Abstract
Member selection to form an effective collaboration new product development (Co-NPD) team is crucial for a successful NPD. Existing researches on member selection mostly focus on the individual attributes of candidates. However, under the background of collaboration, knowledge complementarity and collaboration performance among candidates are important but overlooked. In this paper, we propose a multi-objective optimization model for member selection of a Co-NPD team, considering comprehensively the individual knowledge competence, knowledge complementarity, and collaboration performance. Then, to solve the model, an improved adaptive genetic algorithm (IAGA) is developed. Finally, a real case is provided to illustrate the application of the model, and the IAGA is implemented to select the desired team members for optimal team composition. Additionally, the standard generic algorithm and particle swarm optimization are used to compare with the IAGA to further verify the effectiveness of the IAGA.
1 Introduction
Due to the growing pressure of market competition and customers’ diversified demands, collaboration new product development (Co-NPD) become increasingly important for firms to gain competition advantages [6]. By plunging into Co-NPD, firms attempt to span organizational boundaries, improve utilization efficiency of internal and external resources, and reduce NPD risk and cost [6, 24, 31]. Co-NPD activities are typically executed in a multi-disciplinary team-based manner, and their organizational nucleus is the Co-NPD teams [19, 32]. Co-NPD teams are greatly advantageous since the team members from different organizations can share the complementary knowledge with mutual aims, spark more product innovation inspiration with their multidisciplinary knowledge, and handle the product development complexity [23, 28, 30, 40]. Moreover, the Co-NPD teams are usually organized temporarily in order to quickly respond to the changing NPD conditions by adjusting the composition of Co-NPD team members and optimizing the knowledge structure [39]. Therefore, in order to ensure the NPD success, it is highly important to assemble Co-NPD teams that are able to effectively carry out NPD plans and projects. Within, member selection is a key issue of concern for firms. However, a primary challenge remaining for project managers or other decision makers is to select the team members with desirable qualifications to meet the requirements of the projects.
In the existing research on member selection, the individual performance of each member is focused on; however, the complementarity utility and collaboration performance are overlooked. In fact, there are lots of drawbacks of the simple seeking for the maximum individual performance. The most prominent one is that it fails to consider the synergy among team members. Therefore, it is very necessary to consider the complementarity utility and collaboration performance among members, as the two factors play highly important roles in stimulating the synergy within teams. With this consideration, the objective of this study was to propose a novel approach for member selection of Co-NPD team addressing the individual knowledge competence, the knowledge complementarity, and the collaboration performance of the candidates. In this way, this study tries to provide a new angle and method for decision makers to select desired members with comprehensive advantages to form a more efficient and competitive team in practice.
The remainder of the paper is organized as follows. Section 2 reviews the related work on member selection for teams. In Section 3, the multi-objective model for member selection of Co-NPD teams is built using the attributions of individual knowledge competence, knowledge complementarity, and collaboration performance. Section 4 develops a multi-objective adaptive genetic algorithm (GA) to solve the model. In Section 5, the application of the model and the algorithm in a real-world example is presented to show the practicality of the proposed method. Finally, the main conclusions are summarized in Section 6.
2 Related Work
Member selection of Co-NPD teams is a complex decision problem that needs to consider multiple attributes. Zhang and Zhang [39] discuss the requirements for team members, such as expertise and experience, learning and knowledge sharing, communication, problem solving, and personality characteristics, etc. Lee’s research [18] implies that high NPD team should recruit qualified team members who have adequate knowledge and strong entrepreneurial proclivity. Antoniadis [2] state that work experience, technical and management knowledge, and personal profile are important evaluation criteria for selecting project team members. To meet the project knowledge requirement better, Wi et al. [34] regard knowledge competence as important evaluation criteria for member selection. The above literature reports all state the importance of individual characteristics, especially knowledge competence. Along with that, as Co-NPD is a knowledge-intensive activity, knowledge competence is a vital criterion for selecting members. However, while focusing on individual knowledge competence, from the perspective of synergy within teams, it should also be noted that the collaboration attributions are vital factors that should be taken seriously. In a Co-NPD team, members have to span the organizational boundaries and cooperate with each other to share their knowledge and concerns. Moreover, because of the different background and practice requirements, members’ knowledge needs to be complementary. Only so, the collaboration among members with complementary knowledge can spark newer and more ideas to support product innovation. Therefore, the role of knowledge complementarity and collaboration performance among members in member selection should not be overlooked, and should get as much attention as they deserve.
In the area of knowledge explosion, with the specification of social division of labor, each person can only possess a tiny fragment of all the knowledge of humanity. Therefore, knowledge complementarity is an important property of concern in the environment of collaboration. Xu and Zhao [36] propose the two dimensions of knowledge complementarity – relatedness and differences – and discuss the effects of knowledge complementarity on technology alliance formation and partner selection. By investigating the NPD design industries, Abecassis-Moedas and Mahmoud-Jouini [1] draw a conclusion that the positive relationship between knowledge absorption and NPD performance is moderated by the source-recipient knowledge complementarity. Baum et al. [3] state that the moderate knowledge complementarity can contribute to establish more profitable collaboration partnership. In addition, complementary knowledge provides potential opportunities to inspire members’ cooperation motive, create new and different ideas of NPD, and enhance NPD performance [10, 26]. To sum up, complementary knowledge shared among different members can help generate synergy like 1+1>2.
