

represent the sensitivity of demand to the design innovation

v

and delivery innovation

e

. Based on the reality of green consumption, and also with reference to the research of other scholars [32], this paper assumes that

b < μ

and

b < φ

, meaning that in the service industry, demand is more sensitive to changes in the level of green service than to service prices [13]. Referring to the studies of Wang [1] and Liu, and Weihua [34], this paper assumes that the costs required by the LSI and LSP to achieve the design innovation level and delivery innovation level are

c (v) = \frac{g v^{2}}{2}

and

c (e) = \frac{k e^{2}}{2}

, respectively, where

g

and

k

represent the cost coefficients of LSI and LSP’s level of green innovation. In LSSC, the LSI typically invests significant funds in areas such as operational systems and core business to improve services, thus it is assumed that

g > k

[1].

Let the profit of LSI be

π_{i}

and the profit of LSP be

π_{p}

. Based on the above, we obtain:

π_{i} = (p - w) (a - b p + μ v + φ e) - \frac{g v^{2}}{2}

(1)

π_{p} = (w - c) (a - b p + μ v + φ e) - \frac{k e^{2}}{2} .

(2)

Table 2 lists the notations used in this paper and their explanations.

4. Basic Model Under Contract-Free Coordination

4.1. Model Under Centralized Decision Making

Under centralized decision making, all members of the supply chain are regarded as a single entity, with the goal of maximizing the overall profit of the supply chain to determine the design innovation level

v^{c}

and delivery innovation level

e^{c}

Many studies noted that centralized decision making in supply chains may not be feasible because upstream and downstream enterprises operate independently and may even have competitive relationships, making complete information-sharing collaboration unattainable [35,36]. However, calculating the decision levels under a centralized structure is meaningful as it allows for comparison with decentralized decision making and the game outcomes under various contract coordination mechanisms.

Consequently, the total profit of the green innovation logistics service supply chain under centralized decision making is the sum of the profits of the LSI and LSP, expressed as:

\begin{array}{l} π^{c} = π_{i} {}^{c}+ {π_{p}}^{c} \\ = (p^{c} - c) (a - b p^{c} + μ v^{c} + φ e^{c}) - \frac{{g v}^{c^{2}}}{2} - \frac{{k e}^{c^{2}}}{2} \end{array} .

(3)

Proposition 1.

Under centralized decision making, when

\frac{φ^{2} g + μ^{2} k}{2 g k} < b < \frac{a}{c}

, the optimal LSI design innovation level

v^{c *}

, optimal LSP delivery innovation level

e^{c *}

, optimal GLSP price

p^{c *}

, and optimal supply chain profit

π^{c *}

are as follows (the proof process can be found in the Appendix A):

\begin{matrix} p^{c^{*}} = \frac{b c g k - c g φ^{2} - c k μ^{2} + a g k}{2 b g k - g φ^{2} - k μ^{2}}, v^{c^{*}} = \frac{μ k (a - b c)}{2 b g k - g φ^{2} - k μ^{2}}, \\ e^{c^{*}} = \frac{g φ (a - b c)}{2 b g k - g φ^{2} - k μ^{2}}, π^{c^{*}} = \frac{g k {(a - b c)}^{2}}{2 (2 b g k - g φ^{2} - k μ^{2})} . \end{matrix}

4.2. Model Under Decentralized Decision Making

Under decentralized decision making, the LSI acts as the leader in the Stackelberg game. In the first stage, the LSI determines the market price of green logistics services

p^{d}

and the design innovation level

v^{d}

based on market conditions and its own capabilities. In the second stage, the LSP decides the wholesale price

w^{d}

and delivery innovation level

e^{d}

after observing the LSI’s decisions.

For simplicity in calculation, it is assumed under decentralized decision making that

p = w + θ

, where

θ

represents the unit profit of the LSI. Substituting the expression for

p

into Equations (1) and (2), the profit function for the LSI obtained as:

{π_{i}}^{d} = θ [a - b (w^{d} + θ) + μ v^{d} + φ e^{d}] - \frac{{g v}^{d^{2}}}{2} .

(4)

The profit function of the LSP is:

π_{p}^{d} = (w^{d} - c) [a - b (w^{d} + θ) + μ v^{d} + φ e^{d}] - \frac{{k e}^{d^{2}}}{2} .

(5)

Proposition 2.

Under decentralized decision making, when

\frac{2 φ^{2} g + μ^{2} k}{4 g k} < b < \frac{a}{c}

, the optimal LSI design innovation level

v^{d^{*}}

, optimal LSP delivery innovation level

e^{d^{*}}

, optimal GLSP price

p^{d^{*}}

, optimal wholesale price of wholesale

w^{d^{*}}

, optimal LSP’s profit

{π_{p}}^{d *}

, optimal LSI’s profit are

{π_{i}}^{d *}

, and optimal supply chain profit

π^{d^{*}}

are as follows:

v^{d^{*}} = \frac{k μ (a - b c)}{4 b g k - 2 g φ^{2} - k μ^{2}}, e^{d^{*}} = \frac{g φ (a - b c)}{4 b g k - 2 g φ^{2} - k μ^{2}},

w^{d^{*}} = \frac{k [g (a + 3 b c) - c μ^{2}] - 2 c g φ^{2}}{4 b g k - 2 g φ^{2} - k μ^{2}},

p^{d^{*}} = \frac{a g (3 b k - φ^{2}) + b c (b g k - k μ^{2} - g φ^{2})}{b (4 b g k - k μ^{2} - 2 g φ^{2})},

{π_{i}}^{d *} = \frac{g k {(a - b c)}^{2}}{2 (4 b g k - 2 g φ^{2} - k μ^{2})}, {π_{p}}^{d *} = \frac{g^{2} k {(a - b c)}^{2} (2 b k - φ^{2})}{2 {(4 b g k - 2 g φ^{2} - k μ^{2})}^{2}},

π^{d^{*}} = \frac{{(- c b + a)}^{2} (6 b g k - 3 g φ^{2} - k μ^{2}) g k}{2 {(4 b g k - 2 g φ^{2} - k μ^{2})}^{2}} .

Corollary 1.

Under decentralized decision making, there is

π^{d^{*}} < π^{c^{*}},

v^{d^{*}} < v^{c^{*}}

, and

e^{d^{*}} < e^{c^{*}}

. Therefore, the total profit of the green logistics service supply chain and the green innovation levels of both parties do not reach a coordinated state.

Corollary 2.

When

\frac{μ^{2}}{g} + \frac{φ^{2}}{k} \geq \frac{a}{c}

, the green logistics service market price under decentralized decision making is lower than under centralized decision making. When condition

\frac{μ^{2}}{g} + \frac{φ^{2}}{k} < \frac{a}{c}

is met, the green logistics service market price under decentralized decision making is lower than under centralized decision making only if condition

\frac{φ^{2} g + μ^{2} k}{2 g k} < b < \frac{μ^{2}}{g} + \frac{φ^{2}}{k}

is simultaneously satisfied.

According to Corollaries 1 and 2, when the condition of the existence of an optimal solution is satisfied, the level of green design innovation of LSI, the level of green delivery innovation of LSP, and the overall profit of the supply chain under centralized decision making are greater than those under decentralized decision making. Therefore, the LSSC does not reach an optimal coordination state. At this point, the coordination contract of the supply chain should be actively designed so that the profit and innovation level of the supply chain under decentralized decision making can be improved.

5. Models Under Contractual Coordination

5.1. Model Under Cost-Sharing Contract Coordination

According to Corollary 1 and 2, the total profit of the logistics service supply chain and the green innovation levels of the LSI and LSP under decentralized decision making are lower than those under centralized decision making. Therefore, it is essential to design reasonable supply chain contracts to coordinate the cooperation between the LSI and LSP, enhance green innovation levels, and increase the profits of both parties.

