Chuanrong Wu, Evgeniya Zapevalova Yingwu Chen and Feng Li

1 Introduction

With the advent of the big data era, big data has become one of the most important factors in production. The rational use of big data indicates the new growth of productivity, which will bring new growth for the production and operations of enterprises [Manyika, Chui,Brown et al. (2012)]. Big data knowledge has become an important part of knowledge that enterprises need for innovation. Many scholars have realized the important role of big data in the development of enterprises and countries. To make full use of the big data knowledge,many researchers consider helping enterprises obtain more big data knowledge from big data using some new optimization algorithms or materials [Fu, Ren, Shu et al. (2016); Liu,Cai, Shen et al. (2016); Kong, Zhang and Ye (2016); Kalidindi, Niezgoda, Landi et al.(2010); Yuan, Li, Wu et al. (2017); Cao, Zhou, Sun et al. (2018)]. The MapReduce proposed by Google in 2004 is the most representative data batch processing mode [Dean and Ghemawat (2004); Chen, Alspaugh and Katz (2012)]. Kalidindi [Kalidindi (2010)] built a comprehensive materials knowledge system relying on the use of computationally efficient FFT (Fast Fourier Transforms)-based algorithms for data-mining from large numerical datasets. Some traditional data analysis methods, such as data mining [Wu, Zhu, Wu et al.(2014)], knowledge discovery [Begoli and Horey (2012)], the ontology method [Kuiler(2014)], the statistical analysis method and so on, are applied to acquire knowledge from big data through optimization and adjustment. To ensure the knowledge obtained from big data can be understood and absorbed by enterprises, visualization technology is used to display the final analysis results to the user [Keim, Qu and Ma (2013)].

In the big data environment, the potential intellectual property risk of big data knowledge makes enterprises have to transfer some private knowledge from other organizations while making full use of the big data knowledge [Wu, Chen and Li (2016)]. However, the transfer mode of big data knowledge differs from that of private knowledge. Even though the two types of knowledge are big data knowledge or private knowledge, they are also different from each other in knowledge discovery, the negotiation process and the profit contribution to a new product. Some enterprises need to transfer various types of knowledge in the big data environment. Typically, some types of knowledge are not transferred simultaneously.Enterprises in the big data environment must constantly assimilate private knowledge and big data knowledge through multiple knowledge transfers to maintain their competitive advantage.

Scholars have carried out numerous studies on the influential factors of knowledge transfer and methods to promote the efficiency of knowledge transfer [Khamseh and Jolly (2014);Karlsen and Gottschalk (2015); Szulanski (2000); Burg, Berends and Raaij (2014);Wu and Lee (2015); Hsiao, Chen, Lin et al. (2017); Arteche, Santucci and Welsh (2013); Belso-Martinez (2015); Cowan and Jonard (2004); Fritsch and Kauffeld-Monz (2010); Tang, Mu and Maclachlan (2010); Bagheri, Kusters and Trienekens (2016); Wang and Wang (2017)].Some scholars believe that the selection of the optimal knowledge time is one of the most important factors to improve the efficiency of knowledge transfer. Farzin [Farzin (1996)]constructed a time optimization model for one type of technical knowledge by maximizing the net present value (NPV). Based on the research of Farzin and others, Doraszelski[Doraszelski (2004)] established an optimal adoption time model for a new technology by using the ordinary differential equation method. By considering the influence of an enterprise’s learning effect on the costs, Wu et al. [Wu and Zeng (2009)] proposed a time optimization model of one type of private knowledge in an innovation network. Szulanski[Szulanski (2016)] demonstrated that the proper knowledge transfer time can reduce the transfer difficulties using empirical methods. In previous studies, many scholars noticed the change in knowledge transfer characteristics in the big data environment and the importance of choosing the optimal knowledge transfer time [Wu, Chen and Li (2016);Koman and Kundrikova (2016); Wu (2017)]. However, few researchers have studied the problem of time optimization for multiple knowledge transfers in the big data environment.This paper categorizes multiple knowledge transfers in the big data environment based on the analysis of the complex process and influential factors. By maximizing the present value of the total expected profit of an enterprise, time optimization models for multiple knowledge transfers are established. These models can help enterprises determine the optimal knowledge transfer time. These models will help enterprises choose the optimal time of knowledge transfer according to different circumstances. After introducing the background of multiple knowledge transfers in the big data environment and the necessity of choosing the optimal time of multiple knowledge transfers in Section 1, the circumstances of multiple knowledge transfers and the modeling method are presented in Section 2. A time optimization model of multiple simultaneous knowledge transfers is presented in Section 3. In Section 4, the simulation experiments and experimental results are described. The conclusions and further research are discussed in Section 5.

