Complexity / 2020 / Article
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Complexity, Nonlinear Evolution, Computational Experiments, Agent-Based Modeling and Big Data Modeling for Complex Social Systems

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Research Article | Open Access

Volume 2020 |Article ID 7471948 |

Yi Zheng, Li Liu, Victor Shi, Bin Liu, Wenxing Huang, "Price Cap Models in Pharmaceutical Online-to-Offline Supply Chains", Complexity, vol. 2020, Article ID 7471948, 16 pages, 2020.

Price Cap Models in Pharmaceutical Online-to-Offline Supply Chains

Academic Editor: Peter Bian
Received26 Jun 2020
Revised25 Aug 2020
Accepted15 Sep 2020
Published06 Nov 2020


Pharmaceutical supply chains are often highly complex with conflicting objectives of social welfare and profit maximization. Furthermore, there are various stakeholders including pharmaceutical manufacturer, distributors, retailers, patients, and the government. In this paper, we consider a two-stage supply chain consisting of one pharmaceutical manufacturer and a pharmacy with online and offline channels. We focus on four price cap models: no price cap regulation, pharmaceutical manufacturer’s price cap regulation, pharmacy price cap regulation, and linkage price cap regulation. We apply game theory, investigate how the price cap regulations affect the firms’ pricing, and evaluate the economic performance and social welfare of the dual-channel pharmaceutical supply chain. Our findings show that first, like the single-channel pharmaceutical supply chain, the profit of the regulated firm always decreases and the profit of the unregulated firm always increases when they are under one-sided price cap regulations. Second, the impacts of the linkage price cap regulation on the supply chain are more complicated depending on the linkage coefficient and market share. Overall, our findings can provide theoretical and practical insights to help the government devise price cap regulations for complex modern pharmaceutical supply chains.

1. Introduction

Human health not only affects individual employment and survival but also largely determines a country’s economic growth and prosperity by the United Nations [1]. In turn, human health depends on the improvement of a country’s medical and health system. In 2010, global medical and health expenditures amounted to US $6.5 trillion, accounting for 10.49% of the world’s GDP. The United States spent the world’s highest on medical and health expenditures, reaching US $257.5 billion in 2012, accounting for 17.61% of its GDP [2]. The pharmaceutical industry is a basic component of the medical and health economy. Among all medical and health products, drug expenditure accounts for 20–30% of global medical and health expenditure [3], which is one of the most important expenditures on medical and health [4]. The growth in pharmaceutical spending is attributed to two main reasons: increased pharmaceutical use and the introduction of new higher-priced products. In terms of growth rate, the global pharmaceutical industry grew at a rate of about 3–5% in 2009; it is expected to continue to grow at a rate of 4–6% in the next few years [5].

As a special commodity for curing diseases and saving lives, the quality and safety of medicines are particularly important [6], and the pressure to compress the cost is also very urgent [7]. The high cost of medicines mainly comes from the circulation link [8], which is as high as 40–50% in China [9]. However, medical institutions often take advantage of their monopoly position in the pharmaceutical supply chain to chase high drug profits, deviating from the nature of public welfare, and “expensive medical treatment” has become one of the most prominent social problems in many countries like China [10]. In order to prevent the pharmaceutical supply chain led by medical institutions from chasing high drug profits, the government has adopted price cap regulations. In 2018, “the (4 + 7) Urban Drug Centralized Procurement Documents” was released, and pilot trials of the “volume procurement” policy of public hospitals were started in 11 cities with Shanghai as the representative city, realizing cross-regional joint centralized procurement. This policy has achieved good results and achieved a substantial drop in drug prices. How to ensure the quality of medicines while reducing the price of medicines has become a problem that government departments and patients attach great importance to. In addition, the government’s price limit control for drugs has been constantly reformed in the face of controversy, and various drug price control measures have been implemented, such as comprehensive drug price control, drug retail price control, and price increase rate control [11].

Under the maximum price policy for medicines, a long-term game within the medicine supply chain has gradually formed a balance between profitability and public welfare. Due to the particularity of drugs, traditional distribution channels of drugs are divided into public hospitals and social pharmacies. Therefore, under the government’s control of public hospital bidding and procurement and the control of drug prices in social pharmacies, it is particularly important to consider how drug retailers choose channel sales, how to accurately target consumers, and how to ensure their own profits.