Cost-sharing contract is considered as one of the most effective mechanisms for coordinating supply chain collaboration, especially when enterprises incur significant additional costs [29]. Debabrata et al. [28] investigated the coordination issues within the context of green supply chains, particularly with the impact of cost-sharing contracts on major decisions within the supply chain. This is a highly valuable study that developed the game structure under cost-sharing contracts. This paper draws on the aforementioned study and specifies the game sequence under cost-sharing contracts as follows:

1.: The LSI proposes to share a proportion $γ$ of the green delivery innovation costs with the LSP. If the LSP accepts this cost-sharing proportion, the LSI’s shared delivery innovation cost is $\frac{γ k e^{2}}{2}$ , while the LSP bears the remaining delivery innovation cost $\frac{(1 - γ) k e^{2}}{2}$ , $0 < γ \leq 1$ .
2.: The LSI determines the level of green design innovation $v^{c s}$ and the market price of logistics services $p^{c s}$ based on the cost-sharing ratio and its own circumstances.
3.: The LSP determines its green delivery innovation level $e^{c s}$ and the wholesale price of logistics services $w^{c s}$ based on the cost-sharing ratio and the decisions made by the LSI.

However, the difference from Debabrata ’s study is that this paper considers the LSI’s own green design innovation costs. In other words, under the coordination of the cost-sharing contract, the LSI not only bears its own costs, but also covers a portion of the LSP’s costs. At this point, the profit functions for the LSI and LSP are as follows:

π_{i} {}^{c s}{(w^{c s}, γ)} = (p^{c s} - w^{c s}) [a - b (w^{c s} + θ) + μ v^{c s} + φ e^{c s}] - \frac{{g v}^{{c s}^{2}}}{2} - \frac{γ {k e}^{{c s}^{2}}}{2}

(6)

π_{p} {}^{c s}{(w^{c s}, γ)} = (w^{c s} - c) [a - b (w^{c s} + θ) + μ v^{c s} + φ e^{c s}] - \frac{(1 - γ) {k e}^{{c s}^{2}}}{2} .

(7)

The superscript “

c s

“ denotes the decision variables under the coordination of the cost-sharing contract.

Proposition 3.

Under the cost-sharing contract, when condition

\frac{2 φ^{2} g + μ^{2} k}{4 g k} < b < \frac{a}{c}

is met, the optimal LSI design innovation level

v^{{c s}^{*}}

, the LSP delivery innovation level

e^{{c s}^{*}}

, the optimal GLSP wholesale price

w^{{c s}^{*}}

, and the market price

p^{{c s}^{*}}

can be obtained as follows:

v^{{c s}^{*}} = \frac{k μ (a - b c) {(γ - 1)}^{2}}{g φ^{2} (3 γ - 2) + k (4 b g - μ^{2}) {(γ - 1)}^{2}},

e^{{c s}^{*}} = \frac{φ (γ - 1) (b c - a) g}{g (3 γ - 2) φ^{2} + k {(γ - 1)}^{2} (4 b g - μ^{2})},

w^{{c s}^{*}} = \frac{{(γ - 1)}^{2} ((3 b c + a) g - c μ^{2}) k + c g (3 γ - 2) φ^{2}}{g (3 γ - 2) φ^{2} + k {(γ - 1)}^{2} (4 b g - μ^{2})},

p^{r^{*}} = \frac{b k {(γ - 1)}^{2} (c g b + 3 a g - c μ^{2}) + g φ^{2} ((γ - 1) b c + (2 γ - 1) a)}{b (g φ^{2} (3 γ - 2) + k (4 b g - μ^{2}) {(γ - 1)}^{2})} .

The LSI determines the cost-sharing proportion

γ

based on maximizing its own profit. The optimal cost-sharing proportion chosen by the LSI is:

\begin{matrix} γ^{*} = \underset{0 < γ < 1}{\arg \max} {π_{i}}^{r} \\ s . t . {(γ - 1)}^{2} (4 g b - μ^{2}) k > (2 - 3 γ) g φ^{2} \end{matrix} .

After determining

γ^{*}

, the optimal profits of the LSI and LSP, as well as the overall optimal profit of the supply chain, are as follows:

{π_{i}}^{r *} = \frac{g k {(γ^{*} - 1)}^{2} {(a - b c)}^{2}}{8 b g {(γ^{*} - 1)}^{2} k - 2 ({(γ^{*} - 1)}^{2} k μ^{2} + g (2 - 3 γ^{*}) φ^{2})},

{π_{p}}^{r *} = \frac{k g^{2} {(γ - 1)}^{3} {(a - b c)}^{2} (2 b k (γ - 1) + φ^{2})}{2 {((4 b g - μ^{2}) {(γ - 1)}^{2} k + g φ^{2} (3 γ - 2))}^{2}},

π^{{c s}^{*}} = \frac{g k {(a - b c)}^{2} {(1 - γ)}^{2} ({(1 - γ)}^{2} (6 b g - μ^{2}) k + g φ^{2} (4 γ - 3))}{2 {({(- 1 + γ)}^{2} (4 b g - μ^{2}) k + φ^{2} (3 γ - 2) g)}^{2}} .

Proposition 4.

When condition

γ \in (0, \frac{1}{2})

is met, the market price

p^{{c s}^{*}}

, wholesale price

w^{{c s}^{*}}

, LSI’s design innovation level

v^{{c s}^{*}}

, LSP’s delivery innovation level

e^{{c s}^{*}}

, and LSI’s profit

{π_{i}}^{{c s}^{*}}

under the cost-sharing contract coordination are all higher than under decentralized decision making. When

γ = \frac{1}{3}

, the LSI’s profit reaches its maximum value, which is

\frac{2 k {(b c - a)}^{2}}{16 b g k - 9 g φ^{2} - 4 k μ^{2}}

. As the expression for the difference in provider profits is more complex, its results are discussed in the numerical analysis section.

Proposition 4 indicates that after adopting the cost-sharing contract, the integrator shares part of the delivery innovation cost for the provider, enabling the provider to allocate more funds toward green delivery innovation. This enhances the level of green delivery innovation and improves the quality of logistics services, allowing the integrator to sell to consumers at a higher market price. This paper suggests that the rise in wholesale prices for logistics services is due to two factors: on one hand, the integrator needs to increase the wholesale price to offset the cost-sharing expenditures for the provider; on the other hand, the improved green innovation level enhances the integrator’s brand image, potentially resulting in a brand premium. However, since the cost-sharing contract may incentivize the provider to invest more in higher levels of green innovation, the provider is also likely to raise the wholesale price of logistics services. As a result, the integrator’s profit margin may not increase.

5.2. Model Under Revenue-Sharing Contract Coordination

In addition to cost-sharing contracts, revenue-sharing contracts achieve effective coordination by introducing fewer parameters, making them another effective mechanism for supply chain coordination [37]. Song et al. [38] conducted a highly influential study that examined the revenue-sharing contract model in green supply chains and its impact on overall supply chain performance and internal decision variables. Song et al. developed two game models for revenue-sharing contracts (retailer-led revenue-sharing contracts and negotiated revenue-sharing contracts) and conducted a comparative analysis with game models under centralized control and decentralized decision making. Differing from Song’s study, this paper not only considers the green design innovation cost of the LSI, but also incorporates additional parameters to provide more flexible research conclusions. Based on the above study of revenue-sharing contracts, this paper specifies the game sequence under the coordination of revenue-sharing contracts in the logistics service supply chain as follows:

1.: The LSI allocates a portion of its revenue to the LSP to incentivize the LSP to engage in green innovation. If the LSP accepts this revenue-sharing proportion, the LSP will receive $τ \cdot {π_{i}}^{r s}$ additionally, that is to say, the LSP’s profit is $π_{p} {}^{r s}+ τ \cdot {π_{i}}^{r s}$ , while the LSI receives the remainder of the profits $(1 - τ) \cdot {π_{i}}^{r s}$ .
2.: The LSI determines the level of green design innovation and the wholesale price of logistics services based on its own revenues.
3.: The LSP determines its green delivery innovation level and the wholesale price of logistics services based on the cost-sharing ratio and the decisions made by the LSI.

