- Email: [email protected]
Hybrid modeling and empirical analysis of automobile supply chain network
Accepted Manuscript Hybrid modeling and empirical analysis of automobile supply chain network Sun Jun-yan, Tang Jian-ming, Fu Wei-ping, Wu Bing-ying PII: DOI: Reference:
S0378-4371(17)30036-5 http://dx.doi.org/10.1016/j.physa.2017.01.036 PHYSA 17929
To appear in:
Physica A
Received date: 29 May 2016 Revised date: 19 December 2016 Please cite this article as: J.-y. Sun, J.-m. Tang, W.-p. Fu, B.-y. Wu, Hybrid modeling and empirical analysis of automobile supply chain network, Physica A (2017), http://dx.doi.org/10.1016/j.physa.2017.01.036 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Hybrid modeling and empirical analysis of automobile supply chain network SUN Jun-yan1, 2, TANG Jian-ming3, FU Wei-ping2, Wu Bing-ying1 Faculty of Mechanical and Electronic Engineering, Shaanxi University of Science and Technology, Xi’an 710021, China 2 Faculty of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China 3 Xi’an aerospace precision electromechanical institute, Xi’an 710010, China Abstract: Based on the connection mechanism of nodes which automatically select upstream and downstream agents, a simulation model for dynamic evolutionary process of consumer-driven automobile supply chain is established by integrating ABM and discrete modeling in the GIS-based map. Firstly, the rationality is proved by analyzing the consistency of sales and changes in various agent parameters between the simulation model and a real automobile supply chain. Second, through complex network theory, hierarchical structures of the model and relationships of networks at different levels are analyzed to calculate various characteristic parameters such as mean distance, mean clustering coefficients, and degree distributions. By doing so, it verifies that the model is a typical scale-free network and small-world network. Finally, the motion law of this model is analyzed from the perspective of complex self-adaptive systems. The chaotic state of the simulation system is verified, which suggests that this system has typical nonlinear characteristics. This model not only macroscopically illustrates the dynamic evolution of complex networks of automobile supply chain but also microcosmically reflects the business process of each agent. Moreover, the model construction and simulation of the system by means of combining CAS theory and complex networks supplies a novel method for supply chain analysis, as well as theory bases and experience for supply chain analysis of auto companies. Keywords: complex network, complex self-adaptive system, automobile, supply chain, hybrid modeling, empirical analysis 1. Introduction Node enterprises in supply chains with autonomy, self-organization and self-learning ability, can properly adjust their management strategies according to changes of external environment, and therefore are a complex adaptive system (CAS) [1-3] . The agent-based model (ABM) proposed by R Axelrod [4] shows significant superiority in the modeling of CAS in supply chains. However, the majority of modeling methods based on ABM are centered on the model with one main manufacturer to conduct simulation research for microscopic problems of supply chains (e.g. inventory strategy). The built models have a fixed structure, so it is difficult to establish a dynamic supply chain model reflecting entry and exit mechanisms of node enterprises. Supply chains are not only a CAS but also a network with complexity, which shows typical features including clustering, scale-free and small-world. [5-7]. Some scholars designed macroscopic evolutionary models endowing nodes with entry and quit mechanisms in viewpoint of complex network, but nodes lack of autonomy and self-learning ability [8]. Taking automobile supply chains as research background, a specific simulation model is established to study operation process, evolutionary law and network characteristics of automobile supply chain by comprehensively considering CAS and complex network evolutionary characteristics of supply chains. The established simulation model not only microscopically reflects various main processes (plan, purchase, production and delivery) during operation process of node enterprises in supply chain but also shows dynamic evolutionary process of supply chain macroscopically. The research attempts to provide references for scientific and effective management and design of supply chain, in order to make the automobile manufacturing industry obtain sustainable competition ability. 2. Concept model 2.1 Basic ideas of model design Automobile supply chain is a complex network where competition coexists with cooperation. It is driven by consumer agents, centered on manufacturers, and composed of suppliers, manufacturers and distributors. When secondary suppliers are considered as a category and not regarded as a layer of network, the established network is a four-layer supply chain network, as shown in Figure 1. It primarily reflects competitive relationship among associated nodes in each layer of the network while there is no relationship among non-associated nodes. Each layer of the network is connected with the next layer and by doing so, a local-world is formed. In addition, cooperation relationship is the most important relationship of different network layers in each local-world. Namely, three local-worlds are separately formed between network layers of suppliers and manufacturers, distributors and manufacturers, as well as manufacturers and suppliers, distributors, 1
respectively. The four network layers–suppliers, manufacturers, distributors, and consumers make up the entire network. Node enterprises and consumers of each layer in the supply chain are considered as independent agents which include supplier, manufacturer, distributor, and consumer agents. Independent agents of each layer dynamically and automatically select upstream and downstream agents according to decision rules and their own management conditions, thus forming a dynamic evolutionary network model of supply chain with intelligent agent nodes. Then, actual research data are used to prove the rationality and validity of the above model. Also, the local-world characteristics and overall network features of automobile supply chain are analyzed through complex network theory while its nonlinear characteristic is analyzed by using power spectrum and phase space chart. Consumer
Sub supplier
Supplier
Distributor
Manufacturer
Figure 1 Hierarchical relationship of the automobile supply chain network 2.2 Behaviors of all agents 2.2.1 Consumer agents Consumer agents generally have three behaviors below: (1) Selecting distributors. Consumers’ behaviors of choosing and buying products can be judged by combining distance and consumer utility. Consumer utility can be divided into several components: quality, price, sales, and brand effect. Formula 1 expresses the integration result of utility and distance. U i U Pi U Qi UWi U Ai TU i U i Li st.
Where,
(1)
TU i TU Li
U i refers to the total utility, while U Qi , U Pi , U Ai and UWi respectively manifest various utilities including TU i Li
quality, price, sales and brand effect of consumers. In addition, is distance from customer i to its retail trader,
TU
TU Li
is the overall evaluation on distance and utilities.
is critical purchase point for customer i to buy goods. Consumers
TU
i and comparing i of all distributors. place an order after choosing the maximum (2) Placing orders. Consumers place an order to the nearest distributor of the determined brand of the automobile that they intend to purchase. The consumer directly takes delivery if the distributor has inventory; or, consumers are in wait state. If it needs to wait for more than one month, customers will cancel the order and selects another suitable distributor. (3) Receipt of a car. Consumers’ particular behaviors are shown in Figure 2 (d). 2.2.2 Distributor agents
The main behaviors of distributor agents including (1) selecting manufacturers, (2) purchase, (3) managing inventory, (4) managing orders, and (5) selling and transportation. As for the manufacturer selection, each distributor sells only one determined automobile brand and distributors selling the same brand are supposed to place orders with the nearest manufacturers of the brand according to the principle of proximity. Purchase means that distributors buy finished automobile products. Distributors manage inventory applying the maximum and minimum principle, because distributors store finished automobiles. They handle orders successively following the order time. As to selling and transportation, when there is more than one inventory, customers receive products immediately. Formula 2 shows the amount of orders.
