GENG Chao,QU Shiyou,XIAO Yingying,WANG Mei,SHI Guoqiang,4,LIN Tingyu,4,XUE Junjie,and JIA Zhengxuan

1.Economics and Management School,Harbin Institute of Technology at Weihai,Weihai 264209,China;2.Beijing Complex Product Advanced Manufacturing Engineering Research Center,Beijing Simulation Center,Beijing 100854,China;3.State Key Laboratory of Intelligent Manufacturing System Technology,Beijing Institute of Electronic System Engineering,Beijing 100854,China;4.Science and Technology on Space System Simulation Laboratory,Beijing Simulation Center,Beijing 100854,China

1.Introduction

In line with the strategy of “Internet+manufacturing”,our team builds an industrialized service platform known as cloud manufacturing platform(CMP)[1].Compared with the traditional networked manufacturing model,the platform has three important characteristics:(i)Network effects(NEs)have a strong influence on the platform diffusion.There are three types of roles involved in the platform:operator,demander and provider.This forms a typical bilateral market[2].As a result,its direct network effect d1 and local network effect locallength have an important impact[3]on the critical equilibrium state of the platform diffusion periods,while its indirect network effect d2 leads to the“chicken-and-egg”problem[4]in the early stage of the diffusion process.(ii)Enterprise’s preference heterogeneity(EPH)will affect the success of platform diffusion.Innovators and early enterprises[5](denoted as IATs for immediate acceptance type enterprises)are considered to be the marquee enterprises in the bilateral market,and will affect the selection strategy of the deferred acceptance enterprises(denoted as DATs for deferred acceptance type enterprises),whose proportion is denoted by alpha.At the same time,enterprises’service sharing preference is also an important factor,due to the existence of key content providers(KCPs,ration keytype)whose d2 are stronger and thus have strong influence on decision of other enterprises.(iii)The platform operation strategies,including the supply and demand matching strategy(SDM),the platform quality improvement strategy(PQIm)and initial enterprise guidance strategy(IEG),are key factors to ensuring the sustainable development of the platform.In a word,all the five types of factors above(NEs,EPH,SDM,PQIm,IEG)directly affect the enterprises’utility and the entry/exit decisions,thus affecting the CMP’s diffusion process.

In essence,research on CMP’s diffusion mechanism belongs to the scope of new product diffusion theory.It includes:(i)macroscopic diffusion models[6],which can only be used for post analysis on successfully diffused new products,but cannot predict the success of new product diffusion using different strategies;(ii)complex networks[7],which facilitate the modeling of the dynamic evolution process of the economic network and analysis of the effect of individual decision-making behaviors,providing a useful means[8]for analyzing the new products’diffusion rule.

Therefore,on the basis of the new product diffusion theory,this paper establishes a complex network model to analyze the CMP’s diffusion process and mechanism under the influence of the five factors above.These can provide guidance for the platform operators to choose appropriate strategies to attract enterprises going online and to ensure the profit for operator,demander and provider.

The remainder of this paper is organized as follows.Section 2 presents an investigation on relevant researches on innovation diffusion based on the complex system theory,network effect of platform products and service selection and allocation strategy in CMP.Section 3 introduces the three basic stages of the basic diffusion process of CMP.In Section4,the CMP diffusion model based on complex networks has been constructed with five diffusion forces identified.Simulation results and analysis on the cloud manufacturing(CM)diffusion mechanism are provided in Section 5,and finally conclusions and discussion are drawn in Section 6.

2.Relevant researches

2.1 Innovation diffusion research based on the complex system theory

Duan[9]divided innovation diffusion research based on complex system theory into the following three categories:

(i)Innovation diffusion research based on the fad theory which emphasizes that the proportion of people who use innovation in the surrounding population exerts a social bandwagon pressure on potential users.Pastor-Satorras et al.[10,11]established an infectious disease model based on complex networks;Lopez[12]introduced the traditional game theory into the threshold model and foundthat changes in network structure connectivity and the neighborhood effect will affect the innovation diffusion threshold.

