With the rapid change of business environment and uncertainty of market demand, more and more enterprises are forced to form R&D collaborations with others to obtain complementary resource, to shorten the research & development cycle, and to reduce the cost and share risk. However, the risk still existes in R&D networks. In contrast, enterprises will face more types of risk, for instance, opportunism risk, trust risk, and collaborated risk. Furthermore, due to the complexity collaboration relationship between enterprises, a risk raised in one enterprise may trigger other potential risks of its neighboring enterprises through the R&D collaborations. This phenomenon is called risk propagation. As a result, the R&D network will be collapsed once the major amount of enterprises outbreak risks. Therefore, it is significantly to explore the mechanism of risk propagation in R&D network in order to provide some managerial advices for enterprise.
According to the literature review, many studies have focused their attentions on analyzing risk propagation in R&D network without considering the interrelated relationship between different projects. To fill this gap, the SIS model is adopted to describe risk propagation in R&D network by considering the interrelation between different projects within one enterprise. The sole purpose of our work is to improve the capability of resisting risk and to keep the sustainable development of R&D network.
Firstly, an R&D network is divided into sub-networks according to the number of projects. The adjacency matrixes are denoted as A1
, and the adjacency matrix of the sub-networks is denoted as C
. Secondly, the risk propagation model of R&D network is established by employing the SIS model. In this model, two states are assigned to each enterprise:one is ‘I
’ stands for risk occurred, and another is ‘S
’ stands for risk not occurred. When a risk of one enterprise on a certain project has occurred, then it will trigger its neighboring enterprises in S
state to breakout risk with a specified probability β
. In the meanwhile, the interrelated projects within the same enterprise also will be triggered risk with a probability λβ
. When a risk of one enterprise has been caused, the enterprise will back to normal from risk with probability μ
since some risk control measures took. Therefore, the probability of each enterprise on a specific project can be showed as Eq. (1):
In Eq. (1) aij
are the relationships between enterprises i
respectively, while cij
is the interrelated relationship between different projects within the same enterprise. β
is the triggering probability, and λ
is a controlling parameter which governs the triggering probability between different projects within the same enterprise.μ
is the recovery probability of enterprise.
When risk propagation reaches a stable state, the enterprises' states will not change with the time window t
changing. Then one can obtain the threshold of risk propagation according to the literature of signal network as Eq. (2) shows.
) is the maximum eigenvalue of matrix A
. From Eq. (2), it is obvious that the threshold is determined by the topology of R&D networks and the extent of interrelated between different projects within the same enterprises.
Finally, interrelated R&D network is generated by employing BA model. The partition of failed enterprises at the end of risk propagation is defined by ρI
, which is used to measure the consequence created by risk propagation in R&D network. The mathematical analysis and simulation experiment results show that:(1) the threshold is determined by the sub-networks topology and the degree of the interrelation between different projects in the same enterprise; (2) when considering project interrelated relationship, the threshold is lower than projects interrelated are not considered; (3) by increasing the number of enterprises which existing projects interrelated relationship, the speed and the scope of risk propagation increase rapidly in R&D network; (4) the degree of interrelation between projects within the same enterprise has impact on both the speed and the scope of risk propagation in R&D network.
By taking projects interrelated relationships between different projects within the same enterprises into account, and analyzing how risk propagation influences the robustness of R&D network through analytic and numerical simulation, the research work of this paper will provide some managerial advices for enterprises risk management under context of network.