Coordination of Quantity Discount Contracts With Group Purchasing Organizations and Demand Information Sharing in Pharmaceutical Supply Chains

Abstract

The double-marginal and bullwhip effects caused by information asymmetry are common in the actual operation of pharmaceutical supply chains. Introducing pharmaceutical group purchasing organizations (GPOs) increases the risk of these effects, leading to decision-making failures and reduced operational efficiency in pharmaceutical supply chains. This study addresses these issues by proposing a quantity discount contract coordination model that includes GPOs and incorporates demand information sharing. This model is solved and simulated using a Steinberg game and the inverse induction method. The results show that under certain conditions, demand information sharing increases the demand of each supply chain member and the revenue of pharmaceutical GPOs. However, quantity discount contracts increase the revenue of medical institutions and decrease their procurement costs. Collectively, these effects can reduce the procurement costs of medical institutions and pharmaceutical purchasers, thus enabling the coordinated operation of the pharmaceutical supply chain. These findings reveal potential cost-saving approaches for medical institutions and pharmaceutical purchasers, which are of great significance for promoting the sustainable development of the medical industry. However, the model construction in this study has limitations, and future research could further explore the influence of combination contracts on supply chain coordination.

Introduction

A group purchasing organization (GPO) is a third-party service provider that negotiates purchasing services with suppliers, leveraging the collective purchasing power of multiple members to obtain quantity discounts and more favorable contract terms. Group purchasing is an internationally accepted pharmaceutical procurement model in which a GPO integrates medical institutions’ pharmaceutical needs, negotiates prices with pharmaceutical suppliers with a high degree of centralized purchasing power, and provides medical institutions with quality pharmaceutical procurement services to help reduce pharmaceutical costs and improve the efficiency of pharmaceutical supply chain operations (Nollet & Beaulieu, 2003). Compared to independent procurement, group procurement is more likely to produce a scale effect and significantly affect pharmaceutical procurement prices, transaction costs, and pharmaceutical market development orders.

However, whether pharmaceutical GPO procurement can always yield effects, such as reduced pharmaceutical prices and cost savings, has been controversial (Hu & Schwarz, 2011). The addition of pharmaceutical GPOs increases the number of decision-makers in the pharmaceutical supply chain, and collecting contract management fees and other profit-making behaviors from pharmaceutical manufacturers increases the risk of collusive behavior among members, potentially resulting in higher pharmaceutical prices. However, adding more members to the pharmaceutical supply chain intensifies competition and information asymmetry. If all members seek to maximize their unilateral interests, the overall operating revenue of the pharmaceutical supply chain will likely be lower than the sum of each member’s individual revenue following the introduction of pharmaceutical COPS, creating double marginal bullwhip effects in the pharmaceutical supply chain. These effects can lead to failure in supply chain decisions and reduce operational efficiency (Cachon & Lariviere, 2005). Furthermore, insufficient willingness among members to share information, distortion in the information transmission process, and an imperfect information-sharing mechanism result in unbalanced information distribution in the pharmaceutical supply chain. This information asymmetry makes it challenging for pharmaceutical GPOs to accurately assess medical institutions’ genuine needs. Moreover, pharmaceutical supply chain members have different roles and interests and often reserve key information, such as market demand, production cost, and purchase price, making it difficult for pharmaceutical GPOs to fully comprehend the real supply and demand in the drug market. This not only increases the difficulty of demand consolidation but also makes it harder for supply chain members to reach a consensus when making decisions, thus affecting the operational efficiency and coordination of the entire pharmaceutical supply chain.

Demand consolidation is the main function of pharmaceutical GPOs, and the enormous demand in the pharmaceutical market endows them with a strong advantage in price negotiations. However, in a pharmaceutical supply chain with GPOs, increased information asymmetry among members makes the quantity-for-price problem more complex. Solving this problem requires establishing a mechanism for sharing demand information. This mechanism requires all pharmaceutical supply chain members to share key information, including market demand forecasts and actual sales data, to fully understand market dynamics and patient needs and subsequently make more accurate and wiser decisions. However, against the backdrop of information asymmetry, effectively sharing demand information is not straightforward. Quantity discount contracts can play a vital role as a common supply chain coordination mechanism that encourages buyers to increase their order quantity by providing price concessions, thus realizing the coordinated operation of the supply chain. However, in a pharmaceutical supply chain with asymmetric information, effective implementation of quantity discount contracts faces several challenges. Pharmaceuticals are closely related to human life and health; therefore, without effective quantity discount contracts, fluctuations in the quantity and price of the pharmaceutical supply and failure of pharmaceutical supply chain decisions are likely to lead to a series of governmentally oriented financial and social welfare problems. The quantity–price negotiation advantage of pharmaceutical GPOs can instead become a bottleneck that restricts effective pharmaceutical supply chain operations.

More general research related to the product supply chain indicates that demand information sharing can reduce problems in supply chain operations caused by information asymmetry and enable effective demand forecasting. Dan et al. (2023) suggested that sellers have demand forecast information and can decide whether to share that information with suppliers, and constructed a dynamic game model to analyze the information-sharing strategy in this supply chain and a corresponding demand information-sharing incentive contract. W. L. Wang and Wang (2020) considered competition between two manufacturers, constructed a retailer demand forecasting information-sharing model from the perspective of innovation input, and used Bayesian statistical theory and the Steinberg game approach to explore the effects of competition between manufacturers on retailers’ demand forecasting information sharing. L. Wu et al. (2014) investigated the general role of supply chain partnerships and shared their views on supply chain information sharing. Quantity discount contracts also play an active role in coordination. J. Zhang and Chen (2013) investigated the use of quantity discount contracts to achieve supply chain coordination when demand is uncertain. L. Liu et al. (2021) constructed a supply chain game model with quantity discount contracts to identify intrinsic constraints to achieving supply chain coordination when market demand, price, and risk aversion simultaneously interfere under information asymmetry. However, considering the unique characteristics of pharmaceuticals and the special role of pharmaceutical GPOs in the supply chain, these studies fail to fully explain how demand information sharing and quantity discount contracts influence the coordinated operation of GPO-involved pharmaceutical supply chains. This study addresses this research gap by aiming to resolve the issues of decision-making failures and operational efficiency declines in pharmaceutical supply chains caused by the introduction of GPOs.

This study focuses on the problem in which the introduction of pharmaceutical GPOs may lead to decision-making failures and reduce operational efficiency in the pharmaceutical supply chain. In a four-level supply chain comprising pharmaceutical suppliers, pharmaceutical GPOs, medical institutions, and pharmaceutical buyers, a coordination model of quantity discount contracts in the pharmaceutical supply chain is established, which considers the existence of a GPO under demand information sharing. A Steinberg game model is then used to describe the dynamic interaction process among the main bodies of the pharmaceutical supply chain. Furthermore, the game problem is solved using the inverse solution method, and the effectiveness and practicability of the model are further verified through simulation analysis.

This study makes two main contributions to the literature. First, the members of the pharmaceutical supply chain with GPOs are comprehensively considered using changes in the demand forecast value and actual demand of pharmaceutical GPOs and medical institutions to portray the concept of demand information sharing in a pharmaceutical supply chain with GPOs, and the effects of demand information sharing on the benefits of pharmaceutical GPO supply chain operation are analyzed under various decision scenarios. Second, a quantity discount contract coordination model of the pharmaceutical GPO supply chain under demand information sharing is developed, focusing on the effects of the quantity discount rate, market demand forecast, market competition environment, and degree of demand information sharing on the coordination of pharmaceutical GPO supply chain operations.

Literature Review

This study focuses on pharmaceutical supply chains and selects quantity discount contracts to examine the characteristics of pharmaceutical GPOs for high-volume procurement. Furthermore, the impact of the coordination mechanism of quantity discount contracts on overall supply chain efficiency under demand information sharing is discussed. The literature review considers three main factors based on the content of this study: the role of pharmaceutical GPOs, supply chain information sharing, and quantity discount contracts.

Pharmaceutical Group Procurement

Pharmaceutical group purchasing originated in the United States and is an effective method for controlling pharmaceutical procurement costs and medical expenses in most developed countries. It is also a typical representative of the market-oriented operation of pharmaceutical purchasing (Xu et al., 2020) and a negotiation agent between manufacturers and retailers (Ailawadi et al., 2020). However, the characteristics of pharmaceutical GPOs vary among countries (Vogler et al., 2022). Ahmadi et al. (2019) analyzed the coordinating role of pharmaceutical GPOs in the pharmaceutical supply chain and expounded on the role and principle of GPOs in reducing pharmaceutical prices. In addition to price reduction, pharmaceutical GPO have achieved substantial results in ensuring pharmaceutical supply, standardizing pharmaceutical circulation orders, and simplifying procurement processes (Gao et al., 2020; Xing & Tang, 2021). Despite these advantages, changes in pharmaceutical GPOs may affect hospitals’ supply cost efficiency and their economic benefits, financial status, and service quality (In et al., 2019; Lee et al., 2023; Walker et al., 2021). Furthermore, scholars such as J. C. Lu et al. (2022) have evaluated the influence of pharmaceutical group purchasing policies on pharmaceutical use in public medical institutions, concluding that pharmaceutical group purchasing can gradually concentrate on winning and generic pharmaceuticals, and more importantly, guarantee pharmaceutical quality. From a modeling perspective, Oktay and Barış (2018) developed a two-stage demand, price-stochastic supply chain model comprising multiple buyers, suppliers, and a GPO. Through a case study, they showed that GPOs can help buyers and suppliers effectively reduce demand and price risks and obtain profits. Thus, pharmaceutical GPOs play a crucial role in the pharmaceutical supply chain but also face certain operational challenges.