(ii)Innovation diffusion research based on incremental return theory,that is,potential users decide whether to use innovation through cost-benefit analysis.The most common is the network effect model.Duan et al.[13]constructed a diffusion model with local network effect and indicated that product quality is the key to the success of a new product.Moreover,Woo et al.[14]explored the relationship between technological improvement and innovation diffusion.

(iii)Innovation diffusion research based on the network game theory.In[15]the market evolution trend of CM was presented based on game theory and equilibrium analysis.Fagnani[16]proposed a stochastic network dynamics modeling the spread of a new technological asset based on the word-of-mouth.According to the model,the more the product is diffused,the more intense the persuasion strength is.

In addition to the above-mentioned aspects,more recently,Zhang et al.[17]applied ecological theory to build the ecological evolution mechanism of manufacturing service system(MSS),where a predator-prey model was built to simulate the ecological evolution of MSS.

2.2 Network effect of platform products

Katz and Shapiro[18]formally defined the network effect and divided it into two types:(i)direct network effect where the product value increases as the scale of the users using the product increases; and (ii) indirect network effect where the value of core products comes from the variety of complementary products. Schoder [19] pointed out that the network effect allows the dynamic process of new product diffusion to have macroscopic and microscopic feedback effects,which is consistent with the statement that“macro behavior model emerges from all dynamic behaviors of microscopic subjects”in the complex system theory.

In addition,an important feature of the CMP(a platform product)is the cross network effect where the expectation difference between different groups of users will lead to the “chicken-and-egg”problem.Keller et al.[20]further pointed out that products could be quickly popularized by making use of opinions from opinion leaders and the wordof-mouth effect. Niculescu et al. [21] explored the strategic decision of an incumbent to open a proprietary technology platform in order to allow same-side co-opetition in a market characterized by network effects.

2.3 Service selection and allocation strategy in CMP

(i)Service selection mechanism:Huang et al.[22]and Zhang et al.[23]studied the service portfolio modeling and method based on quality of service(QoS),but they did not consider constantly changing manufacturing service availability.Cao et al.[24]studied the equipment service modeling and their resource selection strategy in CM.Zheng[25]considered design performance in the CM environment,and proposed a QoS-based fuzzy resource service selection method.

(ii)Service allocation strategy:Renna et al.[26]studied the capacity sharing model based on the cooperative game theory,where two cooperation mechanisms of the negotiation method and game theory have been analyzed.Chen et al.[27]proposed four service scheduling models that centered respectively on user,provider,operator,and the whole system in the cloud manufacturing environment,and demonstrated that the last was optimal.Argoneto et al.[28]used the Gale-shapley cooperative game algorithm to explore capacity sharing in the enterprise network.Argoneto et al.[29]further discussed the capacity sharing strategy in cloud manufacturing based on the Gale-shapley algorithm and fuzzy logic.Liu and Tao[30]compared the performance parameters of the traditional manufacturing model and the cloud manufacturing model based on the Gale-Shapley strategy in different task request strategies,and proved the advantages of the cloud manufacturing model on the improvement of resource utilization and demand satisfaction.Su[31]studied the optimization method of resource configuration under the circumstance of possible conflicts between demander and platform operator based on non-cooperative game theory.Tao et al.[32]proposed the concept of manufacturing service supplydemand matching simulator and provided a uniformed research platform for related researchers in both academic and industrial communities.

In a word,complex network theory is an important tool for studying the diffusion mechanism of CMP.The innovation diffusion theories of bandwagon effect,incremental return and network game constitute the theoretical basis of the research in this paper.QoS is the preferentially used method for service selection,and the systemcentered scheduling model and cooperative game are effective strategies for SDM of CMP.

All research above constitutes the basis of this paper,but the CMP’diffusion model considering all the five types of factors above is a new challenge,which will be discussed in the following sections.

3.Basic diffusion process of CMP

In general,the development of the CMP,namely its diffusion process,is a continuous upgrading process mainly including early,mid and late stages.

(i)Concept proposal and early development stage(T0-T1 stage):At this stage,the IATs that have a preference for CMP are guided to enter the platform through policies,thereby driving related enterprises to go online.At this stage,CMP is dominated by social relations like geographical relationship.Meanwhile,studying successful experience of IATs is an important factor for DATs to decide whether to enter the CMP.