With the introduction of the online drug sales policy, drug suppliers such as “Jointown” and “yunnan baiyao” have set up online sales channels and implemented the dual-channel drug sales strategy, thus breaking the traditional balance of interests in the pharmaceutical supply chain. By 2020, more than 1,000 drug suppliers in China have opened online channels. In the context of the dual-channel pharmaceutical supply chain, it has become the focus of social concern whether the price-fixing policy can continue to control drug prices and whether the public welfare of medical institutions can ensure social welfare. In addition, the development of online drug sales channels has broken the monopoly of medical institutions on the drug market, and the dominant position of medical institutions in the pharmaceutical supply chain has been balanced and surpassed by some large drug suppliers. Consequently, drug retailers have become the dominant players in pharmaceutical supply chains [12]. Therefore, it is of great theoretical and practical significance to study drug retailers and their dual-channel supply chains in the context of price cap regulations.

Our research aims to fulfill this gap through addressing the following key questions: what is the best strategy for a pharmaceutical supply chain under price cap regulations? What are the impacts of the price caps on pricing decisions, profits, and social welfare? How does market competition affect a pharmaceutical online-to-offline (O2O) supply chain?

In order to answer these questions, this research focuses on pharmaceutical supply chains under three price cap models. We consider a supply chain with one pharmaceutical manufacturer and one pharmacy with an O2O mixed channel. The pharmacy is the Stackelberg leader, and the pharmaceutical manufacturer is the follower. The pharmacy retailer holds both physical virtual online shops and retail stores. We compare the optimal prices for both online and offline channels, profits, and social welfare under the models without and with price cap regulation.

In this paper, we make the following major contributions. First, our research complements the existing literature by focusing on the pricing strategies from the pharmacy’s point of view in an O2O mixed dual channel. Second, we not only derive the optimal pricing strategies for the pharmaceutical O2O supply chain that operates both online and offline channels to consumers, but also investigate the impacts of three price cap regulations. Third, the three main results provide interesting insights on the appropriate pricing strategies which can support pharmacies who operate or intend to operate an O2O mixed dual channels.

After a review of the literature in Section 2, the model and assumptions are provided in Section 3. In Section 4, the effects of price cap regulation on the pricing, profit, and social welfare are discussed. Section 5 discusses the impact of the linkage coefficient and offline market share on the pharmaceutical supply chain. Finally, we present managerial insights and discuss directions for future work in Section 6.

2. Literature Review

Nowadays, consumers can shop on multiple retailing channels, such as brick-and-mortar stores, online stores, mobile stores, and even social network platforms. Much of the literature relates to the problem of operational decision for pharmaceutical supply chains. Here, we review the studies highly related to our research, which can be classified into two categories: the first is on operations management in O2O supply chain and the second is on operational decisions of the pharmaceutical supply chain.

2.1. Online to Offline

With the rapid development of e-commerce, many retailers such as Wal-Mart, Alibaba, and Noble have opened online channels. As a result, dual-channel supply chains and the term O2O have received more and more research attention [1315]. Tsay and Agrawal [16] find that adding a direct channel is beneficial to the retailer and the manufacturer under certain conditions. Cattani et al. [17] analyzed the potential conflicts between the traditional channel and the direct channel and proposed an equal-pricing strategy to maximize the profit of the manufacturer for O2O channels. Huang and Swaminathan [18] investigated the optimal pricing strategies for the products which are sold via an online channel and a traditional channel. In addition, they also explored the pricing and profit under different degrees of channel competition. Yan and Pei [19] showed that cooperative advertisement can effectively alleviate the channel conflict. Chen et al. [20] derived the optimal prices and profits of a manufacturer and a retailer under different power structures (including Manufacturer-Stackelberg, Retailer-Stackelberg, and Nash) in a retail service supply chain with an O2O mixed dual channel. Xiao and Shi [21] explored the pricing and channel priority strategies of a dual-channel supply chain composed by an online channel and a brick-and-mortar and examined the impacts of channel coordination and time sequence. Although all the aforementioned papers discuss pricing strategies, competition, and cooperation of a dual-channel supply chain in the context of O2O, they omit the impacts of price cap regulations on dual-channel supply chains.

