Service-oriented manufacturing is the new development of manufacturing systems, and manufacturing supply chain service is also an important part of the service-oriented manufacturing systems; hence, the optimal selection of parts suppliers becomes one of key problems in the supply chain system. Complex network theories made a rapid progress in recent years, but the classical models such as BA model and WS model can not resolve the widespread problems of manufacturing supply chain, such as the repeated attachment of edge and fixed number of vertices, but edges increased with preferential connectivity, and flexible edges’ probability. A core model is proposed to resolve the problem in the paper: it maps the parts supply relationship as a repeatable core; a vertex’s probability distribution function integrating the edge’s rate and vertex’s degree is put forward; some simulations, such as the growth of core, the degree distribution characteristics, and the impacting of parameter, are carried out in our experiments, and the case study is set also. The paper proposed a novel model to analyze the manufacturing supply chain system from the insights of complex network.
Manufacturing services spawned the manufacturing system’s range, which needs the dominant firms collaborating with their parts suppliers beyond geographical boundaries, but how to select the most optimal parts suppliers in the supply chain becomes the new difficulty. In order to resolve the problem of optimal selecting part suppliers in manufacturing supply chain, many scholars devote their researches in the topics from those fields.
The first field is the cooperation models in the manufacturing supply chain. Holland proposed the mode of cooperation and collaboration of supply chain management [
The second field is the dynamic analysis, evaluation methods, and the business forecasting in the supply chain. Liang et al. put forward nonlinear programming problems to solve the DEA (Data envelopment analysis) models for supply chain efficiency evaluation [
The third field is the complex network analysis approach and its applications. Stanley Milgram pointed out the famous theories of six degrees of separation; he observed that the distant of human in the world is about six degrees; Watts built a special website to check the theories [
From the reviews above, we can see that the complex network theory and its applications have made a rapid progress in recent years, and it can integrate the system engineering and topology and became a new approach to be used to analyze the part suppliers’ optimal selecting problems of manufacturing supply chain.
But there have been rare reports of complex network theories applied in manufacturing supply chain. Based on the preliminary studies [
The supply relationship of parts in manufacturing system intertwined together and formed a complex relationship network. The dominant firm wants some parts for assembling its production. If there are many parts suppliers meeting the given quality and times requirements, the cost is the key factors to affect their decision that those parts suppliers should to be selected. Supposing the parts consisted of some parts, the parts are made up of subparts and so on; the supply relation forms a supply relationship network, so the manufacturing supply chain has the sketch as Figure
The supply relationship network.
It is not easy to resolve the suppliers selecting problem of the whole network. In the paper, we select one vertex that has many suppliers to analyze; other vertices’ characteristics are easy to arrive using the same method.
Toward the manufacturing supply chain, the similar researches mainly were two famous models, WS model [
Watts and Strogatz reported the WS model firstly in their “Collective dynamics of ‘small-world’ networks” in 1998 (by Nature). Newman and Watts improved it as NW model in 1999 [
The WS model.
The BA model is proposed by Barabási and Albert in their “Emergence of scaling in random networks” in 1999 (by Science) [
The growth of BA model.
Now, let us trace the development of the manufacturing supply chain network from its origin. In Figure
First, both models suppose that the edges attached any two vertices without any repetition, but, in the manufacturing supply chain system, the edges maybe reduplicate, and it usually is repeated many times with the development of the manufacturing supply chain.
Second, in WS model, the attachment probability of new edge is fixed and comes randomly; in BA model, the attachment probability of new edge is be added along with vertices and with preferential connectivity. But those cannot meet the real supply chain network’s request, and the new edges add into the network with preferential connectivity but do not need to add new vertices, so the number of vertices is fixed but the edges will keep increasing with preferential connectivity.
Third, the WS model and the BA model suggested that the edges probability of attachment is constant, but, in supply chain network, because of the limitation of production ability and the distance between them, the probability usually changes periodically. So, it needs a new model to meet the needs of manufacturing supply chains.
In order to resolve the problems mentioned in WS model and BA model, our model maps the supply relationship network from Figure
The core model.
Now, towards Figure
In order to describe the growing process of the manufacturing supply network, we supposed it satisfied the following 4 assumptions. The number of vertices in the network is fixed as It does not allow the edges’ start and end to join the same vertices. The edges of network may grow freely only with preferential connectivity. The probability of changes meets a special function discussed next.
