Knowledge Transfer Optimization Simulation for Innovation Networks

INTRODUCTION

Innovation network is a social context of enterprises and research institutes which are linked to one another to share resources and knowledge to gain critical competencies that contribute to their competitiveness in the marketplace. In this special network, the nodes are enterprises or research institutes, the edges are relations among enterprises or research institutes.

Due to the importance of innovation networks in modern society, various researchers have carried out a lot of researches on the formation and evolution of innovation networks (Debresson and Amesse, 1991; Chang and Harrington, 2007), the factors which influence the knowledge transfer in innovation networks (Cummings and Teng, 2003; Bae and Koo, 2008; Coccia, 2008; Tang et al., 2008) and how to enhance the efficiency of knowledge transfer (Reagans and McEvily, 2003; Kotabe et al., 2003; Hoffmann, 2008). Research has also showed that knowledge transfer plays a key role in innovation networks (Varga, 2000; Hovorka and Larsen, 2005; Knudsen, 2007; Mihelcic et al., 2007). Useful techniques to enhance the efficiency of knowledge transfer have also been developed by Tang et al. (2004), Sabherwal and Sabherwal (2005) and Matsuno et al. (2007).

However, there are few researches on how to determine the optimal time of knowledge transfer to maximize the profit of an enterprise. Taking into account of several important factors such as knowledge absorption capacity, update rate of knowledge in the network, discount rate, market share and life cycle of a product, we will present an optimization model to determine the optimal time of knowledge transfer. A large number of simulated experiments will be carried out to prove the model is feasible as a basis of decision support of time optimization of knowledge transfer for enterprises.

BACKGROUND TO TIME OPTIMIZATION IN KNOWLEDGE TRANSFER

Knowledge transfer can be drawn from the expression: Let G = G (V, E) be an innovation network, where, V = {V_i} is the set of nodes (enterprises or research institutes) in the network, E = {e_{i, j}} is the set of edges (knowledge transfer) between nodes, 1≤ i, ≤ j≤ |V| and |V| is the number of nodes in V.

Knowledge in innovation networks can be divided into two types, common knowledge and private knowledge (Khanna et al., 1998). It is assumed that common knowledge is the knowledge shared freely by all the nodes in the network. The ability to utilize the common knowledge only depends on the absorptive capacity of a node. On the other hand, private knowledge is the knowledge that can bring innovative profits and expand market share for related nodes. If a node wants to get private knowledge from another node, it should pay knowledge transfer cost. We only consider links of nodes based on private knowledge and we shall limit ourselves to the definition 1 below:

Definition 1: Let V_i and V_j be two nodes in G (V, E), if e_{i, j} = 1 then there exists knowledge transfer between V_i and V_j, if e_{i, j} = 0 then there is no knowledge transfer between V_i and V_j.

To make the optimization model simpler and practical, we formulate the following hypothesis.

Hypothesis 1: All the nodes in G (V, E) have only one product, whose marginal cost (Mansfield and Gary, 2003) in the starting period is MC. The marginal cost will decline at a rate of α (0<α<1).

Hypothesis 2: The total market volume of the product is Q. The market share of each node in the starting period is φ. The total market volume increase at a rate of θ₁(0<θ₁<1) in the first L₁ periods and will decrease at a rate of θ (0<θ<1) in other periods.

Hypothesis 3: All nodes in G (V, E) share only one private knowledge whose transfer cost in the starting period is k. If the knowledge is transferred to a node, the market share of this node will increase at a rate of ρ (0<θ₁<ρ<1) in the first L periods immediately after knowledge transfer.

Hypothesis 4: The update rate of the knowledge in G (V, E) is β.

Hypothesis 5: The life cycle of the product in G (V, E) is N, which should be reset after knowledge update.

OPTIMIZATION MODEL

To maximize the profit of a node V_i (enterprise) in G (V, E), a model to determine the optimal time period T to transfer knowledge is presented here.

Given that V_i and V_j are two nodes in G (V, E) and that V_i wants to transfer knowledge from V_j in time period T and that the expected total profits of V_i is denoted as Ψ(T), we shall have Ψ(T) = – K(T)+ξ(T), where, ξ(T) is the expected profit of V_i gotten before knowledge transfer, ξ(T) is the expected profit of V_i gotten after knowledge transfer and K(T) is the cost of absorbing knowledge from V_j. The calculation of ξ(T), ξ(T) and K(T) is derived as follows:

Expected profits before knowledge transfer: Assuming that the price of the product is p, then from hypothesis 2 and 3, the sales revenue in period n can be calculated by:

(1)

From hypothesis 1, the marginal cost in period n is expressed as MCα". Using hypothesis 2, the total production costs in period n can be calculated by:

(2)

Therefore, by subtracting the production cost in Eq. 2 from the sales revenue in Eq. 1, the profit in period n is calculated as follows:

(3)

By discounting the profit in period n to the beginning (with n = 0) at a discount rate r and summing up all the discount profits, the Discount Expectation of Profits (DEP) before knowledge transfer becomes:

(4)

Expected profits after knowledge transfer: If V_i transfers knowledge from V_j in a period of time T, based on hypothesis 2, the market share of V_i in a period of time T can be calculated as follows:

(5)

