Pricing and coordination of product service supply chain under an industrial internet platform environment

Li, Xiangdong; Wu, Xinkun; Wang, Junli; Cui, Linghui

doi:10.1108/MSCRA-09-2023-0037

Purpose

With the development and application of new-generation information technology, a wave of intelligent transformations in enterprise services has emerged. As a combination of various information technologies, industrial Internet platforms are becoming the new engine for driving the intelligent transformation of enterprise services. This paper examines how enterprises address pricing and coordination issues in product–service supply chains under industrial Internet platforms.

Design/methodology/approach

By building a game-theoretic model that includes a manufacturer and seller, with the manufacturer building its own industrial Internet platform, this paper analyzes the changes in service operation modes, service demand and service costs arising from the manufacturer’s service-oriented intelligent transformation.

Findings

First, with higher cost-saving coefficients and greater sensitivity of service intelligence, both wholesale and retail product prices decline, while service prices first rise and then fall as the cost-saving coefficient increases. Second, the effects of both the cost savings coefficient and service intelligence level sensitivity on service prices are related to the cost coefficient of service intelligence transformation. Specifically, in the centralized decision-making scenario, the service intelligence level is the highest, the product price is the lowest and the supply chain node firms and systems are the most profitable. In addition, manufacturers can incentivize sellers to participate in service intelligence transformation through the “cost-sharing-fixed-transfer-payment” agreement.

Originality/value

We incorporate industrial Internet platforms into the product–service supply chain framework by modeling the transformation toward service intelligence and propose coordination mechanisms to improve system performance.

1. Introduction

With the restructuring of the global market economy, traditional manufacturing enterprises are gradually undergoing a servitization transformation to adapt to the change from a product economy to a service economy. Product-service supply chains necessitate that manufacturing firms move beyond merely providing physical products; they must also offer complementary services associated with those products. However, China’s manufacturing enterprises generally face problems such as low service efficiency and low value-added services in the implementation of servitization strategies. As a product of the integration of new-generation information technology and industrial systems, the industrial Internet has become a key engine and important part of the intelligent transformation of the real economy. During a wave of servitization and intelligent transformation in the manufacturing industry, enterprises rely on industrial Internet platforms to collect, process, and analyze product operation data and promote intelligent service transformation by providing intelligent services such as remote monitoring, predictive maintenance, and energy consumption optimization.

With the rapid development of new-generation information technologies, such as big data, Internet of Things, blockchain, and artificial intelligence (AI), service intelligence has become a key target for enterprises to focus on (Jiang et al., 2021). As a new carrier that integrates multiple information technologies, the industrial Internet platform has gradually become a platform for the digital and intelligent transformation of enterprises. Enterprises conduct intelligent service transformation based on industrial internet platforms, reshape the service process and content of enterprises through data-driven intelligent services, change the operation mode of products and services in the value chain, and demonstrate advantages such as quality improvement, operational cost reduction, and an increase in demand for manufacturing enterprises. Specifically, the industrial internet platform is a digital infrastructure that integrates IoT, AI, and cloud computing to connect devices, people, and processes across the manufacturing value chain, enabling smart production and flexible supply chain management. For instance, Haier Group’s industrial internet platform COSMOPlat supports the full lifecycle of manufacturing enterprises, covering design, procurement, production, sales, logistics, and after-sales service. It effectively addresses the growing demand for personalized customization. Built on Huawei Cloud, Huawei’s platform integrates 5G, artificial intelligence, and cloud computing. In partnership with Chinese automotive manufacturers, it enables intelligent manufacturing and efficient supply chain management through real-time data analysis, enhancing demand forecasting, reducing material waste, and improving responsiveness.

However, the high technology content of industrial Internet platforms makes it necessary for enterprises to invest ample capital, technology, and human resources, whether they build their own platforms or rely on third-party platforms for service intelligence transformation. This increases their cost burden and impacts pricing decisions and conflicts of interest among supply chain node enterprises. For enterprises, it is essential to establish clear innovation development strategies and refine organizational structures. This involves progressively increasing investments in scientific and technological innovation, accelerating the enhancement of innovation capabilities, thereby enabling them to assume leadership roles in driving industrial advancement (Chen and Yang, 2022). These efforts will allow enterprises to effectively adapt to service-oriented intelligent transformation within industrial internet platforms. Simultaneously, manufacturers also must consider the advantages and disadvantages and make appropriate decisions.

Given the above background, this study focuses on how firms can effectively respond to the pricing and coordination issues of product-service supply chains in an industrial Internet platform environment, and discusses the following specific questions: (1) How does a manufacturer’s product supply chain embedded in an Industrial Internet Platform shape participants’ decision-making processes in formulating pricing and coordination strategies? (2) What is the impact of a manufacturer’s own industrial Internet platform on the profitability of firms participating in the supply chain?

To solve the above research problems, we develop a Stackelberg game model in which manufacturers and sellers form a two-echelon supply chain, consider the effects of cost, quality, and demand on pricing and coordination strategies for the level of service intelligence, and solve for the optimal product price, service price, and level of service intelligence under both decentralized and centralized decision-making scenarios. In addition, we include the third-party industrial Internet platform operator as an independent decision-making subject in the product and service supply chain and establish a game model consisting of manufacturers, sellers, and the third-party industrial Internet platform operator to analyze the equilibrium solution under different decision-making scenarios.

2. Literature review

In our study, we cover three research areas: the pricing of product-service supply chains, industrial Internet platforms empowering intelligent transformation of enterprise services, and the impact of industrial Internet platforms on product-service supply chains.

2.1 Product-service supply chain

The concept of a product-service supply chain was first proposed by Johnson in 2008 and is considered to be the fusion of the product and service supply chains under service-oriented manufacturing, which is quite different from the traditional product supply chain in terms of demand, uncertainty, and risk tolerance range. This was followed by scholars such as Johson and Mena (2008), Maull et al. (2014), Lockett and Johson (2011), Chen (2010), and Dan et al. (2019) who researched the concept of product-service supply chain from different perspectives, as shown in Table 1.

Table 1

Representative definition of Product Service Supply Chain

Scholars	Definition
Johnsonh and Mena	The fusion of the product and service supply chains
Maull and Smart	Delivering both products and services in the supply chain
Lockett	Build a supply chain network that provides product and service systems to customers with the participation of customers, with the system integrator as the core company
Chen	The product-service supply chain integrates both the product and service supply chains, transforming supply chain offerings from a single product to a product that includes additional services or an integrated solution
Dan	In the context of “Internet +”, and from a value creation perspective, the product-service supply chain is considered a network supported by the Internet platform, oriented toward customer demand. It primarily consists of value-creating entities—namely, product manufacturers and Internet service integrators—working in collaboration with other stakeholders to deliver customized products and services to end users

Scholars	Definition
Johnsonh and Mena	The fusion of the product and service supply chains
Maull and Smart	Delivering both products and services in the supply chain
Lockett	Build a supply chain network that provides product and service systems to customers with the participation of customers, with the system integrator as the core company
Chen	The product-service supply chain integrates both the product and service supply chains, transforming supply chain offerings from a single product to a product that includes additional services or an integrated solution
Dan	In the context of “Internet +”, and from a value creation perspective, the product-service supply chain is considered a network supported by the Internet platform, oriented toward customer demand. It primarily consists of value-creating entities—namely, product manufacturers and Internet service integrators—working in collaboration with other stakeholders to deliver customized products and services to end users

Source(s): Authors’ own creation

Examining how scholars have conceptualized the definition of the product-service supply chain from multiple perspectives reveals that, the concept has become increasingly well-defined and theoretically mature. The enhanced conceptual clarity provides a solid theoretical foundation for the present study.

2.2 Pricing in the product-service supply chain

This paper reviews research on supply chain pricing for products and services, and categorizes the relevant literature into two main categories: product pricing and joint pricing of products and services. The classification is based on two analytical perspectives: the product-service pricing perspective and the intelligent systems context.First, we focus on product-pricing issues. Li et al. (2016) study the impact of service providers on product pricing. Yan et al. (2013) investigate product pricing and supply chain coordination under the separate provision of services by manufacturers and retailers, considering that the demand for a product is affected by its price and the length of the warranty period. The second category focuses on joint pricing of products and services. Under the premise that customers’ expectation of the product failure rate affects their extended warranty service purchase decision, Kou et al. (2020) investigated the joint pricing problem of extended warranty services and products by constructing a customer utility function. Wang et al. (2017) investigated the two-phase dynamics of the manufacturer and service integrator in terms of the strategic waiting behavior of consumers when purchasing product-service system pricing problems. Dan et al. (2017a, b) analyzed the product and service pricing problem of a product-service supply chain consisting of a manufacturer and a sales-service integrator from the perspective of product sales affecting the demand for services, and designed a “price discount-service revenue compensation” contract to realize the coordination of the product-service supply chain. Subsequently, Dan et al. (2017a, b) explored the joint pricing of products and services in a product-service supply chain composed of a manufacturer and a sales-service integrator from the perspective of services promoting product sales.

The continuous development of the new generation of digital technology is changing the form of traditional products and service delivery, and some scholars have been concerned with related pricing decision-making and optimization problems. Thiesse and Köhler (2008) investigated the pricing of smart products based on usage, finding that a new generation of ICT technologies (e.g. Internet of Things, big data, and cloud computing) is transforming the manufacturing industry. Su et al. (2022) considered the impact of product intelligence R&D inputs on the externalities of the product network, product demand, and cost of service. Huang et al. (2020) explored the value measurement and revenue distribution of intelligent Operation and Maintenance (O&M) services using a PaaS model in terms of service outcomes. Tong and Li (2023) studied the pricing decision problem of a dual-channel supply chain based on the impact of 3D printing technology on product production costs and demand.

Recently, scholars have begun to investigate the pricing decision-making and optimization problem of product-service supply chains under the background of digitization and intelligence. However, they mainly study single intelligent product pricing or single intelligent service pricing and seldom involve the co-pricing problem of products and services under the background of intelligence at the same time. Future research may explore the optimization effects of coordinated pricing under contract alignment on pricing decisions within product-service supply chains. For instance, Li et al. (2025) underscore the distinct roles of cost-sharing agreements in enhancing delivery incentives and achieving supply chain coordination.

2.3 Industrial internet platform enables intelligent transformation of enterprise services

With the development of intelligent manufacturing, enterprise service intelligent transformation has become a strategic choice for enterprises to comply with the development trend. The industrial Internet platform, as a key breakthrough tool for the development of intelligent manufacturing, has begun to empower traditional manufacturing enterprises’ intelligent service transformation. When traditional manufacturing enterprises rely on industrial Internet platforms for intelligent service transformation, their product-service supply chain also undergoes certain changes. Intelligent service transformation is an important path for the intelligent transformation of enterprises. From the perspective of complex adaptive systems, Liu (2021) studied how traditional manufacturing enterprises can use the industrial Internet platform to encourage enterprises to comply with the trend of digitization and realize service-oriented transformation, which is a realistic and urgent problem driven by the new industrial revolution. The results showed that manufacturing enterprises can realize product- and user-based servitization through the industrial Internet platform. Cai and Qi (2021) noted that the industrial Internet platform can promote the digital transformation of the manufacturing industry from point to point from the three levels of manufacturing enterprises, industrial chain, and products, and help realize the platformization of the industrial chain, the digitization of the enterprise production process, and product servitization. Xie et al. (2021) stated that an industrial Internet platform can empower manufacturing enterprises from outside the enterprise through the establishment of an industrial Internet platform asset management and tracking system, which helps realize the effective circulation of supply and demand information between the enterprise and the supplier, facilitates the establishment of an efficient negotiation mechanism, and ultimately achieves a win-win situation. Alexopoulos et al. (2018) proposed providing intelligent services to users by constructing an industrial Internet service platform with information-awareness capabilities, thereby realizing personalized customization of industrial needs and increasing enterprise productivity while reducing energy costs.

Earlier studies on industrial Internet platforms have primarily concentrated on their conceptual foundations, architectural models, and key enabling technologies, producing a substantial body of theoretical and technical knowledge. As the industrial Internet continues to evolve, scholarly attention has increasingly shifted toward application contexts, practical implications, and the enabling roles of these platforms. In the context of strong national support for intelligent manufacturing, industrial Internet platforms have come to be regarded as both a methodological framework and a strategic enabler for enterprise-level intelligent transformation. This shift calls for a more in-depth examination of how such platforms contribute to enterprise transformation from the perspective of digital empowerment.

2.4 The impact of industrial internet platforms on product and service supply chains

As the country continues to advocate the development of smart manufacturing and the industrial Internet, scholars have begun to focus on the impact of industrial Internet technologies and platforms on the supply chain of products and services. The research report Supply Chain Innovation and Application Based on Industrial Internet Platforms, 2021, defines the supply chain based on industrial Internet as a digital network structure that uses industrial Internet as the basis and aims to reduce costs and increase efficiency. With big data, AI, and other new-generation information technologies as the means, it realizes the digital network structure of suppliers, manufacturers, distributors, and retailers that is fully connected, efficiently collaborative, and intelligent in decision-making (Alliance of Industrial Internet, 2021). Thus, industrial Internet platforms integrating big data, AI, and other new-generation information technologies have become powerful tools for enterprises to improve supply chain efficiency. The digitization capability of industrial internet platforms has different enhancements for each segment of the enterprise supply chain (Tang et al., 2020), and in the context of big data and AI technologies that constantly influence the servitization of manufacturing, Porter and Heppelmann (2015) noted that after manufacturing enterprises gather full product life cycle data, they can form data barriers to increase buyers’ transfer costs, which in turn reduces buyers’ bargaining power and makes competition move in the direction of high fixed costs and low variable costs. However, the financial position of retailers may also exert influence on the strategic decisions of platforms. Zhang et al. (2025) explore the interactive mechanisms between e-commerce platforms and financially constrained online retailers in terms of financing strategies and channel cooperation contracts. The study highlights the significant impact of the retailer’s working capital on the preferences and operational decisions of both parties. Some scholars have already studied the impact of the industrial Internet platform on the product-service supply chain in terms of reducing enterprise costs, improving enterprise differentiation competitiveness, and increasing the transfer cost of the buyer, for example, Wang et al. (2024) investigate how market thickness and cross-network effects influence the equilibrium order allocation strategies between platforms and firms, as well as the dynamic evolution of their respective profit trajectories. However, at present, the impact of the industrial Internet platform on the product-service supply chain has not yet been systematically analyzed from the perspective of the supply chain service. This study lays the theoretical foundation for the model construction of this study, as well as the wave of intelligent transformation sweeping and the highlighting of the powerful enabling role of the industrial Internet platform.