Supply Chain Information Sharing

Including pharmaceutical GPOs intensifies the bullwhip and double-marginal effects on the supply chain. However, information sharing and establishing a contract model can improve supply chain efficiency to a certain extent. Supply chain information sharing involves exchanging key data (e.g., market demand, inventory levels, costs, and production plans) between upstream and downstream members. This study specifically focuses on demand information sharing because it is most relevant to the coordination of quantity discount contracts in pharmaceutical supply chains with GPOs. W. L. Wang and Wang (2020) examined how an information-sharing model of retailers’ demand forecasts can be built from the perspective of innovation investment in the context of competition between two manufacturers. Furthermore, they used Bayesian statistical theory and the Steinberg game method to explore the influence of competition among manufacturers and their cost reduction innovation on retailers’ demand forecast information sharing. Sun and Cai (2024) found that the preferences of supply chain members with retailer competition under asymmetric demand information are related to the degree of demand uncertainty and intensity of competition. X. M. Zhang et al. (2024) examined the influence of the information-sharing decision of the Cross-border E-commerce Platform on the choice of logistics mode by constructing a multi-stage game model, and found that sharing information is not always beneficial in this context. S. Z. Lu et al. (2024) utilized artificial neural networks and digital twins to build quality models and achieve better management of fresh products in the cold chain.

Some scholars have focused on incentives for information sharing in supply chains. Guan et al. (2019) examined the information sharing and incentive problems in the product-service supply chain when manufacturers provide both products and related services in an uncertain demand environment. By constructing a dynamic game model with incomplete information, the effects of the retailer’s information-sharing level, manufacturer’s service efficiency, and consumer’s service sensitivity on service and information-sharing value were analyzed, and an information-sharing incentive strategy based on two compensation contracts was proposed. Some scholars have focused on the value that information sharing provides. Shi et al. (2019, 2020) studied the influence of the green cost coefficient on information sharing discussed the information sharing of green supply chain demand forecasting under government subsidies and the optimal decision-making and expected profits of upstream and downstream enterprises with and without information sharing, and obtained the value of information sharing by comparing the optimal expected profits.

Quantity Discount Contracts

Effective contract coordination mechanisms and information sharing are important tools for improving supply chain efficiency. Scholars have developed various supply chain contract models, such as quantity discount (Y. W. Zhou et al., 2021), revenue-sharing (Lan et al., 2024), cost-sharing (Jia et al., 2024), return, and quantity flexibility contracts. Among these, quantity discounts can effectively reduce transaction costs and offer sufficient flexibility to achieve profit distribution. Considering that the high-volume procurement characteristic of pharmaceutical GPOs aligns with the core logic of quantity discount contracts, scholars have demonstrated that such contracts can enhance supply chain profit gains and improve operational efficiency. Y. F. Zhang et al. (2020) introduced a quantity discount contract to coordinate the supply chain of time-lagged deteriorating goods and enable the entire supply chain system to achieve an optimal state under centralized decision-making. Zheng et al. (2019) examined the supplier’s optimal pricing decision and the retailer’s optimal purchasing decision under a quantity discount contract for a fresh agricultural product supply chain composed of one supplier and multiple retailers and tested the influence of the deterioration rate on the supply chain’s profits. S. S. Wu and Li (2021) constructed an urgent quantity discount contract and discussed the inherent law of supply chain coordination contracts with stochastic market demand and price and risk-averse suppliers. Furthermore, the risk measurement standard of Conditional Value at Risk has been revised. Blockchain is also expected to solve the problem of transaction resource allocation among several untrusted participants in the fresh fruit supply chain, and smart contracts have been shown to reduce communication and trust costs (Y. Q. Zhang et al., 2022). The influence of the cost advantage on fresh-keeping and outsourcing decision-making considered that the third-party logistics service provider has a cost advantage, and designed a quantity discount contract to develop an improved outsourcing fresh-keeping strategy. They concluded that this strategy can achieve Pareto improvement under an appropriately designed quantity discount incentive contract (G. L. Wang et al., 2023).

The above literature review indicates that domestic and international scholars have conducted several studies on pharmaceutical group procurement, supply chain information sharing, and quantity discount contracts. The findings of these studies hold high reference value; however, several research gaps remain, which are primarily reflected in three aspects. First, research on pharmaceutical GPOs is insufficient, and the literature mainly focuses on the role of the pharmaceutical group procurement model in reducing pharmaceutical prices and ensuring supply, with little research on information sharing between pharmaceutical GPOs and medical institutions. Second, although several studies have examined information sharing in the supply chain, the discussion on information sharing in the pharmaceutical supply chain environment with GPOs remains insufficient. Third, research on the coordination mechanism of pharmaceutical supply chains with GPOs also needs to be expanded, particularly in the context of demand information sharing, while the literature on coordination research using quantity discount contracts is relatively scarce.

Problem Description and Model Building

Problem Description

In a pharmaceutical supply chain involving GPOs, the demand information sharing mechanism between medical institutions and pharmaceutical GPOs is realized by medical institutions sharing their forecasted values of pharmaceutical demand with GPOs. When demand information is shared, pharmaceutical GPOs are consistent with the actual purchase volume of medical institutions. When demand information is not shared, pharmaceutical GPOs decide on the purchasing benchmark quantity based on historical experience, which differs from the actual purchasing quantity of medical institutions. In this study, we consider a pharmaceutical supply chain comprising two medical institutions, a pharmaceutical GPO, a pharmaceutical supplier, and pharmaceutical purchasers. Figure 1 shows a diagram of the procurement process.

Figure 1.

Flowchart of pharmaceutical supply chain procurement with a GPO.

This study draws on prior research methods to establish the models (Ha et al., 2011; Hackner, 1999; Nie & Du, 2017; X. H. Wu & Ai, 2022; Xia et al., 2013; J. H. Zhou & Chang, 2022). We retain the basic concepts and research methods applied in previous research and combine them with the content of this study to establish a quantity discount contract model for a pharmaceutical supply chain involving pharmaceutical purchasers, healthcare providers, pharmaceutical GPOs, and pharmaceutical suppliers. The basic hypotheses of this study are as follows:

• Hypothesis 1: Pharmaceutical purchasers make purchases at medical institutions, and the pharmaceutical GPO aggregates procurement demand from medical institutions before bargaining with suppliers who joined the GPO at a price of ${\mathrm{w}}_{\mathrm{s}}$ .

• Hypothesis 2: The pharmaceutical GPO charges a contract management fee, at which time it sets the contract management fee with the supplier by a certain percentage of the procurement value, percentage parameter $\mathrm{\alpha }$ , and the pharmaceutical supplier provides a volume discount contract to the pharmaceutical GPO at discount rate $\mathrm{k}$ decided independently by the supplier. The final pharmaceutical GPO then sells to medical institutions at wholesale prices ${\mathrm{w}}_1$ and ${\mathrm{w}}_2$ (L. Wu, Guo & Nie, 2023; L. Wu, Guo, Nie & Li, 2023; Zhou, Dan & Zhou, 2017).

• Hypothesis 3: Healthcare providers, pharmaceutical purchasers, and the corresponding pharmaceutical supplier are not directly connected. The pharmaceutical supplier is only directly connected to the pharmaceutical GPO. In addition, both healthcare providers (1 and 2) and the pharmaceutical GPOs are homogeneous.

• Hypothesis 4: The basic expression of the quantity discount contract in this study is ${\mathrm{w}}_{\mathrm{s}}={\mathrm{w}}_0-\mathrm{k}({\mathrm{D}}_1+{\mathrm{D}}_2)$ . Here, $0<{\mathrm{w}}_0<{\mathrm{a}}_0,\mathrm{k}>0$ . ${\mathrm{w}}_0$ is the base price, and $\mathrm{k}$ is the quantity discount rate, which denotes the economies of scale achievable through the GPO-centralized lot size. The larger the discount rate, the higher the economies of scale, with the constraint that ${\mathrm{w}}_{\mathrm{s}}>0$ (Fan et al., 2019; Hu et al., 2012; S. Y. Li et al., 2025).