N Di S D ( K Di K pi NCi )
st. K Di K pi NCi sD
(2)
N Ci is the number of consumer order, N Di is the quantity of distributor order, K pi is the quantity of K Di refers to the actual quantity of distributor inventory. As for S Di and sDi , they represent transportation product, and Where
given maximum value and minimum value of inventory. Distributors’ specific behaviors are shown in Figure 2(c). 2.2.3 Manufacturer agents Manufacturers in a core status of supply chain not only are connected to various suppliers in the upstream but also have a close relationship with distributors of each province in the downstream. A manufacturer's main activities include three points: The first is to select suppliers on the basis of the quality of suppliers’ products and distance from the suppliers. Secondly, manufacturers manage inventory of parts. Currently, manufacturers assemble automobiles after receiving orders placed by distributors. The maximum and minimum principle is applied to manage manufacturers’ parts inventories. Third is purchase. Manufacturers confirm inventories of each kind of required parts, the number of work in process (WIP), in-transit inventory, and the finished inventory. After employing bill of material (BOM) tables to count the quantities of needed parts in each type for unfilled orders at present, manufacturers place an order with suppliers. The order amount is computed using equation 3. N Mi SMi ( K Mi Kbi Kti Z Mi N Di ) (3)
st.
K Mi Kbi Kti Z Mi N Di sMi
Where, N Di is the total quantity of all distributors’ order, N Mi is the amount of a manufacturer’s order, K ti is the amount of parts in transportation, K bi is the inventory amount of parts factories, K Mi is the inventory amount of finished products, and Z Mi is WIP number. SMi and s Mi denote values set for manufacturers’ maximum inventory and minimum inventory. In addition to the above three behaviors, manufacturers produce products, manage orders, and sell and transport. The detailed procedure of manufacturers’ behaviors is illustrated in Figure 2(b). 2.2.4 Supplier agents Suppliers mainly behave as follows: To begin with, they handle orders. Suppliers deal with orders in accordance with the receiving time of orders following first-come-first-served principle. Second, they manage inventories. Suppliers’ inventory means the finished inventory of parts. In the research, the maximum and minimum principle is applied to manage inventory. Suppliers’ raw material always satisfies the requirements for production all the time. In other words, it is not necessary for suppliers to buy raw materials at any time, so suppliers do not have inventory of raw materials. The third behavior of suppliers is production. When the sum of the WIP amount and inventory of parts is less than the ordered one, suppliers begin to produce products. Forth, suppliers also sell and transport products. After receiving orders from manufacturers, suppliers first inspect whether there is enough parts inventory. If the inventory is enough, they make delivery immediately, or not to start production. Figure 2(a) displays the detailed procedure of supplier behaviors.
Consumer
common people
no
whether afford automobiles or not
selecting the sub-suppliers
starting producing
updating inventories
checking inventories
yes
checking whether there are unfilled orders or not
unfilled orders
not satisfied
satisfied
delivering goods and updating the inventory of finished goods and order status
no
exiting
(a) Workflow of suppliers
not sufficient
checking the parts inventories
ordering from suppliers
putting parts in storage and updating the inventory
unfilled orders
<1
checking inventories
starting producing
putting finished goods in storage
yes
satisfied
delivering goods and updating the inventory of finished goods and order status
checking whether there are unfilled orders or not
yes reevaluating the brand in the region to choose the most satisfactory brand
choosing distributors
distributors
not satisfied
manufacturers
suppliers
unfilled orders
choosing manufacturers
ordering from manufacturers
no
putting finished goods in storage and updating the inventory
checking inventories
yes
checking whether there are unfilled orders or not
place orders to chosen distributors
>=1
delivering goods and updating the inventory of finished goods and order status sending the “waiting” information to consumers
whether consumers can directly buying automobiles or not no
yes
consumers picking up automobiles
waiting
yes
no
the waiting time is more than 30 days
no
exiting exiting
updating the satisfaction for the distributor
(b) Workflow of manufacturers (c) Workflow of distributors (d) Workflow of consumers Figure 2 Workflows of different agents in above simulation model 3. Construction of the simulation model 3.1 Construction of visible simulation platform In order to visually reflect spatial dynamic evolution of automobile supply chains, a GIS-based map is imported on the Anylogic simulation platform and then agents of each layer are established at corresponding positions in the GIS-based map according to the research data (as shown in Figure 7). The steps are shown as follows: (1) Location parameters of consumers and various initial parameters of suppliers, manufacturers and distributors (location, price, quality, promotion and reputation) in Excel forms are imported into Anylogic. (2) According to quantity and attribute characteristics of agents in each layer, agents are established at corresponding positions in the GIS-based map. Manufacturer and distributor agents can directly set up agents according to imported coordinate positions from Excel (Xian, Nanjing and so on) while specific positions of suppliers and consumers agents are not defined, so they establish agents in their own provinces. Thus, all agents in the model and their relationships can be displayed in the GIS-based map, which is in favor of observing the evolution process of supply chain’s spatial topological structure. 3.2 Constructing the simulation model In order to comprehensively simulate macroscopic characteristics and microscopic operation process of supply chain, the simulation model is established by combining ABM with discrete event modeling. Automobile-purchasing behaviors of consumer agents are described by using state diagram. Consumers are divided into four categories including ordinary people, potential consumers, people tending to buy certain brand of automobiles, and actual customers. Consumers change their states relying on transition (as shown in Figure 3). We use action diagram to describe distributor agents’ purchasing activities, inventory management activities, and sales activities (Figure 4), while various operating behaviors of manufacturer agents (e.g. production and sale) are expressed by applying discrete event modeling (as shown in Figures 5 and 6). For other behaviors, for example, dealing with orders from manufacturers, are processed by using functions in Java language.