Prior studies have examined the impact of industrial Internet platforms on the product-service supply chain, particularly with respect to cost reduction, enhancement of competitive differentiation, and the increase of buyer switching costs. However, a systematic analysis of their influence on the product-service supply chain from a specific theoretical perspective remains lacking. From the perspective of supply chain services, this study conducts an analysis of how industrial Internet platforms affect the product-service supply chain, providing a theoretical foundation for subsequent model formulation. In addition, with the accelerating trend of intelligent transformation and the expanding role of industrial Internet platforms as enablers, research has increasingly focused on how these platforms facilitate the intelligent transformation of enterprise services. Nevertheless, existing studies have primarily adopted empirical approaches and case studies, while quantitative analysis based on mathematical modeling remains underexplored.

3. Basic model

This section constructs a two-echelon supply chain consisting of a manufacturer and a seller. In the product sales stage, the manufacturer transfers the product to the seller at wholesale price $W$ ⁠, and the seller sells the product to the customer at price $P_{p}$ ⁠. In the service stage, the manufacturer builds its own industrial Internet platform to conduct intelligent service transformation, decides the level of service intelligence $i$ ⁠, provides product after-sales service for the user based on the industrial Internet platform, and decides the price of the service $P_{s}$ ⁠. In an intelligent platform environment, after-sales services can be remotely provided and guided, on-site services simplified, service efficiency improved, and service costs reduced. The framework of the basic model is shown in Figure 1. However, the construction of industrial Internet platform technology requires a large investment in capital, technology, human resources, and other resources. Given that industrial internet platforms are generally regarded as a key component of enterprises’ digital transformation strategies, they also constitute a long-term strategic investment for the enterprise. Accordingly, their operational costs are predominantly borne by platform developers—primarily manufacturers in the context of this study—while governmental entities may provide supplementary support through policy incentives and financial subsidies. For instance, although Haier Group’s COSMOPlat platform has received project-specific funding from local governments, the principal cost burden continues to fall on the platform developers. This will inevitably increase the cost burden of enterprises, in turn affecting pricing decisions and exacerbating the conflict of interest between supply chain nodes.

Figure 1

A diagram shows the basic supply chain model.

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The diagram shows the flow of products and information between a manufacturer, a retailer, an industrial internet platform, and a customer. A solid arrow connection is labeled “Forward sales supply chain.” A dashed arrow connection is labeled “Reverse after-sales service supply chain.” Three vertically arranged boxes are on the left. From top to bottom, the boxes are as follows: “Manufacturer,” “Retailer,” and “Customer.” A solid arrow labeled “W” from “Manufacturer” points to “Retailer.” Another solid arrow labeled “Uppercase P subscript Lowercase p” from “Retailer” points to “Customer.” A box labeled “Industrial Internet Platform” is positioned to the right of “Manufacturer.” “Industrial Internet Platform” points to “Customer” with the dashed arrow labeled “Uppercase P subscript s.” A dashed arrow from “Manufacturer” points to “Industrial Internet Platform.” Above this arrow, a larger arrow points to the text “R and D investment cost,” and “Unit cost of service” is noted.

Diagram of the basic model. Source(s): Authors’ own creation

When purchasing a product, customers consider not only the price of the product but also the quality of the after-sales service (e.g. service reliability and service responsiveness). With the changing consumer purchasing behavior, many consumers now place greater importance on after-sales service quality. As a result, companies typically commit to clear service standards (such as warranty, upgrade support, etc.). Consumers base their purchasing decisions on the brand’s commitments and past service records, which are transparently available. Therefore, consumers are able to make reasonable predictions about the quality of after-sales service. Similar demand function models have been employed in numerous studies, such as studies by Jamali and Rasti-Barzoki. We assume that the product demand function in the industrial Internet platform environment is $D_{p} = a - P_{p} + γ \overset{̅}{q}$ and that the product demand function in the traditional scenario (without service intelligence transformation based on the industrial Internet platform) is ${D_{p}}^{*} = a - P_{p} + γ q$ (Wu, 2017; Zhou et al., 2023). The potential demand for services is closely related to the quantity demanded of the product and is also affected by the price of the service $P_{s}$ and the level of intelligence of the service $i$ ⁠. The demand function for the service is assumed to be $D_{s} = D_{p} - b P_{s} + β i$ (Nie and Deng, 2014; Yi and Yao, 2016). As the level of service intelligence continues to rise, its integration into after-sales services has led to a substantial enhancement in user experience and customer satisfaction, thereby contributing to the sustained growth of service demand. Therefore, Service demand increases with the level of intelligence of the service $i$ ⁠. To better reflect real-world conditions and to ensure that the results of the numerical simulations more accurately capture practical dynamics, we assume that the parameter $β$ lies within the range of 0–1.4. The manufacturer’s costs primarily comprise two parts. The first part is the manufacturer-service intelligent transformation input cost, including the industrial Internet platform infrastructure cost and the platform of the R&D input cost composition, which belongs to the initial one-time investment of fixed costs and cannot be recovered without loss of generality, assumed to be zero. The R&D investment cost of the platform directly affects the level of service intelligence transformation, assuming that the manufacturer’s platform R&D investment cost and the level of service intelligence are in a quadratic relationship $k i^{2} / 2$ (Su et al., 2022). $i$ indicates the level of intelligence of the service. The second part is the manufacturer’s service cost, assuming that the manufacturer’s unit product service cost in an industrial Internet platform environment is $C_{s} (1 - ρ i)$ ⁠. $ρ$ represents the cost-saving factor, while $C_{s}$ denotes the initial unit cost of the service. The formula indicates that in the industrial internet platform environment, a higher level of service intelligence leads to a lower service cost, with the relationship between the two being mediated by the cost-saving coefficient.

The subscripts $m$ and $s$ represent manufacturers and sellers, respectively; superscripts $D$ ⁠, $C$ ⁠, $N D$ ⁠, and $N C$ denote decentralized decision-making in service-intelligent transformation, centralized decision-making in service-intelligent transformation, decentralized decision-making in the traditional scenario, and centralized decision-making in the traditional scenario; superscript $*$ denotes optimality, and profit is denoted by $π$ ⁠. In the traditional scenario, the manufacturer has not undergone service intelligence transformation, and the profit function is influenced solely by product demand and after-sales service. Following the transformation, the manufacturer invests in the development of an industrial internet platform, leading to a significant improvement in service quality, which in turn drives demand growth. This results in a profit function that differs from that in the traditional scenario.

Each parameter and its meaning in the problem description and model assumptions are listed in Table 2.

Table 2

Decision variables and parameters

Symbol	Description	Symbol	Description
$a$	Potential market size of the product	$i$	Service intelligence level
$C_{s}$	Unit cost of service	$W$	Product wholesale prices
$b$	Price sensitivity factor for services(⁠ $b > 1$ ⁠)^*	$P_{p}$	Product price
$ρ$	Cost-saving factor	$P_{s}$	Service price
$β$	Sensitivity of service intelligence level	$D_{p}$	Product demand
$k$	Cost factor of service intelligence transformation	$D_{s}$	Service demand, $D_{s} = D_{p} - b P_{s} + β i$
$γ$	Service quality sensitivity factor	$π_{m}$	Manufacturer profit
$q$	Initial quality of service	$π_{s}$	Seller profit
$\overset{̅}{q}$	Service quality after intelligent transformation of services based on industrial internet platforms	$π_{s c}$	Total supply chain system profit
$D_{p} = a - P_{p} + γ \overset{̅}{q}$	Product demand function in the industrial Internet platform environment	${D_{p}}^{*} = a - P_{p} + γ q$	Product demand function in the traditional scenario
$k i^{2} / 2$	Relationship between manufacturers’ platform R&D investment costs and the level of service intelligence	$C_{s} (1 - ρ i)$	the manufacturer’s unit product service cost in an industrial Internet platform environment

Symbol	Description	Symbol	Description
$a$	Potential market size of the product	$i$	Service intelligence level
$C_{s}$	Unit cost of service	$W$	Product wholesale prices
$b$	Price sensitivity factor for services( $b > 1$ )^*	$P_{p}$	Product price
$ρ$	Cost-saving factor	$P_{s}$	Service price
$β$	Sensitivity of service intelligence level	$D_{p}$	Product demand
$k$	Cost factor of service intelligence transformation	$D_{s}$	Service demand, $D_{s} = D_{p} - b P_{s} + β i$
$γ$	Service quality sensitivity factor	$π_{m}$	Manufacturer profit
$q$	Initial quality of service	$π_{s}$	Seller profit
$\overset{̅}{q}$	Service quality after intelligent transformation of services based on industrial internet platforms	$π_{s c}$	Total supply chain system profit
$D_{p} = a - P_{p} + γ \overset{̅}{q}$	Product demand function in the industrial Internet platform environment	${D_{p}}^{*} = a - P_{p} + γ q$	Product demand function in the traditional scenario
$k i^{2} / 2$	Relationship between manufacturers’ platform R&D investment costs and the level of service intelligence	$C_{s} (1 - ρ i)$	the manufacturer’s unit product service cost in an industrial Internet platform environment

Note(s): *Services are often regarded as value-added offerings provided after the sale of physical products. Consumer demand for such services typically exhibits high price elasticity. Empirical studies indicate that the price elasticity of demand for services tends to be greater than 1

Source(s): Authors’ own creation

4. Pricing and coordination decisions

Based on the model assumptions and parameter settings outlined earlier, this chapter develops the benchmark model (traditional scenario), decentralized decision-making model, and centralized decision-making model. A comparative analysis of the profits within the product-service supply chain is conducted under the benchmark, decentralized, and centralized decision-making models. Furthermore, a “cost-sharing-fixed transfer payment” contract is proposed to enhance the profitability of the product-service supply chain, offering guidance for manufacturing enterprises in their transition to service intelligence when establishing industrial internet platforms, particularly regarding product pricing, service pricing, and coordination.

In practical scenarios, decentralized decision-making typically arises when different parties in the supply chain operate independently. Each decision-maker aims to maximize their individual profit, and although information is shared, conflicts and strategic disagreements may emerge due to differing objectives. In contrast, centralized decision-making assumes that decision-makers align the objectives of all parties and collaborate to maximize overall profit, thereby preventing the conflicts and inefficiencies that may arise in decentralized systems. The distinction between these two decision-making structures reflects varying organizational frameworks within supply chains. While decentralized decision-making is more prevalent, centralized decision-making, as seen in vertically integrated or centrally managed supply chains, contributes to improved system efficiency.

4.1 Benchmark

To provide a benchmark for analyzing the impact of service intelligence transformation supported by industrial Internet platforms on the product-service supply chain, this paper first derives the decision-making outcomes of the product-service supply chain in a traditional scenario. The benchmark model represents a scenario without transformation, with the primary distinction from other scenarios being the inclusion of the industrial internet platform and its resulting impact on service intelligence transformation.

The profit functions for manufacturers and sellers in a traditional decentralized decision-making situation are as follows:

π_{m}^{N D} = W (a - P_{p} + γ q) + (P_{s} - C_{s}) (a - P_{p} + γ q - b P_{s})

π_{s}^{N D} = (P_{p} - W) (a - P_{p} + γ q)

The profit function of the product-service supply chain system under the traditional centralized decision-making situation is as follows:

π_{s c}^{N C} = P_{p} (a + γ q - P_{p}) + (P_{s} - C_{s}) (a + γ q - P_{p} - b P_{s})

The specific calculation procedure is similar to Proposition 1, and this section directly shows the equilibrium outcomes of the product-service supply chain under decentralized and centralized decision-making in the traditional case.

The equilibrium outcome under decentralized decision-making in the traditional case is derived using:

P_{p}^{N D *} = \frac{(6 γ q + C_{s} + 6 a) b - γ q - a}{8 b - 1}, W^{N D *} = \frac{(4 γ q + 2 C_{s} + 4 a) b - γ q - a}{8 b - 1}, P_{s}^{N D *} = \frac{(4 b - 1) C_{s} + γ q + a}{8 b - 1}, D_{p}^{N D *} = \frac{b (2 γ q - C_{s} + 2 a)}{8 b - 1}, D_{s}^{N D *} = \frac{b_{2} (- 4 C_{s} b + γ q + a)}{8 b - 1}, π_{m}^{N D *} = \frac{b (γ^{2} q^{2} + 2 (a - C_{s} / 2) q γ + 2 {C_{s}}^{2} b + a^{2} - C_{s} a)}{8 b - 1}, π_{s}^{N D *} = \frac{b^{2} {(- 2 γ q + C_{s} - 2 a)}^{2}}{{(8 b - 1)}^{2}} 。

The equilibrium result under centralized decision-making in the traditional case is derived using:

P_{p}^{N C *} = \frac{(2 b - 1) (γ q + a) + C_{s} b}{4 b - 1}, P_{s}^{N C *} = \frac{(2 b - 1) C_{s} + γ q + a}{4 b - 1}, D_{p}^{N C *} = \frac{(2 γ q - C_{s} + 2 a) b}{4 b - 1}, D_{s}^{N C *} = \frac{b (- 2 C_{s} b + γ q + a)}{4 b - 1}, π_{s c}^{N C *} = \frac{2 {C_{s}}^{2} b^{2} + 2 (γ q - C_{s} + a) (γ q + a) b}{8 b - 2} 。

Corollary 1.