As for collaboration performance among members, collaboration innovation becomes an emerging trend in NPD, and collaboration among members plays an important role as the success of the teams depend on the smooth connection and good cooperation among all members [4]. Meanwhile, the good collaboration situation among members allows for cross-disciplinary knowledge integration, which may be essential for creating new products [5]. Wi et al. [35] imply that members with good collaboration relationship can mobilize more knowledge resources within collaboration teams. Jiang et al. [14] state that teams are not the simple combination of members, and collaboration is the key to integrate every member and stimulate the potential synergies. Moreover, Fan et al. [9] argue that good collaboration performance between members can enhance team cohesiveness, member tacit agreement and satisfaction, mutual trust, and reduce misunderstanding and conflicts. Therefore, it is a valuable reference for the decision makers to select members based on their prior collaboration information. Above all, from the view of knowledge and collaboration, not only the knowledge competence of individual members but also the knowledge complementarity and collaboration performance among members should be considered in the member selection of a Co-NPD team.
Furthermore, it has been a research trend that many scholars use quantitative methods to solve the member selection problem. Jiang et al. [14] propose a model transition method to reduce the complexity of the member selection problem, and efficiently obtain the optimal solutions of member selection. Shipley and Johnson [29] propose a fuzzy set-based model to select project team members with a preferred cognitive style goal. Yue [38] develops an intuitionistic fuzzy projection-based approach for partner selection. Chen and Lin [8] adopt analytic hierarchy process (AHP) to compare the candidates with their competence in order to select the appropriate members to form a multifunctional team. Zhang and Zhang [39] develop a multi-objective particle swarm optimization (PSO) algorithm to form a multi-objective NPD team. However, in the existing methods for member selection, the individual attributions of candidates are extensively studied, while the knowledge complementarity and collaboration performance of the candidates are seldom considered. Therefore, a comprehensive model and an effective algorithm are required to solve the problem of member selection of a Co-NPD team using the above knowledge and collaboration attributions.
3 Model for Member Selection of a Co-NPD Team
3.1 Problem Statement
This paper focuses on the problem of selecting desired member from candidates affiliated with different organizations to build a Co-NPD team, by using the criteria of the individual knowledge competence, knowledge complementarity, and collaboration performance. In doing so, we attempt to develop a quantitative member selection model. Moreover, the knowledge competence of individual candidates, knowledge complementarity, and collaboration performance between candidates all need to be quantified to evaluate the candidates. Thus, how to quantify the above criteria effectively and then build the mathematical model are the key points in this paper.
The problem of member selection of a Co-NPD team can be described as follows. Suppose that a Co-NPD team needs to select m members from a set of n candidates, namely P={P1, P2, …, Pi, …, Pn}, where Pi represents the ith candidate. The knowledge competence of candidate Pi is denoted as KCi. Let Cij and CPij be as the knowledge complementarity and collaboration performance score between candidates Pi and Pj. In order to choose the appropriate members, form the view of knowledge and collaboration, managers should select the m members with the optimal sum of the knowledge competence KCi, and among the m members, there should be proper knowledge complementarity Cij and optimal collaboration performance CPij.
In order to clearly describe the problem of member selection of a Co-NPD team, the following notations are used throughout the paper:
n: The total number of candidates.
m: The total number of desired members.
M: The total number of knowledge keywords for a certain project.
P={P1, P2, …, Pi, …, Pn}: The set of n candidates.
Pi, Pj: The ith and jth candidates, i, j=1, 2, …, n.
kth: The kth keyword for a certain project, k=1, 2, …, M.
KCi: The knowledge competence value of candidate Pi after normalization.
Cij: The knowledge complementarity between Pi and Pj.
CPij: The knowledge complementarity between Pi and Pj.
Rg: The criterion to measure the individual knowledge competence, g=1, 2, …, q.
wg: The weight of criterion Rg,
Sij: The comparative knowledge advantage of Pi comparing with Pj.
Sk(ij): The comparative knowledge advantage of Pi exceeding Pj for the kth knowledge.
FCij: The formal collaboration performance between Pi and Pj.
Rij, Rji: The proportion of common projects of the candidate Pi and Pj, respectively.
ICij: The informal collaboration performance between Pi and Pj.
Tij, Tji: The proportion of common communication of the candidate Pi and Pj, respectively.
μ, ν: The weights to measure the formal and informal collaboration performance, respectively, μ+ν=1.
xi: 0–1 variable, xi=1 if candidate Pi is selected; xi=0, otherwise.
3.2 Knowledge Competence
It is very advantageous to evaluate the individual knowledge competence, and many scholars attempt various ways to evaluate it [27, 35, 37]. Knowledge competence is the crucial capability of team members to support the effective NPD, because of the knowledge-intensive characteristic of NPD [20]. To obtain the knowledge competence of candidates effectively, this paper builds a decision matrix to evaluate the individual knowledge competence. Let
where
Next, the decision makers should give weight wg to each criterion,
Furthermore, the value of knowledge competence of candidate Pi can be obtained by
To guarantee the knowledge competence score within [0, 1], it should be normalized by the following formula:
where
3.3 Knowledge Complementarity
From the perspective of managers, of course, they hope the Co-NPD team members have as much individual knowledge competence as possible to cope with increasing NPD uncertainty and challenges. However, in the angle of teamwork, there are inevitable disadvantages of simply going after knowledge competence, neglecting the knowledge complementarity among the different members. That is, in the context of Co-NPD, if the members’ knowledge and capabilities are too similar, then there are too many knowledge overlaps, leaving little for mutual learning and hampering the NPD innovation; however, if they are too dissimilar, members will have difficulty in understanding each other, making communicating and learning difficult [3]. The above two situations both make simulating synergy among members difficult. Therefore, successful collaboration depends on the extent to which the members’ knowledge competences both resemble and complement each other.