2.2. Pharmaceutical Supply Chain

In recent years, research related to pharmaceutical supply chains has received increasing attention from scholars [7, 22, 23]. Related papers are reviewed and summarized below.

2.2.1. Distribution Network Design

Sousa et al. [24] studied the dynamic programming problem of the global supply chain configuration of pharmaceutical companies with the goal of profit-maximizing. They developed an effective algorithm to solve it considering production and distribution costs and tax rates in different locations. A. Nagurney and L. S. Nagurney [25] built an easy-to-handle network model and computation method for a medical supply chain. Nagurney et al. [26] studied a pharmaceutical supply chain equilibrium and dynamic network model considering outsourcing, price, and quality competition to find the optimal pharmaceutical logistics that minimizes the total cost. Based on the reality of drug distribution in Europe and the United States, the existing research has studied the design of drug distribution network from the perspective of pharmaceutical companies but not from the perspective of collection and distribution of drug distributors. On the other hand, the unique purpose of drugs to cure patients determines that the design of the drug distribution network should not only pursue low cost but also consider the constraints of service level. de Magalhães and de Sousa [8] used a dynamically designed variable path system to study the optimal distribution path of drugs from the perspective of drug distributors. Liang [27] studied the distribution center planning of pharmaceutical distribution companies in the context of centralized procurement and distribution. The studies above do focus on the design of the drug distribution network from the perspective of drug distributors but do not consider the constraints and impact of service levels. Shang et al. [28] took customer satisfaction rate as the service level constraint and employed noninteger linear programming to design a drug distribution network with the goal of minimizing distribution cost. However, they only consider the demand satisfaction rate and delivery timeliness rate.

2.2.2. Procurement and Distribution Management

Talluri et al. [29] studied the safety inventory management of multinational pharmaceutical companies based on inventory, considering both the variability of demand and supply. Danas et al. [30] applied the Ned-MASTA taxonomy to the inventory management of hospital pharmacies to improve the efficiency of operation management. Boulaksil and Fransoo [31] analyzed the impact of outsourcing on the drug ordering process. Shen et al. [32] proposed an improved pharmaceutical economic production model to minimize the cost of guaranteed inventory in consideration of the minimum inventory constraint. Pazirandeh [33] summarized the strategic procurement and established a decision-making framework for the procurement and distribution of vaccines in developing countries. Zhao et al. [34] studied the multicycle stochastic inventory problem of manufacturers and distributors under the service charge and investment purchase model, derived their optimal strategy, and developed a program to calculate policy parameters. Their research shows that service contract can improve the profit of the whole supply chain. The above studies considered the situation of a single product. Ying and Breen [35] constructed an integrated green drug supply chain model that includes all key stakeholders to improve the environmental, economic, and safety performance of drug management and distribution. Niziolek et al. [36] studied the direct distribution strategy of drugs and discussed the impact of different distribution frequencies and volumes on transportation and inventory costs through simulation. They believed that the mixed distribution strategy significantly reduced the total cost of the drug supply chain. The abovementioned literature separately researches the procurement and distribution of pharmaceutical logistics management.

3. Models and Equilibrium Analysis

3.1. Model Description and Assumptions

We consider a two-echelon dual-channel pharmaceutical supply chain consisting of a pharmaceutical manufacturer and a pharmacy with online and offline channels. Pharmacies often play a leading role in supply chains as the main buyers of pharmaceutical manufacturers. Therefore, we assume the pharmacy as the Stackelberg leader and the pharmaceutical manufacturer as the Stackelberg follower. The pharmacy buys drugs from the pharmaceutical manufacturer at wholesale price and then sells to the patient through the offline channel for the offline retail price or sells to the patient through the online channel for the online retail price . For the pharmaceutical manufacturer, his production cost is denoted as . In addition, regarding the channel setup cost of the pharmacy, the setup cost of the offline channel is denoted as , and the setup cost of the online channel is denoted as . It usually requires more investment and capital to build the online channel, so we assume . Furthermore, in this paper, for clarity, we assume that the offline retailer’s price is higher than the online retail price. That is, . Next, we define parameters and variables as summarized in Table 1. Finally, we assume that the pharmaceutical manufacturer and the pharmacy are rational and self-interested, each aiming for profit-maximizing.