The impacts of the service quality sensitivity coefficient, service quality level, and service cost on the manufacturer’s profit and the supply chain system profit in the traditional scenario postulates. Detailed proof is provided in Appendix (Proof of Corollary 1):

$\frac{\partial π_{m}^{N D *}}{\partial γ} > 0$ ⁠, $\frac{\partial π_{m}^{N D *}}{\partial q} > 0$ ⁠, $\frac{\partial π_{m}^{N D *}}{\partial C_{s}} < 0$ ⁠;
$\frac{\partial π_{s c}^{N D *}}{\partial γ} > 0$ ⁠, $\frac{\partial π_{s c}^{N D *}}{\partial q} > 0$ ⁠, $\frac{\partial π_{s c}^{N D *}}{\partial C_{s}} < 0$

Corollary 1 shows that in the traditional situation, the manufacturer’s profit and the total profit of the supply chain system are positively related to the service quality sensitivity coefficient and service quality level and negatively related to the unit service cost. When the user is more sensitive to service quality and the service quality level is higher, the manufacturer’s profit and supply chain system profit increase, whereas when the unit service cost increases, the manufacturer’s profit and supply chain system profit decrease. As the leader of the supply chain system and the provider of services, manufacturers must make use of big data, AI, cloud computing, and other technologies to conduct the digitalization and intelligent transformation of enterprise products and services, reduce the cost of enterprise products and services, improve the efficiency of services, and satisfy users’ demand for high value-added intelligent services.

4.2 Decentralized decision-making

In this product-service supply chain, the manufacturer and seller form a master-slave game model, where both parties are risk-neutral and fully rational, all the information of both parties is common knowledge, and both parties make decisions based on the principle of maximizing their respective profits. First, the manufacturer decides on the level of service intelligence, wholesale price of the product, and price of the service; then, the seller sets the price of the product according to the manufacturer’s decision, as demonstrated in the equation below:

π_{m} = W (a - P_{p} + γ \overset{̅}{q}) + (P_{s} - C_{s} (1 - ρ i)) (a - P_{p} + γ \overset{̅}{q} - b P_{s} + β i) - \frac{k i^{2}}{2}

π_{s} = (P_{p} - W) (a - P_{p} + γ \overset{̅}{q})

Proposition 1.

The optimal decision of a product-service supply chain under decentralized decision-making is as follows. Detailed proof is provided in Appendix (Proof of Proposition 1):

The manufacturers’ service prices, wholesale product prices, and service intelligence levels are as follows:

P_{s}^{D *} = \frac{(4 b k - 4 β^{2} - k) C_{s} + (k - C_{s} β ρ + {C_{s}}^{2} b ρ^{2}) (γ \overset{̅}{q} + a) - 4 {C_{s}}^{2} b ρ β}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + 2 C_{s} b β ρ - 2 b k + β^{2} + k / 4)}

W^{*} = \frac{(- {C_{s}}^{2} ρ^{2} b + k - C_{s} ρ β) (γ \overset{̅}{q} + a) + C_{s} (4 k b - 4 β^{2} - k) - 4 {C_{s}}^{2} ρ β b}{- 4 {C_{s}}^{2} b^{2} ρ^{2} - 8 C_{s} ρ β b + 8 b_{2} k - 4 β^{2} - k}

i^{D *} = \frac{(C_{s} ρ b + β) (γ \overset{̅}{q} + a - 4 C_{s} b)}{- 4 {C_{s}}^{2} b^{2} ρ^{2} + (- 8 C_{s} ρ β + 8 k) b - 4 β^{2} - k}

The price of the seller’s product is derived using:

P_{p}^{D *} = \frac{(C_{s} k + (6 k - 6 C_{s} ρ β) (γ \overset{̅}{q} + a)) b - (3 β^{2} + k + 3 ρ^{2} {C_{s}}^{2} b^{2}) (γ \overset{̅}{q} + a)}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + (8 C_{s} ρ β - 8 k) b + β^{2} + k / 4)}

Product and service demands are as follows:

D_{p}^{D *} = \frac{(2 k b - 2 C_{s} β ρ b - {C_{s}}^{2} b^{2} ρ^{2} - β^{2}) (γ \overset{̅}{q} + a) - C_{s} k b}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + (2 C_{s} ρ β - 2 k) b + β^{2} + k / 4)}

D_{s}^{D *} = \frac{b k (- 4 C_{s} b + γ \overset{̅}{q} + a)}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + (2 C_{s} ρ β - 2 k) b + β^{2} + k / 4)}

The manufacturer’s, seller’s, and total profits in the product-service supply chain system are as follows:

π_{m}^{D *} = \frac{4 {C_{s}}^{2} b^{2} k + 2 C_{s} k b (γ \overset{̅}{q} + a) - (2 b (k + C_{s} β ρ) + {C_{s}}^{2} b^{2} ρ^{2} + β^{2}) {(γ \overset{̅}{q} + a)}^{2}}{- 8 ({C_{s}}^{2} b^{2} ρ^{2} + (2 C_{s} ρ β - 2 k) b + β^{2} + k / 4)}

π_{s}^{D *} = \frac{{((2 k b - 2 C_{s} β ρ b - {C_{s}}^{2} b^{2} ρ^{2} - β^{2}) (γ \overset{̅}{q} + a) - C_{s} k b)}^{2}}{16 {({C_{s}}^{2} b^{2} ρ^{2} + 2 C_{s} b β ρ - 2 b k + β^{2} + k / 4)}^{2}}

\begin{array}{l} π_{s c}^{D *} = π_{s}^{D *} + π_{m}^{D *} = \frac{{((2 k b - 2 C_{s} β ρ b - {C_{s}}^{2} b^{2} ρ^{2} - β^{2}) (γ \overset{̅}{q} + a) - C_{s} k b)}^{2}}{16 {({C_{s}}^{2} b^{2} ρ^{2} + 2 C_{s} b β ρ - 2 b k + β^{2} + k / 4)}^{2}} \\ + \frac{4 {C_{s}}^{2} b^{2} k + 2 C_{s} k b (γ \overset{̅}{q} + a) - (2 b (k + C_{s} β ρ) + {C_{s}}^{2} b^{2} ρ^{2} + β^{2}) {(γ \overset{̅}{q} + a)}^{2}}{- 8 ({C_{s}}^{2} b^{2} ρ^{2} + (2 C_{s} ρ β - 2 k) b + β^{2} + k / 4)} \end{array}

4.3 Centralized decision-making

To achieve system profit maximization, the centralized decision-making model regards the manufacturer and seller as a unified whole. The profit function of the product-service supply chain system under centralized decision-making is as follows:

π_{s c} = P_{p} (a + γ \overset{̅}{q} - P_{p}) + (P_{s} - C_{s} (1 - ρ i)) (a + γ \overset{̅}{q} - P_{p} - b P_{s} + β i) - \frac{k i^{2}}{2}

Proposition 2.

The optimal decision of a product-service supply chain under centralized decision-making is as follows. Detailed proof is provided in Appendix (Proof of Proposition 2):

Product prices, service prices, and service intelligence levels are as follows:

P_{p}^{C *} = \frac{(C_{s} k + (2 k - 2 C_{s} ρ β) (γ \overset{̅}{q} + a)) b - (β^{2} + k + {C_{s}}^{2} b^{2} ρ^{2}) (γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} ρ^{2} b^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}

P_{s}^{C *} = \frac{- 2 {C_{s}}^{2} b β ρ + (2 b k - 2 β^{2} - k) C_{s} + (- {C_{s}}^{2} ρ^{2} b - C_{s} ρ β + k) (γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} - 4 C_{s} b β ρ + 4 b k - 2 β^{2} - k}

i^{C *} = \frac{(C_{s} ρ b + β) (- 2 C_{s} b + γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}

The demand for products and services is as follows:

D_{p}^{C *} = \frac{(- {C_{s}}^{2} b^{2} ρ^{2} - 2 C_{s} ρ β b + 2 k b - β^{2}) (γ \overset{̅}{q} + a) - C_{s} b k}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}

D_{s}^{C *} = \frac{b k (- 2 C_{s} b + γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}

The total profit of the product-service supply chain system is as follows:

π_{s c}^{C *} = \frac{(- {C_{s}}^{2} b^{2} ρ^{2} + 2 (- C_{s} ρ β b + k b) - β^{2}) {(γ \overset{̅}{q} + a)}^{2} - 2 C_{s} b k (γ \overset{̅}{q} + a) + 2 {C_{s}}^{2} b^{2} k}{- 4 {C_{s}}^{2} b^{2} ρ^{2} + (- 8 C_{s} ρ β + 8 k) b - 4 β^{2} - 2 k}

4.4 Model analysis

4.4.1 Comparison of equalization results

Table 3 presents a comparative analysis of pricing strategies, market demand, and profit margins under centralized and decentralized decision-making systems, implemented through a proprietary Industrial Internet platform developed by the manufacturer.

Table 3

Equilibrium outcomes for a product-service supply chain under a manufacturer’s own industrial internet platform

	Decentralized decision-making	Centralized decision-making
$P_{s}^{D *}$	$\frac{(4 b k - 4 β^{2} - k) C_{s} + (k - C_{s} β ρ + {C_{s}}^{2} b ρ^{2}) (γ \overset{̅}{q} + a) - 4 {C_{s}}^{2} b ρ β}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + 2 C_{s} b β ρ - 2 b k + β^{2} + k / 4)}$	$\frac{- 2 {C_{s}}^{2} b β ρ + (2 b k - 2 β^{2} - k) C_{s} + (- {C_{s}}^{2} ρ^{2} b - C_{s} ρ β + k) (γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} - 4 C_{s} b β ρ + 4 b k - 2 β^{2} - k}$
$W^{*}$	$\frac{(- {C_{s}}^{2} ρ^{2} b + k - C_{s} ρ β) (γ \overset{̅}{q} + a) + C_{s} (4 k b - 4 β^{2} - k) - 4 {C_{s}}^{2} ρ β b}{- 4 {C_{s}}^{2} b^{2} ρ^{2} - 8 C_{s} ρ β b + 8 b_{2} k - 4 β^{2} - k}$	__
$i^{D *}$	$\frac{(C_{s} ρ b + β) (γ \overset{̅}{q} + a - 4 C_{s} b)}{- 4 {C_{s}}^{2} b^{2} ρ^{2} + (- 8 C_{s} ρ β + 8 k) b - 4 β^{2} - k}$	$\frac{(C_{s} ρ b + β) (- 2 C_{s} b + γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}$
$P_{p}^{D *}$	$\frac{(C_{s} k + (6 k - 6 C_{s} ρ β) (γ \overset{̅}{q} + a)) b - (3 β^{2} + k + 3 ρ^{2} {C_{s}}^{2} b^{2}) (γ \overset{̅}{q} + a)}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + (8 C_{s} ρ β - 8 k) b + β^{2} + k / 4)}$	$\frac{(C_{s} k + (2 k - 2 C_{s} ρ β) (γ \overset{̅}{q} + a)) b - (β^{2} + k + {C_{s}}^{2} b^{2} ρ^{2}) (γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} ρ^{2} b^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}$
$D_{p}^{D *}$	$\frac{(2 k b - 2 C_{s} β ρ b - {C_{s}}^{2} b^{2} ρ^{2} - β^{2}) (γ \overset{̅}{q} + a) - C_{s} k b}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + (2 C_{s} ρ β - 2 k) b + β^{2} + k / 4)}$	$\frac{(- {C_{s}}^{2} b^{2} ρ^{2} - 2 C_{s} ρ β b + 2 k b - β^{2}) (γ \overset{̅}{q} + a) - C_{s} b k}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}$
$D_{s}^{D *}$	$\frac{b k (- 4 C_{s} b + γ \overset{̅}{q} + a)}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + (2 C_{s} ρ β - 2 k) b + β^{2} + k / 4)}$	$\frac{b k (- 2 C_{s} b + γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}$
$π_{m}^{D *}$	$\frac{4 {C_{s}}^{2} b^{2} k + 2 C_{s} k b (γ \overset{̅}{q} + a) - (2 b (k + C_{s} β ρ) + {C_{s}}^{2} b^{2} ρ^{2} + β^{2}) {(γ \overset{̅}{q} + a)}^{2}}{- 8 ({C_{s}}^{2} b^{2} ρ^{2} + (2 C_{s} ρ β - 2 k) b + β^{2} + k / 4)}$	__
$π_{s}^{D *}$	$\frac{{((2 k b - 2 C_{s} β ρ b - {C_{s}}^{2} b^{2} ρ^{2} - β^{2}) (γ \overset{̅}{q} + a) - C_{s} k b)}^{2}}{16 {({C_{s}}^{2} b^{2} ρ^{2} + 2 C_{s} b β ρ - 2 b k + β^{2} + k / 4)}^{2}}$	__
$π_{s c}^{D *}$	$π_{s}^{D } + π_{m}^{D }$	$\frac{(- {C_{s}}^{2} b^{2} ρ^{2} + 2 (- C_{s} ρ β b + k b) - β^{2}) {(γ \overset{̅}{q} + a)}^{2} - 2 C_{s} b k (γ \overset{̅}{q} + a) + 2 {C_{s}}^{2} b^{2} k}{- 4 {C_{s}}^{2} b^{2} ρ^{2} + (- 8 C_{s} ρ β + 8 k) b - 4 β^{2} - 2 k}$

Source(s): Authors’ own creation

Proposition 3.