At this point, the profit functions of the LSI and LSP are:

π_{i} {}^{r s}{(w^{r s}, τ)} = (1 - τ) \cdot [θ (a - b (w^{r s} + θ) + μ v^{r s} + φ e^{r s}) - \frac{{g v}^{{r s}^{2}}}{2}]

(8)

\begin{matrix} π_{p} {}^{r s}{(w^{r s}, τ)} = (w^{r s} - c) [a - b (w^{r s} + θ) + μ v^{r s} + φ e^{r s}] - \frac{{k e}^{{r s}^{2}}}{2} \\ + τ \cdot [θ (a - b (w^{r s} + θ) + μ v^{r s} + φ e^{r s}) - \frac{{g v}^{{r s}^{2}}}{2}] \end{matrix} .

(9)

The superscript “

r s

“ denotes the decision variables under the coordination of the revenue-sharing contract.

Proposition 5.

Under the revenue-sharing contract, when condition

\frac{2 (1 - τ) φ^{2} g + μ^{2} k}{4 (1 - τ) g k} < b < \frac{a}{c}

is met, the optimal design innovation level

v^{{r s}^{*}}

, optimal delivery innovation level

e^{{r s}^{*}}

, optimal wholesale price

w^{{r s}^{*}}

, market price

p^{{r s}^{*}}

, optimal LSI profit

{π_{i}}^{{r s}^{*}}

, LSP profit

{π_{p}}^{{r s}^{*}}

, and total supply chain profit

π^{{r s}^{*}}

can be obtained as follows:

v^{r s^{*}} = \frac{(a - b c) k μ}{4 (1 - τ) b k g - 2 (1 - τ) g φ^{2} - k μ^{2}},

e^{{r s}^{*}} = \frac{(1 - τ) (a - b c) g φ}{4 (1 - τ) b k g - 2 (1 - τ) g φ^{2} - k μ^{2}},

w^{{r s}^{*}} = \frac{[c k b^{2} (3 - τ) + a b k (1 - 3 τ) - c b φ^{2} (2 - τ) + a τ φ^{2}] g - b c k μ^{2}}{b [4 (1 - τ) b k g - 2 (1 - τ) g φ^{2} - k μ^{2}]},

p^{{r s}^{*}} = \frac{(1 - τ) [b k (b c + 3 a) - φ^{2} (a - b c)] g - b c k μ^{2}}{[4 (1 - τ) b k g - 2 (1 - τ) g φ^{2} - k μ^{2}] b},

{π_{i}}^{{r s}^{*}} = \frac{(1 - τ) g k {(a - b c)}^{2}}{2 (1 - τ) (4 b k - 2 φ^{2}) g - 2 k μ^{2}},

{π_{p}}^{{r s}^{*}} = \frac{k g {(a - b c)}^{2} [{(1 - τ)}^{2} (2 b k - φ^{2}) g - τ k μ^{2}]}{2 {((1 - τ) (4 b k - 2 φ^{2}) g - k μ^{2})}^{2}},

π^{{r s}^{*}} = \frac{2 k g [(6 b k - φ^{2}) {(1 - τ)}^{2} g - k μ^{2}] {(a - b c)}^{2}}{2 {((4 b k - 2 φ^{2}) (1 - τ) g - k μ^{2})}^{2}} .

Corollary 3.

Under the revenue-sharing contract coordination, the LSP’s delivery innovation level

v^{{r s}^{*}}

, LSI’s design innovation level

e^{{r s}^{*}}

, market price of green logistics services

p^{{r s}^{*}}

, and LSI’s profit

{π_{i}}^{{r s}^{*}}

are all higher than under decentralized decision making, that is to say

v^{{r s}^{*}} > v^{d^{*}},

e^{{r s}^{*}} > e^{d^{*}}

, and

p^{{r s}^{*}} > p^{d^{*}}

, while the wholesale price of green logistics services

w^{{r s}^{*}}

is lower than under decentralized decision making, as

w^{r s^{*}} < w^{d^{*}}

Corollary 3 indicates that when the LSP receives shared revenue from the LSI, it is incentivized to enhance its green delivery innovation level. Distinguishing from Liu [31] et al.’s findings, in this paper’s model, the revenue-sharing contract is able to increase the level of green innovation and profits earned by LSIs. Due to the reduction in revenue, the LSI compensates for the loss by increasing the market price of green logistics services. Contrary to intuition, the LSI also raises its green design innovation level, despite the higher costs associated with it. This paper attributes this to the synergistic effects within the supply chain: the LSI increases its green design innovation level to align with the enhanced green delivery innovation level, thereby improving the overall service quality of the logistics service supply chain. Moreover, the improvement in green design innovation can increase market demand for logistics services. Unlike the cost-sharing contract, the revenue-sharing contract results in the LSI reducing the wholesale price of logistics services. This not only helps the LSP increase its sales volume and market share, but also enhances the LSI’s unit profit.

5.3. Model Under Cost-Sharing and Revenue-Sharing Contract Coordination

Over the past five years, the number of studies on hybrid contracts in supply chains has been increasing in academia. Many scholars, such as Liu, H. [31] and Liu, W.H. [33], demonstrated that the coordination effects of hybrid contracts outperform those of single contracts. Therefore, this paper draws on the research conclusions of the aforementioned studies to design a cost-sharing and revenue-sharing hybrid contract and compares the coordination results of the hybrid contract with those of single contracts. Under the constraints of the hybrid contract, the LSI not only bears part of the LSP’s green delivery innovation cost, but also shares a portion of its revenue with the LSP.

However, differing from the aforementioned studies, this paper not only considers the green design innovation cost of the LSI, but also uses the LSI’s net profit, excluding green design innovation costs, as the basis for revenue sharing in the contract design. This approach aligns better with how enterprises calculate net earnings.

Under the coordination of the cost-sharing and revenue-sharing contract, the game sequence between the LSI and LSP is as follows:

1.: The LSI offers to help the LSP by sharing $γ$ proportion of the green delivery innovation costs and $τ$ proportion of the revenue to incentivize the LSP to engage in green innovation. If the LSP accepts, it will incur a green delivery innovation cost of $\frac{(1 - γ) k e^{2}}{2}$ and receive a shared revenue of $τ \cdot {π_{i}}^{r s}$ from the LSI, while the LSI needs to bear a green delivery innovation cost of $\frac{γ \cdot k e^{2}}{2}$ for the LSP while receiving the remaining revenue of $(1 - τ) \cdot {π_{i}}^{r s}$ .
2.: The LSI determines the level of green design innovation $v^{c r}$ and the market price $p^{c r}$ of logistics services based on its own revenues and cost.
3.: The LSP determines its green delivery innovation level $e^{c r}$ and the wholesale price $w^{c r}$ of logistics services based on the cost-sharing ratio, revenue-sharing ratio, and the decisions made by the LSI.