Some scholars have attempted to define and quantify knowledge complementarity in various kinds of context [3, 7, 21], which contributed noticeably to improving the understanding of knowledge complementarity. However, the existing researches also have their own limitations. Based on the former researches, we attempted to study knowledge complementarity from the view of members’ comparative knowledge advantage. In this work, knowledge complementarity refers to the complementary degree of comparative knowledge advantage among members’ knowledge competence [7]. To quantify knowledge complementarity, firstly suppose that Sij denotes the comparative knowledge advantage of candidate Pi comparing with Pj, and Sij is the sum of knowledge competence value that Pi exceeds Pj. Sk(ij) denotes the comparative knowledge advantage of Pi exceeding Pj for the kth knowledge. Sk(ij) can be obtained by the following formula:
where
Thus, Sij can be obtained by
Cij denotes the knowledge complementarity between candidates Pi and Pj. Moreover, the knowledge complementarity between candidates Pi and Pj are reciprocal, that is, Cij=Cji. The knowledge complementarity between candidates Pi and Pj can be obtained by
Obviously, Cij is within [0, M]. When Cij=0, it means the knowledge background and competence of Pi and Pj is totally same, and when Cij=M, the knowledge background and competence of Pi and Pj is totally different. Based on the above analysis, the knowledge complementarity should be neither too similar nor too far dissimilar among members. Therefore, the knowledge complementarity is profitable if and only if
where
3.4 Collaboration Performance
In the process of Co-NPD, there mainly are two types of collaboration relationship among team members: the formal collaboration relationship and the informal collaboration relationship. The formal collaboration relationship is the cooperation relationship on an NPD project or task, which is determined by the team goal and structure. On the other hand, the informal collaboration relationship implies the social relationship caused by the private communication among members. Researches showed that the good prior cooperation and personal relationship among individuals both contribute to improving their current collaboration [14, 22]. Therefore, the formal and informal prior collaboration information can be made as the valuable reference to evaluate the collaboration performance. In this work, we attempt to investigate the collaboration performance at both sides of the formal and informal collaboration relationship based on members’ collaboration information.
For the formal collaboration relationship, it typically occurs among members in the process of project collaboration of Co-NPD. Some scholars argue that people favor the partners with whom they have successful cooperation before, which can reduce uncertainty regarding potential members’ capabilities and reliabilities [11, 15]. Therefore, we aim to use the prior project cooperation information to obtain the formal collaboration performance. In this work, the formal collaboration performance FCij between Pi and Pj can be measured by their past cooperation information using the following formula [22]:
where Rij and Rji denote the proportion of common projects of candidates Pi and Pj.
For the informal collaboration relationship, it is mainly reflected in the private communication between team members. In this paper, we adopt the frequency of communication among candidates during a specified period of time to measure the informal collaboration relationship. Moreover, the more the frequency of communication is, the tighter the informal relationship is [22].
The informal collaboration performance of candidates Pi and Pj can be measured using the following formula:
where Tij and Tji are the proportions of common communication of candidates Pi and Pj, respectively.
By synthesizing the formal and informal collaboration performance, the collaboration performance of candidates Pi and Pj can be obtained by
where μ and ν are the weights to measure the formal and informal collaboration performance, respectively, and μ+ν=1.
3.5 Model for Member Selection of a Co-NPD Team
Based on the above analysis, to solve the problem of member selection of a Co-NPD team using individual knowledge competence, knowledge complementarity, and collaboration performance, we build the following multi-objective mathematical model:
For models (15) to (19), it is a multi-objective 0–1 quadratic programming model. It is similar to the quadratic 0–1 integer model proposed by Kuo et al. [16] to study the maximum diversity problem, which is proven as an NP-hard problem. On the other hand, the solution space of this model depends on parameters n and m. Let S be the number of solutions in the solution space; there is
Hence, the solution space will approximately exponentially grow with increasing m. For the small-scale problem, that is, n and m are very small, the traditional enumeration method or optimization algorithm may be capable. However, for the large-scale problem, an intelligent optimization algorithm is required. Thus, this paper presents a multi-objective GA in the next section.
4 Improved Adaptive Genetic Algorithm
Member selection for a Co-NPD team is an NP-hard problem of multi-objective combination optimization. The classical optimization methods (including the min-max approach, weighted sum method, ε-constraint method, etc.) can hardly obtain the optimal results quickly. On the other hand, GA is a stochastic search optimization method simulating the process of evolution in nature [12, 17]. GA has a powerful capability of global search. However, weak local search ability and early convergence are the two main defects of GA. In practice, GA often needs to be improved for better search ability. Considering the characteristics of multi-objective non-linear optimization of the proposed model, an improved adaptive GA (IAGA) is designed to solve the proposed model of member selection in a Co-NPD team.
4.1 Coding and Initialization
Binary code is adopted to represent an individual as [1, 0, 0, …, 1, 0] of n genes, where 1 or 0 denotes whether a candidate is chosen or not chosen for the team. For the proposed models (15) to (19), m members need to be selected from n candidates, so there are m genes encoded as 1 in every individual. According to the coding rule, individuals, with parameters of m and n, are randomly generated for initialization
4.2 Fitness Function
For the problem of member selection in Co-NPD team, it is difficult to give the optimal solution for all objectives simultaneously. However, the positive ideal point and negative ideal point of each target can easily be obtained. Therefore, the ideal point method is adopted to design the fitness function.
In the ideal point method, the distance between each target value and the ideal point is used as the criteria to evaluate the plan; that is, the smaller the distance, the better the plan [25]. The ideal points are often determined by the optimal values of each single target. Hereby, according to the ideal point method, the fitness function can be designed as
where
Furthermore, as Z1 and Z2 have different dimension and importance, they should be non-dimensionalized and given the suitable weights. Thus, the fitness function can be revised as
where H is a sufficiently large positive number. γ1 and γ2 are the weights of Z1 and Z2 separately, and γ1+γ2=1.