Therefore,taking appropriate strategies of IEG and EPH are important to solve the“chicken-and-egg”problem.The platform would be guided to enter the following independent development stages,and early investment would result in effective profit.

(ii)Mid development stage(T2 stage):At this stage,network effects among enterprises online and their supporting enterprises or similar enterprises are important to continuously expand the CMP’s network size.Meanwhile,the constantly improved platform quality will also encouragethe entry of new enterprises. Due to DATs’ deferred entering,some enterprises will decide to temporarily exit or not enter the platform because of increased costs,reduced business opportunities,and less available high-quality resources.Therefore,the CMP’s network size is in rapid dynamic evolution.

Therefore,at this phase, the initial network structure,the strategies of SDM,NEs and PQIm will affect the formation of new cooperative relationship and break the“critical mass”to reach a state of stability.

(iii)Late development stage(T3 stage):At this stage,the enterprise network in the platform reaches an equilibrium state with increasing amounts of cooperation,and the network size tends to be steady.At this stage,the network density increases,the cooperation scope becomes wider,the relationship type is more complex,the cooperation intensity becomes higher,and the network is dynamically steady.The evolution indicators could be used to compare the influence of different strategies

4.CMP diffusion model based on complex network

Based on the basic diffusion process introduced in Section 3,a CMP diffusion model described in Fig.1 has been proposed in virtue of complex network theory to analyze from a microscopic view the impacts of five diffusion forces in different development stages.

The modelling process is mainly composed of five parts,namely:initial network generation,initial enterprise guidance,supply and demand matching of CMP,enterprise entry/exit CMP,and PQIm.In the following of this section,details on the modelling of each part are presented.

4.1 Initial network generation

The CMP is a complex transaction network consisting of various enterprises.This paper uses a Barabási-Albert(BA)scale-free network to describe the basic business process between providers and demanders.Enterprises participating in manufacturing activities are represented by“Nodes”in the network,while “Edges”represent various supply and demand relations between enterprises.The BA scale-free network is defined with three elements:

(i)Network size:The total number of enterprises is represented by N.

(ii)Degree of node:It is assumed that the service number owned by an enterprise is represented by the initial degree value of the node,expressed as Ai=kαi,where kiis the degree of node in the BA scale-free network,and α is the service servants owned by enterprise i.

Fig.1 Diffusion model of CMP

(iii)Edge weight of each cooperation pair:Note edges in the network are formed between cooperative enterprises.In this paper,all edge weights between connected nodes are initially set to be 1,and are increased by 1 after each successful transaction.It is assumed that,at each time step t,the ith enterprise service demand,corresponding to certain total number of production tasks(Ri),is calculated through

where s0i∈[0,s],indicating the strength of the service demand.s represents the maximum task intensity.Therefore,when s0i＜1,the enterprise has a certain number of idle services,which isand when s0i＞1,the enterprise needsexternal idle services.

At this point,the enterprises are clearly divided into two types:service demander and service provider.Suppose that at each time step,the probability of an enterprise receiving a production task is pot.Then the total number of demanders is Ndem=N×pot×f(s0＞1),taking up Ddem=Ndem/N in ratio,where f is the proportion of enterprises with service demand strength larger than 1.The total number of providers(Providers consist of two parts:enterprises that have production task themselves but still have idle services and enterprises with no production tasks.)is Npro=Np×f(1＞s0≥0)+N(1-pot),and the ratio is Dpro=Npro/N,where f represents the ratio of enterprises that have idle services.

4.2 Diffusion forces of CMP

Basic complex network model and basic business process of CMP have been defined above;however,its diffusion forces have not yet been discussed.In fact,in the development of CMP,decisions on both entering/exiting the platformand how to share idle services/service demandsin the platform can affect the evolution,diffusion as well as the final state of CMP.In this subsection, five diffusion forces are investigated in detail.