At this point, the profit functions of the LSI and LSP are:

π_{i} {}^{c r}{(w^{c r}, τ)} = (1 - τ) \cdot θ (a - b (w^{c r} + θ) + μ v^{c r} + φ e^{c r} - \frac{{g v}^{{c r}^{2}}}{2}) - \frac{{γ k e}^{{c r}^{2}}}{2}

(10)

\begin{matrix} π_{p} {}^{c r}{(w^{c r}, τ)} = (w^{c r} - c) [a - b (w^{c r} + θ) + μ v^{c r} + φ e^{c r}] - \frac{(1 - γ) {k e}^{{c r}^{2}}}{2} \\ + τ \cdot [θ (a - b (w^{r s} + θ) + μ v^{c r} + φ e^{c r}) - \frac{{g v}^{{c r}^{2}}}{2}] \end{matrix} .

(11)

The superscript “

c r

” denotes the decision variables under the coordination of the cost-sharing and revenue-sharing contract.

Proposition 6.

Under the cost-sharing and revenue-sharing contract, when condition

\frac{μ^{2} {(1 - γ)}^{2} k - g (3 γ - 2) φ^{2} (1 - τ)}{4 g k (1 - τ) {(1 - γ)}^{2}} < b < \frac{a}{c}

is met, the optimal design innovation level

v^{{c r}^{*}}

, optimal delivery innovation level

e^{{c r}^{*}}

, optimal wholesale price

w^{{c r}^{*}}

, market price

p^{{c r}^{*}}

, optimal LSI profit

{π_{i}}^{{c r}^{*}}

, LSP profit

{π_{p}}^{{c r}^{*}}

, and total supply chain profit

π^{{r s}^{*}}

can be obtained as follows:

v^{{c r}^{*}} = \frac{μ k (a - b c) {(1 - γ)}^{2}}{4 g (1 - τ) {(γ - 1)}^{2} b k + (1 - τ) (3 γ - 2) g φ^{2} - μ^{2} k {(γ - 1)}^{2}},

e^{{c r}^{*}} = \frac{(1 - γ) (1 - τ) (a - b c) g φ}{4 b k g {(1 - γ)}^{2} (1 - τ) - (3 γ - 2) (1 - τ) φ^{2} g - k μ^{2} {(1 - γ)}^{2}},

w^{{c r}^{*}} = \frac{b k {(γ - 1)}^{2} [c b g (τ - 3) + a g (3 τ - 1) + c μ^{2}] + φ^{2} g [b c ((τ - 3) γ - τ + 2) + a τ (2 γ - 1)]}{4 g (1 - τ) {(γ - 1)}^{2} b k + (1 - τ) (3 γ - 2) g φ^{2} - μ^{2} k {(γ - 1)}^{2}},

p^{{c r}^{*}} = \frac{(1 - τ) (c k {(γ - 1)}^{2} b^{2} + (3 (γ - 1) a k + c φ^{2}) (γ - 1) b + a (2 γ - 1) φ^{2}) g - b c k μ^{2} {(γ - 1)}^{2}}{b (4 b k g {(1 - γ)}^{2} (1 - τ) - (3 γ - 2) (1 - τ) φ^{2} g - k μ^{2} {(1 - γ)}^{2})},

{π_{i}}^{{c r}^{*}} = \frac{k g {(1 - γ)}^{2} {(a - b c)}^{2} (1 - τ)}{8 b k g {(1 - γ)}^{2} (1 - τ) - 2 φ^{2} g (3 γ - 2) (1 - τ) - 2 k μ^{2} {(1 - γ)}^{2}},

{π_{p}}^{{c r}^{*}} = \frac{({(1 - τ)}^{2} (2 b k (1 - γ) - φ^{2}) g - k μ^{2} τ (1 - γ)) g {(a - b c)}^{2} {(1 - γ)}^{3} k}{2 {((- 1 + τ) (4 b k {(γ - 1)}^{2} + (3 γ - 2) φ^{2}) g + k μ^{2} {(γ - 1)}^{2})}^{2}},

π^{{c r}^{*}} = \frac{g {(- b c + a)}^{2} {(γ - 1)}^{2} k ({(- 1 + τ)}^{2} (6 b {(γ - 1)}^{2} k + (4 γ - 3) φ^{2}) g - k μ^{2} {(γ - 1)}^{2})}{2 {((- 1 + τ) (4 b {(γ - 1)}^{2} k + (3 γ - 2) φ^{2}) g + k μ^{2} {(γ - 1)}^{2})}^{2}} .

Corollary 4.

Under the coordination of the cost-sharing and revenue-sharing hybrid contract, when condition

0 < γ < \frac{1}{2}

is met, the optimal design innovation level of the LSI, the optimal delivery innovation level of the LSP, and the optimal profit of the LSI are all greater than those under single contract coordination, that is to say

v^{{c r}^{*}} > v^{{c s}^{*}},

v^{{c r}^{*}} > v^{{r s}^{*}},

e^{{c r}^{*}} > e^{{c s}^{*}},

e^{{c r}^{*}} > e^{{r s}^{*}},

{π_{i}}^{{c r}^{*}} > {π_{i}}^{{c s}^{*}}

, and

{π_{i}}^{{c r}^{*}} > {π_{i}}^{{r s}^{*}}

. The variation in the LSP’s profit will be discussed in numerical analysis.

Corollary 4 indicates that the coordination ability of the hybrid contract is stronger than that of a single contract. This paper argues that a single contract, such as a cost-sharing contract, may result in one party bearing excessive costs without seeing benefits, while a revenue-sharing contract may cause one party to incur high innovation costs without realizing the expected returns. In contrast, a hybrid contract balances these risks, thereby enhancing the overall economic efficiency of the supply chain.

6. Numerical Analyses

In this section, the validity of the previous propositions is first verified by assigning specific numerical values to the model parameters and conducting simulations using MATLAB 2016b software. Subsequently, sensitivity analysis of key parameters is performed to validate the robustness of the conclusions.

6.1. The Impact of Revenue-Sharing Ratio and Cost-Sharing Ratio

This subsection first analyzes the impact of the proportional coefficients of supply chain contracts on equilibrium outcomes. This study draws on the parameter settings from the research by Wang et al. [32], which primarily explored the key factors and impact mechanisms of implementing green innovation in the logistics industry, with a focus on the roles of relationship strength and overconfidence in green innovation within logistics service supply chains. Wang’s research shares the same contextual background as this paper, making it highly relevant and informative. Subject to the condition that the optimal solution is found, set the parameter value

a = 100

c = 10

φ = 4

μ = 5

b = 3

g = 10

, and

k = 8

The optimal values under centralized and decentralized decision making are calculated separately, and the results are shown in the Table 3 below.

The graphical analysis is as follows (Figure 1):

From Figure 1, it can be observed that as the revenue-sharing ratio (cost-sharing ratio) increases, both the LSI’s green design innovation level and the LSP’s green delivery innovation level show an upward trend, with conditions

v^{c r} > v^{r s} > v^{c s} > v^{d}

and

e^{c r} > e^{c s} > e^{r s} > e^{d}

being satisfied. Overall, hybrid contracts provide the best incentive effects on the green innovation levels of both parties. For single contracts, the two types exhibit different coordination advantages: cost-sharing contracts have a stronger incentive effect on the LSP’s green delivery innovation level, but a weaker effect on the LSI’s green design innovation level. In contrast, revenue-sharing contracts provide a very significant incentive effect on the LSI’s green design innovation level, approaching the performance of hybrid contracts. Therefore, it can be concluded that the LSP is more concerned about innovation costs. Under the coordination of the cost-sharing contract, the LSI directly alleviates the LSP’s financial burden, significantly reducing its short-term expenditures and enhancing its motivation for innovation. On the other hand, the LSI is more focused on long-term returns. Under the coordination of the revenue-sharing contract, the LSI’s profit structure changes, making it more willing to enhance its green design innovation level to increase revenue.