4.3 Selection Strategy
For the selection strategy, the tournament selection method is used. Firstly, select r individuals randomly from the population, generally r=2. Then, according to the fitness function, select the best one from the r individuals to survive to the next generation. Finally, repeat the above steps to get the new population. It should be noted that the tournament selection makes the best individuals alive during all generations. Moreover, tournament selection uses the relative fitness values as the selection standard, which can avoid the influence from super-individuals and reduce the risk of premature convergence to some extent.
4.4 Improved Adaptive Crossover and Mutation Probability
The standard GA (SGA) uses the fixed values of crossover and mutation probability, which can easily cause premature convergence and local convergence. In order to avoid this defect, an IAGA is proposed to select crossover and mutation probability adaptively.
where Pc and Pm are the crossover and mutation probability, respectively. fmax and favg are, respectively, the maximum and average fitness value of the population. f is the higher fitness value of the two crossover individuals. f′ is the fitness value of the mutation individual. Usually, Pc1=0.9, Pc2=0.6, Pm1=0.1, and Pm2=0.01. According to the actual situation, the values can be adjusted properly [33].
The IAGA makes the crossover and mutation probability of the individual with the highest fitness value not equal to 0. It avoids the fine individual lying in a standstill, which is helpful for the algorithm to jump out of partial optimization.
4.5 Crossover Operation
A two-point crossover is adopted. However, for the proposed model, this crossover operator may generate infeasible solutions that do not satisfy the constraints.
For instance, if n=10, m=4, the two parents are represented as
If the crossover points are randomly selected as the fourth and seventh points, the two offspring are represented as
Obviously, the two offspring are infeasible solutions, because they do not satisfy the constraint m=4. Hereby, a reparation strategy for this model is designed to repair the infeasible offspring. Specifically, for the infeasible offspring, the number of genes encoded as 1 should be increased or decreased until it satisfies constraint (18). Meanwhile, the number of genes encoded as 0 should be modified correspondingly. The reparation strategy ensures the number of genes encoded as 1 satisfying constraint (18), and ensures the offspring feasible.
4.6 Mutation Operation
The inversion operator is employed for the individual. For this method, two reversal points in the individual are randomly selected, and then the genes between the two reversal points are reversed in order. Obviously, the inversion operator only changes the order of the genes but cannot increase or decrease the number of the genes with a value of 1. Thus, all the generated solutions satisfy constraint (18).
Furthermore, considering constraint (17) of the proposed model, the solution produced by mutation operation may have the risk of infeasibility; that is, there are existing genes that do not meet the requirement of knowledge complementarity. For example, assume that a solution is represented as
In solution1, suppose the first point and fourth point do not meet constraint (17); namely, the knowledge complementarity between the first candidate and fourth candidate is not appropriate. Thus, a remediation strategy is designed to modify the infeasible solutions. Firstly, find out all the infeasible sets of candidates (genes) that do not meet constraint (17). Then, based on the result of the previous step, the solution produced by mutation operation should be checked on whether it has the infeasible gene sets found in the previous step. If so, the infeasible sets of genes are modified until it satisfies constraint (17). Of course, the modified solution should meet constraint (18) simultaneously. If not, it means that the solution is feasible to retain.
5 Case Study
In this section, we present a real case on member selection of a Co-NPD team for smartphone appearance design, one of the projects that are led by XM Technology Co., Ltd. It is adopted to illustrate the proposed method in this paper. Furthermore, a computational experiment is conducted to test the availability of the proposed IAGA.
XM is one of the most creative mobile Internet companies in China, focusing on the development of intelligent electronic productions, such as smartphone, smartwatch, smartTV, etc. In this electronics industry, the rapid technology update and changing customer demands drive XM to constantly innovate to obtain development advantages. Furthermore, driven by continuous innovation, XM adopts the Internet model to integrate the external resources effectively, and takes the Co-NPD alliance as important strategy to hold its core competence in NPD. Through Co-NPD, XM aims at (i) decreasing the NPD cost, (ii) reducing the NPD developing risk, and (iii) integrating partners’ complementary competence to fill the knowledge gap.
To conduct the project of smartphone appearance design, a Co-NPD team needs to be formed. The required knowledge for the project can be described as the following keywords, i.e. body styling (k1), body dimension (k2), body color (k3), body materials (k4), and artistic quality (k5). In order to form the Co-NPD team, five desired members will be selected from 15 candidates. The decision makers adopt four individual knowledge competence criteria and two collaboration competence criteria to selected members, as shown in Table 1. Herein, the data of criteria R1, C1, and C2 are obtained from the publication retrieval system and database resources. The values on criteria R2, R3, and R4 are given by the decision makers and experts using the values from 1 to 9 (1: very bad, 9: very good). The original data are shown in Tables 2–7.