Decentralized decision-making, compared to centralized decision-making, has the following conclusions. Detailed proof is provided in Appendix (Proof of Proposition 3):

$P_{p}^{D *} > P_{p}^{C *}$ ⁠;
$i^{D *} < i^{C *}$ ⁠, $P_{s}^{D *} < P_{s}^{C *}$ ⁠;
$D_{p}^{D *} < D_{p}^{C *}$ ⁠, $D_{s}^{D *} < D_{s}^{C *}$ ⁠, $π_{s c}^{D *} < π_{s c}^{C *}$

Proposition 3 (1) shows that product prices under decentralized decision-making are higher than those under centralized decision-making. This is because, under centralized decision-making, the manufacturer and seller are in a cooperative relationship; when the supply chain system is a whole, while under decentralized decision-making, the manufacturer and seller make decisions independently based on the principle of maximizing their own profits, and the seller will set a higher price for the product.

Proposition 3 (2) shows that both the level of service intelligence and service price under centralized decision-making are higher than those under decentralized decision-making. Under the guidance of the concept of win-win cooperation, the level of service intelligence under centralized decision-making is higher than that under decentralized decision-making. The higher the level of service intelligence, the greater the degree of service cost savings; however, a higher level of service intelligence also means investing more in service intelligence transformation costs. Therefore, although a higher service intelligence level under centralized decision-making saves more on service costs, the saved service costs are not enough to make up for the invested service intelligence transformation costs. To ensure that their own profits are not harmed, the manufacturers will increase the service prices under centralized decision-making.

Proposition 3 (3) shows that product demand, service demand, and total profit of the supply chain system under decentralized decision-making are smaller than those under centralized decision-making. Because product demand is negatively affected by product price, a higher product price under decentralized decision-making makes product demand under decentralized decision-making smaller than under centralized decision-making. From the expression of service demand, it can be seen that, on the one hand, the lower service price will increase the service demand; on the other hand, the higher product demand and service intelligence level will promote the service demand; on the other hand, due to the larger service demand under centralized decision-making, it can be deduced that the inhibitory effect of the higher service price on service demand is smaller than the promotional effect of the level of service intelligence, and the product needs to increase the demand on service demand, which leads to centralized decision-making under the increase in demand for services.

4.4.2 Sensitivity analysis

Corollary 2.

Impact of cost-saving factors on product prices, service prices, wholesale product prices, product demand, and service demand postulates. Detailed proof is provided in Appendix (Proof of Corollary 2):

Decentralized decision-making model: $\frac{\partial P_{p}^{D *}}{\partial ρ} < 0$ ⁠; $\frac{\partial W^{*}}{\partial ρ} < 0$ ⁠; $\frac{\partial D_{p}^{D *}}{\partial ρ} > 0$ ⁠; $\frac{\partial D_{s}^{D *}}{\partial ρ} > 0$ ⁠; When the condition $k > \frac{2 β^{2} (b - 1 / 8)}{{(b - 1 / 4)}^{2}}$ is satisfied: when $ρ \in (0, ρ_{0}^{D *})$ ⁠, $\frac{\partial P_{s}^{D *}}{\partial ρ} > 0$ ⁠, $ρ \in (ρ_{0}^{D *}, 1)$ ⁠, $\frac{\partial P_{s}^{D *}}{\partial ρ} < 0$ ⁠; When the condition $k \leq \frac{2 β^{2} (b - 1 / 8)}{{(b - 1 / 4)}^{2}}$ , no feasible solution was found within the specified range, making data analysis in this domain impractical.

Centralized decision-making model: $\frac{\partial P_{p}^{C *}}{\partial ρ} < 0$ ⁠; $\frac{\partial D_{p}^{C *}}{\partial ρ} > 0$ ⁠; $\frac{\partial D_{s}^{C *}}{\partial ρ} > 0$ ⁠; When the condition $k > \frac{2 (4 b - 1) β^{2}}{{(2 b - 1)}^{2}}$ is satisfied: when $ρ \in (0, ρ_{0}^{C})$ ⁠, $\frac{\partial P_{s}^{C *}}{\partial ρ} > 0$ ⁠, $ρ \in (ρ_{0}^{C}, 1)$ ⁠, $\frac{\partial P_{s}^{C *}}{\partial ρ} < 0$ ⁠; When $k \leq \frac{2 (4 b - 1) β^{2}}{{(2 b - 1)}^{2}}$ ⁠, no feasible solution exists under the current settings, so analyzing data in this range is not meaningful.

Corollary 2 shows that as the cost-saving coefficient increases, the product price decreases, the service price increases and then decreases, and the product demand and service demand increase under both decentralized and centralized decision-making. This may be because as the cost-saving coefficient increases, the unit product service cost decreases, and the profit margin of the service increases. To promote the sale of services, the manufacturer reduces the product wholesaler, seller, and thus the product price. In addition, due to the enterprise’s self-built platform for intelligent service transformation, the manufacturer invests in a certain cost: when the cost-saving coefficient is small, the manufacturer will increase the price of services, and when the service cost-saving coefficient is larger, the manufacturer will reduce the price of services.

Corollary 3.

Analysis of the impact of service intelligence sensitivity on product prices, service prices, wholesale product prices, product demand, and service demand postulates. Detailed proof is provided in Appendix (Proof of Corollary 3):

Decentralized decision-making model: $\frac{\partial P_{p}^{D *}}{\partial β} < 0$ ⁠; $\frac{\partial W^{*}}{\partial β} < 0$ ⁠; $\frac{\partial D_{p}^{D *}}{\partial β} > 0$ ⁠; $\frac{\partial D_{s}^{D *}}{\partial β} > 0$ ⁠; When the condition $k > 4 C_{s}^{2} ρ^{2} b^{2}$ ⁠, $\frac{\partial P_{s}^{D *}}{\partial β} > 0$ ⁠; When the condition $k \leq 4 C_{s}^{2} ρ^{2} b^{2}$ ⁠, $\frac{\partial P_{s}^{D *}}{\partial β}$ lacks a well-defined solution, therefore its analysis yields no substantive value.

Centralized decision-making model: $\frac{\partial P_{p}^{C *}}{\partial β} < 0$ ⁠; $\frac{\partial P_{s}^{C *}}{\partial β} > 0$ ⁠; $\frac{\partial D_{p}^{C *}}{\partial β} > 0$ ⁠; $\frac{\partial D_{s}^{C *}}{\partial β} > 0$ ⁠; When the condition $k > 2 {C_{s}}^{2} b^{2} ρ^{2}$ ⁠, $\frac{\partial P_{s}^{C *}}{\partial β} > 0$ ⁠; When the condition $k \leq 2 {C_{s}}^{2} b^{2} ρ^{2}$ ⁠, $\frac{\partial P_{s}^{C *}}{\partial β}$ lacks a well-defined solution, therefore its analysis yields no substantive value.

Corollary 3 shows that whether it is a decentralized decision-making mode or centralized decision-making mode, as the sensitivity of the service intelligence level increases, the product price decreases, and the product demand and service demand increase. Under certain conditions, the service price increases with the enhancement of the sensitivity of the service intelligence level, which indicates that when the user’s sensitivity to the service intelligence level increases and they prefer intelligent services, the manufacturer will gradually shift from a product-to service-centered model. The seller will also reduce the product price by reducing the price of the product, promoting product sales, and expanding the service market share. To obtain more profits, the manufacturer will increase the price of the service.

Corollary 4.

Analysis of the influence of the cost-saving coefficient and service intelligence level sensitivity on the service intelligence level postulates. Detailed proof is provided in Appendix (Proof of Corollary 4):

\frac{\partial i^{* D}}{\partial ρ} > 0; \frac{\partial i^{* D}}{\partial β} > 0; \frac{\partial i^{* C}}{\partial ρ} > 0; \frac{\partial i^{* C}}{\partial β} > 0

Corollary 4 shows that the level of service intelligence increases with the increase in the cost-saving coefficient and the sensitivity of the level of service intelligence, regardless of whether it is under decentralized decision-making or centralized decision-making, indicating that the greater the service cost savings when a manufacturer builds its own industrial Internet platform for service intelligence transformation, the more motivated the manufacturer will be to conduct the service intelligence transformation. Moreover, when the customer’s demand for intelligent services is enhanced, to satisfy the consumers’ demand, the manufacturer will actively seek to transform itself intelligently and improve the level of service intelligence.

Corollary 5.

Analysis of the profitability of the cost-saving factor and sensitivity of the service intelligence level postulates. Detailed proof is provided in Appendix (Proof of Corollary 5):

\frac{\partial π_{m}^{D *}}{\partial ρ} > 0; \frac{\partial π_{s}^{D *}}{\partial ρ} > 0; \frac{\partial π_{s c}^{D *}}{\partial ρ} > 0; \frac{\partial π_{m}^{D *}}{\partial β} > 0; \frac{\partial π_{s}^{D *}}{\partial β} > 0; \frac{\partial π_{s c}^{D *}}{\partial β} > 0; \frac{\partial π_{s c}^{C *}}{\partial ρ} > 0; \frac{\partial π_{s c}^{C *}}{\partial β} > 0

Corollary 5 shows that manufacturers, sellers, and supply chain systems can all profit more as the cost-saving factor and sensitivity of the service-intelligence level increase. This also inspires enterprises to actively use technical tools such as big data, AI, and the industrial Internet and conduct digital and intelligent transformation according to the characteristics of the industry, the strengths and weaknesses of their own development, and the need for business development. Especially in industries where the cost of services is relatively large and customers have higher requirements for the level of service intelligence, enterprises should seek intelligent transformation as much as possible to meet the personalized and intelligent needs of customers while earning more profits from products and services for themselves and improving the differentiated competitiveness of enterprises.

4.5 Supply chain coordination

The previous section showed that manufacturers build their own industrial Internet platform to conduct intelligent transformation of services to promote the sale of products and reduce the wholesale price of products, so that the seller’s profit increases and the seller has a certain “free-rider” behavior. Therefore, as the leader of the supply chain, manufacturers should design a reasonable and effective contract mechanism to realize the coordination of the product and service supply chain. Based on this, this section designs a “fixed payment-cost sharing” contract to improve supply chain efficiency. The meaning of a “fixed transfer-cost-sharing” contract is: The manufacturer gives the seller a certain fixed transfer payment $f$ to incentivize the seller to sell the product and reduce the price of the product, while the seller bears a $θ$ proportion of the manufacturer’s service intelligence transformation cost to incentivize the manufacturer to improve service intelligence. There is no constraint on the positivity or negativity of $f$ ⁠. When $f < 0$ ⁠, it can be interpreted as the manufacturer charging the retailer a fixed fee. The superscript $X$ denotes the model under the “cost-sharing-fixed transfer” contract.

Under the “cost-sharing-fixed transfer” contract, the profit function of the manufacturer and the seller are as follows:

π_{m}^{X} = W (a + γ \overset{̅}{q} - P_{p}) + (P_{s} - C_{s} (1 - ρ i)) (a + γ \overset{̅}{q} - P_{p} - b P_{s} + β i) - \frac{(1 - θ) k i^{2}}{2} - f

π_{s}^{X} = (P_{p} - W) (a + γ \overset{̅}{q} - P_{p}) - \frac{θ k i^{2}}{2} + f

The solution steps are similar to those of decentralized decision-making. The optimal wholesale product price, product price, service price, optimal service intelligence level, manufacturer profit, and seller profit under the coordination contract are as follows:

W^{X *} = \frac{(2 {C_{s}}^{2} b^{2} ρ^{2} A + (4 (A + C_{s} / 2) (- 1 + θ) k + 4 ρ C_{s} β A) b - A ((- 1 + θ) k - 2 β^{2}))}{4 {C_{s}}^{2} b^{2} ρ^{2} + ((8 θ - 8) k + 8 ρ C_{s} β) b + (1 - θ) k + 4 β^{2}}

P_{s}^{X *} = \frac{{C_{s}}^{2} ρ b (A ρ + 4 β) + ((4 b - 1) (θ - 1) k + (A ρ + 4 β) β) C_{s} + k (- 1 + θ) A}{4 {C_{s}}^{2} b^{2} ρ^{2} + 8 C_{s} b β ρ + ((8 b - 1) (θ - 1)) k + 4 β^{2}}

i^{X *} = \frac{(ρ C_{s} b + β) (- 4 C_{s} b + A)}{- 4 {C_{s}}^{2} b^{2} ρ^{2} - (8 ρ C_{s} β + 8 (- 1 + θ) k) b - 4 β^{2} + (- 1 + θ) k}

D_{p}^{X *} = \frac{({C_{s}}^{2} b^{2} ρ^{2} A + (2 (- 1 + θ) (A - C_{s} / 2) k + 2 ρ C_{s} β A) b + A β^{2})}{4 {C_{s}}^{2} b^{2} ρ^{2} + ((8 θ - 8) k + 8 ρ C_{s} β) b + (1 - θ) k + 4 β^{2}}

D_{s}^{X *} = \frac{b k (- 1 + θ) (- 4 C_{s} b + A)}{4 {C_{s}}^{2} b^{2} ρ^{2} + (8 ρ C_{s} β + 8 k θ - 8 k) b - k θ + 4 β^{2} + k}

π_{m}^{X *} = \frac{{C_{s}}^{2} b^{2} (4 (- 1 + θ) k + ρ^{2} A^{2}) + 2 ((- 1 + θ) (A - C_{s}) k + ρ C_{s} β A) A b + β^{2} A^{2}}{8 {C_{s}}^{2} b^{2} ρ^{2} + (16 (- 1 + θ) k + 16 ρ C_{s} β) b + 2 (1 - θ) k + 8 β^{2}} - f

\begin{array}{l} π_{s}^{X *} = \frac{{({C_{s}}^{2} b^{2} ρ^{2} A + ((- 1 + θ) (2 A - C_{s}) k + 2 ρ C_{s} β A) b + A β^{2})}^{2}}{{(4 {C_{s}}^{2} b^{2} ρ^{2} + 8 b ((- 1 + θ) k + ρ C_{s} β) + (1 - θ) k + 4 β^{2})}^{2}} \\ - \frac{θ k {(ρ C_{s} b + β)}^{2} {(- 4 C_{s} b + A)}^{2}}{2 {((- 1 + θ) (8 b - 1) k + 4 {(ρ C_{s} b + β)}^{2})}^{2}} + f \end{array}

Notes: $A = a + γ \overset{̅}{q}$ ⁠.