Figure 5 Productive processes of manufacturers
Figure 3 States of consumers
Figure 4 Actions of distributors
Figure 6 Transport processes of manufacturers
Apart from the above three layers of agents and consumer agents, two assistive agents are also established. One is message agent, which represents orders while the other is environment demand agent which denotes market demand in the model. The latter is used for describing marketing mix utility of certain a consumer for a specific distributor, which is also one of the judgment conditions for consumers to choose distributors. Finally, agents of different layers can transfer information by using “linking to agents” tool of Anylogic. 4. Empirical analysis An automobile mainly consists of seven parts including an engine, an automobile body, drive, traveling, steering and braking systems, and an electric device. That is, suppliers are split into seven classifications. Manufacturers only take responsible for assembling finished automobiles but not produce these parts, and they purchase the seven parts from different suppliers. The research data of top twelve car brands of Chinese market in recent five years are used as basic parameters to construct networks of supply chain. The initial conditions for the simulation are set as follows: There are 12 brands and 32 manufacturer agents; each automobile brand can be sold only by one distributor in each of 30 provinces and regions in China, so each brand of automobiles has 30 distributors and there are totally 360 distributors in China. Moreover, there are 5 suppliers for same parts, so there are 35 suppliers and 427 agents in China. Consumer agents are set as 13,529 per 100,000 persons. Figure 7 displays the simulated GIS-based network structure where supplier agents are displayed by yellow houses while manufacturers and distributors are shown as red and green, respectively. Also, consumer agents are shown as spots, for which different colors indicate that consumers are in different states. The agents are connected with lines when they have transaction behaviors while those without connections don't belong to the network. Simulation results show that the supply chain network has 155 nodes, which contain100 distributor nodes, 29 manufacturer nodes, and 26 supplier nodes.
Figure 7 Simulation result of automobile supply chain in China based on GIS 4.1 Model verification 4.1.1 Verification of sale volumes Table 1 displays data of sale volumes for the engine, automobile body, electrical equipment, drive, traveling, steering, and braking systems of suppliers, manufacturers and distributors. Table 1 Total Sales of Each Type of Parts Supplier
Manufacturer
Distributor
sale Automobile sale Electrical sale Traveling sale Transmission sale Steering sale Braking sale sale sale sale sale Engine brand brand brand brand volume body volume equipment volume system volume system volume system volume system volume volume volume volume volume S0
10506
S5
5966
S10
0
S15
13296
S20
0
S25
14090
S30
321
Car0
2974
Car6
1567
Car0
2818
Car6
1510
S1
0
S6
0
S11
12740
S16
12854
S21
1972
S26
3649
S31
10846
Car1
2049
Car7
1432
Car1
1953
Car7
1290
S2
4332
S7
8804
S12
3729
S17
0
S22
5494
S27
0
S32
10851
Car2
1026
Car8
2049
Car2
946
Car8
1920
S3
14126
S8
0
S13
11762
S18
0
S23
14210
S28
1429
S33
4432
Car3
1748
Car9
1348
Car3
1682
Car9
1253
S4
1972
S9
16903
S14
1827
S19
0
S24
9285
S29
10728
S34
11063
Car4
845
Car10
2087
Car4
792
Car10 2010
Total
30938
Total
26673
Total
30058
Total
26084
Total
30961
Total
29896
Total
37531
Car5
844
Car11
1701
Car5
812
Car11 1607
The minimum of parts:26084
Total
19670
Total
18593
It can be seen from Table 1 that: (1) There are 35 suppliers in which 9 suppliers are not contained in the supply chain network while 26 are contained, which conforms to the law of survival of the fittest. (2) The ratio of parts in the BOM table is 1:1, so sale volumes of the seven parts are basically the same (about 30,000). However, the total quantities have differences, which conform to the rule of orders of manufacturers. (3) The table also shows that the maximum finished products assembled with parts bought from suppliers is 26,084 which is larger than the cumulative sale amount of manufacturers (19,670), letting alone the sale volume (18,593) of distributors. Such results are accordance with the substantive condition of the supply chain, that is, suppliers are expected to have larger sale volumes than manufacturers, who also have larger sale volumes than distributors. (4) The sale volumes of distributors and manufacturers are compared in Figure 8. Based on the figure, it can be found that manufacturers and distributors occupy basically equal market proportions for each brand, but the sale volume of a manufacturer is generally greater than that of a distributor for every brand. This result is consistent with the foundational condition of the supply chain.
sale volumes ：
the accumulative sale volumes of automobiles of the 12 brands
market s h a r e： s %
16
the market shares of automobiles of the 12 brands
2000 car0 car3 car6 car9
car1 car4 car7 car10
car2 car5 car8 car11
car0 car3 car6 car9
14
12
car1 car4 car7 car10
car2 car5 car8 c a r 11
1500
10
8
1000
6
4
500
2 time step
0
time step
0 0
1000
2000
3000
4000
5000
0
1000
2000
3000
4000
5000
Figure 8 Trend charts of market shares and cumulative sales for twelve automobile brands As shown in Figure 8, the cumulative sales of all brands increase with time as a whole. While, automobiles of different brands are sold in dissimilar volumes which also increase in different ranges; at the same time, each brand also present continuously changes ranks and market shares which stabilize after certain periods of time. This matches with the actual situation. The validity of the model is therefore verified by doing so. 4.1.2 Verification for the variation of agents’ main parameters (1) Supplier agents’ variation Time lines of suppliers 28 and 12 are demonstrated in Figures 9, respectively. The above and below figures have the following common points: (1) all the total sale volumes increase; (2) unfilled orders have similar curves with WIP inventory; and (3) unfilled orders reduce, while the total sale volumes increase, by corresponding values with the decline of the finished inventory. The difference is that supplier 12 always manufactures products in the simulation; in contrast, supplier 28 merely manufactures products on occasions. This is because that supplier 12 obtains more orders than its production capacity. As a result, the amount of its unfinished orders is always higher than zero. At the same time, supplier 28 gets a smaller number of orders, resulting in production halting. During the halt, the finished inventory, the unfilled orders, and WIP are zero. This conforms to the previous setting of relevant rules, and proves the correctness and rationality of the model. unfilled orders
total sale volumes
finished inventory
WIP
supplier 28
supplier 12
Figure 9 Main data of suppliers 28 and 12 (2) Manufacturer agents’ variation As shown in Figure 10, the WIP amount increases only when the in-transit inventories of all the seven parts close to the
minimum. This suggests that manufacturers do not produce products before buying parts from suppliers. The model specifies suppliers' production principle is to produce in line with orders. However, a manufacturer's production is decided by existing inventory of parts. When a manufacturer has less unfinished orders than finished inventory, it is expected to deliver products directly; otherwise, manufacturers only order from suppliers when they lack of goods and produce goods after receiving parts. The rule can be observed from Figure 10. This conforms to the previous setting of relevant rules, and proves the correctness and rationality of the model. engine
automobile body
steering system
braking system
electrical equipment
traveling system
transmission system
manufacturer 6
finished inventory
unfilled orders
total sale volumes
WIP
manufacturer 6
Figure 10 The in-transit inventory and main parameters changes of manufacturer 6 (3) Distributor agents’ variation The variations in main parameters of distributors 7 and 32 are illustrated in Figures 11, respectively. The two figures show that distributor 32 does not obtain orders from consumers while consumers place orders with distributor 7 in the initial stage of the simulation. It shows that the time is different for customers accessing the model. This conforms to the previous setting of relevant rules, and proves the correctness and rationality of the model. unfilled orders
finished inventory
in-transit inventory
total sale volumes
distributor 7
distributor 32
Figure 11 Variation trends of distributors 7 and 32 The discussions above analyze the model from sales and variations of several agents. In this way, it is verified that the
model established is correct and reasonable. 4.2 Network characteristics of the case. Pajek software is used to draw the network structure. Figure 12 shows an annular chart in which spots represent node enterprises while the nodes at dense blue lines indicate manufacturer agents. In order to see the structure clearly, the authors use Kamada-Kawai algorithm to draw the space layout (Figure 13). In the figure, nodes from 1 to 29 represent manufacturers, 30 to 57 are suppliers, and nodes from 58 to155 represent distributors.
