Qiao Zelin,Huang Zhe

(School of Business Administration,Shenyang Pharmaceutical University,Shenyang 110016,China)

Abstract Objective To study the reasonable pricing strategy to effectively reduce the risk of drug supply disruption.This paper studies the vertical competition between drug purchasers and pharmaceutical enterprises,and the horizontal competition between different pharmaceutical enterprises.Based on the wholesale price of drugs made by pharmaceutical enterprises,drug purchasers adopt different procurement strategies.Methods A multi-stage game model was used to analyze the collusion and competition between two drug procurement parties.Results and Conclusion (1) Enterprise B can choose the optimal game strategies according to the stability of enterprise A; (2)Two procurement parties should choose collusion when the risk of supply interruption is low; (3) Emergency dual sourcing strategy is better than single sourcing strategy; (4) The optimal procurement quantity is irrelevant to the monotonicity of the stability of enterprise A in Cournot game.Through numerical analysis,the optimal decisions of pharmaceutical enterprises and drug purchasers are obtained respectively.

Keywords:drug; procurement with target quantity; multi-stage game model; sustainability

1 Introduction

Drug procurement with target quantity is a new concept proposed in 2018 based on centralized drug procurement in China.In the process of negotiation and bidding for centralized drug procurement,the information such as variety and quantity of drugs to be purchased is clarified.Finally,the pharmaceutical enterprise with a lower price will win the bid[1].

On November 15,2018,the Office of China National Joint Procurement issued the “Document of 4+7 City Centralized Drug Procurement on the official website of Shanghai Sunshine Medical Procurement”[2],which marked the formal introduction of the longbrewing policy of procurement with target quantity.The pilot area covered 11 cities (4+7 cities) including Beijing,Tianjin,Shanghai,Chongqing,Shenyang,Dalian,Xiamen,On December 6,2018,the bidding results of drug procurement in “4+7 city” were released.Compared with the lowest drug price in the domestic market in the same period,the decrease was up to more than 95%[3].

In September 2019,the “Document on Centralized Drug Procurement in the Alliance Area” was officially released.On the basis of the existing 4+7 cities,85% of provincial-level administrative units form alliances in China to conduct centralized procurement with target quantity in the cross-regional alliance.In August 2020,the results of the third round of drug purchase with quantity was released,and the price of selected drugs dropped by more than 50%.On the one hand,drug procurement with target quantity solved the problem of high drug price,but it also increased the risk of drug supply interruption.In January 2019,due to the rising cost,the nimesulide dispersible tablet of HONZ Pharmaceutical Co.,Ltd.could not be supplied at the original price and it was disqualified from the bid.Therefore,how to balance the low price and sustainable supply of drugs has become an urgent problem to be solved.

From the perspective of enterprise,its quotations determine the probability of winning the bid.Enterprises not only play the game with other enterprises,but also consider the tender probability and the expected profit.From the perspective of government,it should avoid such situation that in the past centralized procurement mode,in order to successfully win the bid,some pharmaceutical enterprises adopted measures such as using inferior substances or simplifying the process flow to reduce costs,thus capturing the market at a low price,which can lead to the phenomenon of “bad money drives good money out of circulation”.

At present,China’s pharmaceutical industry has both opportunities and risks.Therefore,making a reasonable and scientific quotation will determine pharmaceutical enterprise to win the bid and obtain monopoly profits.At the same time,the government must effectively reduce the risk of supply disruptions by developing appropriate procurement strategies.Based on this situation,this paper studies drug pricing decision for sustainable supply under the mode of procurement with target quantity.

2 Analysis methods

Nowadays,with the development of economic globalization,unstable factors in the supply chain have also increased.Chopra pointed out that supply disruption caused by many emergencies such as war,disaster and strike movement had greatly impacted the related industries[4].As a special commodity,it is unacceptable to have drug supply disruption.

There are usually two ways to solve the problem of supply disruptions,one is to scientifically formulate procurement strategy,and the other is to formulate good quotation strategy[5-9].For example,Yu evaluated the impact of single or double procurement strategy on demand instability and price sensitivity of two supply chain models under the risk of supply disruption.By comparing the expected profit functions of the two procurement models,the key values affecting the final procurement strategy are determined[10].Sun Shennan et al.discussed how to reduce the risk of supply disruption in product price adjustment by studying the price adjustment strategy (PS strategy),which aimed at reducing the loss of market share[11].

Besides our study,several scholars also studied the procurement model under the risk of supply disruption[12-13].Burke studied the selection of single or multi-source procurement mode,considering factors such as supplier cost,supply capacity and supply stability in the case of uncertain demand[14].On the other hand,some scholars have studied the risk of supply disruptions from the perspective of inventory.For example,Chi and Chen determined the critical value of the inventory system.When the stock falls below a threshold,it is necessary to issue an order to the emergency supplier to reduce the risk[15].In addition,there are a few scholars who studied the restoration of normal production after supply disruptions[16].