From Figure 2, it is evident that regardless of whether it is a single contract or a hybrid contract, the market price of logistics services increases with the revenue-sharing ratio (cost-sharing ratio), with condition

p^{c r} > p^{r s} > p^{c s} > p^{d}

being satisfied. As for the wholesale price, revenue-sharing contracts and hybrid contracts significantly reduce it, while cost-sharing contracts lead to an increase. Therefore, under the coordination of revenue-sharing contracts and hybrid contracts, the unit profit margin of the integrator increases. This paper attributes this to the fact that, under a revenue-sharing contract, part of the LSI’s sales revenue in the market flows back to the LSP. As a result, the LSP is willing to lower the wholesale price to encourage the LSI to increase its procurement of logistics services, thereby also improving its own market share. Under a cost-sharing contract, although the LSI bears part of the LSP’s green delivery innovation costs, the provider still increases the wholesale price to offset its cost expenditures.

From Figure 3a, it can be observed that under the coordination of revenue-sharing contracts and hybrid contracts, the LSI’s profit shows a gradual upward trend as the revenue-sharing ratio (cost-sharing ratio) increases. However, under the coordination of cost-sharing contracts, the LSI’s profit first increases and then decreases. Overall, hybrid contracts provide the best incentive effect on the LSI’s profit, while cost-sharing contracts have a relatively weaker effect, satisfying condition

π_{i} {}^{c r}> π_{i} {}^{r s}> π_{i} {}^{c s}> {π_{i}}^{d}

. From Figure 3b, under the coordination of the three types of contracts, the LSP’s profit exhibits a trend of first increasing and then decreasing as the revenue-sharing ratio (cost-sharing ratio) increases. Among these, hybrid contracts still provide the best incentive effect, satisfying condition

π_{p} {}^{c r}> π_{p} {}^{r s}> π_{p} {}^{c s}> {π_{p}}^{d}

for the maximum LSP profit. Combined with Figure 4, hybrid contracts have the best incentive effect on total supply chain profit, followed by revenue-sharing contracts, and lastly cost-sharing contracts. Under hybrid contracts, the total supply chain profit reaches its peak; however, this peak cannot be realized because the LSP’s profit at this point is lower than under decentralized decision making. Based on the above conclusions, under the coordination of the three types of contracts, the LSI consistently achieves higher profits. However, for the LSI to realize profit increases, strict requirements must be imposed on the setting of revenue-sharing and cost-sharing ratios. If these ratios are set too high, the LSI’s profit may fall below that of decentralized decision making, potentially terminating the collaboration between the LSI and LSP. Although counterintuitive, this paper attributes this conclusion to the fact that when the revenue-sharing and cost-sharing ratios are set too high, the LSI must allocate substantial costs and revenues to support the LSP. This prompts the LSI to increase the market price of logistics services to offset its losses. However, excessively high prices reduce market demand, thereby lowering the LSP’s profit.

6.2. Sensitivity Analysis Results

This section analyzes the impact of key model parameter assignments on equilibrium outcomes to demonstrate the robustness of the conclusions.

First, the cost coefficients

g

and

k

of green innovation for the LSI and LSP are selected as independent variables to examine their impact on the levels of green design innovation, green delivery innovation, and the profits of both supply chain parties. To ensure that the LSI and LSP achieve profit growth under the coordination of the contracts, this subsection selects a cost-sharing ratio

γ = 0.15

and a revenue-sharing ratio

τ = 0.15

. The remaining parameters are set based on the study by Wang et al. [39]:

a = 100

b = 3

c = 10

φ = 4

, and

μ = 5

From Figure 5, it can be observed that the levels of green delivery innovation and green design innovation decrease as the cost coefficient

k

increases, with conditions

e^{c r} > e^{c s} > e^{r s} > e^{d}

and

v^{c r} > v^{r s} > v^{c s} > v^{d}

consistently holding within the given range. Similarly, from Figure 6, it is evident that the levels of green delivery innovation and green design innovation decrease as the cost coefficient

g

increases, with conditions

e^{c r} > e^{c s} > e^{r s} > e^{d}

and

v^{c r} > v^{r s} > v^{c s} > v^{d}

consistently holding within the range, thereby verifying the robustness of the previous conclusions. Additionally, it can be inferred that as the cost coefficients increase, the incentive effects of the three types of contracts on the levels of green delivery innovation and green design innovation weaken accordingly.

From Figure 7, it can be observed that the profits of the LSI and LSP decrease as the cost coefficient

k

increases, with conditions

π_{i}^{c r} > π_{i}^{r s} > π_{i}^{c s} > π_{i}^{d}

and

π_{p}^{c r} > π_{p}^{r s} > π_{p}^{c s} > π_{p}^{d}

consistently holding within the given range. Similarly, from Figure 8, the profits of the LSI and LSP decrease as the cost coefficient

g

increases, with conditions

π_{i}^{c r} > π_{i}^{r s} > π_{i}^{c s} > π_{i}^{d}

and

π_{p}^{c r} > π_{p}^{r s} > π_{p}^{c s} > π_{p}^{d}

consistently holding, thereby validating the robustness of the previous conclusions. This conclusion aligns with intuition and indicates that the coordination of all three types of contracts can increase the profits of both the LSI and LSP, thereby achieving Pareto improvement in the supply chain.

Next, this subsection takes the sensitivity coefficients

μ

and

φ

of market demand to green innovation levels as independent variables to examine their impact on the levels of green design innovation, green delivery innovation, and the profits of both supply chain parties.

From Figure 9, it can be observed that as the demand sensitivity coefficients

μ

increase, the levels of green design innovation and green delivery innovation rise accordingly, with conditions

e^{c r} > e^{c s} > e^{r s} > e^{d}

and

v^{c r} > v^{r s} > v^{c s} > v^{d}

consistently holding within the given range. Similarly, from Figure 10, as the demand sensitivity coefficients increase, the levels of green design innovation and green delivery innovation also rise, with conditions

e^{c r} > e^{c s} > e^{r s} > e^{d}

and

v^{c r} > v^{r s} > v^{c s} > v^{d}

consistently holding within the given range. Therefore, this validates the robustness of the previous conclusions.

From Figure 11, it can be observed that as the demand sensitivity

μ

coefficients increase, the profits of the LSI and LSP also increase, with conditions

π_{i}^{c r} > π_{i}^{r s} > π_{i}^{c s} > π_{i}^{d}

and

π_{p}^{c r} > π_{p}^{r s} > π_{p}^{c s} > π_{p}^{d}

consistently holding within the given range. Similarly, from Figure 12, as the demand sensitivity

φ

coefficients increase, the profits of the LSI and LSP also rise, with conditions

π_{i}^{c r} > π_{i}^{r s} > π_{i}^{c s} > π_{i}^{d}

and

π_{p}^{c r} > π_{p}^{r s} > π_{p}^{c s} > π_{p}^{d}

consistently holding within the given range. Therefore, this validates the robustness of the previous conclusions. Additionally, this conclusion aligns with intuition: when the demand for logistics services is highly sensitive to green innovation levels, the LSI and LSP can efficiently stimulate market demand by enhancing their green innovation levels, thereby increasing revenue.