Pharmaceutical manufacturer’s unit production cost
Offline channel’s unit cost
Online channel’s unit cost
Pharmaceutical manufacturer’s unit wholesale cost
Pharmacy’s unit offline retail price;
Pharmacy’s unit online retail price;
Wholesale price cap imposed by the government
Retail price cap imposed by the government
The customer demand via offline
The customer demand via online
Linkage coefficient between the wholesale price cap and the retail price cap under the linkage price cap regulation,
Pharmaceutical manufacturer’s profit
Pharmacy’s profit
Total profit of the pharmaceutical supply chain,
The patient surplus
Social welfare,

Following Mukhopadhyay et al. [37], Shang et al. [38], and Chen et al. [39], we assume that the customer demand via the offline channel is , and the customer demand via the online channel is , . In the demand functions, means the base market, represents the offline market share, and represents the online market share. means the self-price sensitivity and means the cross-price sensitivity. means the self-price sensitivity is higher than the cross-price sensitivity. Based on the demand functions above, the pharmaceutical manufacturer’s profit is

The first and second parts of (2) represent the pharmaceutical manufacturer’s profit from the pharmacy’s offline and online sales, respectively. The marginal profit of the offline channel is and the marginal profit of the online channel is . The pharmaceutical manufacturer’s profit can be expressed as

The pharmacy’s profit is

The first and second parts of this formula represent the pharmacy’s profit from the offline and online sales, respectively. Social welfare consists of the patient surplus, the profit of the pharmaceutical manufacturer, and the profit of the pharmacy. Following Cowan et al. [40] and Jin et al. [41], the patient surplus can be written as

3.2. Price Cap Models

In this model, the pharmacy is the leader and the pharmaceutical manufacturer is the follower, which means that pharmacy plays a leadership role when they are making their decisions, the sequence of events is as follows. Firstly, the pharmaceutical manufacturer decides the wholesale price given the pharmacy’s retail price. Then, the pharmacy decides his offline and online retail prices in response to the pharmaceutical manufacturer so as to maximize his profit. Finally, when the customer demand is realized, the pharmaceutical manufacturer and the pharmacy will gain their revenues. There are several potential situations in the pharmaceutical supply chain:(i)RN model: in a RN model, the government has no price cap regulation on the pharmaceutical manufacturer and the pharmacy. The pharmaceutical manufacturer’s profit-maximizing problem isThe pharmacy’s profit-maximizing problem is(ii)RM model: in a RM model, the government regulates only the upstream pharmaceutical manufacturer by setting a wholesale price cap, . It means that the pharmaceutical manufacturer’s wholesale price cannot exceed the wholesale price cap. The pharmaceutical manufacturer’s profit-maximizing problem isThe pharmacy’s profit-maximizing problem is(iii)RR model: in a RR model, the government regulates only the downstream pharmacy by setting a retail price cap, . It means that the pharmacy’s retail price cannot exceed the retail price cap. The pharmaceutical manufacturer’s profit-maximizing problem isThe pharmacy’s profit-maximizing problem is(iv)RL model:in a RL model, the government regulates both the upstream pharmaceutical manufacturer and the downstream pharmacy and is the linkage coefficient to maintain a connection between the two price caps, . The purpose of this linkage price cap regulation is to regulate the entire supply chain, and the pharmaceutical manufacturer’s wholesale price and the pharmacy’s retail price will be constrained by price cap. The pharmaceutical manufacturer’s profit-maximizing problem is

The pharmacy’s profit-maximizing problem is

Now, we can derive the optimal wholesale price and the optimal retail prices for the RN, RM, RR, and RL models () which are summarized in Table 2. Hence, the pharmaceutical manufacturer’s optimal wholesale price and the pharmacy’s optimal offline and online retail prices exist and are unique in these price cap models.


RN model;
RM model

RR model

RL model,


Based on the optimal pricing decisions in Table 2, we can derive the optimal profits of the pharmaceutical manufacturer and the pharmacy for the RN, RM, RR, and RL models which are summarized in Table 3.


RN model
RM model
RR model
RL model