2 Modeling method of multiple knowledge transfer in the big data environment

Big data knowledge has the characteristics of being open-source, dynamic, scalable and multi-source heterogeneous [Lohr (2012)]. That makes the process of big data knowledge transfer are significantly different from the process of private knowledge transfer. Big data knowledge transfers have intersectionality and complexity [Wu, Chen and Li (2016)]. An enterprise that transfers one types of big data knowledge has difficulties clearly defining the source of the knowledge transfer. However, the private knowledge transfer is usually a process of knowledge transferring from one organization to another organization [Alavi and Leidner (2001)]. Therefore, the big data knowledge and the private knowledge are the two dominant types of knowledge that enterprises need for innovation.

A new product of an enterprise usually needs various types of knowledge. These types of knowledge may be many types of private knowledge, may be many types of big data knowledge, or may be a variety of mixed knowledge. In addition, these types of knowledge may not be concurrently transferred. Knowledge transfer in the big data environment is a complex process of multiple knowledge transfers among many organizations.

Multiple knowledge transfers in the big data environment can be divided into two circumstances. One is the simultaneous transfer of various types of knowledge, and the other is various types of knowledge transfers at different time points. With the first circumstance, the weights of various types of simultaneous knowledge transfers can be determined by the profit contribution rate of each type of knowledge. Then, the multiple simultaneous knowledge transfers can be seen as a one-time knowledge transfer. By analyzing the influential factors of knowledge transfers, a time optimization model of multiple simultaneous knowledge transfers in the big data environment can be established based on the maximization of the total DEP of a new product. The total DEP includes the DEP before knowledge transfer, the DEP after knowledge transfer and the transfer costs.With the second circumstance, the problem of multiple knowledge transfers in the big data environment can be decomposed into many knowledge transfers. Various types of multiple simultaneous knowledge transfers still can be seen as a one-time knowledge transfer. The DEP after each knowledge transfer can be seen as the DEP before knowledge transfer of the next knowledge transfer. Then, the optimal time of multiple knowledge transfers at different time points in the big data environment can be obtained. The modeling idea and method are as shown in Fig. 1.

Figure 1: Model method

According to the modeling concept in Fig. 1, various types of knowledge transfers at different time points in the big data environment can be decomposed into many simultaneous knowledge transfers. Therefore, the most important thing for the time optimization of multiple knowledge transfers in the big data environment is to find the optimal time of the one-time knowledge transfer of various types of knowledge.

3 Time optimization model of multiple simultaneous knowledge transfers

3.1 Model hypotheses

This model is based on previous research. The same assumptions and variables remain unchanged as follows. The expression of an innovation network in the big data environment is. An enterprisewill produce only one product. The total market volume of the new product is, the price of the product is, and the marginal cost in the starting period is. The knowledge absorption capacity is. The market share ofin the starting period is. The market share ofincreases at a rate ofin the firstperiods and decreases at a rate ofin the other periods. The discount rate is, the life cycle of the product is，andis renumbered after each knowledge transfer. For the details on assumptions, see to the research of Wu et al. [Wu, Chen and Li (2016); Wu and Zeng (2009)]. In addition, six new hypotheses are proposed:

Hypothesis 1.is an enterprise in.needs to transfertypes of private knowledge from other enterprises, andalso needs to transfertypes of big data knowledge from the big data knowledge providers. All the private knowledge and the big data knowledge will transfer simultaneously at time period (0＜T＜NT ).