First, this contract is valid and ensures that the total profit of the supply chain system increases after the implementation of the optimization contract.

π_{m}^{X *} + π_{s}^{X *} > π_{m}^{D *} + π_{s}^{D *}

Second, owing to the existence of individual rationality, the manufacturer and seller are willing to cooperate in the implementation of this contract only if the post-contractual profit is not less than the pre-contractual profit, which must be guaranteed.

π_{m}^{X *} > π_{m}^{D *}

π_{s}^{X *} > π_{s}^{D *}

Given the complexity of the profit functions of the manufacturer and seller under this contract, it is difficult to directly find the specific analytical intervals of $θ$ and $f$ ⁠. Therefore, the relevant conclusions are solved and analyzed through the method of arithmetic example analysis (Dan et al., 2017a, b), and the specific procedure is described in Section 5.4.

5. Numerical analysis

According to the model assumptions, the parameters $ρ$ ⁠, $β$ ⁠, and $γ$ are all greater than 0, and $b > 1$ ⁠. To ensure that the manufacturers and sellers have positive profits and there is an optimal solution for the model, the values of each parameter need to satisfy the condition $2 C_{s} b β ρ - 2 b k + {C_{s}}^{2} b^{2} ρ^{2} + β^{2} + k < 0$ ⁠, $C_{s} β ρ + {C_{s}}^{2} ρ^{2} b - k < 0$ ⁠, and $γ \overset{̅}{q} + a - 4 C_{s} b > 0$ ⁠. According to the relevant information on the websites of industrial Internet platforms, such as Khaos and RootsCloud, as well as the reference to relevant literature (Kou et al., 2020; Zhang and Wei, 2021), without loss of generality, it is assumed that the parameter values are taken as follows: $a = 100$ ⁠, $b = 1.2$ ⁠, $C_{s} = 2$ ⁠, $γ = 0.6$ ⁠, $β = 0.49$ ⁠, $ρ = 0.5$ ⁠, $k = 6$ ⁠, $q = 3$ ⁠, $\overset{̅}{q} = 3.9$ ⁠.

5.1 Profit comparison of transformation

As the analytical formula is too complicated to compare the results of decentralized and centralized decision-making in the traditional situation with those after intelligent service transformation based on the industrial Internet platform through mathematical derivation, in this section, we compare the profits of the supply chain system and the profits of supply chain node enterprises before and after intelligent service transformation using arithmetic analysis and derive the significance and value of intelligent service transformation based on the industrial Internet platform. In order to ensure that the manufacturer and seller profits are positive and that there exists an optimal solution to the model, $ρ > 0$ ⁠, $β > 0$ ⁠, $γ > 0$ and $b > 1$ ⁠.

Figures 2 and 3 demonstrate the changes in the manufacturer’s, seller’s, and supply chain system’s profit margins with the cost-saving factor and the sensitivity of the level of service intelligence before and after the transformation of service intelligence.

Figure 2

Two graphs (a) and (b) illustrate the impact of the cost-saving factor on profit margins.

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The horizontal for both graphs is labeled “rho” and ranges from 0 to 1 in increments of 0.2 units. (a): Profit difference in supply chain system: The vertical axis is labeled “delta pi subscript S C” and ranges from 0 to 1800 in increments of 200 units. It shows two curves. A solid red curve is labeled “delta pi superscript C subscript S C minus delta pi superscript N C subscript S C. This curve starts near zero and rises at an accelerating rate as rho increases, ending with a value over 1750 at rho equals 1. A dashed blue line is labeled ”delta pi superscript D subscript S C minus pi superscript N D subscript S C.“ This curve also starts near zero and rises, but it is consistently below the red curve, reaching a value of approximately 580 at rho equals 1. (b): Profit difference in node enterprises: The vertical axis is labeled ”delta pi subscript m minus delta pi subscript s“ and ranges from 0 to 350 in increments of 50 units. It shows two curves. A dashed blue line is labeled ”delta pi superscript D subscript m.“ This curve starts near zero and rises at an accelerating rate as rho increases, ending with a value of approximately 315 at rho equals 1. A dotted blue line is labeled ”delta pi superscript D subscript s.“ This curve is nearly identical to the manufacturer‘s curve, starting near zero and rising to a value just below 250 at rho equals 1. The two curves almost overlap completely across the entire range of rho. Note: All numerical values are approximated.

Impact of cost-saving factor on profit margin before and after service intelligent transformation. Source(s): Authors’ own creation

Figure 3

Two graphs (a) and (b) illustrate the impact of service intelligence level sensitivity on profit difference.

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The horizontal for both graphs is labeled “beta” and ranges from 0 to 1.4 in increments of 0.2 units. (a): Profit difference in supply chain system: The vertical axis is labeled “delta pi subscript S C” and ranges from 0 to 1600 in increments of 200 units. It shows two curves. A Solid red curve is labeled “delta pi superscript C subscript S C minus delta pi superscript N C subscript S C. This curve starts near 200 and rises at an accelerating rate as beta increases, ending with a value over 1550 at beta equals 1. A dashed blue line is labeled ”delta pi superscript D subscript S C minus pi superscript N D subscript S C.“ This curve starts near 80 and rises, but it is consistently below the red curve, reaching a value of approximately 500 at rho equals 1. (b): Profit difference in node enterprises: The vertical axis is labeled ”delta pi subscript m minus delta pi subscript s“ and ranges from 0 to 300 in increments of 50 units. It shows two curves. A dashed blue line is labeled ”delta pi superscript D subscript m.“ This curve starts near 35 and rises at an accelerating rate as beta increases, ending with a value of approximately 275 at beta equals 1. A dotted blue line is labeled ”delta pi superscript D subscript s.“ This curve is nearly identical to the manufacturer‘s curve, starting near 34 and rising to a value of 225 at beta equals 1. The two curves almost overlap completely across the range of rho between 0 and 0.6. Note: All numerical values are approximated.

Impact of service intelligence level sensitivity on profit difference before and after service intelligence transformation. Source(s): Authors’ own creation

Before and after service intelligence transformation, the profit differences of the supply chain system, manufacturer, and seller are all positive, indicating that it is beneficial for the manufacturer to build its own industrial Internet platform for service intelligence transformation. This not only improves the manufacturer’s own profit but also the profits of other members in the supply chain system. In addition, under the premise that the cost-saving coefficient and sensitivity of the service-intelligence level are the same, the seller’s profit difference is larger than that of the manufacturer. This is because when the manufacturer builds its own platform to conduct service intelligent transformation, it bears all the costs alone, whereas the seller only needs to make a capital investment.
Figures 2a and 3a show that the profit difference between the supply chain system before and after the service intelligence transformation gradually expands, indicating that when the customer’s demand for the level of service intelligence increases or the effect of the service intelligence transformation on the improvement of service cost improves, the manufacturer achieves a more significant effect on the service intelligence transformation based on the industrial Internet platform, which leads to a more obvious increase in the profit of the supply chain system.
Figures 2b and 3b reveal that, as the cost-saving coefficient and sensitivity of the service intelligence level increase, the manufacturer’s profit difference and the seller’s profit difference before and after the transformation of service intelligence show an increasing trend. Second, when the cost-saving coefficient or service intelligence level sensitivity is less than a certain threshold, the value of the manufacturer’s profit growth exceeds that of the seller. This indicates that when the user is less sensitive to the level of service intelligence or the service cost saved by the service intelligence transformation for the manufacturer is low, the manufacturer’s level of service intelligence and the cost investment are low, which leads to a manufacturer’s profit growth value being greater than the seller’s profit growth value. When the cost-saving coefficient or sensitivity of the service intelligence level exceeds a certain threshold, the seller’s profit growth value exceeds that of the manufacturer. Hence, when users are more sensitive to the level of service intelligence, or when the service cost saved by service intelligence transformation is higher for manufacturers, they will actively conduct service intelligence transformation to improve the level of service intelligence, and thus increase the sales of their products and services. However, this also means that manufacturers need to undertake higher costs, which strengthens the “free-riding” behavior of sellers, resulting in the profit growth value of manufacturers being smaller than that of sellers. Therefore, to promote long-term cooperation among supply chain members, sellers should take the initiative to assist manufacturers in building industrial Internet platforms, bear certain intelligent service transformation costs, and reduce the financial pressure on manufacturers. Simultaneously, as the dominant player in the supply chain, manufacturers should design an effective coordination contract mechanism to avoid damaging their earnings.

5.2 Impact of cost-saving factors

Figures 4 and 5 show the impact of the cost-savings factor on product and service prices under the decentralized and centralized decision-making models, revealing that product prices decrease as the cost-savings factor increases, and service prices increase and then decrease as the cost-savings factor increases under the two decision-making models, an observation that is consistent with Corollary 2.

Figure 4

A graph shows the impact of product price on the cost-saving factor.

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The horizontal axis is labeled “rho” and ranges from 0 to 1 in increments of 0.1 units. The vertical axis is labeled “Uppercase p subscript Lowercase p” and ranges from 0 to 80 in increments of 10 units. The graph shows two distinct curves: A dashed blue curve is labeled “Uppercase P superscript D subscript Lowercase p. This curve is nearly flat and horizontal, starting at a value of approximately 75 on the vertical axis and slightly decreasing to a value around 70 as rho increases. A solid red curve is labeled ”Uppercase P superscript C subscript Lowercase p. This curve starts at a value of around 38 and gradually decreases as rho increases. The decrease accelerates as rho approaches 1, with the curve ending near a value of 0.

Impact of product price with cost-saving factor. Source(s): Authors’ own creation

Figure 5

Two graphs (a) and (b) illustrate the impact of the cost-saving factor on service price.

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The horizontal for both graphs is labeled “rho” and ranges from 0 to 0.2 in increments of 0.05 units. (a): Service price under decentralized decision: The vertical axis is labeled “P superscript D subscript S” and ranges from 12.86 to 13 in increments of 0.02 units. The graph shows a single, dashed blue line that forms a gentle, inverted U-shape. The line starts at a price of approximately 12.99, rises slightly to a peak of about 12.992 at a rho value just below 0.05, and then steadily decreases to a value of approximately 12.88 at rho equals 0.2. (b): Service price under centralized decision: The vertical axis is labeled “P superscript C subscript S” and ranges from 28.16 to 28.28 in increments of 0.02 units. The graph displays a single, solid red line that also forms a very gentle, inverted U-shape. This curve starts at a price of approximately 28.22, rises to a peak of about 28.27 at a ρ value of approximately 0.08, and then declines to a value of about 28.17 at rho equals 0.2.

Impact of cost-saving factor on service price. Source(s): Authors’ own creation

Figure 6 shows the impact of the cost-saving coefficient on manufacturer, seller, and supply chain system profits. First, Figure 6a shows that the total profit of the product-service supply chain system increases with an increase in the cost-saving coefficient under decentralized and centralized decision-making. Meanwhile, the cost-saving coefficient has a greater impact on the total profit of the supply chain system under centralized decision-making and a smaller impact on the total profit of the supply chain system under decentralized decision-making. Second, as seen in Figure 6b, with an increase in the cost-saving coefficient, both the manufacturer’s profit and seller’s profit increase, and their growth rate is gradually accelerated. This indicates that the magnitude of service cost improvement has a significant impact on the profits of manufacturers and sellers when manufacturers build their own industrial Internet platforms for service intelligence transformation. Additionally, the extent to which the cost-saving coefficient affects the seller’s profit is greater than that to which it affects the manufacturer’s profit. This is mainly because in the case where manufacturers invest in building their own industrial Internet platforms for service intelligent transformation, sellers do not have to bear the costs of service intelligent transformation, and therefore there is more significant “free-rider” opportunistic behavior.

Figure 6

Two graphs (a) and (b) illustrate the impact of the cost-saving factor on profit.

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The horizontal for both graphs is labeled “rho” and ranges from 0 to 1 in increments of 0.2 units. (a): The profit of supply chain system: The vertical axis is labeled “pi subscript S C” and ranges from 2000 to 5000 in increments of 500 units. It shows two distinct curves: A solid red curve is labeled “pi superscript C subscript S C.” This curve starts at a profit of approximately 3250 and gradually rises, with the increase becoming more pronounced as rho approaches 1. It ends at a value of around 5000. A dashed blue curve is labeled “pi superscript D subscript S C.” This curve starts at a profit of approximately 2250 and also rises as rho increases, but at a slower rate than the red line. It ends at a value of around 2750. (b): The profit of node enterprises: The vertical axis is labeled “pi subscript m minus pi subscript s” and ranges from 800 to 1700 in increments of 100 units. It shows two distinct curves: A dotted blue curve is labeled “pi superscript D subscript m.” This curve starts at a profit of approximately 1440 and rises at an accelerating rate as rho increases, ending at a value of 1660. A dashed blue curve is labeled “pi superscript D subscript s.” This curve starts at a profit of approximately 800 and rises at an accelerating rate as rho increases, ending at a value of 1100.

Impact of cost-saving factor on profit. Source(s): Authors’ own creation

5.3 Impact of service intelligence level sensitivity

Figure 7 shows the impact of service intelligence level sensitivity on product and service prices. First, as the sensitivity of the service intelligence level increases, the product price decreases, and the service price increases. This indicates that when customers are more sensitive to the level of service intelligence and tend to choose services with high levels of intelligence, supply chain node enterprises can adopt a pricing strategy of “low product and high service prices.” Second, the service price (product price) under decentralized decision-making is always lower (higher) than under centralized decision-making, which is consistent with Proposition 3.

Figure 7

Two graphs (a) and (b) illustrate the impact of product price and service price with service intelligence level sensitivity.