However,all the above studies are about how to reduce the impact of disruptions from an individual enterprise pricing decision.At present,there is no literature to analyze strategic interactions between enterprises such as two retailers/manufacturers and two suppliers.Under this background,this paper discusses the horizontal and vertical competition between the supply chains formed by two pharmaceutical enterprises and two types of procurement (one procurement with target quantity and the other without).Procurement with target quantity adopts emergency dual sourcing strategy while the other adopts single sourcing strategy.This paper discusses the results of the above two procurement strategies under different circumstances in order to provide reasonable suggestions for relevant policies.

3 Description and establishment of model

There are two pharmaceutical enterprises(hereinafter referred as enterprise A and enterprise B) on the market that have passed the quality and efficacy consistency evaluation of generic drug,as well as procurement with target quantity and procurement without target quantity (hereinafter called as procurement party 1 and procurement party 2).The drug supply model under the risk of supply disruption is shown in Fig.1.Enterprise A wins the bid due to low quotation,but there is a risk of supply disruption.On the contrary,enterprise B doesn’t win the bid because of higher quotation.Therefore,it has no risk of supply disruption.The procurement mode of procurement party 1 is defined as emergency dual sourcing strategy,and the procurement mode of procurement party 2 is defined as single sourcing strategy.The collusion and Cournot game between two pharmaceutical enterprises reflect the influence of the policy of procurement with target quantity on pharmaceutical industry.We definePas the drug price,λas a fixed market capacity,andQas the quantity of drugs on the market.The demand function isP=λ-Q,which means that the price of drugs decreases with the increase of the quantity of drugs on the market.Based on the background of drug supply disruption,this paper analyzes the impact of different strategies on the decisions made by procurement parties and the pricing decisions of enterprises.In order to simplify the analysis,this paper assumes that enterprise A has no production cost and enterprise B has sufficient drug supply capacity.

Fig.1 Drug supply model under the risk of supply disruption

3.1 Parametric hypothesis

b:probability of stable drug supply for enterprise A,b∈ (0,1).1q:procurement quantity of procurement party 1 from enterprise A.q2:procurement quantity of procurement party 2 from enterprise B.uq:emergency procurement quantity of procurement party 1 from enterprise B.ΠB:expected profit of enterprise B.Π1:expected profit of procurement party 1.Π2:expected profit of procurement party 2.2β:wholesale price of enterprise B.2γ:unit cost of enterprise B.

3.2 Decision-making process

The drug circulation process is shown in Fig.2.Enterprise B sets the wholesale price2β,and then procurement party1 purchase1qdrug from enterprise A,while procurement party 2 purchasesq2drug from enterprise B.This is an ordinary drug supply model.In our assumptions,the supply of drugs in enterprise A is interrupted,so procurement party 1 urgently purchases uqdrugs from enterprise B,and then the supply and demand of drugs attain a balance.

Fig.2 The decisions of drug procurement

3.3 Collusion of two procurement parties

When two procurement parties believe that cooperation will enable each party to obtain the maximum expected prof it,they reach the basic condition for collusion.At this time,the prof it function is:

3.4 Cournot game situation of procurement parties

When the supply of the drug has no t been interrupted,procurement party 1 purchases drugs from enterprise A,at this timequ=0.When the drug supply is interrupted,the expected profit function of procurement part 1 is:

Before starting drug supply,procurement party 2 knows the strategy of procurement party 1 and purchasesq2drug to maximize profits. The expected profit function of procurement part 2 is:

When the supply capacity of enterprise A is relatively stable,if the unit cost of enterprise B increases,the advantage of enterprise A is significantly higher than enterprise B.Therefore,the procurement quantity of procurement party 1 from enterprise A increases,the emergency procurement quantity of procurement party 1 from enterprise B decreases,and the procurement quantity of procurement party 2 from enterprise B decreases.Substituteq*1,q*2q,*quinto equation (2) and (4),we can get the maximum expected profits of procurement parties 1 and 2,like the following:

3.5 Comparison of collusion and Cournot game between two procurement parties

Theorem 6:the expected total output of pharmaceutical enterprises in collusion is smaller than that in Cournot game.The expected market price of pharmaceutical enterprises in collusion is higher than that in Cournot game.