Figure 12 Annular chart Figure 13 Space layout drawn by Kamada-Kawai algorithm By comprehensively analyzing Figures 12, 13 and 1, the constructed network of automobile supply chain has the following characteristics: (1) The network shows a dumbbell-shaped structure. The network displays a dumbbell-shaped structure with large both ends and a small middle section on the whole. This is because more consumer and secondary supplier nodes lie in the both ends of the supply chain and they update rapidly, while manufacturers, suppliers for parts and distributors in the core layer are relatively stable and these nodes enter and exit relatively slowly. (2) Self-similarity of nodes in the same category. Same category of nodes such as supplier, manufacturer and distributor agents in different layers show self-similarities including similar functions, core businesses, local-worlds, connections, and competitive environments. Therefore, in terms of choosing upstream suppliers and competing for downstream clients, nodes in the same category generally compete with each other. In addition, nodes playing a dominant role have priority in choice and therefore occupy more market shares. (3) Multilayer of local-world; in the supply chain network, the nodes with the same layer show the same local-world while those with different layers exhibit different local-worlds. (4) High clustering of core enterprises. In the supply chain network, manufacturer agents are at the core status, on which other nodes depend on. In the manufacturer network, a core manufacturer or minor core manufacturers show large market superiority and hold large market shares, which exert a significant effect on the property and the structure of supply chain network. Similarly, there are always one or several enterprises with competitive superiority in the levels of supplier and distributor agents, which occupy large market shares. According to the law of market competition, the enterprises with competitive superiority are chosen preferentially. Therefore, minor nodes in the supply chain show high degrees, which exhibits high-clustering characteristic of core enterprises. (5) High dynamics of network topology. Nodes in the network have independent judgment, behavior, adaption and learning capacities. During mutual competition, choosing, and being chosen, nodes follow the rule of survival of the fittest, that is, nodes with good adaptive and learning capacities grow. On the contrary, nodes with poor adaptation are eliminated or replaced by some new nodes. Therefore, the whole network topology exhibits a high dynamics. The distances, degrees and clustering coefficients of each node can be calculated by applying Pajek. Next, through data statistics and numerical fitting using Matlab, network characteristics of whole and local-worlds are obtained. Table 2 Average distances and clustering coefficients of nodes of the whole network and local area networks in each layer Whole network Distance
Clustering
Local world of manufacturers Distance
coefficient 3.89
0.00124
Clustering
Local world of suppliers Distance
coefficient 2.32339
0.414217823
Clustering
Local world of distributors Distance
coefficient 2.56147
0.277985165
Clustering coefficient
2.24063
0.429115
Table 2 displays the average distances and clustering coefficients of nodes. From Table 2, local-worlds in different layers all show short average distances and large clustering coefficients, which indicates that local area networks in each
layer of the system exhibit a small-world characteristic. The whole network contains numerous consumers and secondary suppliers while few connections between the both types of nodes, so the whole network shows small clustering coefficients and long average distances. 1.E+00
1.E-01
γ=3.319
1.E-02
Degree distribution 乘幂(度分布图)
度分布图
1.E-03
Fitting curve (power law)
拟合曲线（幂律）
1.E-04
1.E-05 1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Figure 14 Degree distribution As shown in Figure 14, the network displays an overall distribution conforming to power-law distribution of f ( x) x and 3.319 can be obtained through simulation, which shows that the network has a typical characteristic of
scale-free networks on the whole. Numerous nodes in the network have a few connections while a few nodes (manufacturers 1-29, suppliers 30, 43, 45 and 50) have the majority of connections in the network. Due to this characteristic, when the nodes with high degrees are attacked, the whole network may be rapidly broken down. The nodes with high degrees play an important role in trouble-free running of the network, so they should be paid more attention in the maintenance. 4.3 Analysis from CAS The power spectra are drawn in Figures 15 based on inventories and orders of distributor 7, separately. No obvious peaks are observed, and the power spectral values are connected into one piece. Based on this, the system can be identified as a nonlinear one where its movement presents chaotic state. power /dB
power /dB
-15
40
-20
30 20
-25
10 -30 0 -35 -10 -40 -20 -45
-30
-50 -55
-40
0
100
200
300
400
500
600
700
800
900
1000
f/Hz
-50
0
100
200
300
400
500
600
700
800
900
1000
f/Hz
Figure 15 Power spectra drawn on the basis of the inventories and orders of distributor 7 The three-dimensional (3D) phase spaces obtained by combining the inventories, orders, and sales amount of manufacturer 21 and distributor 7 are shown Figures 16, separately. It can be seen from the figures that the 3D phase space charts are basically open and contain irregularly and disorderedly distributed helical curves. This suggests that the network is shown to move chaotically.