7. Discussion

To address the coordination issues in logistics service supply chains within the context of green innovation, this paper focuses on a two-level logistics service supply chain consisting of a single LSI and a single LSP. A Stackelberg game model is constructed, with the LSI as the leader and the LSP as the follower. The game outcomes are calculated under centralized decision-making, decentralized decision-making, and cost-sharing, revenue-sharing, and cost-sharing-revenue-sharing hybrid contracts. Through model solving and case analysis, this study specifically compares the effects of the three contracts on incentivizing green innovation levels and profits for both supply chain parties, as well as their impact on the wholesale price and market price of logistics services.

The conclusions of this study are as follows: First, hybrid contracts provide the best incentive effects on the green innovation levels of both the LSI and LSP, while cost-sharing contracts show relatively weaker effects on incentivizing the LSI’s green design innovation level. Second, the application of all three contracts leads to an increase in the market price of logistics services, but revenue-sharing and hybrid contracts effectively reduce the wholesale price of logistics services. Finally, under the coordination of the three contracts, the supply chain achieves Pareto improvement but fails to reach the optimal state of centralized decision making. Moreover, the LSP has strict requirements for the application of these contracts.

Currently, similar research exists in academia. Liu et al. [31] explored how to promote the intelligent transformation of logistics service supply chains through the design of incentive contracts, focusing on the impact of cost-sharing contracts, revenue-sharing contracts, and hybrid contracts on the intelligent transformation of logistics service providers. Their research found that single contracts struggle to achieve comprehensive supply chain coordination, and cost-sharing contracts reduce the profit of the LSP. In contrast, hybrid contracts significantly balance the interests of all parties, enhance the level of intelligence, and increase overall profits, achieving perfect supply chain coordination. Differing from Liu’s conclusions, our research finds that under the solutions of this model, cost-sharing contracts also have a profit-enhancing effect on the LSP, albeit weaker than that of revenue-sharing and hybrid contracts. Moreover, hybrid contracts cannot achieve Pareto optimality for the supply chain. This paper attributes these differing conclusions to the inclusion of the LSI’s green innovation costs in this model, which better aligns with the research context of this study and is likely the primary reason for the discrepancy. Additionally, this model incorporates more parameters for practitioners, offering a broader range of application scenarios.

The second study similar to this paper is the article by Liu et al. [33]. Liu’s research primarily explored the adoption of blockchain technology collaboration between core enterprises and SMEs through supply chain contracts involving cost-sharing, revenue-sharing, and hybrid contracts. Their study used a Stackelberg game model to describe the leader–follower relationship between enterprises and analyzed the blockchain development levels and supply chain profits under different contract models. Their findings reveal that the coordination effect of cost-sharing contracts was superior to revenue-sharing contracts, and only hybrid contracts could enable the supply chain to achieve the optimal level under centralized decision making. Unlike this study, Liu’s research considered the synergistic effects between upstream and downstream enterprises in the supply chain, positing that the blockchain development level upstream influences the downstream development. This is a valuable research perspective that could potentially be adopted in future studies of this paper. Additionally, their study included the blockchain credit evaluation system, regarded as another component of enterprise revenue, which might be one of the reasons for the differences between the conclusions of this study and theirs.

8. Conclusions and Future Research

With the growing global awareness of environmental protection, environmental issues in the logistics industry have become a critical topic in corporate management. Green innovation in logistics services is not only an inevitable response to increasingly stringent environmental regulations and policies, but also a key approach for enterprises to enhance competitiveness and fulfill social responsibility. However, the cost of green innovation in logistics services is substantial, and decentralized decision making alone makes it challenging for supply chain enterprises to achieve efficient innovation. Based on this, this chapter constructs a two-level logistics service supply chain Stackelberg game model under the context of green innovation, consisting of an LSI as the leader responsible for green design innovation and an LSP as the follower responsible for green delivery innovation. It examines the coordination effects of cost-sharing contracts, revenue-sharing contracts, and cost-sharing-revenue-sharing hybrid contracts on the supply chain, aiming to provide theoretical insights for managers.

8.1. Main Conclusions

The conclusions of this paper are as follows:

First, under decentralized decision making without contractual coordination, the green innovation levels and profits of the integrator and provider are lower than those under centralized decision making, highlighting the critical importance of proper contractual coordination.

Second, all three contracts can incentivize the LSI and LSP to improve their respective green innovation levels, with hybrid contracts providing the best incentive effects. However, the cost-sharing contract shows relatively weak incentive effects on the LSI’s green design innovation level. This is because a single cost-sharing contract does not provide sustained incentives for green innovation, causing the LSI to focus more on incurred costs rather than the benefits of innovation, thus lacking motivation to enhance its green design innovation level.

Third, all three contracts increase the market price of logistics services, but revenue-sharing and hybrid contracts effectively reduce the wholesale price of logistics services. Green innovation incurs additional costs for the LSI and LSP, which are partially transferred to consumers through higher market prices. However, under the coordination of revenue-sharing and hybrid contracts, the wholesale price of logistics services is reduced, thereby expanding the profit margin for the LSI.

Finally, under the coordination of the three contracts, the profits of both the LSI and LSP are improved, achieving Pareto improvement in the supply chain. However, the LSP has strict requirements for cost-sharing and revenue-sharing ratios, and the profit-enhancing effects of the three contracts are more significant for the LSI than for the LSP. Additionally, the total profit of the supply chain is highest under hybrid contracts, while among single contracts, the coordination effect of the revenue-sharing contract is superior to that of the cost-sharing contract. Due to its weaker position in the game, the LSP struggles to fully benefit from the coordination process, as the LSI, controlling the final stages close to consumers, has greater flexibility in market pricing and green innovation decisions.

8.2. Management Insights

This paper examines the coordination effects of different contracts on logistics service supply chains in the context of green innovation, providing the following managerial insights for practitioners:

First, contractual coordination is crucial for incentivizing green innovation. Research shows that in the context of green innovation, contractual coordination plays a decisive role in motivating the innovation behaviors of both supply chain parties. Therefore, supply chain managers should prioritize the introduction of contract mechanisms when designing cooperation agreements to encourage integrators and providers to jointly invest in green innovation and to incentivize innovation through fair profit distribution.

Second, logistics service providers are in a weaker position in the supply chain and may struggle to achieve high returns through bargaining, which could affect their motivation for innovation. Thus, logistics service integrators should engage in contract negotiations to establish reasonable cost-sharing and revenue-sharing ratios, balancing costs and benefits between the parties. Additionally, integrators can support providers by offering technical assistance and sharing resources to help reduce green innovation costs and enhance their motivation for innovation.

Last but not least, hybrid contracts offer the best coordination effects. Among the three types of contracts, hybrid contracts most effectively incentivize both parties to improve their innovation levels, increase their profits, and achieve Pareto improvement in the supply chain. This indicates that managers should strive to combine the coordination advantages of different contracts to design flexible hybrid contracts, ensuring that all supply chain parties can control costs in the short term while achieving sustainable innovation benefits in the long term.

8.3. Limitrations and Future Research

Despite the conclusions and managerial insights presented in this paper, there are still some limitations: (1) Model limitations: First, this study only considers a logistics service supply chain comprising a single integrator and a single provider, whereas in reality, multiple competing providers often exist. Second, scenarios where the provider has greater power and leads the game may occur. (2) Limitations of the cost-sharing contract: In practice, it is challenging for the integrator to fully monitor the provider’s innovation costs, making the implementation of cost-sharing contracts difficult. Future research could explore different power structures and supply chains with competition, as well as other coordination contracts.

Author Contributions

Conceptualization, Y.S. and W.C.; validation, Y.S. and X.Z.; writing—original draft, Y.S.; writing—review and editing, Y.S., X.Z. and X.H.; supervision, W.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

Proof of Proposition 1.