Criteria for Member Selection of the Research and Development Team.
| Objectives | Criteria | Descriptions |
|---|---|---|
| Individual knowledge competence | Publications (R1) | Quantity of publications about certain knowledge |
| Experience (R2) | The experience or abilities about certain knowledge obtained in practice | |
| Implicit knowledge (R3) | The knowledge not expressed in publications or patents, citation patterns, and others | |
| Know-who knowledge (R4) | The awareness of others’ tacit knowledge stocks | |
| Collaboration competence | Cooperation projects (C1) | The cooperation on projects between candidates |
| Communication (C2) | The mutual communication between candidates |
Original Data on Criteria R1.
| Candidates | k1 | k2 | k3 | k4 | k5 | Candidates | k1 | k2 | k3 | k4 | k5 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| P1 | 6 | 4 | 0 | 2 | 3 | P9 | 2 | 2 | 3 | 2 | 6 |
| P2 | 4 | 6 | 1 | 6 | 2 | P10 | 2 | 1 | 5 | 2 | 8 |
| P3 | 0 | 0 | 8 | 1 | 4 | P11 | 2 | 0 | 1 | 8 | 0 |
| P4 | 4 | 3 | 7 | 0 | 6 | P12 | 1 | 1 | 6 | 0 | 4 |
| P5 | 4 | 3 | 5 | 2 | 4 | P13 | 6 | 3 | 1 | 3 | 3 |
| P6 | 7 | 5 | 4 | 3 | 2 | P14 | 4 | 3 | 1 | 6 | 3 |
| P7 | 2 | 1 | 8 | 2 | 4 | P15 | 2 | 1 | 7 | 2 | 3 |
| P8 | 2 | 1 | 0 | 9 | 0 |
Original Data on Criteria R2.
| Candidates | k1 | k2 | k3 | k4 | k5 | Candidates | k1 | k2 | k3 | k4 | k5 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| P1 | 8 | 5 | 2 | 7 | 8 | P9 | 7 | 5 | 5 | 4 | 8 |
| P2 | 7 | 9 | 3 | 8 | 6 | P10 | 4 | 2 | 7 | 6 | 9 |
| P3 | 5 | 2 | 9 | 4 | 7 | P11 | 4 | 1 | 2 | 9 | 2 |
| P4 | 6 | 6 | 9 | 1 | 9 | P12 | 3 | 3 | 7 | 1 | 7 |
| P5 | 7 | 8 | 6 | 4 | 6 | P13 | 8 | 5 | 3 | 5 | 7 |
| P6 | 9 | 6 | 6 | 6 | 5 | P14 | 7 | 7 | 3 | 8 | 6 |
| P7 | 5 | 6 | 9 | 5 | 6 | P15 | 4 | 1 | 9 | 4 | 6 |
| P8 | 5 | 5 | 1 | 9 | 2 |
Original Data on Criteria R3.
| Candidates | k1 | k2 | k3 | k4 | k5 | Candidates | k1 | k2 | k3 | k4 | k5 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| P1 | 7 | 7 | 3 | 9 | 7 | P9 | 8 | 6 | 7 | 6 | 8 |
| P2 | 6 | 8 | 5 | 7 | 8 | P10 | 6 | 2 | 8 | 8 | 9 |
| P3 | 7 | 3 | 8 | 5 | 8 | P11 | 4 | 1 | 3 | 8 | 3 |
| P4 | 6 | 7 | 9 | 2 | 9 | P12 | 5 | 4 | 8 | 3 | 7 |
| P5 | 6 | 7 | 5 | 5 | 7 | P13 | 9 | 6 | 4 | 6 | 7 |
| P6 | 8 | 5 | 6 | 7 | 4 | P14 | 7 | 8 | 6 | 8 | 7 |
| P7 | 6 | 6 | 8 | 6 | 5 | P15 | 5 | 1 | 8 | 5 | 6 |
| P8 | 5 | 6 | 1 | 8 | 3 |
Original Data on Criteria R4.
| Candidates | k1 | k2 | k3 | k4 | k5 | Candidates | k1 | k2 | k3 | k4 | k5 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| P1 | 7 | 4 | 4 | 8 | 7 | P9 | 7 | 6 | 6 | 5 | 9 |
| P2 | 6 | 8 | 4 | 7 | 8 | P10 | 5 | 3 | 8 | 8 | 8 |
| P3 | 6 | 3 | 8 | 5 | 8 | P11 | 5 | 3 | 1 | 8 | 3 |
| P4 | 7 | 7 | 8 | 2 | 7 | P12 | 7 | 4 | 2 | 4 | 6 |
| P5 | 8 | 7 | 7 | 5 | 7 | P13 | 9 | 6 | 4 | 5 | 6 |
| P6 | 8 | 7 | 8 | 5 | 6 | P14 | 6 | 7 | 4 | 8 | 7 |
| P7 | 4 | 8 | 9 | 7 | 7 | P15 | 3 | 1 | 9 | 5 | 4 |
| P8 | 4 | 4 | 1 | 8 | 2 |
Original Data on Criteria C1.
| P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | P9 | P10 | P11 | P12 | P13 | P14 | P15 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| P1 | 14 | 7 | 3 | 6 | 2 | 8 | 6 | 5 | 7 | 4 | 1 | 6 | 4 | 2 | 8 |
| P2 | 7 | 19 | 9 | 8 | 6 | 8 | 10 | 7 | 4 | 6 | 4 | 5 | 7 | 3 | 7 |
| P3 | 3 | 9 | 13 | 2 | 3 | 6 | 2 | 7 | 6 | 7 | 5 | 3 | 4 | 2 | 4 |
| P4 | 6 | 8 | 2 | 14 | 1 | 5 | 3 | 4 | 5 | 4 | 7 | 2 | 4 | 6 | 1 |
| P5 | 2 | 6 | 3 | 1 | 15 | 3 | 7 | 3 | 2 | 6 | 7 | 2 | 7 | 6 | 3 |
| P6 | 8 | 8 | 6 | 5 | 3 | 17 | 8 | 7 | 2 | 6 | 4 | 2 | 3 | 5 | 3 |
| P7 | 6 | 10 | 2 | 3 | 7 | 8 | 16 | 6 | 2 | 9 | 2 | 3 | 5 | 6 | 2 |
| P8 | 5 | 7 | 7 | 4 | 3 | 7 | 6 | 15 | 4 | 8 | 0 | 6 | 5 | 4 | 6 |
| P9 | 7 | 4 | 6 | 5 | 2 | 2 | 2 | 4 | 15 | 3 | 7 | 2 | 4 | 5 | 4 |
| P10 | 4 | 6 | 7 | 4 | 6 | 6 | 9 | 8 | 3 | 20 | 8 | 6 | 7 | 5 | 6 |
| P11 | 1 | 4 | 5 | 7 | 7 | 7 | 2 | 0 | 7 | 8 | 16 | 7 | 4 | 4 | 5 |
| P12 | 6 | 5 | 3 | 2 | 2 | 2 | 3 | 6 | 2 | 6 | 7 | 14 | 7 | 5 | 2 |
| P13 | 4 | 7 | 4 | 4 | 7 | 3 | 5 | 5 | 4 | 7 | 4 | 7 | 18 | 3 | 7 |
| P14 | 2 | 3 | 2 | 6 | 6 | 5 | 6 | 4 | 5 | 5 | 4 | 5 | 3 | 16 | 6 |
| P15 | 8 | 7 | 4 | 1 | 3 | 3 | 2 | 6 | 4 | 6 | 5 | 2 | 7 | 6 | 18 |
The data on the diagonal line presents the total number of projects joined by candidate Pi, that is, pri.