Z: sale volume
Z: sale volume 250
150
200
100
150
100 50
50
0
0
250
150
200
250
150 100
150
200 100
X: orders
100
150 100 50
50 0
0
Y: inventory
X: orders
50 50
0
Y: i n v e n t o r y
0
Figure 16 Phase spaces of manufacturer 21 and distributor 7 After calculating the Lyapunov index with the application of WOLF algorithm, the maximum values of these data are normalized. Thereinto, inventories, orders, and sale volumes show the maximum Lyapunov exponents of 0.00104, 0.00152, and 0.00086, respectively. As these maximum exponents are larger than zero, it suggests that the system is in chaotic state. Besides, it has CAS’s nonlinear characteristics. 5 Conclusions (1) The simulation system is constructed using hybrid modeling method (integrating ABM and discrete event modeling). It presents the operation process of all agents microscopically, which preferably reflects the business process of supply chain. Also, the model shows the overall evolutionary characteristic of automobile supply chain network in the macroscopic level. The modeling idea provides bases for establishing evolutionary mechanism of supply chain and studying bottom-up emergence mechanisms. (2) As for model verification, the changes and relationships of various parameters of all agents including the orders, sales amount, transportation inventory, factory inventory and WIP are analyzed. On this basis, the authors simulate parameter changes during business process of automobile supply chain and verify the correctness and rationality of the model (3) In terms of analysis, the system is comprehensive studied in terms of the CAS and the complex network. Moreover, the authors explore the system macrocosmically and microcosmically. With regard to the analysis of complex network, the relationships of nodes in the supply chain network are analyzed. In this way, it can be obtained that the nodes of all local area networks in the supply chain have short average distances, large average clustering coefficients, and specific features of small-world networks. In addition, supply chain network exhibits scale-free characteristic on the whole and the degree distribution accords with power-law distribution. Besides, the supply chain it proved to show chaotic motion by analyzing the power spectra, Lyapunov exponents, and phase spaces. Furthermore, the system has CAS’s nonlinear characteristics. (4) Future works are supposed to be conducted from the following aspects: it is necessary to introduce learning system for agents [9] and develop a proper intelligent algorithm. In addition, the emergence and clustering characteristics of the supply chain network need to be studied from the CASs and the complex networks. Acknowledgements The work was supported by NSFC (No. 51275407, No. 11072192). Reference [1] Souad Benomrane, Zied Sellami, Mounir Ben Ayed. An ontologist feedback driven ontology evolution with an adaptive multi-agentsystem. Advanced Engineering Informatics, 2016, 30(3): 337-353. [2] Sun Jun-yan, Wang Wen, Fu wei-ping, Yao Dan. Evolution of car supply chain complex adaptive system. Computer Integrated Manufacturing Systems, 2016, 22(8):2011-2022 (in Chinese). [3] Nicolas Couellan, Sophie Jan, Tom Jorquera, Jean-Pierre Georgé. Self-adaptive Support Vector Machine: A multi-agent optimization perspective. Expert Systems with Applications, 2015, 42(9):4284-4298. [4] R Axelrod . Advancing the art of simulation in the social sciences. Complexity , 1997 , 3(2) : 16-22 . [5] Songjing Wang, Lifeng Xi, Hui Xu, Lihong Wang. Scale-free and small-world properties of Sierpinski networks. Physica A: Statistical Mechanics and its Applications, 2017, 465(1): 690-700. [6] Paul Kim, Sangwook Kim. Detecting community structure in complex networks using an interaction optimization
process. Physica A: Statistical Mechanics and its Applications, 2017, 465(1): 525-542. [7] Zhou He, Shouyang Wang, T.C.E. Cheng. Competition and evolution in multi-product supply chains: An agent-based retailer model [J].International Journal of Production Economics, 2013, 146(1): 325-336. [8] Georg Weichhart, Wided Guédria, Yannick Naudet. Supporting interoperability in complex adaptive enterprise systems: A domain specific language approach. Data & Knowledge Engineering, 2016, 105(9): 90-106. [9] Tao You, Hui-Min Cheng, Yi-Zi Ning, Ben-Chang Shia, Zhong-Yuan Zhang. Community detection in complex networks using density-based clustering algorithm and manifold learning. Physica A: Statistical Mechanics and its Applications, 2016, 464(15): 221-230.
Highlights
The model construction and simulation of the system by means of combining CAS theory and complex networks The hybrid modeling method (integrating ABM and discrete event modeling). The modeling method based on GIS. The macroscopically illustrates and microcosmically reflect of the system. The local area networks have typical characteristics of small-world networks. The whole network exhibits scale-free characteristic and accords with power-law distribution. The supply chain show chaotic motion and has CAS’s nonlinear characteristics.
S0378-4371(17)30036-5 http://dx.doi.org/10.1016/j.physa.2017.01.036 PHYSA 17929
To appear in:
Physica A
Received date: 29 May 2016 Revised date: 19 December 2016 Please cite this article as: J.-y. Sun, J.-m. Tang, W.-p. Fu, B.-y. Wu, Hybrid modeling and empirical analysis of automobile supply chain network, Physica A (2017), http://dx.doi.org/10.1016/j.physa.2017.01.036 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Hybrid modeling and empirical analysis of automobile supply chain network SUN Jun-yan1, 2, TANG Jian-ming3, FU Wei-ping2, Wu Bing-ying1 Faculty of Mechanical and Electronic Engineering, Shaanxi University of Science and Technology, Xi’an 710021, China 2 Faculty of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China 3 Xi’an aerospace precision electromechanical institute, Xi’an 710010, China Abstract: Based on the connection mechanism of nodes which automatically select upstream and downstream agents, a simulation model for dynamic evolutionary process of consumer-driven automobile supply chain is established by integrating ABM and discrete modeling in the GIS-based map. Firstly, the rationality is proved by analyzing the consistency of sales and changes in various agent parameters between the simulation model and a real automobile supply chain. Second, through complex network theory, hierarchical structures of the model and relationships of networks at different levels are analyzed to calculate various characteristic parameters such as mean distance, mean clustering coefficients, and degree distributions. By doing so, it verifies that the model is a typical scale-free network and small-world network. Finally, the motion law of this model is analyzed from the perspective of complex self-adaptive systems. The chaotic state of the simulation system is verified, which suggests that this system has typical nonlinear characteristics. This model not only macroscopically illustrates the dynamic evolution of complex networks of automobile supply chain but also microcosmically reflects the business process of each agent. Moreover, the model construction and simulation of the system by means of combining CAS theory and complex networks supplies a novel method for supply chain analysis, as well as theory bases and experience for supply chain analysis of auto companies. Keywords: complex network, complex self-adaptive system, automobile, supply chain, hybrid modeling, empirical analysis 1. Introduction Node enterprises in supply chains with autonomy, self-organization and self-learning ability, can properly adjust their management strategies according to changes of external environment, and therefore are a complex adaptive system (CAS) [1-3] . The agent-based model (ABM) proposed by R Axelrod [4] shows significant superiority in the modeling of CAS in supply chains. However, the majority of modeling methods based on ABM are centered on the model with one main manufacturer to conduct simulation research for microscopic problems of supply chains (e.g. inventory strategy). The built models have a fixed structure, so it is difficult to establish a dynamic supply chain model reflecting entry and exit mechanisms of node enterprises. Supply chains are not only a CAS but also a network with complexity, which shows typical features including clustering, scale-free and small-world. [5-7]. Some scholars designed macroscopic evolutionary models endowing nodes with entry and quit mechanisms in viewpoint of complex network, but nodes lack of autonomy and self-learning ability [8]. Taking automobile supply chains as research background, a specific simulation model is established to study operation process, evolutionary law and network characteristics of automobile supply chain by comprehensively considering CAS and complex network evolutionary characteristics of supply chains. The established simulation model not only microscopically reflects various main processes (plan, purchase, production and delivery) during operation process of node enterprises in supply chain but also shows dynamic evolutionary process of supply chain macroscopically. The research attempts to provide references for scientific and effective management and design of supply chain, in order to make the automobile manufacturing industry obtain sustainable competition ability. 