Demand Function Construction

Referring to Yan et al. (2019) and P. Liu et al. (2023), the inverse demand function for supply chain members is as follows:

$$\begin{array}{c}\multicolumn{1}{c}{{\mathrm{D}}_1=\mathrm{a}-{\mathrm{p}}_1+\mathrm{\gamma }{\mathrm{p}}_2}\\ \multicolumn{1}{c}{{\mathrm{D}}_2=\mathrm{a}-{\mathrm{p}}_2+\mathrm{\gamma }{\mathrm{p}}_1}\end{array}$$

where $\mathrm{\gamma }(0<\gamma <1)$ is the coefficient of the effect of competitors’ outputs on price. Here, a larger $\mathrm{\gamma }$ indicates less differentiation between the two products and more intense competition between healthcare providers (Qi & Zhang, 2024; X. F. Wang et al., 2024). Potential market demand ${\mathrm{a}}_1$ and ${\mathrm{a}}_2$ are random variables, in that $\mathrm{a}={\mathrm{a}}_0+\mathrm{\xi }$ , where $\mathrm{\xi }$ represents demand uncertainty following a normal distribution with an expectation of 0 and a variance of $\mathrm{v}$ . In the face of uncertain market demand, healthcare organizations make market demand forecasts, thereby facilitating informed decision-making. Assume that the market forecast value is $\mathrm{f}$ , while $\mathrm{f}=\mathrm{a}+\mathrm{\zeta }$ , $\mathrm{\zeta }$ represents the forecast error term of healthcare providers with an expectation of 0 and a variance of $\mathrm{s}$ , where $\mathrm{v}$ and $\mathrm{s}$ are independent of each other (Tan et al., 2024; Yang et al., 2021; Zhou, Dan, Ma & Xumei, 2017). Following L. Li (2002), we obtain the following:

$$\mathrm{E}(\mathrm{a}|\mathrm{f})=\frac{\mathrm{s}{\mathrm{a}}_0}{\mathrm{v}+\mathrm{s}}+\frac{\mathrm{vf}}{\mathrm{v}+\mathrm{s}}=\mathrm{A}$$

$$\mathrm{E}\left({(\mathrm{f}-{\mathrm{a}}_0)}^2\right)=\mathrm{v}+\mathrm{s}$$

Let $\mathrm{t}=\frac{\mathrm{v}}{\mathrm{v}+\mathrm{s}}\in (0,1)$ , which indicates the market prediction accuracy of the healthcare provider. The larger $\mathrm{t}$ is, the more accurate the healthcare provider’s market prediction and vice versa. Thus, we obtain the following:

$$\mathrm{E}(\mathrm{a}|\mathrm{f})=(1-\mathrm{t}){\mathrm{a}}_0+\mathrm{tf}=\mathrm{A}$$

When $\mathrm{f}>{\mathrm{a}}_0$ , the forecast value of the market demand by medical institutions is greater than the average value of the potential market size. Then, medical institutions become optimistic about the forecasted market demand. When $\mathrm{f}<{\mathrm{a}}_0$ , the value of the market demand forecasted by medical institutions is less than the average value of the potential market size. Then, medical institutions are pessimistic about the forecasted market demand.

Symbol Description

Table 1 provides descriptions of the symbols used for the main variables in this study.

Table 1.

Description of Model Symbols.

${\mathrm{D}}_1$ , ${\mathrm{D}}_2$	Procurement requirements of medical institutions 1 and 2
${\mathrm{w}}_{\mathrm{s}}$	The price at which a pharmaceutical GPO purchases a pharmaceutical from a supplier
$\mathrm{k}$	Quantity discount rates offered by suppliers
θ	Fixed membership fees that providers must pay to pharmaceutical GPOs
$\mathrm{\gamma }$	Coefficient of the impact of competitors’ output on price
$\mathrm{a}$	Potential market demand
$\mathrm{\xi }$	Demand uncertainty, which obeys a normal distribution with an expectation of 0 and a variance of $\mathrm{v}$
$\mathrm{f}$	Market forecast for medical institutions
$\mathrm{\zeta }$	Prediction error term for medical institutions with an expectation of 0 and a variance of $\mathrm{s}$
$\mathrm{t}$	Market forecast accuracy for medical institutions
${\mathrm{a}}_0$	Average potential market size
${\mathrm{p}}_1$ , ${\mathrm{p}}_2$	Consumer purchase prices at medical institutions 1 and 2
${\mathrm{w}}_1$ , ${\mathrm{w}}_2$	The purchase price at the pharmaceutical GPO for healthcare providers 1 and 2
α	The pharmaceutical GPO and the supplier set the contract management fee according to a certain percentage of the purchase value (i.e., parameter α)

Quantitative Discount Contract Model Construction and Solution Results

Quantity Discount Contract Model Construction and Solution Results Without Information Sharing

According to the above, the profit composition of the medical institution acquires revenue from pharmaceutical sales and procurement costs through the pharmaceutical GPO and membership fee $\mathrm{\theta }$ paid to the GPO. In this study, we consider several aspects of the profit composition of medical institutions more comprehensively than has been done in prior research, similar to L. Wu, Guo and Nie (2023); L. Wu, Guo, Nie and Li (2023) However, this study considers the membership fees paid by medical institutions to pharmaceutical GPO in greater depth. Without demand information sharing, the demand for pharmaceuticals at medical institutions 1 and 2 represents the market forecast values ${\mathrm{D}}_1|\mathrm{f}$ and ${\mathrm{D}}_2|\mathrm{f}$ , respectively, and ${\mathrm{w}}_1$ and ${\mathrm{w}}_2$ are the procurement prices for medical institutions 1 and 2 through the pharmaceutical GPO, respectively. Thus, the profit functions of medical institutions 1 and 2 are expressed as follows:

$$\begin{array}{c}\multicolumn{1}{c}{\underset{{\mathrm{D}}_1}{max}{\mathrm{\pi }}_{\mathrm{h}1}=({\mathrm{p}}_1-{\mathrm{w}}_1){\mathrm{D}}_1|\mathrm{f}-\mathrm{\theta }}\\ \multicolumn{1}{c}{\underset{{\mathrm{D}}_2}{max}{\mathrm{\pi }}_{\mathrm{h}2}=({\mathrm{p}}_2-{\mathrm{w}}_2){\mathrm{D}}_2|\mathrm{f}-\mathrm{\theta }}\end{array}$$

The profit composition of the pharmaceutical GPO consists of membership fees collected from medical institutions, contract management fees collected from suppliers, revenue from selling pharmaceuticals to medical institutions, and supplier procurement costs. Here, ${\mathrm{w}}_{\mathrm{s}}$ represents the price at which the pharmaceutical GPO procures pharmaceuticals from suppliers. The pharmaceutical GPO and suppliers set contract management fees following a certain percentage of the purchase value (i.e., ratio parameter $\mathrm{\alpha }$ ). At this time, the demand for the pharmaceutical GPO is its independent market forecast (i.e., ${\mathrm{D}}_1$ and ${\mathrm{D}}_2$ ), and the profit function of the GPO is as follows:

$$\underset{{\mathrm{w}}_1,{\mathrm{w}}_2}{max}{\mathrm{\pi }}_{\mathrm{g}}=(1-\mathrm{\alpha })(({\mathrm{w}}_1-{\mathrm{w}}_{\mathrm{s}}){\mathrm{D}}_1+({\mathrm{w}}_2-{\mathrm{w}}_{\mathrm{s}}){\mathrm{D}}_2)+2\mathrm{\theta }$$

The medical institutions, pharmaceutical GPOs, consumers, and suppliers in the pharmaceutical supply chain with GPOs comprise the Steinberg game. Pharmaceutical GPOs play the dominant role in this supply chain; therefore, they act as game leaders. The inverse induction method is used to solve the game, which yields expressions of profits among supply chain members and expressions of price and demand under the equilibrium solution (see the Appendix for the proof process), as follows:

$${\mathrm{w}}_{\mathrm{s}}^{*}={\mathrm{w}}_0+\frac{\mathrm{k}({\mathrm{a}}_0(-1+\mathrm{t}(-1+\mathrm{\gamma }))-(\mathrm{ft}+{\mathrm{w}}_0)(-1+\mathrm{\gamma }))}{2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma }}$$