4.2.1 IEG

Generally,at the initial stage(T0),cooperation is mostly carried out through the guidance of local government and industry associations,which attracts initial enterprises to go online through the“1+N”method i.e.,leading enterprises guide small and medium enterprises(SMEs).The guidance strategy of initial enterprises choice between providers and demanders is the key point in addressing the“chicken-and-egg”problem.For example,the platform can inject magnetic attraction force by means of sharing lots of demands to attract enterprises’entry.However,some scholars hold that“He who masters the supply side will win in face of competition”.Therefore,guidance strategies to be verified in this paper could be summarized as:

Strategy 1Provider priority:Priority is given to encouraging service providers to go online first,thereby attracting the entry of relevant demanders.

Strategy 2Demander priority:Priority is given to encouraging relevant demanders to release demands first,thereby attracting the entry of relevant service providers.

Strategy 3No priority:Enterprises are guided to go online without distinguishing demanders and providers.

At initial time T0,a certain number(NT=0,with proportion p)of enterprises are guided to enter the platform according to the three strategies above.

4.2.2 SDM of CMP

During operation of the CMP(T0-T3),the cooperation among enterprises is a dynamic game process affected by the cooperation utility and different matching strategies.

The cooperation utility defined in this paper is com-posed of two parts as follows:

Utility of fixed-term(UF)is related to the acceptance preference riof enterprises for CMP,platform quality qtand NEs including d1,local strength and d2.The demander and provider’s UF are respectively defined by(2)and(3).

Utility for each trade(UT)is measured by comprehensive QoS,including cost costj,service quality Qj,request/idle servicedistance dijand cooperation weight wijbetween the cooperating enterprises,and enterprise scale represented by service number Ai.

ωdc,ωdQ,ωdq,ωdd,ωdw,ωpq,ωps,ωpdand ωpwindicate respectively the weights of each item.

Therefore,for each service request,the candidate cooperation providers are evaluated by cooperation utility.The matching strategy will affect the final matching between each service request and candidate provider.In this paper,we mainly focus on the following two matching strategies.

Strategy 1Deferred-acceptance strategy.In this case,the platform utilizes the Gale-Shapley algorithm to find the best matching strategy for stable matches.Each demander i(or provider j)will choose the provider j(or demander i)with maximum cooperation utility and refuse other requests.In this algorithm,cooperation requests will not be accepted immediately,i.e.,if the provider j has still established a cooperation intention with another demander k,it can choose the one with maximum transaction utility between i and k.The rejected enterprise can choose yet another enterprise it has intention to cooperate with until there is no enterprise intending to make a new cooperation request.

Strategy2Immediate-acceptance strategy.In this case,the demander i must find the best matching provider in this time.As the name suggests,the difference between this strategy and the aforementioned deferred-acceptance strategy is that once the intentional cooperation is established between enterprises,they must accept the matched cooperation.In this algorithm,the enterprises providing demands early are more likely to reach cooperation with maximum benefits due to having more choices.Therefore,the algorithm can also be considered as a first-come first served cooperation mode.

4.2.3 Enterprise entry/exit CMP under the influence of NEs and EPH

After the initial time T0,all enterprises will decide whether to enter/exit the platform or continue to stay through comparison of profits obtained in CMP and the traditional mode,combined with their own preferences and experiences of other associated enterprises during the diffusion.Therefore,the network size of CMP is dynamically changing.When the scales of entering and exiting enterprises are equal,the network reaches an equilibrium state.In this paper,the basic enter/exit strategy is described in Fig.2.

Fig.2 CMP entry/exit decision making of enterprise i

Fig.2 corresponds to the module“Enterprise enter/exit CMP”between A and B marked in Fig.1.In details,three statistical parameters (the total utility of successful transactions in the traditional manufacturing modethe total utility of successful transactions in CMPand the utility of fixed-term UFi)will be calculated in each simulation period,according to the type of enterprise i(DAT of IAT).Then,the entry/exit decision making of enterprise i can be represented with the following flowchart shown in Fig.2.Specially,DCNidenotes the ratio of enterprises that are in CMP in enterprise-i’slocal network,which will be updated according to the number of entry/exit enterprises.