2. Concept model 2.1 Basic ideas of model design Automobile supply chain is a complex network where competition coexists with cooperation. It is driven by consumer agents, centered on manufacturers, and composed of suppliers, manufacturers and distributors. When secondary suppliers are considered as a category and not regarded as a layer of network, the established network is a four-layer supply chain network, as shown in Figure 1. It primarily reflects competitive relationship among associated nodes in each layer of the network while there is no relationship among non-associated nodes. Each layer of the network is connected with the next layer and by doing so, a local-world is formed. In addition, cooperation relationship is the most important relationship of different network layers in each local-world. Namely, three local-worlds are separately formed between network layers of suppliers and manufacturers, distributors and manufacturers, as well as manufacturers and suppliers, distributors, 1
respectively. The four network layers–suppliers, manufacturers, distributors, and consumers make up the entire network. Node enterprises and consumers of each layer in the supply chain are considered as independent agents which include supplier, manufacturer, distributor, and consumer agents. Independent agents of each layer dynamically and automatically select upstream and downstream agents according to decision rules and their own management conditions, thus forming a dynamic evolutionary network model of supply chain with intelligent agent nodes. Then, actual research data are used to prove the rationality and validity of the above model. Also, the local-world characteristics and overall network features of automobile supply chain are analyzed through complex network theory while its nonlinear characteristic is analyzed by using power spectrum and phase space chart. Consumer
Sub supplier
Supplier
Distributor
Manufacturer
Figure 1 Hierarchical relationship of the automobile supply chain network 2.2 Behaviors of all agents 2.2.1 Consumer agents Consumer agents generally have three behaviors below: (1) Selecting distributors. Consumers’ behaviors of choosing and buying products can be judged by combining distance and consumer utility. Consumer utility can be divided into several components: quality, price, sales, and brand effect. Formula 1 expresses the integration result of utility and distance. U i U Pi U Qi UWi U Ai TU i U i Li st.
Where,
(1)
TU i TU Li
U i refers to the total utility, while U Qi , U Pi , U Ai and UWi respectively manifest various utilities including TU i Li
quality, price, sales and brand effect of consumers. In addition, is distance from customer i to its retail trader,
TU
TU Li
is the overall evaluation on distance and utilities.
is critical purchase point for customer i to buy goods. Consumers
TU
i and comparing i of all distributors. place an order after choosing the maximum (2) Placing orders. Consumers place an order to the nearest distributor of the determined brand of the automobile that they intend to purchase. The consumer directly takes delivery if the distributor has inventory; or, consumers are in wait state. If it needs to wait for more than one month, customers will cancel the order and selects another suitable distributor. (3) Receipt of a car. Consumers’ particular behaviors are shown in Figure 2 (d). 2.2.2 Distributor agents
The main behaviors of distributor agents including (1) selecting manufacturers, (2) purchase, (3) managing inventory, (4) managing orders, and (5) selling and transportation. As for the manufacturer selection, each distributor sells only one determined automobile brand and distributors selling the same brand are supposed to place orders with the nearest manufacturers of the brand according to the principle of proximity. Purchase means that distributors buy finished automobile products. Distributors manage inventory applying the maximum and minimum principle, because distributors store finished automobiles. They handle orders successively following the order time. As to selling and transportation, when there is more than one inventory, customers receive products immediately. Formula 2 shows the amount of orders.
N Di S D ( K Di K pi NCi )
st. K Di K pi NCi sD
(2)
N Ci is the number of consumer order, N Di is the quantity of distributor order, K pi is the quantity of K Di refers to the actual quantity of distributor inventory. As for S Di and sDi , they represent transportation product, and Where
given maximum value and minimum value of inventory. Distributors’ specific behaviors are shown in Figure 2(c). 2.2.3 Manufacturer agents Manufacturers in a core status of supply chain not only are connected to various suppliers in the upstream but also have a close relationship with distributors of each province in the downstream. A manufacturer's main activities include three points: The first is to select suppliers on the basis of the quality of suppliers’ products and distance from the suppliers. Secondly, manufacturers manage inventory of parts. Currently, manufacturers assemble automobiles after receiving orders placed by distributors. The maximum and minimum principle is applied to manage manufacturers’ parts inventories. Third is purchase. Manufacturers confirm inventories of each kind of required parts, the number of work in process (WIP), in-transit inventory, and the finished inventory. After employing bill of material (BOM) tables to count the quantities of needed parts in each type for unfilled orders at present, manufacturers place an order with suppliers. The order amount is computed using equation 3. N Mi SMi ( K Mi Kbi Kti Z Mi N Di ) (3)
st.
K Mi Kbi Kti Z Mi N Di sMi
Where, N Di is the total quantity of all distributors’ order, N Mi is the amount of a manufacturer’s order, K ti is the amount of parts in transportation, K bi is the inventory amount of parts factories, K Mi is the inventory amount of finished products, and Z Mi is WIP number. SMi and s Mi denote values set for manufacturers’ maximum inventory and minimum inventory. In addition to the above three behaviors, manufacturers produce products, manage orders, and sell and transport. The detailed procedure of manufacturers’ behaviors is illustrated in Figure 2(b). 2.2.4 Supplier agents Suppliers mainly behave as follows: To begin with, they handle orders. Suppliers deal with orders in accordance with the receiving time of orders following first-come-first-served principle. Second, they manage inventories. Suppliers’ inventory means the finished inventory of parts. In the research, the maximum and minimum principle is applied to manage inventory. Suppliers’ raw material always satisfies the requirements for production all the time. In other words, it is not necessary for suppliers to buy raw materials at any time, so suppliers do not have inventory of raw materials. The third behavior of suppliers is production. When the sum of the WIP amount and inventory of parts is less than the ordered one, suppliers begin to produce products. Forth, suppliers also sell and transport products. After receiving orders from manufacturers, suppliers first inspect whether there is enough parts inventory. If the inventory is enough, they make delivery immediately, or not to start production. Figure 2(a) displays the detailed procedure of supplier behaviors.