$$\begin{array}{c}\multicolumn{1}{c}{{\mathrm{p}}_1^{*}={\mathrm{p}}_2^{*}=\frac{1}{2}(\frac{\mathrm{A}-2{\mathrm{a}}_0\mathrm{k}+{\mathrm{w}}_0}{2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma }}-\frac{{\mathrm{a}}_0}{-1+\mathrm{\gamma }})}\\ \multicolumn{1}{c}{{\mathrm{D}}_1^{*}={\mathrm{D}}_2^{*}=\frac{-{\mathrm{a}}_0(-2+\mathrm{\gamma })+\mathrm{A}(-1+\mathrm{\gamma })+{\mathrm{w}}_0(-1+\mathrm{\gamma })}{4+4\mathrm{k}(-1+\mathrm{\gamma })-2\mathrm{\gamma }}}\\ \multicolumn{1}{c}{\begin{array}{c}\multicolumn{1}{c}{{\mathrm{D}}_1^{*}|\mathrm{f}={\mathrm{D}}_1^{*}|\mathrm{f}=}\\ \multicolumn{1}{c}{\frac{\mathrm{A}(3+4\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })+{\mathrm{w}}_0(-1+\mathrm{\gamma })+{\mathrm{a}}_0(-2+4\mathrm{k}+\mathrm{\gamma }-4\mathrm{k}\mathrm{\gamma })}{4+4\mathrm{k}(-1+\mathrm{\gamma })-2\mathrm{\gamma }}}\end{array}}\\ \multicolumn{1}{c}{\begin{array}{c}\multicolumn{1}{c}{{\mathrm{\pi }}_{\mathrm{h}1}^{*}={\mathrm{\pi }}_{\mathrm{h}2}^{*}=}\\ \multicolumn{1}{c}{\frac{{(\mathrm{A}(3+4\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })+{\mathrm{w}}_0(-1+\mathrm{\gamma })+{\mathrm{a}}_0(-2+4\mathrm{k}+\mathrm{\gamma }-4\mathrm{k}\mathrm{\gamma }))}^2}{4{(-2-2\mathrm{k}(-1+\mathrm{\gamma })+\mathrm{\gamma })}^2}-\mathrm{\theta }}\end{array}}\\ \multicolumn{1}{c}{{\mathrm{\pi }}_{\mathrm{g}}^{*}=(\mathrm{\alpha }-1)\frac{{(\mathrm{A}-2{\mathrm{a}}_0+{\mathrm{w}}_0-(\mathrm{A}-{\mathrm{a}}_0+{\mathrm{w}}_0)\mathrm{\gamma })}^2}{2(2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })(-1+\mathrm{\gamma })}+2\mathrm{\theta }}\end{array}$$

Quantity Discount Contract Model Construction and Solution With Demand Information Sharing

Likewise, the profit function of the medical institution is obtained as follows:

$$\begin{array}{c}\multicolumn{1}{c}{\underset{{\mathrm{D}}_1}{max}{\mathrm{\pi }}_{\mathrm{h}1}=({\mathrm{p}}_1-{\mathrm{w}}_1){\mathrm{D}}_1|\mathrm{f}-\mathrm{\theta }}\\ \multicolumn{1}{c}{\underset{{\mathrm{D}}_2}{max}{\mathrm{\pi }}_{\mathrm{h}2}=({\mathrm{p}}_2-{\mathrm{w}}_2){\mathrm{D}}_2|\mathrm{f}-\mathrm{\theta }}\end{array}$$

With demand information sharing, the demand for pharmaceutical GPOs is the forecasted value of the demand shared by healthcare providers with the GPO (i.e., ${\mathrm{D}}_1|\mathrm{f}$ and ${\mathrm{D}}_2|\mathrm{f}$ ). The profit function of the pharmaceutical GPO is as follows:

$$\underset{{\mathrm{w}}_1,{\mathrm{w}}_2}{max}{\mathrm{\pi }}_{\mathrm{g}}=(1-\mathrm{\alpha })\left(({\mathrm{w}}_1-{\mathrm{w}}_{\mathrm{s}}){\mathrm{D}}_1|\mathrm{f}+({\mathrm{w}}_2-{\mathrm{w}}_{\mathrm{s}}){\mathrm{D}}_2|\mathrm{f}\right)+2\mathrm{\theta }$$

Similarly, the supply chain profit and price and demand expressions with demand information sharing (see the Appendix for the proof process) can be obtained as follows:

$$\begin{array}{c}\multicolumn{1}{c}{{\mathrm{p}}_1^{*}={\mathrm{p}}_2^{*}=\frac{1}{2}(\frac{\mathrm{A}-2\mathrm{Ak}+{\mathrm{w}}_0}{2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma }}-\frac{\mathrm{A}}{-1+\mathrm{\gamma }})}\\ \multicolumn{1}{c}{{\mathrm{D}}_1^{*}|\mathrm{f}={\mathrm{D}}_2^{*}|\mathrm{f}=\frac{\mathrm{A}+{\mathrm{w}}_0(-1+\mathrm{\gamma })}{4+4\mathrm{k}(-1+\mathrm{\gamma })-2\mathrm{\gamma }}}\\ \multicolumn{1}{c}{{\mathrm{\pi }}_{\mathrm{h}1}^{*}={\mathrm{\pi }}_{\mathrm{h}2}^{*}=\frac{{(\mathrm{A}+{\mathrm{w}}_0(-1+\mathrm{\gamma }))}^2}{4{(-2-2\mathrm{k}(-1+\mathrm{\gamma })+\mathrm{\gamma })}^2}-\mathrm{\theta }}\\ \multicolumn{1}{c}{{\mathrm{\pi }}_{\mathrm{g}}^{*}=\frac{(1-\mathrm{\alpha }){(\mathrm{A}+{\mathrm{w}}_0(-1+\mathrm{\gamma }))}^2}{2(2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })(1-\mathrm{\gamma })}+2\mathrm{\theta }}\end{array}$$

Analysis of the Results

Sensitivity Analysis

The relationships between price, demand, and key factors, such as market forecast values, with and without demand information sharing, are analyzed to explore the impact on each member’s price and demand. Detailed proofs are provided in the Appendix.

Proposition 1: With demand information sharing, market forecast values and demand are always positively correlated. Consumer prices, which were previously constant with respect to forecasts, become positively correlated under conditions $0<\mathrm{\gamma }\le \frac{1}{2}$ , $0<k<\frac{-3+2\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ , and $\frac{1}{2}<\gamma <1$ . Thus, information sharing generally increases demand for medical institutions and GPOs, lowers consumer purchase costs, raises institutional procurement costs, and increases GPO revenue.

Analysis Without Demand Information Sharing

$$\frac{\partial {\mathrm{w}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\mathrm{t}(-2-4\mathrm{k}(-1+\mathrm{\gamma })+\mathrm{\gamma })}{4+4\mathrm{k}(-1+\mathrm{\gamma })-2\mathrm{\gamma }}$$

(1)

The partial derivation of the purchase price for medical institutions considering the market forecast value shows that when $0<\mathrm{\gamma }\le \frac{2}{3}$ , if $0<\mathrm{k}<\frac{-2+\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ , that is, when the market competition and quantity discount rate are low, $\frac{\partial {\mathrm{w}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{N}}}{\partial \mathrm{f}}<0$ . Then, the purchase price for medical institutions decreases with an increase in the market forecast value. Otherwise, $\frac{\partial {\mathrm{w}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{N}}}{\partial \mathrm{f}}>0$ . When $\frac{2}{3}<\gamma <1$ , that is when the market competition is high, $\frac{\partial {\mathrm{w}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{N}}}{\partial \mathrm{f}}<0.$

$$\frac{\partial {\mathrm{p}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{p}}_2^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\mathrm{t}}{4+4\mathrm{k}(-1+\mathrm{\gamma })-2\mathrm{\gamma }}>0.$$

(2)

Here, the results are constantly greater than 0, indicating a positive correlation. The greater the market forecast value, the higher the consumer purchase price.

$$\frac{\partial {\mathrm{D}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\mathrm{t}(-1+\mathrm{\gamma })}{4+4\mathrm{k}(-1+\mathrm{\gamma })-2\mathrm{\gamma }}<0$$

(3)

Here, the results are constantly less than 0, indicating a negative correlation. The larger the market forecast value of pharmaceutical GPOs, the lower the demand.

$$\frac{\partial {\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\mathrm{t}(3+4\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })}{4+4\mathrm{k}(-1+\mathrm{\gamma })-2\mathrm{\gamma }}$$

(4)

When $0<\mathrm{\gamma }\le \frac{1}{3}$ , if $0<\mathrm{k}<\frac{-3+\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ , that is, when market competition and volume discount rates are low, $\frac{\partial {\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}>0$ . Here, the demand for healthcare facilities increases with the market forecast. Otherwise, $\frac{\partial {\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}<0$ . When $\frac{1}{3}<\gamma <1$ , $\frac{\partial {\mathrm{w}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{N}}}{\partial \mathrm{f}}>0$ if market competition is high.