According to(2),(3),(5),(6)and the flowchart above,it is not difficult to see that the CMP entry/exit decision making of enterprises is related to the diffusion forces of EPH(alpha,keytype)and NEs(d1,d2,localstrenth).In details,(i)alpha can affect CMP enter/exit through controlling the size of IATs.(ii)keytype is the proportion of KCPs,which is randomly selected from the number of initial guided enterprises(NT=0),which can affect enter/exit decision through NEs value of d2(d2 keytype=2?d2).(iii)NEs(d1,d2,localstrenth)can affect the value of UF.At the same time,the number of initial guided enterprises(NT=0)is determined by the IEG strategy in subsection 4.2.1,the SDM strategy in subsection 4.2.2 can affect the value of UT.Thus,EPH,NEs,IEG,SDM can affect the evolution of the entire network.

4.2.4 PQIm

In the whole process of platform development(T0-T3),the continuous PQIm is a key factor in attracting the entry of new enterprises,but it also means increasing investment in the platform.Taking appropriate PQIm speed(denoted as c)and maximum quality objectives qmaxto match the development speed of the platform is the key to ensuring that the platform can sustain its power under cost constraints.

Strategy 1Platform quality priority:Giving priority to improving the platform quality.The PQIm of the platform in the whole process(T0-T3)is continuous and fast under this strategy,and the maximum quality objective of the platform is also high.

Strategy 2Guiding enterprises priority:Giving priority to guiding enterprises to go online:The investment in the early stage(T0-T1)under the strategy focuses on guiding enterprises to go online.By this strategy,only in the mid and late stages T2-T3 of platform development,related investment in PQIm gradually increases to promote continuous quality improvement.

According to(2)–(4),apparently,PQIm(c,qmax)can affect qt,thus affecting the value of UF.Thus,the parameters c and qmaxcan affect the process of CMP entry/exit of enterprises,and have influence on the evolution of CMP.

5.Simulation results and analysis

On the basis of our proposed diffusion model of CMP,simulation analysis has been carried out on the diffusion mechanism through C++programming.During the simulation,different strategies have been explored and the corresponding evolutions of CMP are evaluated through statistical indicators.

5.1 Simulation parameters and evaluation indicators

According to the diffusion model defined in Section 4.2,relevant simulation parameters and their initial values are shown in Table 1.

In order to analyze the efficiency of CMP and the effects of different strategies,the evolution of CMP is evaluated by the following statistical indicators.

(i)Ratio of enterprises entering CMP

Nprepresents the enterprise number in CMP.

(ii)Overall service utilization rate

(iii)Overall demand fulfillment rate

(iv)Total utility of providers

(v)Total utility of demanders

Table 1 Initial simulation parameters

(vi)Total utility of enterprises

5.2 Advantages of CMP

Reference[30]has performeda study on the resource sharing(RS)model in the cloud manufacturing(CM)and in advanced networked manufacturing(NM),indicating the main differences shown in Table 2,in terms of framework,operating mechanism and strategy of matching between demanders and providers.According to the study in paper[30],enterprises in CM are thoroughly connected through resource service pool,compared to those in NM.This in turn,results in complete resource scheduling and sharing mechanisms and more extensive demander-provider matching strategies,which forms the basis of the amelioration of the resource utilization rate and the demands at is faction rate of CM compared to NM.

Table 2 Comparison between CM and NM

In this paper,however,the RS model of NM defined in the literature is adopted as the benchmark to compare with that of CM diffused by our newly proposed diffusion model of CMP.(Refer to initial values in Table 1 for parameter settings).The results are shown in Fig.3 and Fig.4.

Fig.3 Comparison of service utilization rate and demand satisfaction rate(CM parameter settings:qmax=12,c=0.05,alpha=0.5,key type=1,d1=1,d2=2,local strenth=1,S-DStra=1,Guid Stra=1)

Fig.4 Enlarged views of Rsand Ruat different times

The statistical results in Fig.3 cover the evolution of Ruand Rsunder CM and benchmark.It can be seen from the results that Ruand Rsof the benchmark are stable,as conforming services are only searched within a fixed local range for enterprise demands.The Ruand Rsin the CM have a typical evolution process,which is divided into:

(t=0):The CM and the benchmark have the same Ruand Rs.