Supposing the core has
The first factor to be considered is the degree of vertex; it means the truth, cooperation times, or selection history. Obviously, the selection process is a binomial distribution function, as in the following formula:
The normalized result is the following formula:
However, the degree can not involve all the factors. It is only an experiment index; a bigger degree means the supplier has more experiment of operation, or it has more relation resources or skills. The edges rate should to be taken into consideration, and it is a cost index; it is to be decided by such as transportation costs of the parts, ready resources, and other costs. So, the relationship between the vertices degree and the edges rates should be taken into consideration. The preresearch shows that it is a linear function if only it is taken into consideration one factor of the vertex degree or the edges rates individually. Toward the vertex, the vertex degree and the edges rates are a binomial distribution; the probability distribution meets the function as in formula
The normalized results may be expressed as
Formula (
If the time is unlimited, the parts supply chain plan tends to the most effective route, and other suppliers have no chances to obtain the orders. So, the operation cost is
Therefore,
On the contrary, if the time is very urgent, the time should exceed the shortest time request so as to finish all the parts of the batch. Maybe, the cost is the largest one:
Usually, the optimal plan is between the two extreme cases, which means the operation tending to some effective suppliers and other suppliers may allocate fewer amounts of orders.
Now, let us study the core model in simulation to check it. In our experience, the rate of edges (the reciprocal of transportation costs) came from random number between 0 and 1; each vertex has initial degree of 1.
The growth of core is studied first in our experiment, and the results are shown in Figures
The growth of the core.
Initial status
Degree = 30
Degree = 40
Degree = 1000
The degree distribution of the core while time = 1000.
Where the adjustable parameter of degree and edge is
From Figure
The degree distribution of growing process is shown in Figure
Figure
The cooperation relationship and tendency.
Figure
Formula (
The impact of edge’s rate.
The rates of edge are constant
The rates of edge are not constant
The rates of edge are constant (3D)
The rates of edge are not constant (3D)
It shows that the degree distribution is a single peak function when the rates of edge are constant; it is obviously different from the rates of edge which are not constant. It may be explained from formula (
The adjustable parameter
The impact of adjustable parameter.
Figure
The growth process and tendency of the core.
The simulations show that the supply chain is a power law network, and the selecting amount tends differently with the time. A little amount of vertices supply the most amount of parts; on the contrary, most of the vertices have little chances to attend the supply chain, and the supply relationship is the effect of Matthew; on the other hand, if a supplier improved their product and reduced the cost of parts, they have the chance to attend the supply chain network. So, the supply chain network is dynamic and clustered.
Formula (
The simulations also show the difference between the model proposed in the paper and the traditional model: our model disclosed the running principle of the supply chain and gives the ways to how to improve the chance to obtain the orders, so it is a novel and practical method to analyze the supply chain.
The IT manufacturing industry of Chongqing China was very weak at 2000, but it had a rapid expansion while Hewlett-Packard (Chongqing) Co., Ltd, and Acer (Chongqing) Co., Ltd, began to produce the notebook computer in recent years and the notebook computer accounts for one-fifth of global production [
Why did it expand so quickly? It clustered 5 large computer enterprises, 6 large foundries, and 817 parts manufacturers in Xiyong Chongqing till February 11, 2014, and the industry gathering circle is about 1 hour drive. One very interesting phenomenon is that these companies are new plants following the large enterprises such as HP, Acer, and Cisco. The foundries and parts manufacturers built new production plant in Chongqing in order to decrease the transportation costs to the lowest level, so they have the lowest, calculated from formula (
Jiangmen Hi-tech Development Zone began at 1992 [
Aiming at the three difficulties of classical complex network theories to resolve the optimal selection of parts suppliers, a core model is proposed in the paper after reviewing famous BA model and WS model; it maps the parts supply relationships of manufacturing supply chain as a repeatable core. A vertex’s probability distribution formula is put forward; it mainly involves the edge’s rate and vertex’s degree. Some simulation studies, such as the growth of core, the degree distribution characteristics, and the impacting of parameter experiment, were carried out. At last, two cases were set out to prove the correctness in the paper. The core model can be used to resolve some difficulties—with repeating edge attachment, fixed vertices number but increasing edges with preferential connectivity, and flexible edges probability.
It did not consider the interactions of other cores and the consistency of costs in our experiments; the calculating results may be a little deviated, and we plan to resolve those problems in next steps.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research is supported by the Natural Sciences Fund of China (Grant no. 51275547) and the Natural Science Fund Projects in Chongqing (Grant no. cstc2012gg-yyjs40019, CSTCjjA1481).