Analysis With Demand Information Sharing

$$\frac{\partial {\mathrm{w}}_1^{\mathrm{SG}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{SG}}}{\partial \mathrm{f}}=\mathrm{t}(\frac{1}{2-2\mathrm{\gamma }}-\frac{\mathrm{k}}{2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma }})$$

(1)

When $0<\mathrm{\gamma }\le \frac{2}{3}$ , $0<\mathrm{k}<\frac{-2+\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ , when the market competition and quantity discount rate are low, $\frac{\partial {\mathrm{w}}_1^{\mathrm{SG}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{SG}}}{\partial \mathrm{f}}>0$ . Here, the purchase price for medical institutions increases with the market forecast value; no demand information sharing can further reduce the purchase price, and vice versa. When market competition and the quantity discount rates are high, $\frac{\partial {\mathrm{w}}_1^{\mathrm{SG}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{SG}}}{\partial \mathrm{f}}<0$ , at which point demand information sharing can reduce the purchase price to some extent. When $\frac{2}{3}<\gamma <1$ , we obtain $\frac{\partial {\mathrm{w}}_1^{\mathrm{SG}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{SG}}}{\partial \mathrm{f}}>0$ . Thus, when market competition is high, the purchase price for medical institutions increases with the market forecast value.

$$\frac{\partial {\mathrm{p}}_1^{\mathrm{SG}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{p}}_2^{\mathrm{SG}}}{\partial \mathrm{f}}=\frac{1}{2}(\frac{\mathrm{t}-2\mathrm{kt}}{2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma }}-\frac{\mathrm{t}}{-1+\mathrm{\gamma }})$$

(2)

When $0<\mathrm{\gamma }\le \frac{1}{2}$ , if $0<\mathrm{k}<\frac{-3+2\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ , that is, when market competition and quantity discount rates are low, $\frac{\partial {\mathrm{p}}_1^{\mathrm{SG}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{p}}_2^{\mathrm{SG}}}{\partial \mathrm{f}}>0$ . Here, the consumer purchase price is positively correlated with the market forecast value; otherwise, $\frac{\partial {\mathrm{p}}_1^{\mathrm{SG}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{p}}_2^{\mathrm{SG}}}{\partial \mathrm{f}}<0$ . When $\frac{1}{2}<\gamma <1$ , $\frac{\partial {\mathrm{p}}_1^{\mathrm{SG}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{p}}_2^{\mathrm{SG}}}{\partial \mathrm{f}}>0$ if market competition is high.

$$\frac{\partial {\mathrm{D}}_1^{\mathrm{SG}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{SG}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\mathrm{t}}{4+4\mathrm{k}(-1+\mathrm{\gamma })-2\mathrm{\gamma }}>0.$$

(3)

With demand information sharing, the demand among medical institutions and pharmaceutical GPOs is the same and positively correlated with the market forecast value (i.e., the higher the market forecast value, the higher the demand).

This study is consistent with Zhang and Chen (2013) and L. Liu et al. (2021), who have emphasized the potential of quantity discount contracts to improve supply chain efficiency and realize coordination. However, this study not only analyzes the influence of quantity discount contracts on supply chain coordination but also discusses the role of demand information sharing in depth. Comparatively, prior studies have often considered only quantity discount contracts or information sharing.

Contrast Analysis

Comparative Analysis of Purchasing Prices

Here, we compare procurement prices with and without demand information sharing to evaluate the effects on price levels.

• Proposition 2: When $\mathrm{f}>{\mathrm{a}}_0$ , medical institutions are optimistic about market demand and information sharing reduces procurement prices.

w_s Comparison

• Corollary 1:  ${\mathrm{w}}_{\mathrm{s}}^{\mathrm{N}}-{\mathrm{w}}_{\mathrm{s}}^{\mathrm{S}}=\frac{({\mathrm{a}}_0-\mathrm{f})\mathrm{kt}(\mathrm{\gamma }-2)}{2+2\mathrm{k}(\mathrm{\gamma }-1)-\mathrm{\gamma }}$

${\mathrm{w}}_{\mathrm{s}}^{\mathrm{S}},{\mathrm{w}}_{\mathrm{s}}^{\mathrm{N}}$ indicate the purchase prices for pharmaceutical GPOs with and without demand information sharing, respectively. When $\mathrm{f}>{\mathrm{a}}_0$ , ${\mathrm{w}}_{\mathrm{s}}^{\mathrm{N}}-{\mathrm{w}}_{\mathrm{s}}^{\mathrm{S}}<0$ , that is, when the forecast value of market demand by medical institutions is greater than the mean potential market size, medical institutions become optimistic about market demand forecasts, and demand information sharing can increase purchase prices for pharmaceutical GPOs. Conversely, ${\mathrm{w}}_{\mathrm{s}}^{\mathrm{N}}-{\mathrm{w}}_{\mathrm{s}}^{\mathrm{S}}>0$ , that is, when the market demand forecast is pessimistic, demand information sharing can decrease purchase prices for pharmaceutical GPOs.

w Comparison

• Corollary 2:  ${\mathrm{w}}_1^{\mathrm{N}}-{\mathrm{w}}_1^{\mathrm{S}}={\mathrm{w}}_2^{\mathrm{N}}-{\mathrm{w}}_2^{\mathrm{S}}=\frac{({\mathrm{a}}_0-\mathrm{f})\mathrm{t}(2+4\mathrm{k}(\mathrm{\gamma }-1)-\mathrm{\gamma })(2-\mathrm{\gamma })}{2(2+2\mathrm{k}(\mathrm{\gamma }-1)-\mathrm{\gamma })(1-\mathrm{\gamma })}$

${\mathrm{w}}_1^{\mathrm{N}}$ , ${\mathrm{w}}_1^{\mathrm{S}}$ , ${\mathrm{w}}_2^{\mathrm{N}}$ , and ${\mathrm{w}}_2^{\mathrm{S}}$ denote the purchase prices for medical institutions with and without demand information sharing. When $0<\mathrm{\gamma }\le \frac{2}{3}$ and $0<\mathrm{k}<\frac{-2+\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ , or when $\frac{2}{3}<\gamma <1$ , if $\mathrm{f}>{\mathrm{a}}_0$ , ${\mathrm{w}}_1^{\mathrm{N}}-{\mathrm{w}}_1^{\mathrm{S}}={\mathrm{w}}_2^{\mathrm{N}}-{\mathrm{w}}_2^{\mathrm{S}}<0$ , that is, when market competition and the quantity discount rates are low or market competition is high, if medical institutions are optimistic about market demand forecasts, their purchase prices under demand information sharing are higher; otherwise, ${\mathrm{w}}_1^{\mathrm{N}}-{\mathrm{w}}_1^{\mathrm{S}}={\mathrm{w}}_2^{\mathrm{N}}-{\mathrm{w}}_2^{\mathrm{S}}>0$ .

When $0<\mathrm{\gamma }\le \frac{2}{3}$ and $\frac{-2+\mathrm{\gamma }}{-4+4\mathrm{\gamma }}<\mathrm{k}<1$ , if $\mathrm{f}>{\mathrm{a}}_0$ , ${\mathrm{w}}_1^{\mathrm{N}}-{\mathrm{w}}_1^{\mathrm{S}}={\mathrm{w}}_2^{\mathrm{N}}-{\mathrm{w}}_2^{\mathrm{S}}>0$ , that is, when the market competition is low, and the quantity discount rate is high, demand information sharing will increase medical institutions’ procurement costs if they are optimistic about market demand forecasts. Otherwise, ${\mathrm{w}}_1^{\mathrm{N}}-{\mathrm{w}}_1^{\mathrm{S}}={\mathrm{w}}_2^{\mathrm{N}}-{\mathrm{w}}_2^{\mathrm{S}}<0$ .

p Contrast

• Corollary 3:  ${\mathrm{p}}_1^{\mathrm{N}}-{\mathrm{p}}_1^{\mathrm{S}}={\mathrm{p}}_2^{\mathrm{N}}-{\mathrm{p}}_2^{\mathrm{S}}=\frac{({\mathrm{a}}_0-\mathrm{f})\mathrm{t}(2+4\mathrm{k}(\mathrm{\gamma }-1)-\mathrm{\gamma })}{2(2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })(1-\mathrm{\gamma })}$

When $0<\mathrm{\gamma }\le \frac{2}{3}$ and $0<\mathrm{k}<\frac{-2+\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ or when $\frac{2}{3}<\gamma <1$ , if $\mathrm{f}>{\mathrm{a}}_0$ , we obtain ${\mathrm{p}}_1^{\mathrm{N}}-{\mathrm{p}}_1^{\mathrm{S}}={\mathrm{p}}_2^{\mathrm{N}}-{\mathrm{p}}_2^{\mathrm{S}}<0$ . That is, when market competition and quantity discount rates are low or market competition is high, demand information sharing increases consumer purchase prices if providers are optimistic about market demand forecasts. Otherwise, ${\mathrm{p}}_1^{\mathrm{N}}-{\mathrm{p}}_1^{\mathrm{S}}={\mathrm{p}}_2^{\mathrm{N}}-{\mathrm{p}}_2^{\mathrm{S}}>0$ .

When $0<\mathrm{\gamma }\le \frac{2}{3}$ and $\frac{-2+\mathrm{\gamma }}{-4+4\mathrm{\gamma }}<\mathrm{k}<1$ , if $\mathrm{f}>{\mathrm{a}}_0$ , we obtain ${\mathrm{p}}_1^{\mathrm{N}}-{\mathrm{p}}_1^{\mathrm{S}}={\mathrm{p}}_2^{\mathrm{N}}-{\mathrm{p}}_2^{\mathrm{S}}>0$ . That is, when market competition is low and the quantity discount rate is high, if six medical institutions are optimistic about market demand forecasts, demand information sharing will reduce consumer purchase prices. Otherwise, ${\mathrm{p}}_1^{\mathrm{N}}-{\mathrm{p}}_1^{\mathrm{S}}={\mathrm{p}}_2^{\mathrm{N}}-{\mathrm{p}}_2^{\mathrm{S}}<0$ .