Hypothesis 2.ω11, ω12,… ω1Aare the weights of A types of private knowledge, andare the weights of B types of big data knowledge

Hypothesis 3.The update rate of the first type of private knowledge from another enterprise is, the update rate of the second type of private knowledge is, and the update rate of theAth type of private knowledge is. The update rate of the first type of big data knowledge from big data knowledge provider is, the update rate of the second type of big data knowledge is, and the update rate of theBth type of big data knowledge is. The update rate of all external new knowledge at time periodis.

Hypothesis 4.The fixed transfer cost of the first type of private knowledge is, the fixed transfer cost of the second type of private knowledge is, and the fixed transfer cost of theAth type of private knowledge is. The fixed transfer cost of the first type of big data knowledge is, the fixed transfer cost of the second type of big data knowledge is, and the fixed transfer cost of theBth type of big data knowledge is.All the fixed transfer costs are constants.

Hypothesis 5.is the total growth rate of the market share ofin the firstperiods immediately aftertransfers various types of knowledge at the time period.is the growth rate of the market share ofin the firstperiods immediately afteronly transfers the first type of private knowledge at the time period.is the growth rate of the market share ofin the firstperiods immediately afteronly transfers the second type of private knowledge at the time period.is the growth rate of the market share ofin the firstperiods immediately afteronly transfers theAth type of private knowledge at the time period.,, …are the respective growth rates of the market share of each type of big data knowledge afteronly transfers each type of big data knowledge at the time period

Hypothesis 6.s the DEP ofbefore transferring new knowledge,is the DEP ofreceived after transferring various types of new knowledge at time point,andis the knowledge transfer cost of all external new knowledge. The total DEP ofis denoted asand.

3.2 DEP before multiple simultaneous knowledge transfers

Because there is no new knowledge before knowledge transfer,produces new product using prior knowledge. From the previous hypotheses, the market share changes from growth to decay at time periodherefore, the entire life cycle of the product can be divided into two phases:ndhe net profit ofduring this period can be calculated by subtracting the total production cost from the total sales revenues.Then, the total DEP ofbefore various types of simultaneous knowledge transfers can be obtained by discounting the net profits of each phase to the starting point. The DEP before knowledge transfer is as shown in Eq. (1). The detailed calculation method is introduced by Wu et al. [Wu and Zeng (2009)].

3.3 Transfer cost of various types of knowledge

From hypotheses 2-4, the variable cost can be computed by Eq. (4), whereis the coefficient of variable cost, anda constant.

After discounting the transfer cost to the starting point, the total transfer cost of various types of knowledge can be expressed as Eq. (5).

3.4 DEP after multiple simultaneous knowledge transfers

From hypothesis 3, the update rate of all external new knowledge at time periodis. Considering the time cumulative effect, the external new knowledge at time periodhas been updated by, which can make the marginal cost ofat time periodreduce to. The knowledge absorption capacity ofis. Then, the marginal cost ofat time periodwill becomeBy replacingwith Eq. (3), the marginal cost at time periodofcan be calculated by Eq. (8).

The total production cost at time periodafter knowledge transfer is. By subtracting the total production cost from the sales revenue, the profit at time periodafter knowledge transfer can be obtained by Eq. (9)

Through discounting the profits in period n to the starting point by multiplying Equation(9) withand summing up all the discounted profits in the life cycle, the DEP after knowledge transfer is as shown in Eq. (10)

By using Eqs. (7) and (10), the expected profits after knowledge transfer can be expressed as Eq. (11)

3.5 Total DEP model

From the modeling idea and methods, the time optimization problem of multiple simultaneous knowledge transfer of various types of knowledge must find the maximum of the total DEPoffor the given parameters. Therefore, the optimization model of multiple simultaneous knowledge transfer can be expressed as Eq. (12).

4 Simulation experiments

4.1 Model solution

It can be seen from Eq. (12) thatis a piecewise continuous differential function of. Therefore,can reach its maximum in a closed intervalnd the maximum profits in the life cycle of the product can be found. Then, the optimal time of multiple knowledge transfers can be obtained.

MATLAB 7.0 has been used to compile a program that considers the power of the numerical calculation and simulation functions. Some simulation experiments of actual situations could be conducted by adjusting the model’s parameters.