From hypothesis 2 and 3, the market share of V_i will increase at a rate of ρ in the L periods immediately after the time period T and it will then decay at a rate of θ. Hence, the market share of V_i in period n can be denoted as follows:

(6)

From hypothesis 4, the knowledge adopted by V_i in period T has been updated by β^T, which will make the marginal cost in period T reduce to MCβ^T. If we renumber the periods after knowledge transfer as n starting from 1 to N, where, N is the life circle of the product defined in hypothesis 5, the marginal cost in period n becomes MCβ^Tαⁿ. Hence, the total production cost in period n after knowledge transfer is Qλ(n, T)MCβ^Tαⁿ. By subtracting the total production cost Qλ(n, T)MCβ^Tαⁿ from the sales revenue pQλ(n, T), the profit in period n after knowledge transfer is as follows:

(7)

Discounting the profits in period n to the starting point by multiplying Eq. 7 by r^Trⁿ and summing up all the N discount profits, the Discount Expectation of Profits (DEP) after knowledge transfer becomes:

(8)

Using Eq. 6 and 8, the expected profits after knowledge transfer can be expressed as follows:

(9)

Transfer cost: The transfer cost of node V_i is composed of two parts, the fixed transfer cost k defined in hypothesis 3 and the variable cost. The variable cost is related to the gap between the inside and outside knowledge level. We may compute the variable cost as F(α^T – β^T), where, F is a constant. After discounting the transfer cost to the starting point, it can be expressed as follows:

(10)

The total discount expectation of profits model: Given that V_i and V_j are two nodes in G (V, E), V_i wants to transfer knowledge from V_j in time period T, the optimization problem of knowledge transfer will be to find the optimal time T to maximize – K (T)+ζ (T)+ξ (T). Therefore, the optimization model of knowledge transfer can be expressed as:

(11)

From Eq. 4, 9 and 10, the Eq. 11 becomes:

(12)

OPTIMALITY OF THE MODEL

The model itself: From Eq. 12, it is easy to see that Ψ(T) is a piecewise continuous differential function of T. Therefore, Ψ(T) can reach its maximum in a closed interval 1≤ T≤ N. That is to say, we can find the optimal knowledge transfer time in the life circle N of the product.

Moreover, since generally N is not very large, there is no need to find a higher and efficient algorithm to get the optimal solution, as exhaustive method is enough. Therefore, considering the powerfulness of the numerical calculation and simulation functions of Matlab, we only compiled a very simple program by Matlab.

Fig. 1:	Changes in total DEP

Table 1:	Profit and cost of knowledge transfer

We made lots of experiments to test the model by adjusting its parameters.

Simulation experimental results: To simulate the practical innovation networks, a great deal of combinations of values of parameters of the model are chosen for testing. One of the sets of parameters considered is: Q = 1000, φ = 8%, θ₁ = 3%, p = 60, ρ = 6%, θ = 3%, MC = 40, k = 300, F = 1000, α = 95%, β = 88%, N = 10, r = 0.9. We assume the unit of the time period T is year.

Figure 1 and Table 1 show the experimental results of the model and a set of values of parameters used. The results in Table 1 and Fig. 1 imply that the discount expectation of profits is maximal at T = 6 and that the optimal knowledge transfer time is the 6th period.

3-DIMENSIONAL SIMULATION EXPERIMENTS

In order to find the influence of the parameters on the optimal knowledge transfer time, one of the parameters was set as a variable with time period set in turn.

Fig. 2:	Changes in EDP with α

In this way, so many 3-dimensional simulation experiments were carried out at the same time. The 3-dimensional simulation results do not only further verify the correctness of the model but also provide decision support for enterprise management.

Simulation with α as a variable: To find the influence of α on the optimal knowledge transfer time, all the parameters except α were set with the same values like the earlier mentioned. Figure 2 shows the Discount Expectation of Profits (DEP) with α varying from 0.88 to 0.99 and T varying from 1 to 10. From Fig. 2, it can be seen that the smaller the α the later the optimal knowledge transfer time becomes.

Simulation with β as a variable: To find the influence of β on the optimal knowledge transfer time, all the parameters except β were set with the same values as indicated in the previous section. Figure 3 shows the Discount Expectation of Profits (DEP) with β varying from 0.75 to 0.95 and T varying from 1 to 10. It can be seen that the smaller the β the earlier the optimal knowledge transfer time becomes.

Simulation with θ as a variable: To find the influence of θ on the optimal knowledge transfer time, all the parameters except θ were set with the same values as earlier mentioned.

Figure 4 shows the Discount Expectation of Profits (DEP) with θ varying from 0 to 0.15 and T varying from 1 to 10. From Fig. 4, it can be seen that the smaller the θ the later the optimal knowledge transfer time becomes.

Simulation with ρ as a variable: To find the influence of ρ on the optimal knowledge transfer time, all the parameters except ρ were set with the same values as earlier mentioned.

Fig. 3:	Changes in EDP with β

Fig. 4:	Changes in EDP with θ

Figure 5 shows the Discount Expectation of Profits (DEP) with ρ varying from 0.03 to 0.15 and T varying from 1 to 10. From Figure 5, we can see that the smaller the ρ the later the optimal knowledge transfer time becomes.