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The horizontal for both graphs is labeled “beta” and ranges from 0 to 1.4 in increments of 0.2 units. (a): Product price: The vertical axis is labeled “Uppercase P subscript Lowercase p” and ranges from 0 to 80 in increments of 10 units. It shows two distinct curves: A solid red curve is labeled “Uppercase P superscript C subscript Lowercase p.” This curve is relatively flat, starting around 73 and gradually decreasing to about 70 as beta increases. A dashed blue curve is labeled “Uppercase P superscript D subscript Lowercase p.” This curve starts at approximately 36 and steadily decreases to a value near 8 as beta increases. (b): Service price: The vertical axis is labeled “Uppercase P subscript s” and ranges from 10 to 40 in increments of 5 units. It shows two distinct curves: A solid red curve is labeled “Uppercase P superscript C subscript s.” This curve starts at about 24 and rises dramatically, reaching a value of approximately 40 as beta increases. A dashed blue curve is labeled “Uppercase P superscript D subscript s.” This curve starts at a price of about 11 and gradually rises to approximately 14.

Impact of product price and service price with service intelligence level sensitivity. Source(s): Authors’ own creation

Figure 8 demonstrates the impact of service intelligence level sensitivity on the manufacturer’s profit, seller’s profit, and total supply chain system profit. First, with an increase in service-intelligence level sensitivity, the profit and total system profit of supply chain node enterprises increase, and their growth rates gradually accelerate. This indicates that when a manufacturer conducts service intelligence transformation through a self-built industrial Internet platform, it not only increases the manufacturer’s profit but also increases the profit of other node enterprises in the supply chain. Second, under the decentralized decision-making model, sellers’ profit growth rates exceed those of manufacturers.

Figure 8

Two graphs (a) and (b) illustrate the Impact of service intelligence level sensitivity on profit.

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The horizontal for both graphs is labeled “beta” and ranges from 0 to 1.4 in increments of 0.2 units. (a): The profit of supply chain system: The vertical axis is labeled “pi subscript S C” and ranges from 2000 to 5000 in increments of 500 units. It shows two distinct curves: A solid red curve is labeled “pi superscript C subscript S C.” This curve starts at a profit of approximately 3350 and gradually rises, with the increase becoming more pronounced as rho approaches 1. It ends at a value of around 4750. A dashed blue curve is labeled “pi superscript D subscript S C.” This curve starts at a profit of approximately 2300 and also rises as rho increases, but at a slower rate than the red line. It ends at a value of around 2700. (b): The profit of node enterprises: The vertical axis is labeled “pi subscript m minus pi subscript s” and ranges from 800 to 1700 in increments of 100 units. It shows two distinct curves: A dotted blue curve is labeled “pi superscript D subscript m.” This curve starts at a profit of approximately 1460 and rises at an accelerating rate as beta increases, ending at a value of 1640. A dashed blue curve is labeled “pi superscript D subscript s.” This curve starts at a profit of approximately 820 and rises at an accelerating rate as beta increases, ending at a value of 1070.

Impact of service intelligence level sensitivity on profit. Source(s): Authors’ own creation

5.4 Analysis of coordination mechanisms

This section further verifies the validity of the “cost-sharing-fixed transfer” contract using example analysis. The same parameters are taken as above, and based on the above hypothetical data, the price, demand, and profit under decentralized decision-making are: product price 72.96, service price 11.31, wholesale product price 43.59, service intelligence level 4.88, product demand 29.38, service demand 18.14, manufacturer profit 1484.95, and seller profit 862.92. Under the “cost-sharing-fixed transfer” coordination contract, we analyze the effects of different values of $θ$ on the fixed transfer $f$ ⁠, product price $P_{p}^{X *}$ ⁠, service price $P_{s}^{X *}$ ⁠, wholesale product price $W^{X *}$ ⁠, service intelligence level $i^{X *}$ ⁠, product demand $D_{p}^{X *}$ ⁠, service demand $D_{s}^{X *}$ ⁠, as well as the difference $Δ π$ between the total profit of the supply chain system after the coordination contract and that under decentralized decision-making, as shown in Table 4.

Table 4

The value of $f$ and post-contract optimal decision under different $θ$

$θ$	$P_{p}^{X *}$	$P_{s}^{X *}$	$W^{X *}$	$i^{X *}$	$D_{p}^{X *}$	$D_{s}^{X *}$	$Δ π$	$f$
0.05	72.88	11.20	43.42	5.25	29.46	18.59	4.58	(−0.74, 3.84)
0.1	72.78	11.07	43.23	5.67	29.55	19.05	9.19	(−0.89, 8.30)
0.15	72.67	10.92	43.00	6.18	29.67	19.60	13.65	(−0.08, 13.56)
0.2	72.54	10.73	42.73	6.78	29.80	20.45	17.57	(2.28, 19.85)
0.25	72.37	10.51	42.40	7.52	29.97	21.04	20.29	(7.21, 27.51)
0.3	72.17	10.23	41.99	8.43	30.17	22.03	20.54	(26.28, 37.02)
0.35	71.90	9.88	41.47	9.60	30.44	23.28	15.78	(33.39, 49.17)
0.4	71.56	9.41	40.78	11.14	30.78	24.95	0.79	(64.43, 65.22)

$θ$	$P_{p}^{X *}$	$P_{s}^{X *}$	$W^{X *}$	$i^{X *}$	$D_{p}^{X *}$	$D_{s}^{X *}$	$Δ π$	$f$
0.05	72.88	11.20	43.42	5.25	29.46	18.59	4.58	(−0.74, 3.84)
0.1	72.78	11.07	43.23	5.67	29.55	19.05	9.19	(−0.89, 8.30)
0.15	72.67	10.92	43.00	6.18	29.67	19.60	13.65	(−0.08, 13.56)
0.2	72.54	10.73	42.73	6.78	29.80	20.45	17.57	(2.28, 19.85)
0.25	72.37	10.51	42.40	7.52	29.97	21.04	20.29	(7.21, 27.51)
0.3	72.17	10.23	41.99	8.43	30.17	22.03	20.54	(26.28, 37.02)
0.35	71.90	9.88	41.47	9.60	30.44	23.28	15.78	(33.39, 49.17)
0.4	71.56	9.41	40.78	11.14	30.78	24.95	0.79	(64.43, 65.22)

Source(s): Authors’ own creation

As can be seen from Table 2:

When the product-service supply chain adopts the “cost-sharing-fixed-transfer-payment” contract, the level of service intelligence improves compared with decentralized decision-making, the selling price of the product decreases, the demand for the product and the demand for the service rise, and the total profit of the supply chain improves; therefore, the “cost-sharing-fixed-transfer-payment” contract is effective in realizing the coordination of the product-service supply chain, and it also further demonstrates that the manufacturer can adopt the “cost-sharing-fixed-transfer-payment” contract to motivate the seller to cooperate with him to conduct a joint transformation of the service intelligence, which in turn will improve the level of service intelligence, increase the demand for the product and the demand for the service, and improve the efficiency of the supply chain.
As $θ$ increases, the level of service intelligence continues to increase, leading to a sustained decline in wholesale product, product, and service prices, as well as an increase in the scope of adjustments to fixed transfers. This is because manufacturers are driven by the incentive to increase their level of service intelligence as sellers bear the increased cost of service intelligence transformation. As this study assumes $ρ = 0.6$ and $β = 0.49$ ⁠, the service costs saved by the intelligent transformation of services are higher and users are more sensitive to the level of service intelligence. Therefore, the manufacturer reduces the service price under the dual effect of the seller bearing part of the cost of intelligent transformation and the higher service cost saved through intelligent transformation. In addition, the manufacturer reduces the wholesale price of the product due to the increased profit margins of the service and the sensitivity of users to the level of service intelligence. Although sellers bear a portion of the service intelligence transformation costs, thereby increasing their own costs, manufacturers lowering the wholesale prices of their products have a greater impact on sellers. As a result, the seller reduces the product price to boost product demand and, in turn, service demand. As rational individuals, sellers will only be willing to cooperate in implementing the contract if the profit under the contract is higher than the profit before the contract; as the seller bears the cost of service intelligence transformation for the manufacturer, the manufacturer will provide more fixed fees to the seller to ensure that the seller’s profit is not damaged.
As $θ$ increases, the incremental profit of the product-service supply chain under the pact shows a tendency to first increase and then decrease. This is because, in the process of gradually increasing the proportion of service intelligence transformation costs borne by the seller, the level of service intelligence of the manufacturer continues to improve, gradually making the profit reduction effect of the increase in service intelligence transformation costs exceed the profit promotion effect of the increase in product demand and service demand. Therefore, manufacturers should design a reasonable cost-sharing ratio to maximize the total profit of the entire supply chain.

6. Extensions

In this section, we discuss the key modeling assumptions and related issues. Specifically, in Section 6.1, we include the third-party industrial Internet platform operator as an independent decision-making subject in the product-service supply chain to explore how this model affects the product-service supply chain pricing strategy under the different decision-making scenarios described in Sections 6.2–6.4. In addition, we analyze the impact of the model parameters in Section 6.5.

6.1 Supply chain environment

In a real market environment, small- and medium-sized manufacturers with insufficient funds or weak information technology will cooperate with third-party industrial Internet platform operators to conduct an intelligent transformation of services. Third-party industrial Internet platform operators will provide manufacturers with intelligent transformation solutions of services according to their needs, so that manufacturers can use the third-party industrial Internet platform to provide users with intelligent services such as failure early warning, predictive maintenance, and asset management, remotely guide product repair and maintenance services, and precisely deliver spare parts and other products and services to users based on platform data. The manufacturer can then use the third-party industrial Internet platform to provide users with intelligent services such as failure warnings, predictive maintenance, asset management, and remote guidance for product repair and maintenance services, and accurately push spare parts and other products and services for users based on platform data. At this time, the third-party industrial Internet platform operator participates in the product-service supply chain and becomes an independent decision-maker in the product service supply chain. In this product-service supply chain system, the manufacturer is responsible for producing products and transferring them to the seller at the wholesale price $W$ ⁠. At the same time, it is responsible for selling the service and deciding the service price $P_{s}$ ⁠. Second, it has to pay the platform service price $h i$ to the third-party industrial Internet platform operator, which decides the unit platform service price $h$ ⁠; the third-party industrial Internet platform operator is responsible for providing the manufacturer with the service intelligent transformation solution, and according to the platform service price paid by the manufacturer, as well as the maintenance cost of the platform itself and the investment cost of technology research and development, it weighs the pros and cons and decides the level of service intelligentization $i$ ⁠; which is responsible for the sales of the product, which decides the product price $P_{p}$ ⁠.

Customers will consider not only product price but also after-sales service quality (e.g. service reliability and service responsiveness) when purchasing a product, assuming that the product demand function in the industrial Internet platform environment is $D_{p} = a - P_{p} + γ \overset{̅}{q}$ (Wang et al., 2022; Wu, 2017; Zhou et al., 2023). The service demand function is assumed to be $D_{s} = D_{p} - b P_{s} + β i$ (Nie and Deng, 2014; Yi and Yao, 2016). Due to the low marginal production cost and high marginal service cost of the intelligent transformation solution service provided by the third-party industrial Internet platform operator for manufacturers, the cost of the industrial Internet platform operator was assumed to be $k i^{2} / 2$ (Pan, 2022; Wu et al., 2023). The manufacturer’s cost consists of the platform service price paid to the third-party industrial Internet platform operator and the product service cost. Referring to the assumptions regarding the prices charged by industrial Internet platforms when they provide value-added services to manufacturers, the platform service price paid by the manufacturer to the third-party industrial Internet platform operator is $h i$ (Pan, 2022); The manufacturer’s unit cost of service is assumed to be $(1 - ρ i) C_{s}$ ⁠. To ensure that the profits of the manufacturer, seller, and third-party industrial Internet platform operator are greater than zero, and that the model has an optimal solution, it is necessary to satisfy ${C_{s}}^{2} b^{2} ρ^{2} + 2 C_{s} b β ρ - 2 b k + β^{2} + k / 2 < 0$ ⁠, ${C_{s}}^{2} ρ^{2} + 8 C_{s} β ρ - 8 k < 0$ ⁠, and ${C_{s}}^{2} b ρ^{2} + C_{s} β ρ - k < 0$ ⁠.

In the following, the subscript $j = m, s, p$ stands for manufacturer, seller, and third-party industrial Internet platform operators, respectively; the superscripts $D$ ⁠, $L$ ⁠, and $C$ denote decentralized, collaborative, decentralized, and centralized decision-making; the superscript * denotes optimal and $π$ denotes profit.

The new parameter symbols and their meanings are as follows.

$h$ ⁠: Unit platform service price; $π_{p}$ ⁠: Third-party industrial Internet platform operator profits.

6.2 Decentralized decision-making

In a product-service supply chain under decentralized decision-making, the manufacturer and third-party industrial Internet platform operators constitute a Stackelberg game relationship, and the manufacturer and seller also constitute a Stackelberg game relationship. The manufacturer first determines the wholesale price of the product $W$ ⁠, service price $P_{s}$ ⁠, and unit platform service price $h$ ⁠. The third-party industrial Internet platform operator then decides the service intelligence level $i$ based on the unit platform service price paid by the manufacturer, and the seller decides the product price $P_{p}$ based on the manufacturer’s decision. The profit functions of the manufacturer, third-party industrial Internet platform operator, and seller under decentralized decision-making are as follows:

π_{m}^{D} = W (a + γ \overset{̅}{q} - P_{p}) + (P_{s} - C_{s} (1 - ρ i)) (a + γ \overset{̅}{q} - P_{p} - b P_{s} + β i) - h i

π_{p}^{D} = h i - \frac{k i^{2}}{2}

π_{s}^{D} = (P_{p} - W) (a + γ \overset{̅}{q} - P_{p})

Proposition 4.