Original Data on Criteria C2.
| P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | P9 | P10 | P11 | P12 | P13 | P14 | P15 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| P1 | 471 | 56 | 7 | 21 | 51 | 11 | 110 | 24 | 81 | 13 | 4 | 50 | 35 | 6 | 52 |
| P2 | 56 | 736 | 106 | 48 | 50 | 104 | 76 | 63 | 41 | 52 | 16 | 33 | 62 | 29 | 91 |
| P3 | 7 | 106 | 472 | 20 | 12 | 51 | 8 | 37 | 46 | 53 | 31 | 26 | 33 | 18 | 24 |
| P4 | 21 | 48 | 20 | 439 | 7 | 36 | 26 | 32 | 40 | 33 | 103 | 11 | 35 | 41 | 11 |
| P5 | 51 | 50 | 12 | 7 | 613 | 20 | 81 | 29 | 9 | 58 | 64 | 13 | 76 | 53 | 41 |
| P6 | 11 | 104 | 51 | 36 | 20 | 590 | 55 | 58 | 21 | 56 | 45 | 13 | 24 | 51 | 25 |
| P7 | 110 | 76 | 8 | 26 | 81 | 55 | 648 | 57 | 21 | 89 | 33 | 11 | 17 | 26 | 45 |
| P8 | 24 | 63 | 37 | 32 | 29 | 58 | 57 | 581 | 36 | 56 | 2 | 42 | 36 | 45 | 53 |
| P9 | 81 | 41 | 46 | 40 | 9 | 21 | 21 | 36 | 478 | 32 | 34 | 14 | 16 | 21 | 21 |
| P10 | 13 | 52 | 53 | 33 | 58 | 56 | 89 | 56 | 32 | 689 | 61 | 63 | 39 | 35 | 29 |
| P11 | 4 | 16 | 31 | 103 | 64 | 45 | 33 | 2 | 34 | 61 | 495 | 36 | 16 | 24 | 36 |
| P12 | 50 | 33 | 26 | 11 | 13 | 13 | 11 | 42 | 14 | 63 | 36 | 462 | 72 | 39 | 19 |
| P13 | 35 | 62 | 33 | 35 | 76 | 24 | 17 | 36 | 16 | 39 | 16 | 72 | 611 | 94 | 56 |
| P14 | 6 | 29 | 18 | 41 | 53 | 51 | 16 | 45 | 21 | 35 | 24 | 39 | 94 | 511 | 49 |
| P15 | 52 | 91 | 24 | 11 | 41 | 25 | 45 | 53 | 21 | 29 | 36 | 19 | 56 | 49 | 564 |
The above data is one random month’s set of data, and the data on the diagonal denotes the times of communication of candidate Pi, that is, Ni.
The weights of criteria R1, R2, R3, and R4 are obtained as W=(0.30, 0.20, 0.30, 0.20) by AHP. Moreover, based on the original data of criteria R1, R2, R3, and R4, the value of individual knowledge competence is obtained. Using the above data and computed results, the knowledge complementarity among candidates can be obtained by Eqs. (6) to (8). Finally, the overall values of individual knowledge competence and knowledge complementarity are shown in Table 8.
Overall Values of Individual Knowledge Competence and Knowledge Complementarity.