(t=1-3):Ruand Rsof CM increase rapidly at an extremely high speed as shown in Fig.4(a)and Fig.4(d),Ruincreases from 0.16 to nearly 0.23,and Rsincreases from 0.2 to 0.6.This is mainly due to the demand release by the guidance strategy in the early stage(GuidStra=1),which quickly guides related provider online for transactions.

(t=4-100):Ruand Rsof CM increase slowly as shown in Fig.4(b)and Fig.4(e),Ruincreases from 0.23 to near 0.26,and Rsincreases from 0.6 to 0.66.This is mainly due to the gradual consumption of initially released demands and bad matching between limited demands and services,while the increase of CMP scale results from EPH and NEs in this stage.

(t=100-150):Ruand Rsof CM regain rapid increase as shown in Fig.4(c)and Fig.4(f),with Ruincreasing from 0.26 to near 0.35 and Rsincreasing from 0.66 to higher than 0.9.This is mainly due to continuous PQIm which attracts the entry of new enterprises,and the increased network size which enhances d1/d2/localstrength to rapidly break through the critical mass.The platform gathers a large number of demands and services,which is conducive to looking for a suitable match in a larger range,improving the service utilization rate and demand satisfaction rate of enterprises.

(t=150-200):Enter the equilibrium state.After rapid growth,due to the limit of the total network size,both the number of enterprises entering the platform and demands and services tend to be stable.Rsis almost as high as 100%,indicating that some enterprises still have some remaining services to be used under the task intensity of simulation parameters in this paper.Therefore,Ruis stable at around 0.35.

In short,the results of Fig.3 and Fig.4 show that the over all service utilization rate and demand satisfaction rate of the enterprises are improved in CM compared with NM.

Fig.5(a)plots the growth curves of three utilities of the CM and the benchmark.As is indicated by the results,the three utilities in the CM are higher than those in the benchmark,which is consistent with the growth of Ruand Rsshown in Fig.3.Fig.3 and Fig.5(a)show that the platform will take about 150 simulation steps to reach equilibrium state under the current simulation parameterization.Fig.5(b)shows the distribution of enterprise utility.It is clear that most enterprises entering the CMP will have a higher utility.However,not all enterprises entering the CMP can get better profits;the utility of some enterprises is even at the bottom.However,in general,more enterprises will have higher utility in the CMP.

The results above show that the global sharing mechanism of CM can improve the service utilization and demand satisfaction rate of enterprises,and improve their profitability.

Fig.5 Comparison of utility

5.3 Impacts of diffusion forces

The above subsection analyzes the advantages of the CM mode under standard parameters.This subsection explores the impacts of diffusion forces mentioned in subsection 4.2.All parameters are fixed to initial values given in Table 1 except relevant impact factor parameters.The impact of each factor is analyzed in detail below.

(i)Impact of NEs(standard d1 = 1,d2 = 2,localstrenth=1)

This part analyzes the impact of localstrength(value set to be an integer in 1–5),d2(value set to be an integer in 1–5)and d1(value set to be an integer in 1–5).

From the results in Fig.6,it can be noted that localstrength has a great impact on platform diffusion.Specifically,although localstrength has almost no impact on the final ratio when the platformreaches an equilibrium state,it has a great impact on the speed in achieving an equilibrium state.The greater localstrength is,the shorter the time for the platform to diffuse to a stable state is,and the higher the speed is.

Fig.6 Impact of localstrength

As can be seen from the results in Fig.7,d2 has less impact on platform diffusion.Only when the platform grows rapidly(t=100-150),could larger d2 value result in shorter time and higher speed of diffusion to stable state.

Fig.7 Impact of d2

The results in Fig.8 indicate that d1 has a great impact on platform diffusion.Similar to the impact of localstrength,a larger d1 also results in a shorter time and higher speed of diffusion to equilibrium state.However,when d1 is larger than 3,the time gap from diffusion to stability becomes small.