4 Data analysis

4.1 The expected profit comparison of collusion and competition between two procurement parties

Letλ=100,which denotes the difference between the expected profit of two cites in collusion and that in Cournot game.Fig.3 (a) below shows the changing trend of Δ with valuebwhenγ2=5.It can be seen that Δ ＞ 0 and monotonically increases with valueb.Therefore,the higher the supply stability of enterprise A is,the more cooperation should be developed between two procurement parties.Fig.3 (b) below shows the changing trend of Δwithγ2whenb=0.9.It can be seen that Δ ＞ 0 and monotonically decreases with valueγ2.Therefore,the lower the unit cost of enterprise B is,the more cooperation should be developed between two procurement parties,because the monopoly profit in the cooperation is greater than the profit in the competition.We regard the supply stability of enterprise A and the cost of enterprise B as two characteristics of differentiated competition.When other characteristics stay the same,the supply stability of the enterprise A increases (or the cost of the enterprise B decreases),the difference between two enterprises decreases while the homogenization competition increases.In a word,collusion can eliminate the increasing homogeneous competition,thus increasing the advantage of collusion.

Fig.3 (a) Change trend of the difference between two situations with value b; (b) Change trend of the difference between two situations with value γ2

4.2 Parameter analysis under Competition

4.2.1 The influence of parameters on the optimal purchase quantity

Fig.4 (a) Change trend of the optimal procurement quantity with value b; (b) Change trend of the optimal procurement quantity with value γ2

4.2.2 The influence of parameters on the expected profits of procurement parties

Fig.5 (a) below shows the changing trend of expected profits of procurement party 1 with valueband valueγ2.It can be seen that expected profits of procurement party 1 monotonically increase with valueband valueγ2.But the former has increased more than the latter.This indicates that the supply stability of enterprise A has greater impact on expected profits of procurement party 1 than the cost advantage of enterprise A.Fig.5 (b) below shows the changing trend of expected profits of procurement party 2 with valueband valueγ2.It can be seen that expected profits of procurement party 2 monotonically decrease with valueγ2and first decrease,and then increase with valueb.When valuebexceeds the threshold,the optimal procurement of procurement party 1 decreases,while the optimal procurement of procurement party 2 increases,and the expected profits of procurement party 2 increase.Therefore,the expected profit of procurement party 2 is not a monotonic function related tob.

Fig.5 (a) Change trend of the expected profits of procurement party 1 with value b and value γ2; (b) Change trend of the expected profits of procurement party 2 with value b and value γ2

4.2.3 The expected profit difference between procurement party 1 and procurement party 2

Fig.6 (a) below shows the changing trend of the difference of expected profit between procurement party 1 and procurement party 2 with valuebwhenγ2=5.It can be seen that the difference monotonically increases with valueb.Therefore,the procurement party 1 that implements a contingency dual sourcing strategy has much advantage.Fig.6 (b) below shows the changing trend of the expected profit difference between procurement party 1 and procurement party 2 with valuebwhenb=0.9.It can be seen that the difference monotonically increases with valueγ2.The superiority of the contingency dual sourcing strategy has been proved again.In reality,unless the valuebis very low,the emergency dual sourcing strategy must be better than the single sourcing strategy.In addition,since drug is a special commodity,if the supply stability is low,it is difficult to establish a long-term cooperation with medical institutions.

Fig.6 (a) Change trend of the difference of expected profits between two procurement parties with value b; (b)Change trend of the difference of expected profits between two procurement parties with value γ2

5 Conclusion

Through the above theory and data analysis,we can get the following conclusions:

(1) When the supply stability of enterprise A is high,the competition between the two procurement parties is more favorable for enterprise B.When the supply stability of enterprise A is low,the collusion between two procurement parties is more favorable for enterprise B.

(2) When the supply stability of enterprise A is high,collusion between two procurement parties can bring higher expected profits.

(3) According to the theory of management,it is better to adopt emergency dual sourcing strategy than single sourcing strategy.

(4) If the cost of enterprise B rises,it will benefit procurement party 1.If the supply stability of enterprise A is high,the expected profits of procurement party 2 may increase.

(5) The optimal procurement quantity is irrelevant to the monotonicity ofbin Cournot game.When supply stability is high,a slight decrease inq1can help increase the profit of procurement party 1.

This paper discusses the vertical competition and the horizontal competition between two pharmaceutical enterprises and two procurement parties under the background of the risk of drug supply disruptions.In order to minimize the impact of drug supply disruption,procurement party 1 has adopted the emergency dual sourcing strategy,while procurement party 2 has adopted the single sourcing strategy.This paper discusses the optimum decision of pharmaceutical enterprises and procurement parties in collusion and Cournot game.Through the comparative analysis of two cases,the relevant conclusions are obtained.Through data analysis,the influence of the parameters of cost and supply stability on the optimal purchase quantity and the influence of different purchase strategies on the expected profit of procurement parts are discussed.The conclusion of this paper is of great significance to the operation management of cities facing the risk of supply disruptions.

This paper assumes that enterprise B has no capacity constraints.If we let loose the supposition,procurement party 2 can limit the quantity of drugs that procurement party 1 can get from enterprise B by purchasing more drugs from enterprise B.In this way,the advantages of emergency dual source ordering strategy may be greatly reduced or even lost.We expect that such strategic interaction will bring about different results.This will be the next step in the direction of this paper.