According to function (3), the Hessian matrix of

π

with respect to the variables

p

v

, and e is solved as follows:

H_{1} = [\begin{matrix} \frac{\partial π^{2}}{\partial p^{2}} & \frac{\partial π^{2}}{\partial p \partial v} & \frac{\partial π^{2}}{\partial p \partial e} \\ \frac{\partial π^{2}}{\partial v \partial p} & \frac{\partial π^{2}}{\partial v^{2}} & \frac{\partial π^{2}}{\partial v \partial e} \\ \frac{\partial π^{2}}{\partial e \partial p} & \frac{\partial π^{2}}{\partial e \partial v} & \frac{\partial π^{2}}{\partial e^{2}} \end{matrix}] = [\begin{matrix} - 2 b & φ & μ \\ φ & - g & 0 \\ μ & 0 & - k \end{matrix}] .

In order for

π (p, v, e)

to have a unique optimal solution, the Hessian matrix needs to be negative definite, that is

- 2 b < 0

2 b g - φ^{2} > 0

, and

- 2 b g k + φ^{2} g + μ^{2} k < 0

. By solving the system of three equations involving

\frac{\partial π}{\partial p} = 0

\frac{\partial π}{\partial v} = 0

, and

\frac{\partial π}{\partial e} = 0

, the optimal price

p^{c^{*}}

of GLSP, the optimal LSI design innovation level

v^{c^{*}}

, and the optimal LSP delivery innovation level

e^{c^{*}}

under centralized decision making can be determined. Substituting the equilibrium price

p^{c^{*}}

of GLSP, the equilibrium design innovation level

v^{c^{*}}

of LSI, and the equilibrium delivery innovation level

e^{c^{*}}

of LSP into Equations(3), the optimal profit of the green logistics service supply chain under centralized decision making can be obtained. □

Proof of Proposition 2.

Similarly to the proof process of Proposition 1. □

Proof of Corollary 1.

v^{d^{*}} - v^{c^{*}} = \frac{k μ g (a - b c) (φ^{2} - 2 b k)}{(4 b g k - 2 g φ^{2} - k μ^{2}) (2 b g k - g φ^{2} - k μ^{2})}

From

\frac{φ^{2} g + μ^{2} k}{2 g k} < b < \frac{a}{c}

, there is

2 b k > φ^{2} + \frac{μ^{2} k}{g}

, so that

φ^{2} - 2 b k < 0

v^{d^{*}} - v^{c^{*}} < 0

, that is

v^{d^{*}} < v^{c^{*}}

Similarly, it can be proven that:

e^{d^{*}} < e^{c^{*}}

and

π_{d}^{*} < π_{c}^{*}

. □

Proof of Corollary 2.

p^{d^{*}} - p^{c^{*}} = \frac{(a - b c) g (2 b k - φ^{2}) ((b g - μ^{2}) k - g φ^{2})}{b (4 b g k - 2 g φ^{2} - k μ^{2}) (2 b g k - g φ^{2} - k μ^{2})}

According to the proof of Corollary 1, there is

2 b k - φ^{2} > 0

. For

p^{d^{*}} < p^{c^{*}}

to hold, it is necessary to satisfy

(b g - μ^{2}) k - g φ^{2} < 0

and

\frac{φ^{2} g + μ^{2} k}{2 g k} < b < \frac{a}{c}

, so that

b < \frac{μ^{2}}{g} + \frac{φ^{2}}{k}

. Therefore, when

\frac{μ^{2}}{g} + \frac{φ^{2}}{k} \geq \frac{a}{c}

and

\frac{φ^{2} g + μ^{2} k}{2 g k} < b < \frac{μ^{2}}{g} + \frac{φ^{2}}{k}

holds, there

p^{d^{*}} < p^{c^{*}}

. When

\frac{μ^{2}}{g} + \frac{φ^{2}}{k} < \frac{a}{c}

occurs,

p^{d^{*}} < p^{c^{*}}

can only be achieved if

\frac{φ^{2} g + μ^{2} k}{2 g k} < b < \frac{μ^{2}}{g} + \frac{φ^{2}}{k}

. □

Proof of Proposition 3.

Similarly to the proof process of Proposition 1. □

Proof of Proposition 4.

e^{r^{*}} - e^{d^{*}} = \frac{φ g γ ((1 - γ) (4 b g - μ^{2}) k - g φ^{2}) (a - b c)}{2 ((4 b g - μ^{2}) k - 2 g φ^{2}) ({(γ - 1)}^{2} (4 b g - μ^{2}) k + φ^{2} (3 γ - 2) g)}

For the part of the molecule, let

A = (1 - γ) (4 b g - μ^{2}) k - g φ^{2}

, so that

\frac{\partial A}{\partial γ} = - (4 b g - μ^{2}) k

. Let

(4 b g - μ^{2}) k - 2 g φ^{2} > 0

, so that

\frac{\partial A}{\partial γ} < 0

. That is,

A (γ)

is monotonically decreasing on the interval

(0, 1)

. Let

e^{r^{*}} - e^{d^{*}} = 0

; it can be solved that

γ = 1 - \frac{g φ^{2}}{(4 b g - μ^{2}) k}

. Let

(4 b g - μ^{2}) k - 2 g φ^{2} > 0

, so that

1 - \frac{g φ^{2}}{(4 b g - μ^{2}) k} > \frac{1}{2}

. □

w^{r^{*}} - w^{d^{*}} = \frac{γ k φ^{2} g^{2} (1 - 2 γ) (a - b c)}{((4 b g - μ^{2}) {(γ - 1)}^{2} k + φ^{2} g (3 γ - 2)) ((4 b g - μ^{2}) k - 2 g φ^{2})}

v^{r^{*}} - v^{d^{*}} = \frac{γ g k μ φ^{2} (1 - 2 γ) (a - b c)}{((4 b g - μ^{2}) {(γ - 1)}^{2} k + (3 γ - 2) g φ^{2}) ((4 b g - μ^{2}) k - 2 g φ^{2})}

p^{r^{*}} - p^{d^{*}} = \frac{g γ φ^{2} (a - b c) ((b (3 - 2 γ) k - φ^{2}) g - γ k μ^{2})}{b ((4 b g - μ^{2}) {(γ - 1)}^{2} k + (3 γ - 2) g φ^{2}) ((4 b g - μ^{2}) k - 2 g φ^{2})} .

When

0 < γ < \frac{1}{2}

, there is

w^{r^{*}} > w^{d^{*}}

v^{r^{*}} > v^{d^{*}}

; when

\frac{1}{2} < γ < 1

, there is

w^{r^{*}} < w^{d^{*}}

and

v^{r^{*}} < v^{d^{*}}

Let

(b (3 - 2 γ) k - φ^{2}) g - γ k μ^{2} = 0

, it can be solved that

γ = \frac{3 b k g - g φ^{2}}{2 b k g + k μ^{2}}

. Because

(4 b g - μ^{2}) k - 2 g φ^{2} > 0

, then

\frac{3 b k g - g φ^{2}}{2 b k g + k μ^{2}} > \frac{1}{2}

. Compute the first derivative of

{π_{i}}^{r}

with respect to

γ

\frac{\partial {π_{i}}^{r}}{\partial γ} = \frac{φ^{2} g^{2} k (3 γ - 1) (γ - 1) {(a - b c)}^{2}}{8 {({(γ - 1)}^{2} (4 b g - μ^{2}) k + φ^{2} g (3 γ - 2))}^{2}}

. When

0 < γ < 1

holds,

\frac{\partial {π_{i}}^{r}}{\partial γ}

first increases and then decreases. So that when

γ = \frac{1}{3}

{π_{i}}^{r}

attains its maximum value.

Proof of Proposition 5.