The above analysis shows that large localstrength and d1 have significant promotion effects on the diffusion rate of the platform,while d2 has fewer effects.Only when the platform reaches a certain scale will it promote the diffusion rate.Furthermore,no matter how the above three strengths change in their respective ranges, the ratio is kept at about 0.92 when reaching an equilibrium state.This is mostly due to the difficulty for the enterprises that have not yet entered the late stage to find a provider to meet their demands.Additionally,they can not use their own idle service to get benefits.Therefore,they cannot get benefit higher than that in traditional mode,and those enterprises will never enter the platform.

Fig.8 Impact of d1

(ii)Impact of EPH(standard alpha=0.5,keytype=1)

This part analyzes the effect of ratio of DATs(alpha)and the ratio of the KCPs(keytype).Based on the standard parameters in subsection 5.2,this part analyzes the evolutional structure of the entry ratio of enterprises when the value of alpha and the value of keytype are in[0,1].The results are shown in Fig.9 and Fig.10.

Fig.9 Impact of alpha

The simulation results shown in Fig.9 indicate that alpha has a great impact on both the diffusion speed of the platform when reaching an equilibrium state and the entry ratio of enterprises under equilibrium state. The smaller alpha is,the larger the ratio is,the higher the speed is,and the shorter the time required for reaching an equilibrium state is.When alpha is less than 0.3,the impact on the platform evolution becomes weaker with the ratio stabilized above 0.9 and the time required for reaching an equilibrium state stabilized about t=100.Fig.10 shows that keytype has limited impact on the ratio at the initial time and fluctuates near the standard curve of alpha=0.5.In general,when alpha＜0.5,the ratio increases faster than in the case where alpha＞0.5.

Fig.10 Impact of keytype

The analysis above shows that alpha has an obvious impact on the platform diffusion speed and ratio when CMP is in an equilibrium state.When alpha＜0.3,the platform can achieve an equilibrium state and has a higher value of ratio.However,keytype has less impact.

(iii)Impact of SDM strategy

This part performs an analysis on the impact of the first come first-served algorithm based immediate-acceptance strategy and the gale-shaply algorithm based deferred acceptance strategy.The results are shown in Fig.11.

Fig.11 Impact of SDM strategy on the growth speed and scale of CMP

It can be seen in Fig.11 that both strategies have a positive effect on the promotion of enterprises to enter the CMP.In general,the time to reach an equilibrium state under both strategies is about t= 150.The deferredacceptance strategy,on the other hand,has a better promotion effect on the ratio,indicating that it can attract more enterprises to enter the platform.

The statistics of the inter- firm cooperation time and distribution diagram under the two strategies in Fig.12 show that the inter- firm cooperation time under the deferred-acceptance strategy(Gale-shapley)is uniformly distributed.Although the maximum cooperation time(ct=53)under this strategy is less than that under the immediate-acceptance strategy(ct=26)(the first come first served),on the whole,the opportunities for all enterprises under the deferred-acceptance strategy are relatively equal,and the competition among enterprises is more intensive.This can benefit the oligopoly situation and facilitate the promotion of maximization of overall utility throughout the entire network.

Fig.12 Statistics of cooperation times and distribution diagram

The analysis above shows that the deferred-acceptance strategy can avoid disequilibrium cooperation opportunities due to strong nodes in the network,and thus can promote more enterprises to enter the CMP.

(iv)Impact on IEG strategy

This part analyzes the demander priority strategy(dem)and the provider priority strategy(pro).The results are shown in Fig.13.

Fig.13 Number of demanders and providers newly entering the platform

Fig.13 shows the net increase in the number of demanders(nbDemander)and the number of providers(nbProvider)when two strategies are adopted during the platform diffusion process.The enlarged view shows the net increase at the early stage of development,indicating that:(i)under the dem strategy,the net increase of nbDemander is firstly changed and drives the increase of providers,but the net increase of nbProvider is more than that of nbDemander;(ii)under the pro strategy,the net growth of nbProvider is firstly changed and drives the increase of demanders,but the net growth of nbDemander is more than that of nbProvider.