By comparing the purchase price without demand information sharing, we find that information sharing can reduce purchase costs for pharmaceutical buyers, which is consistent with some previous studies (e.g., L. Wu, Guo, Nie, & Li, 2023). However, this study further indicates that under the joint action of information sharing and quantity discount contracts, medical institutions may face rising procurement costs under certain conditions, depending on the market competition environment and quantity discount rate.

Demand Forecast Analysis

Here, we compare member demand levels with and without information sharing.

• Proposition 3: When $\mathrm{f}>{\mathrm{a}}_0$ , information sharing increases the demand across all supply chain members. The details are as follows:

D|f——Forecast of demand by medical institutions

• Corollary 4:  ${\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}=-\frac{({\mathrm{a}}_0-\mathrm{f})\mathrm{t}(2+4\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })}{2(2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })}$

When $0<\mathrm{\gamma }\le \frac{2}{3}$ and $0<\mathrm{k}<\frac{-2+\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ or when $\frac{2}{3}<\gamma <1$ , if $\mathrm{f}>{\mathrm{a}}_0$ , we obtain ${\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}>0$ . Thus, when market competition and quantity discount rates are low or market competition is high, demand information sharing can increase the demand purchase volume for medical institutions if they are optimistic about the demand forecasts of the market. Otherwise, ${\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}<0$ .

When $0<\mathrm{\gamma }\le \frac{2}{3}$ and $\frac{-2+\gamma }{-4+4\gamma }\mathrm{<k}\mathrm{<}1$ , if $\mathrm{f}>{\mathrm{a}}_0$ , we obtain ${\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}<0$ . That is, when market competition is low and the quantity discount rate is high, if medical institutions are optimistic about market demand forecasts, demand information sharing can increase their demand. Otherwise, ${\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}>0$ .

D——GPOs’ forecasts of market demand

• Corollary 5:  ${\mathrm{D}}_1^{\mathrm{N}}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}=\frac{({\mathrm{a}}_0-\mathrm{f})\mathrm{t}(2-\mathrm{\gamma })}{2(2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })}$

When there is no demand information sharing, the demand for pharmaceutical GPOs is ${\mathrm{D}}_1^{\mathrm{N}},{\mathrm{D}}_2^{\mathrm{N}}$ . When $\mathrm{f}>{\mathrm{a}}_0$ , ${\mathrm{D}}_1^{\mathrm{N}}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}<0$ , that is when healthcare providers are optimistic about market demand forecasts, demand information sharing can increase the demand for pharmaceutical GPOs. Otherwise, ${\mathrm{D}}_1^{\mathrm{N}}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}>0$ .

Supply Chain Revenue Analysis

Here, we examine revenue changes caused by information sharing.

• Proposition 4: Demand information sharing increases the GPO’s revenue when forecasts are optimistic. Under certain conditions, competition combined with quantity discount contracts also increases institutional revenue. The details are as follows:

Profit analysis of medical institutions

• Corollary 6: $\begin{array}{c}\multicolumn{1}{c}{{\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{S}}={\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{S}}=}\\ \multicolumn{1}{c}{\frac{-{({\mathrm{a}}_0-{\mathrm{a}}_0\mathrm{t}+\mathrm{ft}+{\mathrm{w}}_0(-1+\mathrm{\gamma }))}^2+{({\mathrm{a}}_0+\mathrm{ft}(3+4\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })+{\mathrm{w}}_0(-1+\mathrm{\gamma })+{\mathrm{a}}_0\mathrm{t}(-3-4\mathrm{k}(-1+\mathrm{\gamma })+\mathrm{\gamma }))}^2}{4{(2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })}^2}}\end{array}$

When $\mathrm{f}>{\mathrm{a}}_0$ , if $0<\mathrm{\gamma }\le \frac{2}{3}$ and $0<\mathrm{k}<\frac{-2+\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ or $\frac{2}{3}<\gamma <1$ , we obtain ${\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{S}}={\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{S}}>0$ , that is, when providers have optimistic forecasts of market demand, demand information sharing reduces provider revenue if market competition and volume discount rates are low or market competition is high. Otherwise, ${\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{S}}={\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{S}}<0$ .

When $0<\mathrm{f}<\frac{{\mathrm{a}}_0(2+4\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })-2{\mathrm{w}}_0(-1+\mathrm{\gamma })}{4+4\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma }}$ , if $\frac{2({\mathrm{a}}_0+{\mathrm{w}}_0(-1+\mathrm{\gamma }))}{({\mathrm{a}}_0-\mathrm{f})(4+4\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })}<\mathrm{t}<1$ , $0<\mathrm{\gamma }\le \frac{2}{3}$ , and $0<\mathrm{k}<\frac{-2+\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ , or $\frac{2}{3}<\gamma <1$ , we obtain ${\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{S}}={\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{S}}>0$ . Thus, when the provider’s forecast of market demand is extremely low, the provider becomes extremely pessimistic about potential market demand. If the provider’s forecast of market demand is low and market competition and quantity discount rates are low, or if market competition is high, demand information sharing will reduce the provider’s revenue. Otherwise, ${\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{S}}={\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{S}}<0$ .

Pharmaceutical GPO Profit Analysis

• Corollary 7: ${\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{S}}=\frac{({\mathrm{a}}_0-\mathrm{f})\mathrm{t}(1-\mathrm{\alpha })(2-\mathrm{\gamma })(2{\mathrm{w}}_0(-1+\mathrm{\gamma })+\mathrm{ft}\mathrm{\gamma }+{\mathrm{a}}_0(2-\mathrm{t}\mathrm{\gamma }))}{2(2+2\mathrm{k}(-1+\mathrm{\gamma })-\mathrm{\gamma })(1-\mathrm{\gamma })}$

When $\mathrm{f}>{\mathrm{a}}_0$ , ${\pi }_{\mathrm{g}}^{\mathrm{N}}-{\pi }_{\mathrm{g}}^{\mathrm{S}}\mathrm{<}0$ . Thus, when healthcare providers are optimistic about the market demand forecast, demand information sharing can increase the pharmaceutical GPO’s revenue. Otherwise, ${\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{S}}>0$ .

Above, the income changes for each member of the pharmaceutical supply chain are compared without demand information sharing. The results indicate that demand information sharing can increase the income of pharmaceutical GPO and medical institutions under certain conditions. This finding supports previous research conclusions that information sharing can increase the overall income of the supply chain (e.g., Shi et al., 2019, 2020; Zhou, Dan, & Yu, 2017). However, the difference is that this study further considers the role of the quantity discount rate and finds that information sharing and quantity discount contracts can collectively increase supply chain revenue.

Numerical Simulation Analysis

We conduct a numerical simulation analysis using MATLAB to better illustrate the effects of market demand forecasts, quantity discount rates, market competition, and other factors on prices, demand, and revenue in the pharmaceutical supply chain. This analysis validates the main propositions derived in the previous section. All the parameters are set within the previously established ranges: $\mathrm{t}=\frac{1}{2},{\mathrm{a}}_0=10,{\mathrm{w}}_0=5,\mathrm{f}=8$ . The red surfaces in the figures represent the reference planes (value = 0). Parameter values are determined based on in-depth interviews with personnel from five hospitals and eight enterprises and incorporate actual data, such as those on market demand, historical forecasts, procurement prices, and contract management fees. The specific rationale for each parameter is as follows. (1) $\mathrm{t}=\frac{1}{2}$ , indicating that medical institutions demonstrate moderate accuracy in forecasting market demand. This setting is based on a comparative analysis of the historical forecast data of medical institutions and actual market demand. The market forecast accuracy of most medical institutions is found to be at a medium level; thus, $\mathrm{t}$ is set to $\frac{1}{2}$ . (2) ${\mathrm{a}}_0=10$ , which reflects the comprehensive situation of the current pharmaceutical market scale and future growth potential. This value is determined based on extensive market research, including information collection and analysis of the scale, growth rate, and competition patterns in the pharmaceutical market. Simultaneously, we refer to the relevant literature (L. Wu, Guo, Nie, & Li, 2023; Zhou, Dan, & Yu, 2017), evaluate and predict the potential market size, and finally set average potential market size a₀ to 10. (3) ${\mathrm{w}}_0=5$ , representing the general trading level of pharmaceuticals in the market. By consulting several pharmaceutical price databases (including government-guided prices and market transaction prices) and referring to price data in industry reports, we sort and analyze the collected price data, including removing abnormal values and calculating average values. Based on the sorted price data, benchmark price ${\mathrm{w}}_0$ is set to 5. (4) $\mathrm{f}=8$ and $\mathrm{f}=13$ are used to reflect of medical institutions’ pessimistic and optimistic expectations for current market demand, respectively. These two values are randomly determined based on ${\mathrm{a}}_0=10$ to simulate the impact under different market expectation scenarios.