The optimal decision for a product-service supply chain under decentralized decision-making is as follows. Detailed proof is provided in Appendix (Proof of Proposition 4):

Under decentralized decision-making, the service price, wholesale product price, per-unit platform service price of the manufacturer, product price of the seller, and service intelligence level of the third-party industrial Internet platform operator are as follows:

P_{s}^{D *} = \frac{- ρ b (A ρ + 4 β) {C_{s}}^{2} + (- A β ρ + 8 b k - 4 β^{2} - 2 k) C_{s} + 2 A k}{- 4 {C_{s}}^{2} b^{2} ρ^{2} - 8 C_{s} b β ρ + 16 b k - 4 β^{2} - 2 k}

W^{D *} = \frac{(- {C_{s}}^{2} b^{2} ρ^{2} + (- 2 C_{s} β ρ + 4 k) b - β^{2} - k) A + 2 C_{s} b k}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} β ρ + 8 k) b - 2 β^{2} - k}

h^{D *} = \frac{k (- 4 {C_{s}}^{2} b^{2} ρ + A C_{s} b ρ - 4 C_{s} b β + A β)}{- (4 {C_{s}}^{2} b^{2} ρ^{2} + 8 C_{s} b β ρ - 16 b k + 4 β^{2} + 2 k)}

P_{p}^{D *} = \frac{(- 3 {C_{s}}^{2} b^{2} ρ^{2} + (- 6 C_{s} β ρ + 12 k) b - 3 β^{2} - 2 k) A + 2 C_{s} b k}{- 4 {C_{s}}^{2} b^{2} ρ^{2} + (- 8 C_{s} β ρ + 16 k) b - 4 β^{2} - 2 k}

i^{D *} = \frac{(C_{s} b_{2} ρ + β) (- 4 C_{s} b_{2} + A)}{- 4 {C_{s}}^{2} {b_{2}}^{2} ρ^{2} + (- 8 C_{s} β ρ + 16 k) b_{2} - 4 β^{2} - 2 k}

Under decentralized decision-making, product demand and service demand are as follows:

D_{p}^{D *} = \frac{- A {C_{s}}^{2} {b_{2}}^{2} ρ^{2} + ((- 2 A β ρ - 2 k) C_{s} + 4 A k) b_{2} - A β^{2}}{- 4 {C_{s}}^{2} {b_{2}}^{2} ρ^{2} + (- 8 C_{s} β ρ + 16 k) b_{2} - 4 β^{2} - 2 k}

D_{s}^{D *} = \frac{b_{2} k (- 4 C_{s} b_{2} + A)}{- 2 {C_{s}}^{2} {b_{2}}^{2} ρ^{2} + (- 4 C_{s} β ρ + 8 k) b_{2} - 2 β^{2} - k}

Under decentralized decision-making, the manufacturer’s profit, third-party industrial Internet platform operator’s profit, and seller’s profit are as follows:

π_{m}^{D *} = \frac{- {C_{s}}^{2} (A^{2} ρ^{2} - 8 k) {b_{2}}^{2} + ((- 2 A^{2} β ρ - 4 A k) C_{s} + 4 A^{2} k) b_{2} - A^{2} β^{2}}{- 8 {C_{s}}^{2} {b_{2}}^{2} ρ^{2} + (- 16 C_{s} β ρ + 32 k) b_{2} - 8 β^{2} - 4 k}

π_{p}^{D *} = \frac{k {(C_{s} b_{2} ρ + β)}^{2} {(- 4 C_{s} b_{2} + A)}^{2}}{8 {(- 2 {C_{s}}^{2} {b_{2}}^{2} ρ^{2} - 4 C_{s} b_{2} β ρ + 8 b_{2} k - 2 β^{2} - k)}^{2}}

π_{s}^{D *} = \frac{{(A {C_{s}}^{2} {b_{2}}^{2} ρ^{2} + 2 A C_{s} b_{2} β ρ - 4 A b_{2} k + A β^{2} + 2 C_{s} b_{2} k)}^{2}}{4 {(2 {C_{s}}^{2} {b_{2}}^{2} ρ^{2} + 4 C_{s} b_{2} β ρ - 8 b_{2} k + 2 β^{2} + k)}^{2}}

Notes: $A = a + γ \overset{̅}{q}$ ⁠.

6.3 Collaborative decision-making

This section considers the cooperation between manufacturers and sellers to form an alliance system to jointly face the third-party industrial Internet platform operator to seek service intelligent transformation, and although still decentralized decision-making, there is manufacturer and seller cooperation. The alliance state of manufacturers and sellers is called collaborative decision-making. Owing to full cooperation between manufacturers and sellers, the wholesale price of the product will no longer be considered. The order of decision-making under collaborative decision-making is as follows. First, the alliance composed of manufacturers and sellers decides the product price, service price, and the unit platform service price to be paid to the third-party platform operator, which then determines the service intelligence level according to the decision-making of the alliance system.

The profit function of the consortium of manufacturers and sellers under collaborative decision-making and the third-party industrial Internet platform operator is as follows:

π_{m s}^{L} = P_{p} (a + γ \overset{̅}{q} - P_{p}) + (P_{s} - C_{s} (1 - ρ i)) (a + γ \overset{̅}{q} - P_{p} - b P_{s} + β i) - h i

π_{p}^{L} = h i - \frac{k i^{2}}{2}

Proposition 5.

The optimal decision of a product-service supply chain under collaborative decision-making is as follows. Detailed proof is provided in Appendix (Proof of Proposition 5):

Under collaborative decision-making, product prices, service prices, unit platform service prices, and service intelligence levels are as follows.

P_{p}^{L *} = \frac{(2 C_{s} (k - A β ρ) + 4 A k) b - A (β^{2} + 2 k + {C_{s}}^{2} b^{2} ρ^{2})}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 8 k) b - 2 β^{2} - 2 k}

P_{s}^{L *} = \frac{(- A β ρ + 4 b k - 2 β^{2} - 2 k) C_{s} + 2 A k - {C_{s}}^{2} ρ b (A ρ + 2 β)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} - 4 C_{s} b β ρ + 8 b k - 2 β^{2} - 2 k}

h^{L *} = \frac{k (C_{s} ρ b + β) (A - 2 C_{s} b)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 8 k) b - 2 β^{2} - 2 k}

i^{L *} = \frac{(A - 2 C_{s} b) (C_{s} ρ b + β)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 8 k) b - 2 β^{2} - 2 k}

Product and service demands are as follows:

P_{p}^{L *} = \frac{(4 A k - (2 A β ρ + 2 k) C_{s}) b - A (β^{2} + {C_{s}}^{2} b^{2} ρ^{2})}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 8 k) b - 2 β^{2} - 2 k}

D_{s}^{L *} = \frac{b k (A - 2 C_{s} b)}{- {C_{s}}^{2} b^{2} ρ^{2} + (- 2 C_{s} ρ β + 4 k) b - β^{2} - k}

The profits of the alliance system consisting of manufacturers and sellers and those of the third-party industrial Internet platform operator are as follows:

π_{m s}^{L *} = \frac{- {C_{s}}^{2} (A^{2} ρ^{2} - 4 k) b^{2} + ((- 2 A^{2} β ρ - 4 A k) C_{s} + 4 A^{2} k) b - A^{2} β^{2}}{- 4 {C_{s}}^{2} b^{2} ρ^{2} + (- 8 C_{s} ρ β + 16 k) b - 4 β^{2} - 4 k}

π_{p}^{L *} = \frac{k {(C_{s} ρ b + β)}^{2} {(- 2 C_{s} b + A)}^{2}}{2 {(- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 8 k) b - 2 β^{2} - 2 k)}^{2}}

6.4 Centralized decision-making

Centralized decision-making views manufacturers, sellers, and third-party industrial Internet platform operators as one system, with profit maximization of the supply chain system as the primary criterion and decision-making by a unified control center. The profit function of the product and service supply chain is as follows:

π_{s c}^{C} = P_{p} (a + γ \overset{̅}{q} - P_{p}) + (P_{s} - C_{s} (1 - ρ i)) (a_{s} - P_{p} + γ \overset{̅}{q} - b P_{s}) - \frac{k i^{2}}{2}

Proposition 6.

The optimal decision for a product-service supply chain under centralized decision-making is as follows. Detailed proof is provided in Appendix (Proof of Proposition 6):

Under centralized decision-making, the product, service, and service intelligence levels are as follows.

p_{p}^{C *} = \frac{((- 2 A β ρ + k) C_{s} + 2 A k) b - (β^{2} + k + {C_{s}}^{2} b^{2} ρ^{2}) A}{- 2 {C_{s}}^{2} {b_{2}}^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}

P_{s}^{C *} = \frac{(2 b k - A β ρ - 2 β^{2} - k) C_{s} + A k - {C_{s}}^{2} ρ b (A ρ + 2 β)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} - 4 C_{s} b β ρ + 4 b k - 2 β^{2} - k}

i^{C *} = \frac{(C_{s} ρ b + β) (A - 2 C_{s} b)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}

Product and service demands are as follows:

D_{p}^{C *} = \frac{(2 A k - (2 A β ρ + k) C_{s}) b - A (β^{2} + {C_{s}}^{2} b^{2} ρ^{2})}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}

D_{s}^{C *} = \frac{b k (A - 2 C_{s} b)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}

Total profit of the product-service supply chain system

π_{s c}^{C *} = \frac{{C_{s}}^{2} b^{2} (2 k - A^{2} ρ^{2}) + 2 (A k - (A β ρ + k) C_{s}) A b - A^{2} β^{2}}{- 4 {C_{s}}^{2} b^{2} ρ^{2} + (- 8 C_{s} ρ β + 8 k) b - 4 β^{2} - 2 k}

6.5 Sensitivity analysis

Corollary 6.

The impacts of the cost-saving factor on wholesale product prices, product prices, service prices, service intelligence levels, per-unit platform service prices, product demand, service demand, and profits under decentralized decision-making are as follows:

$\frac{\partial P_{p}^{* D}}{\partial ρ} < 0$ ⁠; $\frac{\partial W^{D *}}{\partial ρ} < 0$ ⁠; $\frac{\partial i^{D *}}{\partial ρ} > 0$ ⁠; $\frac{\partial h^{D *}}{\partial ρ} > 0$
$k > k_{a}$ ⁠, $ρ \in (0, ρ_{1})$ ⁠, $\frac{\partial P_{s}^{D *}}{\partial ρ} > 0$ ⁠, and $ρ \in (ρ_{1}, 1)$ ⁠, $\frac{\partial P_{s}^{D *}}{\partial ρ} < 0$
$\frac{\partial D_{p}^{D *}}{\partial ρ} > 0$ ⁠; $\frac{\partial D_{s}^{D *}}{\partial ρ} > 0$ ⁠; $\frac{\partial π_{m}^{D *}}{\partial ρ} > 0$ ⁠; $\frac{\partial π_{p}^{D *}}{\partial ρ} > 0$ ⁠; $\frac{\partial π_{s}^{D *}}{\partial ρ} > 0$

Corollary 6 (1) shows that under decentralized decision-making, the wholesale price of products, product price, and cost-saving coefficient are inversely proportional to each other, and the level of service intelligence, the unit platform service price, and the cost-saving coefficient are positively proportional to each other. This indicates that with an increase in the cost-saving coefficient, more service costs are saved by the manufacturer relying on the third-party industrial Internet platform’s service intelligence transformation, and the manufacturer is willing to pay the third-party industrial Internet platform the unit platform service price more. To promote the sale of services, manufacturers and sellers adopt a product price reduction strategy to reduce the wholesale price of the service product.

Corollary 6 (2) shows that, when the cost coefficient of intelligent service transformation meets certain conditions, the service price first increases and then decreases with an increase in the cost-saving coefficient. When the cost-saving coefficient is small (i.e. the cost effect of service intelligent transformation on service cost improvement is not obvious), the manufacturer will increase the service price to ensure that its own profit will not be lost; when the cost-saving coefficient is large, the cost of the product service is small, and the manufacturer will choose to reduce the price of the service to improve customer stickiness.

Corollary 6 (3) shows that as the cost-saving coefficient increases, manufacturers save on service costs through intelligent service transformation, which promotes the growth of demand for products and services and expands the scale of production and sales, thereby increasing the profits of manufacturers, sellers, and third-party industrial Internet platform operators. Manufacturers are willing to pay higher service prices to third-party industrial Internet platform operators, incentivizing them to provide smart services. Although the third-party industrial Internet platform operator bears more of the costs of smart transformation, the platform service price it receives from the manufacturer increases as the smartness level of its services increases, which, in turn, increases profits.

Corollary 7.

The analysis of the impact of service-intelligence level sensitivity on wholesale product price, product price, service price, service-intelligence level, service price per unit of platform, product demand, service demand, and profit under decentralized decision-making are as follows:

$\frac{\partial i^{D *}}{\partial β} > 0$ ⁠; $\frac{\partial P_{p}^{D *}}{\partial β} < 0$ ⁠; $\frac{\partial W^{D *}}{\partial β} < 0$ ⁠; $\frac{\partial h^{D *}}{\partial β} > 0$
$k \leq C_{s}^{2} ρ^{2} (\frac{8 b - 1}{6})$ ⁠, $\frac{\partial P_{s}^{D *}}{\partial β} < 0$ ⁠; when $C_{s}^{2} ρ^{2} (\frac{8 b - 1}{6}) < k < 2 {C_{s}}^{2} b^{2} ρ^{2}$ ⁠: then $β \in (0, β_{1}^{D})$ ⁠, $\frac{\partial P_{s}^{D *}}{\partial β} < 0$ ⁠, $β \in (β_{1}^{D}, \frac{k - C_{s}^{2} ρ^{2} b^{2}}{C_{s} ρ})$ ⁠, $\frac{\partial P_{s}^{D *}}{\partial β} > 0$ ⁠; when $k > 2 {C_{s}}^{2} b^{2} ρ^{2}$ ⁠, and $\frac{\partial P_{s}^{D *}}{\partial β} \geq 0$
$\frac{\partial D_{p}^{D *}}{\partial β} > 0$ ⁠; $\frac{\partial D_{s}^{D *}}{\partial β} > 0$ ⁠; $\frac{\partial π_{p}^{D}}{\partial β} > 0$ ⁠; $\frac{\partial π_{m}^{D}}{\partial β} > 0$ ⁠; $\frac{\partial π_{s}^{D}}{\partial β} > 0$

Corollary 7 (1) shows that under decentralized decision-making, the service intelligence level and unit platform service price are positively related to service intelligence sensitivity, whereas the product wholesale price and product price are negatively related to service intelligence level sensitivity. When the service intelligence level sensitivity increases, manufacturers increase the service intelligence transformation to meet user demand, increasing the unit platform service price paid to third-party industrial Internet platform operators. For products in the product-service supply chain, manufacturers and sellers will choose the price reduction strategy to reduce the wholesale price of products and the sales price of products; the intelligent service transformation of the manufacturer saves the service cost and expands the profit margin of the service, and the sensitivity of the user to the level of service intelligence increases, so that the price reduction promotes the sales of products and stimulates the demand for services to increase the profits of the enterprise, and the profit growth center is gradually transformed from products to services.