In short,when the pro/dem strategy is used,the corresponding providers/demanders will take the lead in entering the platform,and guide more demanders/providers to enter the platform.From the perspective of the overall trend,obvious guidance effect comes from t=1-60,and is not visible between t=60-120.After t=150,the entry/exit number of enterprises tends to be 0,the CMP network reaches the equilibrium state.

As shown in Fig.14,according to different ratios in corresponding guidance strategies,the dem can accelerate the process of bringing enterprises online(in other words,the platform can achieve an equilibrium state in a shorter time),and its ratio of entry enterprises is higher than that of the pro when the platform is in an equilibrium state.When using the strategy of enterprise priority,the increasing speed of ratio is between the other two strategies.

Fig.14 Impact of different guidance strategies

As shown in Fig.15,according to the cumulative chart of“enter/exit”enterprises in two strategies,the enterprises enter/exit more frequently from the platform under pro(in other words,the enter/exit number of enterprises is larger),and the time required for equilibrium(t=150)is longer than that required by dem(t=75).

The analysis above shows that dem can get more enterprises online faster,and the entry/exit decision of enterprises shows little changes and randomness.The similar ratio in equilibrium state can be achieved under the pro, but needs longer time as the entry/exit decision of enterprises shows larger changes and a higher degree of randomness.

Fig.15 “Entry/exit” cumulative graph

(v)Impact of PQIm strategy(standard qmax= 12,c=0.05)

This part analyzes the impact of maximum quality qmaxand platform learning speed c on the platform diffusion process.The results are as follows in Fig.16.

Fig.16 Impact of qmax

According to Fig.16,qmaxhas a relatively large impact on the ratio and the speed of achieving the equilibrium state.When qmax≤10,the higher qmax,the shorter time required for the equilibrium state and the larger of the ratio.When qmax＞10,the same impact is applied on the speed of achieving the equilibrium state,but less impact is applied on the ratio(values close to 0.9).

According to Fig.17,c has no impact on the equilibrium state,but c has an important effect on the speed of achieving the equilibrium state.The larger c is,the shorter the time required is.

Fig.17 Impact of c

The analysis shows that the space and speed of PQIm are important factors which affect the equilibrium state and the speed of platform diffusion.In the development of CMP,the platform quality must be improved continuously to keep consistently attracting enterprises to enter the CMP.In short,the time required to achieve the equilibrium state and the growth rate of the network size depends on different strategies.Specifically,(i)three types of NEs are important;(ii)the ratio of deferred acceptance type enterprises has more effects than the ratio of KCPs;(iii)the Gale-Shapley algorithm based deferred-acceptance strategy and continuously improvement of CMP’s quality should be used in CMP.

6.Conclusions and discussions

This paper discusses the innovation diffusion process and dynamic mechanism of CMP.More specifically, first,the three-stage basic evolution process of CMP has been in novatively proposed.Second,an evolution model of CMP has been established for the first time with theoretical analysis on five diffusion forces in the diffusion process performed.Third,through simulation,evaluations on resource sharing indicators of the network manufacturing model and the proposed model have been compared,proving better resource utility and user satisfaction of the CM mode.Besides,simulation based analysis on the five diffusion forces’in fl uence on CMP diffusion has also been conducted.These analyses finally improve that CMP could create a stable supply and demand matching ecosystem,and break the inherent formation mechanism of the enterprise alliance.Therefore,a trans-regionally,dynamically and virtually open online cooperation environment could be reformed.

However,there are still many deficiencies in this model,mainly including:(i)this paper only selects several typical diffusion forces of CMP,and many other factors can be extended,e.g.,penetration pricing strategy to promote online trades;(ii)many other strategies of the five discussed factors should be analyzed,e.g.,SDMs based on non-cooperative game or various auction algorithms,and many kinds of social network phenomena,e.g.,word of mouth effect,vanity effect;(iii)more complex business scenarios can be considered,e.g.,batch and rolling demand,different cooperation degree between different types of nodes;(iv)random variables can be considered in the model;(v)the flexible index of the evaluation index system of CMRSC could be further considered;(vi)CMP diffusion model should be refined according to real scenarios.

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