Similarly to the proof process of Proposition 1. □

Proof of Corollary 3.

v^{{r s}^{*}} - v^{d^{*}} = \frac{2 k g μ τ (2 b k - φ^{2}) (a - b c)}{(4 b g k - 2 g φ^{2} - k μ^{2}) [(1 - τ) (4 b k - 2 φ^{2}) g - k μ^{2}]} > 0

e^{{r s}^{*}} - e^{d^{*}} = \frac{τ μ^{2} k g φ (a - c b)}{(4 b g k - 2 g φ^{2} - k μ^{2}) [(1 - τ) (4 b k - 2 φ^{2}) g - k μ^{2}]} > 0

p^{{r s}^{*}} - p^{d^{*}} = \frac{τ μ^{2} g k (a - c b) (3 b k - φ^{2})}{4 b (4 b g k - 2 g φ^{2} - k μ^{2}) [(1 - τ) (4 b k - 2 φ^{2}) g - k μ^{2}]} > 0

{π_{i}}^{{r s}^{*}} - {π_{i}}^{d *} = - \frac{g k^{2} {(- b c + a)}^{2} μ^{2} τ}{32 ((b k - \frac{φ^{2}}{2}) (τ - 1) g + \frac{k μ^{2}}{4}) ((b k - \frac{φ^{2}}{2}) g - \frac{k μ^{2}}{4})} > 0

w^{{r s}^{*}} - w^{d^{*}} = \frac{τ g (a - c b) [μ^{2} k (3 b k - φ^{2}) - 2 {(2 b k - φ^{2})}^{2} g]}{b (4 b g k - 2 g φ^{2} - k μ^{2}) [(1 - τ) (4 b k - 2 φ^{2}) g - k μ^{2}]}

Sitio Let

A = μ^{2} k (3 b k - φ^{2}) - 2 {(2 b k - φ^{2})}^{2} g

, so that

b = \frac{8 φ^{2} k g + 3 μ^{2} k^{2}}{16 g k^{2}}

. Because

\frac{8 φ^{2} k g + 3 μ^{2} k^{2}}{16 g k^{2}} < \frac{2 (1 - τ) φ^{2} g + μ^{2} k}{4 (1 - τ) g k}

, then

w^{{r s}^{*}} < w^{d^{*}}

. □

Proof of Proposition 6.

Similarly to the proof process of Proposition 1. □

Proof of Corollary 4.

Similarly to the proof process of Corollary 3. □

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Figure 1. (a) The impact of the revenue-sharing (cost-sharing) coefficient on the level of green design innovation. (b) The impact of the revenue-sharing (cost-sharing) coefficient on the level of green delivery innovation.

Figure 2. (a) The impact of the revenue-sharing (cost-sharing) coefficient on the wholesale price. (b) The impact of the revenue-sharing (cost-sharing) coefficient on the market price.

Figure 3. (a) The impact of the revenue-sharing (cost-sharing) coefficient on the LSP’s profit. (b) The impact of the revenue-sharing (cost-sharing) coefficient on the LSI’s profit.

Figure 4. The impact of the revenue-sharing coefficient (cost-sharing coefficient) on the profit of LSSC.

Figure 5. (a) The impact of cost coefficient k on the level of green delivery innovation. (b) The impact of cost coefficient k on the level of green design innovation.

Figure 6. (a) The impact of cost coefficient g on the level of green delivery innovation. (b) The impact of cost coefficient g on the level of green design innovation.

Figure 7. (a) The impact of cost coefficient k on the LSI’s profit. (b) The impact of cost coefficient k on the LSP’s profit.

Figure 8. (a) The impact of cost coefficient g on the LSI’s profit. (b) The impact of cost coefficient g on the LSP’s profit.

Figure 9. (a) The impact of demand sensitivity coefficient μ on the level of green delivery innovation. (b) The impact of demand sensitivity coefficient μ on the level of green design innovation.

Figure 10. (a) The impact of demand sensitivity coefficient ϕ on the level of green delivery innovation. (b) The impact of demand sensitivity coefficient ϕ on the level of green design innovation.

Figure 11. (a) The impact of demand sensitivity coefficient μ on the LSI’s profit. (b) The impact of demand sensitivity coefficient μ on the LSP’s profit.

Figure 12. (a) The impact of demand sensitivity coefficient ϕ on the LSI’s profit. (b) The impact of demand sensitivity coefficient ϕ on the LSP’s profit.

Table 2. Description of Notations.

Notation	Description
$a$	Potential market demand
$b$	Sensitivity coefficient of demand to price
$p$	Market price per unit of green logistics service
$w$	Wholesale price per unit of green logistics services
$c$	Cost of Service for LSPs
$v$	Level of design innovation
$e$	Level of delivery innovation
$μ$	Sensitivity coefficient of demand to the level of design innovation
$φ$	Sensitivity coefficient of demand to the level of delivery innovation
$g$	Cost coefficients for design innovation
$k$	Cost coefficients for delivery innovation
$γ$	Proportionality factor in cost-sharing contract
$τ$	Proportionality factor in revenue-sharing contract
$θ$	The unit profit of the LSI
$π_{i}$	LSI’s profits
$π_{p}$	LSP’s profits

Table 3. Optimal values of centralized and decentralized decision model.

	$p$	$w$	$v$	$e$	$π_{i}$	$π_{p}$	$π$
Centralized decision model	64.90 ¹	/	21.96	34.31	/	/	1921.60
Decentralized decision model	43.03	26.87	6.75	10.54	590.36	408.99	999.35

¹ Rounded to two decimal places.

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Sun, Y.; Zhang, X.; Huang, X.; Cao, W. Research on Logistics Service Supply Chain Coordination in the Context of Green Innovation. Sustainability 2025, 17, 646. https://doi.org/10.3390/su17020646

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Sun Y, Zhang X, Huang X, Cao W. Research on Logistics Service Supply Chain Coordination in the Context of Green Innovation. Sustainability. 2025; 17(2):646. https://doi.org/10.3390/su17020646

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Sun, Yuxiang, Xiaopu Zhang, Xirou Huang, and Wenbin Cao. 2025. "Research on Logistics Service Supply Chain Coordination in the Context of Green Innovation" Sustainability 17, no. 2: 646. https://doi.org/10.3390/su17020646

APA Style

Sun, Y., Zhang, X., Huang, X., & Cao, W. (2025). Research on Logistics Service Supply Chain Coordination in the Context of Green Innovation. Sustainability, 17(2), 646. https://doi.org/10.3390/su17020646

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Research on Logistics Service Supply Chain Coordination in the Context of Green Innovation

Abstract

1. Introduction

2. Literature Review

2.1. Logistics Service Supply Chain

2.2. Green Innovation in Logistics Services

2.3. Research on Stackelberg Game

2.4. Research on Supply Chain Coordination Contracts

3. Research Methodology and Model Construction

4. Basic Model Under Contract-Free Coordination

4.1. Model Under Centralized Decision Making

4.2. Model Under Decentralized Decision Making

5. Models Under Contractual Coordination

5.1. Model Under Cost-Sharing Contract Coordination

5.2. Model Under Revenue-Sharing Contract Coordination

5.3. Model Under Cost-Sharing and Revenue-Sharing Contract Coordination

6. Numerical Analyses

6.1. The Impact of Revenue-Sharing Ratio and Cost-Sharing Ratio

6.2. Sensitivity Analysis Results

7. Discussion

8. Conclusions and Future Research

8.1. Main Conclusions

8.2. Management Insights

8.3. Limitrations and Future Research

Author Contributions

Funding

Institutional Review Board Statement

Informed Consent Statement

Data Availability Statement

Conflicts of Interest

Appendix A

References

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