4.2 Simulation experiments

4.2.1 Common parameter setting and simulation

To simulate multiple knowledge transfer in the big data environment, several common parameters are chosen for testing. The values of some common parameters are set the same as those of Wu et al. [Wu, Chen and Li (2016)] and are as shown in Tab. 1.

Table 1: Values of common parameter

Table 2: Model validation with ω11=0.6,ω21=0.4

Figure 2: Changes in DEPs and transfer costs with ω11=0.6,ω21=0.4

Table 3: Model validation with ω11=0.4,ω21=0.6

Figure 3: Changes of DEPs and transfer costs when ω11=0.4,ω21=0.6

4.2.2 Simulation of withA=2,B=1

Table 4: Parameter values when A=2, B=1

Tab. 5 and Fig. 4 show the changes of DEPb, DEPa, transfer costs and the total DEPs of. The optimal time for knowledge transfer is. When comparing the experimental results with those in Tab. 2 and Fig. 2, despite the increase in the transfer costs of one type of private knowledge, the total DEPs increase with the efficiency of the private knowledge.The optimal time for knowledge transfer changes fromto. The reason is that private knowledge is usually the core patent knowledge, which can greatly improve the technology innovation performance of the enterprise. The more efficient the private knowledge is, the greater the total DEP, and the earlier that knowledge transfer occurs.

Table 5: DEPs and transfer costs with A=2, B=1

Figure 4: Changes of DEPs and transfer costs when A=2, B=1

4.2.3 Simulation of with A=2,B=1

Table 6: Parameter values when A=1, B=2

Tab. 7 and Fig. 5 show the experimental results of DEPb, DEPa, transfer costs and the total DEPs of. The optimal time for knowledge transfer is. Comparing the experimental results with those in Tab. 3 and Fig. 3, although the transfer costs of one type of big data knowledge are reduced, the total DEPs have also declined. The optimal time for knowledge transfer changes fromto. The reason is that the fixed costs of big data knowledge are extremely low, and the marginal costs are almost negligible. The efficiency of big data knowledge having lower transfer costs is limited to the profits growth of the enterprise. If the expected profits are not large enough, the enterprise will delay knowledge transfer.

Table 7: DEP and transfer cost with A=1, B=2

Figure 5: Changes of DEPs and transfer costs when A=1, B=2

5 Conclusion

This paper analyzed the time optimization problem of multiple knowledge transfer in the big data environment. Based on the analysis of the complex process and influential factors of multiple knowledge transfers in the big data environment, the activities of multiple knowledge transfer are divided into two categories. One is the simultaneous transfers of various types of knowledge, and the other one is that multiple knowledge transfers of various types of knowledge at different time points. Taking into consideration the influential factors, such as the knowledge type, knowledge structure, knowledge absorptive capacity, knowledge update rate, discount rate, market share, profit contribution of each type of knowledge, transfer cost, product life cycle and so on, time optimization models of multiple knowledge transfers are presented by maximizing the total DEP of an enterprise.Some simulation experiments have been performed to verify the validity of models, and the models can help enterprises determine the optimal time of complex multiple knowledge transfers in the big data environment.

The proposed models in this paper have several limitations, and further research is needed.Multiple knowledge transfers at different time points in the big data environment are just decomposed into many times of simultaneous knowledge transfers. However, the optimal time for the first knowledge transfer usually affects the second knowledge transfer in realworld circumstances if the time interval is not too long. Enterprises have to comprehensively determine the optimal time for multiple knowledge transfers. Compared with the profits, the transfer costs are set too low, especially the transfer costs of private knowledge. Therefore, the transfer costs should be adjusted to discover their impact on the total DEPs. Additionally, our assumptions that the enterprise only produces one product and the price remains flat can be relaxed to accommodate more realistic circumstances.

Acknowledgment:This research is supported by the National Natural Science Foundation of China (Grant No. 71704016,71331008, 71402010), the Natural Science Foundation of Hunan Province (Grant No. 2017JJ2267), the Educational Economy and Financial Research Base of Hunan Province (Grant No. 13JCJA2), and the Project of China Scholarship Council for Overseas Studies (201508430121, 201208430233).

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