Consumer
common people
no
whether afford automobiles or not
selecting the sub-suppliers
starting producing
updating inventories
checking inventories
yes
checking whether there are unfilled orders or not
unfilled orders
not satisfied
satisfied
delivering goods and updating the inventory of finished goods and order status
no
exiting
(a) Workflow of suppliers
not sufficient
checking the parts inventories
ordering from suppliers
putting parts in storage and updating the inventory
unfilled orders
<1
checking inventories
starting producing
putting finished goods in storage
yes
satisfied
delivering goods and updating the inventory of finished goods and order status
checking whether there are unfilled orders or not
yes reevaluating the brand in the region to choose the most satisfactory brand
choosing distributors
distributors
not satisfied
manufacturers
suppliers
unfilled orders
choosing manufacturers
ordering from manufacturers
no
putting finished goods in storage and updating the inventory
checking inventories
yes
checking whether there are unfilled orders or not
place orders to chosen distributors
>=1
delivering goods and updating the inventory of finished goods and order status sending the “waiting” information to consumers
whether consumers can directly buying automobiles or not no
yes
consumers picking up automobiles
waiting
yes
no
the waiting time is more than 30 days
no
exiting exiting
updating the satisfaction for the distributor
(b) Workflow of manufacturers (c) Workflow of distributors (d) Workflow of consumers Figure 2 Workflows of different agents in above simulation model 3. Construction of the simulation model 3.1 Construction of visible simulation platform In order to visually reflect spatial dynamic evolution of automobile supply chains, a GIS-based map is imported on the Anylogic simulation platform and then agents of each layer are established at corresponding positions in the GIS-based map according to the research data (as shown in Figure 7). The steps are shown as follows: (1) Location parameters of consumers and various initial parameters of suppliers, manufacturers and distributors (location, price, quality, promotion and reputation) in Excel forms are imported into Anylogic. (2) According to quantity and attribute characteristics of agents in each layer, agents are established at corresponding positions in the GIS-based map. Manufacturer and distributor agents can directly set up agents according to imported coordinate positions from Excel (Xian, Nanjing and so on) while specific positions of suppliers and consumers agents are not defined, so they establish agents in their own provinces. Thus, all agents in the model and their relationships can be displayed in the GIS-based map, which is in favor of observing the evolution process of supply chain’s spatial topological structure. 3.2 Constructing the simulation model In order to comprehensively simulate macroscopic characteristics and microscopic operation process of supply chain, the simulation model is established by combining ABM with discrete event modeling. Automobile-purchasing behaviors of consumer agents are described by using state diagram. Consumers are divided into four categories including ordinary people, potential consumers, people tending to buy certain brand of automobiles, and actual customers. Consumers change their states relying on transition (as shown in Figure 3). We use action diagram to describe distributor agents’ purchasing activities, inventory management activities, and sales activities (Figure 4), while various operating behaviors of manufacturer agents (e.g. production and sale) are expressed by applying discrete event modeling (as shown in Figures 5 and 6). For other behaviors, for example, dealing with orders from manufacturers, are processed by using functions in Java language.
Figure 5 Productive processes of manufacturers
Figure 3 States of consumers
Figure 4 Actions of distributors
Figure 6 Transport processes of manufacturers
Apart from the above three layers of agents and consumer agents, two assistive agents are also established. One is message agent, which represents orders while the other is environment demand agent which denotes market demand in the model. The latter is used for describing marketing mix utility of certain a consumer for a specific distributor, which is also one of the judgment conditions for consumers to choose distributors. Finally, agents of different layers can transfer information by using “linking to agents” tool of Anylogic. 4. Empirical analysis An automobile mainly consists of seven parts including an engine, an automobile body, drive, traveling, steering and braking systems, and an electric device. That is, suppliers are split into seven classifications. Manufacturers only take responsible for assembling finished automobiles but not produce these parts, and they purchase the seven parts from different suppliers. The research data of top twelve car brands of Chinese market in recent five years are used as basic parameters to construct networks of supply chain. The initial conditions for the simulation are set as follows: There are 12 brands and 32 manufacturer agents; each automobile brand can be sold only by one distributor in each of 30 provinces and regions in China, so each brand of automobiles has 30 distributors and there are totally 360 distributors in China. Moreover, there are 5 suppliers for same parts, so there are 35 suppliers and 427 agents in China. Consumer agents are set as 13,529 per 100,000 persons. Figure 7 displays the simulated GIS-based network structure where supplier agents are displayed by yellow houses while manufacturers and distributors are shown as red and green, respectively. Also, consumer agents are shown as spots, for which different colors indicate that consumers are in different states. The agents are connected with lines when they have transaction behaviors while those without connections don't belong to the network. Simulation results show that the supply chain network has 155 nodes, which contain100 distributor nodes, 29 manufacturer nodes, and 26 supplier nodes.