| P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | P9 | P10 | P11 | P12 | P13 | P14 | P15 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| P1 | 0.75 | 1.13 | 2.36 | 1.98 | 1.06 | 1.34 | 1.68 | 1.32 | 1.21 | 1.88 | 1.41 | 1.58 | 0.68 | 0.75 | 2.58 |
| P2 | 1.13 | 0.92 | 2.03 | 2.01 | 1.16 | 1.62 | 1.70 | 1.24 | 1.36 | 2.03 | 1.22 | 1.68 | 1.14 | 0.43 | 1.97 |
| P3 | 2.36 | 2.03 | 0.71 | 1.17 | 1.34 | 2.17 | 1.06 | 2.78 | 1.23 | 0.68 | 2.15 | 0.67 | 2.02 | 1.97 | 0.46 |
| P4 | 1.98 | 2.01 | 1.17 | 0.82 | 0.98 | 1.89 | 1.46 | 2.96 | 0.96 | 1.81 | 2.74 | 0.98 | 1.93 | 1.84 | 1.42 |
| P5 | 1.06 | 1.16 | 1.34 | 0.98 | 0.94 | 1.02 | 1.13 | 2.22 | 0.67 | 1.62 | 2.38 | 0.48 | 0.97 | 0.96 | 1.32 |
| P6 | 1.34 | 1.62 | 2.17 | 1.89 | 0.41 | 0.92 | 1.43 | 1.94 | 1.34 | 2.01 | 1.89 | 1.41 | 1.07 | 1.22 | 1.48 |
| P7 | 1.68 | 1.70 | 1.06 | 1.46 | 0.51 | 0.66 | 0.85 | 1.88 | 1.25 | 1.18 | 1.86 | 0.56 | 1.46 | 1.52 | 0.49 |
| P8 | 1.32 | 1.24 | 2.78 | 1.39 | 1.08 | 0.96 | 0.90 | 0.49 | 1.89 | 1.96 | 0.46 | 2.02 | 1.87 | 0.97 | 2.42 |
| P9 | 1.21 | 1.36 | 1.23 | 0.46 | 0.30 | 0.64 | 0.56 | 0.99 | 0.90 | 1.23 | 2.04 | 0.71 | 1.12 | 1.23 | 1.46 |
| P10 | 1.88 | 2.03 | 0.68 | 0.82 | 0.79 | 1.00 | 0.58 | 0.98 | 0.57 | 0.86 | 1.52 | 1.06 | 2.34 | 1.86 | 0.97 |
| P11 | 1.41 | 1.22 | 2.15 | 1.33 | 1.09 | 0.96 | 0.91 | 0.24 | 1.04 | 0.74 | 0.47 | 2.21 | 1.79 | 1.03 | 1.71 |
| P12 | 1.58 | 1.68 | 0.67 | 0.41 | 0.17 | 0.61 | 0.25 | 1.03 | 0.31 | 0.40 | 1.04 | 0.55 | 1.75 | 1.46 | 1.17 |
| P13 | 0.68 | 1.14 | 2.02 | 0.93 | 0.47 | 0.40 | 0.72 | 0.93 | 0.54 | 1.02 | 0.94 | 0.74 | 0.83 | 0.98 | 1.99 |
| P14 | 0.75 | 0.43 | 1.97 | 0.89 | 0.43 | 0.60 | 0.73 | 0.48 | 0.58 | 0.93 | 0.42 | 0.70 | 0.45 | 0.95 | 2.04 |
| P15 | 2.58 | 1.97 | 0.46 | 0.71 | 0.61 | 0.75 | 0.26 | 1.15 | 0.70 | 0.41 | 0.83 | 0.51 | 0.99 | 1.00 | 0.67 |
The data on the diagonal line denotes the overall scores of individual knowledge competence.
Considering the proper knowledge complementarity and the sufficient number of candidates comprehensively, the decision makers and experts finalize the floor and ceiling values as
The original data of criteria C1 and C2 is processed by Eqs. (10) to (14). The weights of C1 and C2 are given as μ=0.65, ν=0.35 by AHP. Thus, the total values of collaboration performance are obtained and shown in Table 9.
Total Values of Collaboration Performance.
| P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | P9 | P10 | P11 | P12 | P13 | P14 | P15 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| P1 | – | 0.67 | 0.32 | 0.66 | 0.34 | 0.68 | 0.83 | 0.53 | 0.91 | 0.34 | 0.10 | 0.76 | 0.43 | 0.20 | 0.77 |
| P2 | 0.67 | – | 0.93 | 0.72 | 0.57 | 0.83 | 0.89 | 0.67 | 0.42 | 0.53 | 0.34 | 0.48 | 0.65 | 0.30 | 0.73 |
| P3 | 0.32 | 0.93 | – | 0.27 | 0.32 | 0.65 | 0.21 | 0.75 | 0.71 | 0.66 | 0.55 | 0.39 | 0.43 | 0.24 | 0.41 |
| P4 | 0.66 | 0.72 | 0.27 | – | 0.12 | 0.53 | 0.34 | 0.47 | 0.60 | 0.40 | 0.95 | 0.23 | 0.43 | 0.66 | 0.12 |
| P5 | 0.34 | 0.57 | 0.32 | 0.12 | – | 0.30 | 0.80 | 0.35 | 0.21 | 0.58 | 0.78 | 0.23 | 0.74 | 0.67 | 0.35 |
| P6 | 0.68 | 0.83 | 0.65 | 0.53 | 0.30 | – | 0.78 | 0.73 | 0.23 | 0.56 | 0.51 | 0.21 | 0.30 | 0.55 | 0.30 |
| P7 | 0.83 | 0.89 | 0.21 | 0.34 | 0.80 | 0.78 | – | 0.66 | 0.24 | 0.83 | 0.26 | 0.30 | 0.43 | 0.57 | 0.28 |
| P8 | 0.53 | 0.67 | 0.75 | 0.47 | 0.35 | 0.73 | 0.66 | – | 0.47 | 0.70 | 0.01 | 0.68 | 0.49 | 0.48 | 0.62 |
| P9 | 0.91 | 0.42 | 0.71 | 0.60 | 0.21 | 0.23 | 0.24 | 0.47 | – | 0.32 | 0.71 | 0.23 | 0.37 | 0.50 | 0.38 |
| P10 | 0.34 | 0.53 | 0.66 | 0.40 | 0.58 | 0.56 | 0.83 | 0.70 | 0.32 | – | 0.72 | 0.62 | 0.58 | 0.45 | 0.49 |
| P11 | 0.10 | 0.34 | 0.55 | 0.95 | 0.78 | 0.51 | 0.26 | 0.01 | 0.71 | 0.72 | – | 0.72 | 0.36 | 0.42 | 0.50 |
| P12 | 0.76 | 0.48 | 0.39 | 0.23 | 0.23 | 0.21 | 0.30 | 0.68 | 0.23 | 0.62 | 0.72 | – | 0.76 | 0.56 | 0.23 |
| P13 | 0.43 | 0.65 | 0.43 | 0.43 | 0.74 | 0.30 | 0.43 | 0.49 | 0.37 | 0.58 | 0.36 | 0.76 | – | 0.50 | 0.68 |
| P14 | 0.20 | 0.30 | 0.24 | 0.66 | 0.67 | 0.55 | 0.57 | 0.48 | 0.50 | 0.45 | 0.42 | 0.56 | 0.50 | – | 0.61 |
| P15 | 0.77 | 0.73 | 0.41 | 0.12 | 0.35 | 0.30 | 0.28 | 0.62 | 0.38 | 0.49 | 0.50 | 0.23 | 0.68 | 0.61 | – |
Based on the above processed data, the model for member selection of Co-NPD team in the real case can be built as follows:
The IAGA developed in Section 4 is implemented to solve the above model. The parameters are set as Popsize=100, Maxgen=200, where Popsize is the population size and Maxgen is the number of generations. The weights of the two objective functions are obtained as γ1=0.4, γ2=0.6 by direct assignment of the decision maker by weighing and balancing the project requirement. Furthermore, H=100. Meanwhile, the ideal point values of the two single objective function is (4.57, 7.27). By repeated testing, the parameters Pc1=0.78, Pc2=0.49, Pm1=0.12, and Pm2=0.01 are most efficient. The IAGA is coded by the MATLAB R2010a, and run 30 times to select the best one. Finally, the obtained solution is [1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]. The solution represents that the first, second, fourth, seventh, and ninth candidates are selected to form the smartphone appearance design team, which combines the better individual knowledge competence and collaboration performance. The best fitness value is 99.8922. Correspondingly, the individual knowledge competence value and the collaboration performance value are 4.34 and 6.28, respectively. The optimized solution is obtained at the 108th generation. Figure 1 shows the fitness values of the best gene of the IAGA in each generation.