Sensitivity Analysis

Quantity Discount Contracts Without Demand Information Sharing

Figures 2 to 5 depict the relationships among prices, demand, market demand forecasts, market competition, and quantity discount rates for supply chain members in the presence of a pharmaceutical GPO without demand information sharing. With the red surface as the reference, as shown in Figure 2, when market competition is low, and the quantity discount rate is high, $\frac{\partial {\mathrm{w}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{N}}}{\partial \mathrm{f}}>0$ , indicating that an increase in market forecast value will lead to a decrease in the purchase price of medical institutions. As shown in Figures 3 and 4, $\frac{\partial {\mathrm{p}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{p}}_2^{\mathrm{N}}}{\partial \mathrm{f}}>0$ , $\frac{\partial {\mathrm{D}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{N}}}{\partial \mathrm{f}}<0$ . The result of $\frac{\partial {\mathrm{p}}_1^N}{\partial f}=\frac{\partial {\mathrm{p}}_2^N}{\partial f}$ is always greater than 0, which is positively correlated, indicating that the greater the market forecast value, the higher the purchasing price of pharmaceutical buyers. The constant value of $\frac{\partial {\mathrm{D}}_1^N}{\partial f}=\frac{\partial {\mathrm{D}}_2^N}{\partial f}$ is less than 0, which is negatively correlated, indicating that the greater the market forecast value, the lower the demand for pharmaceutical GPO. This is possibly because when the market forecast value increases, buyers may be more inclined to wait for better purchasing opportunities or seek more favorable prices, thus reducing the current purchasing volume. As Figure 5 shows, when market competition is low, and the quantity discount rate is high, $\frac{\partial {\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}<0$ , that is, the demand of medical institutions decreases as market forecast value increases. Otherwise, $\frac{\partial {\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}>0$ .

Figure 2.

Graph of the variation of $\frac{\partial {\mathrm{w}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{N}}}{\partial \mathrm{f}}$ .

Figure 3.

Graph of the variation of $\frac{\partial {\mathrm{p}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{p}}_2^{\mathrm{N}}}{\partial \mathrm{f}}$ .

Figure 4.

Graph of the variation of $\frac{\partial {\mathrm{D}}_1^{\mathrm{N}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{N}}}{\partial \mathrm{f}}$ .

Figure 5.

Graph of the variation of $\frac{\partial {\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}}{\partial \mathrm{f}}$ .

Quantity Discount Contracts With Demand Information Sharing

Figures 6 to 8 illustrate the relationships among the price, demand, market demand forecast value, market competition, and quantity discount rate for each member of the pharmaceutical supply chain with pharmaceutical GPOs and demand information sharing. As Figure 6 shows, when market competition is low, and the quantity discount rate is high, $\frac{\partial {\mathrm{w}}_1^{\mathrm{S}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{S}}}{\partial \mathrm{f}}<0$ , indicating that, with an increase in market forecast value, the price of medical institutions purchasing from the GPO will decrease. At this time, if medical institutions share demand information, their purchasing prices will further decrease because information sharing will help the GPO more accurately predict market demand and thus optimize purchasing and pricing strategies. Otherwise, $\frac{\partial {\mathrm{w}}_1^{\mathrm{S}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{S}}}{\partial \mathrm{f}}>0$ . As Figure 7 shows, when market competition is low, and the quantity discount rate is high, $\frac{\partial {\mathrm{p}}_1^{\mathrm{S}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{p}}_2^{\mathrm{S}}}{\partial \mathrm{f}}<0$ . Otherwise, $\frac{\partial {\mathrm{p}}_1^{\mathrm{S}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{p}}_2^{\mathrm{S}}}{\partial \mathrm{f}}>0$ . As Figure 8 shows, when $\frac{\partial {\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}}{\partial \mathrm{f}}>0$ , the demand of medical institutions and the pharmaceutical GPO is positively correlated with the market forecast value. Thus, with an increase in market forecast value, the demand of medical institutions and pharmaceutical GPO will increase accordingly. This finding emphasizes the importance of demand information sharing in promoting synergy among supply chain members and improving market demand response ability. The phenomena shown in Figures 6 to 8 are consistent with Proposition 1.

Figure 6.

Graph of the variation of $\frac{\partial {\mathrm{w}}_1^{\mathrm{S}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{w}}_2^{\mathrm{S}}}{\partial \mathrm{f}}$ .

Figure 7.

Graph of the variation of $\frac{\partial {\mathrm{p}}_1^{\mathrm{S}}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{p}}_2^{\mathrm{S}}}{\partial \mathrm{f}}$ .

Figure 8.

Graph of the variation of $\frac{\partial {\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}}{\partial \mathrm{f}}=\frac{\partial {\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}}{\partial \mathrm{f}}$ .

Contrast Analysis

Supply Chain Price and Revenue Analysis Under Pessimistic Market Demand Forecast

When $\mathrm{f}<{\mathrm{a}}_0$ , the forecasted market demand value among medical institutions is less than the average potential market size. Thus, we compare the changes in the purchase price and revenue of each member with and without demand information sharing, considering a pessimistic forecast of market demand from medical institutions (parameter settings: $\mathrm{t}=\frac{1}{2},{\mathrm{a}}_0=10,{\mathrm{w}}_0=5,\mathrm{f}=8$ ), to explore the impact of demand information sharing and quantity discount contracts on supply chain prices and revenue, as shown in Figures 9 to 14. As Figure 9 shows, ${\mathrm{w}}_{\mathrm{s}}^{\mathrm{N}}-{\mathrm{w}}_{\mathrm{s}}^{\mathrm{S}}<0$ , indicating that the pharmaceutical GPO’s purchase price has increased compared to that without information sharing. As Figures 10 and 11 show, when market competition is low, and the quantity discount rate is high, ${\mathrm{w}}_1^{\mathrm{N}}-{\mathrm{w}}_1^{\mathrm{S}}={\mathrm{w}}_2^{\mathrm{N}}-{\mathrm{w}}_2^{\mathrm{S}}<0$ , ${\mathrm{p}}_1^{\mathrm{N}}-{\mathrm{p}}_1^{\mathrm{S}}={\mathrm{p}}_2^{\mathrm{N}}-{\mathrm{p}}_2^{\mathrm{S}}<0$ . This indicates that with demand information sharing, the purchase prices of medical institutions and pharmaceutical buyers increase. This phenomenon is likely because with the improved transparency facilitated by information sharing, the pharmaceutical GPO’s procurement cost increases correspondingly owing to the increase in procurement price. To maintain its profit margins, the pharmaceutical GPO will tend to transfer this part of its increased costs to downstream medical institutions. Facing pressure from rising upstream costs, medical institutions may increase the selling price of pharmaceuticals to ensure operational stability and profitability. Therefore, the purchase prices of medical institutions and pharmaceutical buyers will finally increase as a result of the cost transmission mechanism of the entire supply chain. Figures 12 and 13 show that when market competition is low, and the quantity discount rate is high, ${\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}>0$ , ${\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{S}}={\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{S}}>0$ . Currently, the volume of drugs purchased by medical institutions decreases when demand information is shared and their income declines. This phenomenon is likely because of the decrease in the purchasing volume of medical institutions, which directly leads to a decrease in their total income or profit space. Figure 14 shows that when ${\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{S}}>0$ , if medical institutions are pessimistic about the market demand forecast, demand information sharing is always unfavorable to pharmaceutical GPOs, regardless of changes in market competition and quantity discount rates. This phenomenon may be because when medical institutions are pessimistic about the market demand forecast, they will decrease their purchase quantity to reduce the inventory risk, and the premise for the pharmaceutical GPO to obtain price concessions through centralized procurement is sufficient purchase quantity. Thus, a decrease in purchase quantity may weaken the bargaining power between pharmaceutical GPO and suppliers, thus increasing purchase costs. Furthermore, the results shown in Figures 9 to 14 are consistent with Propositions 2 to 4.

Figure 9.

Graph of the variation of ${\mathrm{w}}_{\mathrm{s}}^{\mathrm{N}}-{\mathrm{w}}_{\mathrm{s}}^{\mathrm{S}}$ .

Figure 10.

Graph of the variation of ${\mathrm{w}}_1^{\mathrm{N}}-{\mathrm{w}}_1^{\mathrm{S}}={\mathrm{w}}_2^{\mathrm{N}}-{\mathrm{w}}_2^{\mathrm{S}}$ .

Figure 11.

Graph of the variation of ${\mathrm{p}}_1^{\mathrm{N}}-{\mathrm{p}}_1^{\mathrm{S}}={\mathrm{p}}_2^{\mathrm{N}}-{\mathrm{p}}_2^{\mathrm{S}}$ .

Figure 12.

Graph of the variation of ${\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}$ .

Figure 13.

Graph of the variation of ${\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{S}}={\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{S}}$ .

Figure 14.

Graph of the variation of ${\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{S}}$ .

Supply Chain Price and Revenue Analysis Under an Optimistic Market Demand Forecast

When $\mathrm{f}>{\mathrm{a}}_0$ , the forecast value of the market demand among medical institutions is greater than the average value of the potential market size, that is, medical institutions are optimistic about potential market demand forecasts (parameter settings: $\mathrm{t}=\frac{1}{2},{\mathrm{a}}_0=10,{\mathrm{w}}_0=5,\mathrm{f}=13$ ).