Corollary 7 (2) reveals the relationship between service price and sensitivity to service intelligence level. The effect of service-intelligence level sensitivity on service price is related to the service-intelligence transformation cost coefficient, cost-saving coefficient, and service-price sensitivity coefficient. From the perspective of convenience, assuming that the cost-saving coefficient and service price sensitivity coefficient are certain, we mainly analyze the impact of service-intelligence level sensitivity on service price when the service-intelligence cost coefficient changes. Specifically, when the service intelligence transformation cost coefficient is small (⁠ $k \leq C_{s}^{2} ρ^{2} (8 b - 1) / 6$ ⁠), the service price is always negatively correlated with the service intelligence level sensitivity, indicating that under other conditions remaining unchanged, when the service intelligence transformation cost coefficient is low, with an increase in the service intelligence level sensitivity, the manufacturer chooses to reduce the service price to promote demand for services; when the service intelligence transformation cost coefficient is moderate (⁠ $C_{s}^{2} ρ^{2} (8 b - 1) / 6 < k < 2 {C_{s}}^{2} b^{2} ρ^{2} \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ ⁠), the service price decreases first and then increases with the increase of service intelligence level sensitivity, which indicates that when the service intelligence transformation input cost is moderate, the manufacturer will formulate the service price strategy according to the size of the service intelligence sensitivity; when the cost coefficient of service intelligent transformation is high, the service price is always positively correlated with the sensitivity of service intelligence level, which indicates that when the cost of service intelligent transformation input is high (⁠ $k > 2 {C_{s}}^{2} b^{2} ρ^{2}$ ⁠), in order to ensure that the profit will not be lost, the manufacturer will increase the service price with the increase of service intelligence sensitivity.

Corollary 7 (3) indicates that product demand, service demand, manufacturer profit, seller profit, and third-party industrial Internet platform operator profit positively correlate with service intelligence level sensitivity. This is because, as the sensitivity of the service intelligence level increases, the wholesale price of products and product prices decrease, and the service intelligence level increases, which leads to an increase in product market demand and service market demand. However, the positive effect of increased demand for products and services outweighs the negative effect of lower prices on profits, and the manufacturers’ and sellers’ profits increase. The profits of third-party industrial Internet platform operators also increase due to an increase in the level of service intelligence and the unit platform service price.

7. Conclusion

7.1 Conclusion

This study identified the following points:

It is advantageous for manufacturers to opt for a service-intelligent transition that increases their own profits and those of the entire supply chain. In addition, in the case of the manufacturer’s own platform, there is a certain degree of “free-riding” behavior of the seller, the degree of which is strengthened with the increase of the cost-saving factor and the sensitivity of the service intelligence level. To maintain long-term cooperation among supply chain members, sellers should take the initiative to bear a certain amount of service intelligence transformation costs to reduce the financial pressure on manufacturers.
Whether it is a self-built platform or a third-party platform, the impact of the cost-saving factor and sensitivity of the level of service intelligence on the wholesale price of products and price of products is more complicated. In the case of the manufacturer’s self-built platform, the service price increases and then decreases with an increase in the cost-saving coefficient and increases with an increase in the sensitivity of the service intelligence level. When relying on third-party platforms, the service price increases, and subsequently decreases with an increase in the cost-saving coefficient. The impact of the service-intelligence level sensitivity on service prices is closely related to the service-intelligence transformation cost coefficient. When the cost coefficient of service intelligent transformation is small, the service price decreases with an increase in service intelligence level sensitivity; when the cost coefficient is moderate, the service price decreases first and then increases with an increase in service intelligence level sensitivity; when the cost coefficient is large, the manufacturer raises the service price to ensure that profit is not lost.
Whether it is a self-built platform or a third-party platform, the centralized decision-making mode has the highest level of service intelligence, lowest product price, and highest profit of the supply chain node enterprises, as well as system profit. In the case of the manufacturer’s self-built platform, the service price under centralized decision-making is the highest, while in the case of relying on the third-party platform, the service price under collaborative decision-making is always higher than the service price under decentralized decision-making. This indicates that cooperation between manufacturers and sellers in intelligent service transformations can increase service prices. The size of the relationship between service price under collaborative decision-making and service price under centralized decision-making is related to the sensitivity of the service intelligence level, unit service cost savings, and service price sensitivity coefficient.
With the development of intelligent transformations, users gradually recognize the value of intelligent services and prefer high-level services. Manufacturers gradually reduce the prices of their products to promote sales, thereby expanding the potential size of the service market. This indicates that with the development of intelligent transformation, the market logic of manufacturers has changed from “product-driven logic” to “service-driven logic.”

7.2 Managerial implications

7.2.1 Management implications for manufacturers

Enhancing awareness of the intelligent transformation of services: In the context of implementing a digital economy strategy, intelligent transformation has become necessary for the transformation and upgrading of traditional manufacturing enterprises. Enterprises should enhance the willingness and motivation for intelligent transformation and move from passive to active transformation to comply with the development trend of the digital economy era, and manufacturers should develop different service pricing strategies at different stages of intelligent service transformation. At the primary stage, the platform technology level is low, the service cost savings are small, and the manufacturer can adopt a high service price strategy. With the development of technology and the reduction of transformation costs, the manufacturer can adjust the service price according to the sensitivity of the level of service intelligence. At the advanced stage, the platform technology is highly developed, the savings in service costs are extremely high, and the manufacturer can reduce the service price to expand the market share. Further, as a leading enterprise in the supply chain, the manufacturer should commit to developing the supply chain from a completely uncooperative state to a partially cooperative state or even a completely cooperative state. Large-scale manufacturing enterprises that can build their own industrial Internet platforms can design a “cost-sharing-fixed transfer payment” contract, but they need to set the cost-sharing ratio carefully to promote win-win cooperation.

7.2.2 Management implications for third-party industrial Internet platform operators

Platform technology development should be accelerated, and platform services and management capabilities should be strengthened. As important carriers for enterprises to conduct intelligent service transformation, the technical level and service management capability of industrial Internet platforms directly affect the cost of intelligent transformation and the level of intelligence of enterprises. Therefore, the platform should increase R&D investment in key technologies, such as industrial mechanism models, edge computing, and big data analysis, and improve its data processing, analysis, and decision-making capabilities. In addition, the platform should establish a unified standard data interoperability interface and data parsing protocol, and develop modeling tools and common methods. Simultaneously, as a provider of intelligent transformation solutions, an industrial Internet platform operator should enhance its own platform service and management capabilities, accumulate manufacturing knowledge, gain a deeper understanding of the business processes and modes of traditional manufacturing enterprises, and continue to cultivate standardized and low-cost solutions to encourage enterprises to actively use the platform for digital and intelligent transformation activities. Doing so will not only help enterprises maximize their revenues but also help platform operators maximize their own interests.

7.2.3 Management implications for vendors

Sellers should cooperate actively with manufacturers’ service-intelligent transformation activities. By comparing and analyzing the profits and system profits of supply chain node enterprises before and after intelligent service transformation, we learn that it is beneficial for manufacturers to conduct intelligent service transformation based on industrial Internet platforms, which can improve the profits of sellers. Therefore, sellers should actively cooperate with manufacturers to support the intelligent transformation of their services. First, the seller can help the manufacturer share part of the transformation cost, thus reducing financial pressure on the manufacturer. Second, sellers can provide the service intelligence transformation data required by manufacturers to expand the data scale further. Finally, sellers should actively cooperate with manufacturers to deal with third-party industrial internet platform operators and improve the competitiveness of the supply chain.

7.2.4 Suggested responses from government departments

Governments should take measures to provide policy subsidies to third-party industrial Internet platforms and enterprises undergoing smart transformation to promote the dynamism of the smart transformation market and reduce the financial pressure and cost burden faced by enterprises in the transformation process. Specific measures include direct financial allocations or low-interest loan schemes to provide financial support for the implementation of intelligent transformation, lowering the tax burden on enterprises by providing tax relief or tax incentives to help enterprises save costs and use more funds for transformation, facilitating cooperation between third-party industrial Internet platforms and enterprises, and helping enterprises interface with suitable industrial Internet platforms through the establishment of partnerships or the provision of project support to promote information sharing. Internet platforms promote information sharing and resource integration and further promote the intelligent transformation market.

In the context of smart manufacturing, the government is a favorable promoter of the development and implementation of the industrial Internet platform and plays an important role in the intelligent transformation of the supply chain. The government can not only influence the level of intelligent service transformation of manufacturers through punishment and subsidy policies, but can also influence the user’s preference for intelligent services and thus market demand through various channels; therefore, it is very meaningful to study the inclusion of the government as the main body in intelligent service transformation.

7.3 Limitations and future research

This paper investigates the impact of service intelligence transformation—driven by industrial Internet platforms—on service demand, cost, and quality. It also examines the pricing and coordination mechanisms of the product-service supply chain within this context. Nevertheless, due to limitations in research scope and time, the study has certain shortcomings. Future research can be expanded in the following directions:

This research assumes a linear relationship between the level of service intelligence and its impact on service demand and cost efficiency. However, real-world interactions are often more complex than this assumption suggests. Future research should explore pricing strategies and coordination mechanisms within nonlinear modeling frameworks.

This research considers the impact of service intelligence transformation primarily in terms of cost, demand, and quality. However, its effects extend beyond these dimensions to include market expansion and the enhancement of network externalities. Future research should therefore aim to develop more comprehensive models that capture the broader implications of service intelligence transformation, thereby improving alignment with real-world operational dynamics.

Moreover, under the paradigm of intelligent manufacturing, government plays a pivotal role as a facilitator in the development and implementation of industrial Internet platforms. In the context of supply chain intelligence transformation, governmental influence is twofold: on the one hand, it can shape the manufacturer’s level of service intelligence through regulatory instruments such as subsidies and penalties; on the other hand, it can influence consumer preferences for intelligent services through various policy channels, thereby indirectly affecting market demand. As such, incorporating the role of government into the analysis of service intelligence transformation represents a meaningful direction for future research.

The supplementary material for this article can be found online.

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Pricing and coordination of product service supply chain under an industrial internet platform environment

1. Introduction

2. Literature review

2.1 Product-service supply chain

2.2 Pricing in the product-service supply chain

2.3 Industrial internet platform enables intelligent transformation of enterprise services

2.4 The impact of industrial internet platforms on product and service supply chains

3. Basic model

4. Pricing and coordination decisions

4.1 Benchmark

4.2 Decentralized decision-making

4.3 Centralized decision-making

4.4 Model analysis

4.4.1 Comparison of equalization results

4.4.2 Sensitivity analysis

4.5 Supply chain coordination

5. Numerical analysis

5.1 Profit comparison of transformation

5.2 Impact of cost-saving factors

5.3 Impact of service intelligence level sensitivity

5.4 Analysis of coordination mechanisms

6. Extensions

6.1 Supply chain environment

6.2 Decentralized decision-making

6.3 Collaborative decision-making

6.4 Centralized decision-making

6.5 Sensitivity analysis

7. Conclusion

7.1 Conclusion

7.2 Managerial implications

7.2.1 Management implications for manufacturers

7.2.2 Management implications for third-party industrial Internet platform operators

7.2.3 Management implications for vendors

7.2.4 Suggested responses from government departments

7.3 Limitations and future research

References

Further reading

Supplementary data

Email Alerts

Cited By

Pricing and coordination of product service supply chain under an industrial internet platform environment

1. Introduction

2. Literature review

2.1 Product-service supply chain

2.2 Pricing in the product-service supply chain

2.3 Industrial internet platform enables intelligent transformation of enterprise services

2.4 The impact of industrial internet platforms on product and service supply chains

3. Basic model

4. Pricing and coordination decisions

4.1 Benchmark

4.2 Decentralized decision-making

4.3 Centralized decision-making

4.4 Model analysis

4.4.1 Comparison of equalization results

4.4.2 Sensitivity analysis

4.5 Supply chain coordination

5. Numerical analysis

5.1 Profit comparison of transformation

5.2 Impact of cost-saving factors

5.3 Impact of service intelligence level sensitivity

5.4 Analysis of coordination mechanisms

6. Extensions

6.1 Supply chain environment

6.2 Decentralized decision-making

6.3 Collaborative decision-making

6.4 Centralized decision-making

6.5 Sensitivity analysis

7. Conclusion

7.1 Conclusion

7.2 Managerial implications

7.2.1 Management implications for manufacturers

7.2.2 Management implications for third-party industrial Internet platform operators

7.2.3 Management implications for vendors

7.2.4 Suggested responses from government departments

7.3 Limitations and future research

References

Further reading

Supplementary data

Email Alerts

Suggested Reading

Related Chapters

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Cited By

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