Fitness Values of the Best Gene in Every Iteration of the IAGA.
Then, to further test the performance of the IAGA, we compare the IAGA with the SGA and PSO to illustrate their relative merits. Using the same parameters of population size and maximum evolution generation, the above algorithms are used to solve the problem of Co-NPD team member selection, and independent running is 30 times. The running results can be obtained as shown in Figure 2 and Table 10. According to Figure 2 and Table 10, the IAGA can obtain a better solution, with a higher fitness value, than the SGA and PSO. Meanwhile, the optimal solution is obtained at the average evolution generation 105 using the IAGA. However, the average evolution generation is 158 by the SGA and 147 by PSO. Moreover, the SGA and PSO need more time than the IAGA to obtain the optimal solution. Obviously, for the problem of Co-NPD team member selection, it is not hard to conclude that the IAGA has more advantages on the convergence rate and running efficiency than the SGA and PSO, along with a better solution.
Comparative Running Results of the IAGA, SGA, and PSO.
Comparison of the Performance of the IAGA, SGA, and PSO.
| Algorithm | Optimal result | Iteration number | Running time |
|---|---|---|---|
| IAGA | 99.8922 | 107 | 4.08 |
| SGA | 99.8702 | 158 | 5.75 |
| PSO | 99.8572 | 147 | 5.51 |
6 Conclusions
Facing the complex and changing marketplace, the challenges to achieve a successful NPD project have put forward more demands for the multi-disciplinary and cross-functional knowledge of team members. To assemble an effective and cooperative Co-NPD team, not only the knowledge competence of individual members but also the knowledge complementarity and collaboration performance among members are important for member selection to form a Co-NPD team. In this way, team members with more comprehensive ability of knowledge and collaboration can be discovered, and a Co-NPD team with more collaboration efficiency can be formed. For this aim, this paper proposes a method to select the appropriate members of a Co-NPD team combining the individual knowledge competence of member, the knowledge complementarity, and collaboration performance. Several valuable conclusions of this study are refined as follows.
Firstly, from the perspective of knowledge and collaboration, it is a practical idea to synthetically consider the individual knowledge competence, the knowledge complementarity, and collaboration performance between members. It reflects well the comprehensive attributes of candidates in the formation of a Co-NPD team. Therefore, it can help improve the reliability of the member selection plan for the Co-NPD team. Combining the above attributes, the selected Co-NPD team members can carry out the knowledge coordination more effectively, apart from their outstanding personal knowledge competence. Obviously, it will be a sound situation that managers would really like to see in Co-NPD.
Secondly, the individual knowledge competence, knowledge complementarity, and collaboration performance between members are quantified and considered together. Then, a multi-objective 0–1 programming model is established to select great members with different knowledge backgrounds. However, the proposed model is an NP-hard problem. Therefore, an IAGA is presented to solve the model, which improves the SGA with the adaptive crossover and mutation probability. It effectively enhances the global searching ability and convergence ability. The real example along with the comparison with the SGA and PSO verify the advantages of the IAGA.
Finally, a real case of a Co-NPD team for smartphone appearance design in XM Technology Co., Ltd. is proposed to apply the presented model and algorithm. The result shows that it can well select the excellent members with desired comprehensive attributes for the formation of Co-NPD team. Additionally, the Co-NPD team member selection method can be extended to other team-based backgrounds such as cross-functional team, research and development team, and concurrent engineering team, etc., by adjusting goals or constraints.
Acknowledgments
The authors are grateful to the support of the National Science Foundation of China (project no. 71571023) and the Chongqing Graduate Student Research Innovation Project (project no. CYB15018).
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