We then compare the changes in the procurement price and revenue for each member with and without demand information sharing to explore the effects of demand information sharing and quantity discount contracts on supply chain prices and revenues when the market demand forecast is optimistic, as shown in Figures 15 to 20. Figure 15 shows that when ${\mathrm{w}}_{\mathrm{s}}^{\mathrm{N}}-{\mathrm{w}}_{\mathrm{s}}^{\mathrm{S}}>0$ (i.e., when the market demand forecast is optimistic), demand information sharing can reduce the pharmaceutical GPO’s purchase price. Figures 16 and 17 show that, in the context of demand information sharing, when the competition between two products is low, and the quantity discount rate is high, ${\mathrm{w}}_1^{\mathrm{N}}-{\mathrm{w}}_1^{\mathrm{S}}={\mathrm{w}}_2^{\mathrm{N}}-{\mathrm{w}}_2^{\mathrm{S}}>0$ , ${\mathrm{p}}_1^{\mathrm{N}}-{\mathrm{p}}_1^{\mathrm{S}}={\mathrm{p}}_2^{\mathrm{N}}-{\mathrm{p}}_2^{\mathrm{S}}>0$ , the purchasing prices of medical institutions and pharmaceutical buyers follow a downward trend, which directly reflects the effective role of demand information sharing in reducing these two parties’ purchasing costs of. These decreases in procurement costs are rooted in the ability of demand information sharing to enable the pharmaceutical GPO to predict and respond to market demand more accurately, thereby reducing procurement costs. When the pharmaceutical GPO’s purchasing costs decrease, medical institutions and pharmaceutical buyers, as downstream purchasers, can also obtain more favorable purchasing prices, thus realizing the linkage in the reduction of costs across the entire supply chain. As Figures 18 and 19 show, when the competition between two products is low, and the quantity discount rate is high, ${\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}<0$ , ${\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{S}}={\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{S}}<0$ . Thus, the demand and revenue of medical institutions’ pharmaceutical procurement are increasing, possibly because information sharing improves the efficiency of the pharmaceutical supply chain, allowing medical institutions to obtain more pharmaceuticals at a lower cost, thus increasing revenue. Figure 20 shows that if ${\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{S}}<0$ , when medical institutions are optimistic about the market demand forecast, demand information sharing can always increase the pharmaceutical GPO’s revenue, regardless of changes in market competition or the quantity discount rate.

Figure 15.

Graph of the variation of ${\mathrm{w}}_{\mathrm{s}}^{\mathrm{N}}-{\mathrm{w}}_{\mathrm{s}}^{\mathrm{S}}$ .

Figure 16.

Graph of the variation of ${\mathrm{w}}_1^{\mathrm{N}}-{\mathrm{w}}_1^{\mathrm{S}}={\mathrm{w}}_2^{\mathrm{N}}-{\mathrm{w}}_2^{\mathrm{S}}$ .

Figure 17.

Graph of the variation of ${\mathrm{p}}_1^{\mathrm{N}}-{\mathrm{p}}_1^{\mathrm{S}}={\mathrm{p}}_2^{\mathrm{N}}-{\mathrm{p}}_2^{\mathrm{S}}$ .

Figure 18.

Graph of the variation of ${\mathrm{D}}_1^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_1^{\mathrm{S}}|\mathrm{f}={\mathrm{D}}_2^{\mathrm{N}}|\mathrm{f}-{\mathrm{D}}_2^{\mathrm{S}}|\mathrm{f}$ .

Figure 19.

Graph of the variation of ${\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}1}^{\mathrm{S}}={\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{h}2}^{\mathrm{S}}$ .

Figure 20.

Graph of the variation of ${\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{N}}-{\mathrm{\pi }}_{\mathrm{g}}^{\mathrm{S}}$ .

Conclusions and Future Outlook

Conclusions

In this study, to weaken the double-marginal effect, information asymmetry, and bullwhip effect in the pharmaceutical supply chain after the introduction of GPOs, as well as to solve the problems of decision failure and reduced operational efficiency in the pharmaceutical GPO supply chain, a four-level supply chain comprising pharmaceutical suppliers, pharmaceutical GPOs, medical institutions, and pharmaceutical buyers is used as the research object. Furthermore, a quantity discount contract coordination model of the pharmaceutical supply chain with GPOs and demand information sharing is established, solved, and simulated using a Steinberg game and inverse induction method. The following conclusions can be drawn based on our results.

First, with demand information sharing, the higher the market forecast value, the higher the demand and consumer purchase prices. In addition, the pharmaceutical purchaser purchase price is positively correlated with the market forecast value under two conditions: $0<\mathrm{\gamma }\le \frac{1}{2}$ , $0<\mathrm{k}<\frac{-3+2\mathrm{\gamma }}{-4+4\mathrm{\gamma }}$ , and $\frac{1}{2}<\gamma <1$ . Thus, demand information sharing can increase demand among medical institutions and pharmaceutical GPOs to some extent, thereby reducing the purchase costs for pharmaceutical purchasers and increasing them for medical institutions, increasing pharmaceutical GPOs’ gains.

Second, within a certain range of conditions, demand information sharing can reduce purchase prices for healthcare organizations and increase demand for each supply chain member if $\mathrm{f}>{\mathrm{a}}_0$ , and healthcare organizations are optimistic about market demand forecasts. Moreover, demand information sharing can increase pharmaceutical GPOs’ revenue. Within a certain range of conditions, a competitive market environment and volume discount contracts can collectively increase the revenue of healthcare organizations.

This study’s findings indicate that the information-sharing mechanism between medical institutions and pharmaceutical GPOs can be optimized and improved. In practice, pharmaceutical GPOs can design a reasonable quantity discount contract system based on parameters such as the quantity discount rate and market competition intensity. This system can be flexibly adjusted according to different purchasing quantities and market competition environments to encourage medical institutions to share their real and accurate pharmaceutical demand information more actively, thereby increasing the income of pharmaceutical GPOs. Furthermore, medical institutions with optimistic market demand forecasts, under the combined effect of the market competition environment and quantity discount contracts, should take full advantage of the favorable conditions of demand information sharing to cooperate with pharmaceutical GPOs in depth and further reduce procurement costs by sharing demand information, thus achieving revenue growth. Furthermore, pharmaceutical GPOs can use technologies such as big data, cloud computing, and artificial intelligence to build an efficient information-sharing platform, quickly and accurately collect and integrate pharmaceutical demand forecast information from medical institutions, and reduce the bullwhip effect caused by information asymmetry. In the process of building an information-sharing platform, pharmaceutical GPOs should also consider information security and privacy protection to ensure that information from medical institutions is not leaked or misused.

Limitations

Although this study provides meaningful findings on the influence of quantity discount contracts on the coordination of pharmaceutical GPO supply chains with demand information sharing, it has some limitations.

First, this study mainly focuses on the quantity discount contract, which is flexible in reducing procurement costs and increasing revenue, and has certain applicability in the context of large-scale procurement. However, when there are large fluctuations or high uncertainty in market demand, a single-quantity discount contract may be insufficient to coordinate the supply chain effectively.

Second, to simplify the problem, this study assumes that the membership fee paid by medical institutions is constant in the model. This hypothesis helps us focus on the influence of demand information sharing and quantity discount contracts on supply chain coordination in the theoretical analysis. However, in practice, medical institutions of various sizes may pay different membership fees or membership fees may be adjusted according to changes in order quantity. This may affect the purchasing decisions and cost structures of medical institutions, thereby affecting the coordinated operation of the entire supply chain.

Future Outlook

The coordinated operation of the pharmaceutical group purchasing supply chain requires effective collaboration among all participants, extending beyond just medical institutions and Group Purchasing Organizations (GPOs), to achieve the goals of cost reduction and efficiency improvement. This is consistent with Michael Porter’s concept of value-based healthcare. In light of rising global medical inflation and growing risks of supply chain disruptions, it is urgent to integrate the operation of pharmaceutical group purchasing supply chains with the principles of value-based healthcare. Future efforts may focus on the following areas to build a more effective healthcare order.

First, measuring value-based healthcare performance in pharmaceutical group purchasing. Research should follow the principles of value-based healthcare, align with the operational characteristics of group purchasing, consider the guiding role of medical insurance payment mechanisms and the service value provided by GPOs, clarify the logical links between member collaboration and value-based healthcare goals, and develop clear objectives and corresponding measurement indicators.

Second, formation mechanisms of collaborative behavior among supply chain members. It is essential to clarify the interests of supply chain members as well as stakeholders such as insurers and patients, identify common and conflicting interests, focus on value-based healthcare objectives, determine the factors influencing collaborative behavior, and reveal the conditions and patterns governing its formation and evolution.

Third, Incentive mechanisms for collaboration in value-based pharmaceutical group purchasing. Research should account for the progressive nature of value-based healthcare objectives, define stages of collaboration, introduce new theories and methods for profit-sharing and cooperative games, and identify profit distribution schemes and contractual arrangements that maximize incentives at each stage.