Figure 7 Simulation result of automobile supply chain in China based on GIS 4.1 Model verification 4.1.1 Verification of sale volumes Table 1 displays data of sale volumes for the engine, automobile body, electrical equipment, drive, traveling, steering, and braking systems of suppliers, manufacturers and distributors. Table 1 Total Sales of Each Type of Parts Supplier
Manufacturer
Distributor
sale Automobile sale Electrical sale Traveling sale Transmission sale Steering sale Braking sale sale sale sale sale Engine brand brand brand brand volume body volume equipment volume system volume system volume system volume system volume volume volume volume volume S0
10506
S5
5966
S10
0
S15
13296
S20
0
S25
14090
S30
321
Car0
2974
Car6
1567
Car0
2818
Car6
1510
S1
0
S6
0
S11
12740
S16
12854
S21
1972
S26
3649
S31
10846
Car1
2049
Car7
1432
Car1
1953
Car7
1290
S2
4332
S7
8804
S12
3729
S17
0
S22
5494
S27
0
S32
10851
Car2
1026
Car8
2049
Car2
946
Car8
1920
S3
14126
S8
0
S13
11762
S18
0
S23
14210
S28
1429
S33
4432
Car3
1748
Car9
1348
Car3
1682
Car9
1253
S4
1972
S9
16903
S14
1827
S19
0
S24
9285
S29
10728
S34
11063
Car4
845
Car10
2087
Car4
792
Car10 2010
Total
30938
Total
26673
Total
30058
Total
26084
Total
30961
Total
29896
Total
37531
Car5
844
Car11
1701
Car5
812
Car11 1607
The minimum of parts:26084
Total
19670
Total
18593
It can be seen from Table 1 that: (1) There are 35 suppliers in which 9 suppliers are not contained in the supply chain network while 26 are contained, which conforms to the law of survival of the fittest. (2) The ratio of parts in the BOM table is 1:1, so sale volumes of the seven parts are basically the same (about 30,000). However, the total quantities have differences, which conform to the rule of orders of manufacturers. (3) The table also shows that the maximum finished products assembled with parts bought from suppliers is 26,084 which is larger than the cumulative sale amount of manufacturers (19,670), letting alone the sale volume (18,593) of distributors. Such results are accordance with the substantive condition of the supply chain, that is, suppliers are expected to have larger sale volumes than manufacturers, who also have larger sale volumes than distributors. (4) The sale volumes of distributors and manufacturers are compared in Figure 8. Based on the figure, it can be found that manufacturers and distributors occupy basically equal market proportions for each brand, but the sale volume of a manufacturer is generally greater than that of a distributor for every brand. This result is consistent with the foundational condition of the supply chain.
sale volumes ：
the accumulative sale volumes of automobiles of the 12 brands
market s h a r e： s %
16
the market shares of automobiles of the 12 brands
2000 car0 car3 car6 car9
car1 car4 car7 car10
car2 car5 car8 car11
car0 car3 car6 car9
14
12
car1 car4 car7 car10
car2 car5 car8 c a r 11
1500
10
8
1000
6
4
500
2 time step
0
time step
0 0
1000
2000
3000
4000
5000
0
1000
2000
3000
4000
5000
Figure 8 Trend charts of market shares and cumulative sales for twelve automobile brands As shown in Figure 8, the cumulative sales of all brands increase with time as a whole. While, automobiles of different brands are sold in dissimilar volumes which also increase in different ranges; at the same time, each brand also present continuously changes ranks and market shares which stabilize after certain periods of time. This matches with the actual situation. The validity of the model is therefore verified by doing so. 4.1.2 Verification for the variation of agents’ main parameters (1) Supplier agents’ variation Time lines of suppliers 28 and 12 are demonstrated in Figures 9, respectively. The above and below figures have the following common points: (1) all the total sale volumes increase; (2) unfilled orders have similar curves with WIP inventory; and (3) unfilled orders reduce, while the total sale volumes increase, by corresponding values with the decline of the finished inventory. The difference is that supplier 12 always manufactures products in the simulation; in contrast, supplier 28 merely manufactures products on occasions. This is because that supplier 12 obtains more orders than its production capacity. As a result, the amount of its unfinished orders is always higher than zero. At the same time, supplier 28 gets a smaller number of orders, resulting in production halting. During the halt, the finished inventory, the unfilled orders, and WIP are zero. This conforms to the previous setting of relevant rules, and proves the correctness and rationality of the model. unfilled orders
total sale volumes
finished inventory
WIP
supplier 28
supplier 12
Figure 9 Main data of suppliers 28 and 12 (2) Manufacturer agents’ variation As shown in Figure 10, the WIP amount increases only when the in-transit inventories of all the seven parts close to the
minimum. This suggests that manufacturers do not produce products before buying parts from suppliers. The model specifies suppliers' production principle is to produce in line with orders. However, a manufacturer's production is decided by existing inventory of parts. When a manufacturer has less unfinished orders than finished inventory, it is expected to deliver products directly; otherwise, manufacturers only order from suppliers when they lack of goods and produce goods after receiving parts. The rule can be observed from Figure 10. This conforms to the previous setting of relevant rules, and proves the correctness and rationality of the model. engine
automobile body
steering system
braking system
electrical equipment
traveling system
transmission system
manufacturer 6
finished inventory
unfilled orders
total sale volumes
WIP
manufacturer 6
Figure 10 The in-transit inventory and main parameters changes of manufacturer 6 (3) Distributor agents’ variation The variations in main parameters of distributors 7 and 32 are illustrated in Figures 11, respectively. The two figures show that distributor 32 does not obtain orders from consumers while consumers place orders with distributor 7 in the initial stage of the simulation. It shows that the time is different for customers accessing the model. This conforms to the previous setting of relevant rules, and proves the correctness and rationality of the model. unfilled orders
finished inventory
in-transit inventory
total sale volumes
distributor 7
distributor 32
Figure 11 Variation trends of distributors 7 and 32 The discussions above analyze the model from sales and variations of several agents. In this way, it is verified that the
model established is correct and reasonable. 4.2 Network characteristics of the case. Pajek software is used to draw the network structure. Figure 12 shows an annular chart in which spots represent node enterprises while the nodes at dense blue lines indicate manufacturer agents. In order to see the structure clearly, the authors use Kamada-Kawai algorithm to draw the space layout (Figure 13). In the figure, nodes from 1 to 29 represent manufacturers, 30 to 57 are suppliers, and nodes from 58 to155 represent distributors.
Figure 12 Annular chart Figure 13 Space layout drawn by Kamada-Kawai algorithm By comprehensively analyzing Figures 12, 13 and 1, the constructed network of automobile supply chain has the following characteristics: (1) The network shows a dumbbell-shaped structure. The network displays a dumbbell-shaped structure with large both ends and a small middle section on the whole. This is because more consumer and secondary supplier nodes lie in the both ends of the supply chain and they update rapidly, while manufacturers, suppliers for parts and distributors in the core layer are relatively stable and these nodes enter and exit relatively slowly. (2) Self-similarity of nodes in the same category. Same category of nodes such as supplier, manufacturer and distributor agents in different layers show self-similarities including similar functions, core businesses, local-worlds, connections, and competitive environments. Therefore, in terms of choosing upstream suppliers and competing for downstream clients, nodes in the same category generally compete with each other. In addition, nodes playing a dominant role have priority in choice and therefore occupy more market shares. (3) Multilayer of local-world; in the supply chain network, the nodes with the same layer show the same local-world while those with different layers exhibit different local-worlds. (4) High clustering of core enterprises. In the supply chain network, manufacturer agents are at the core status, on which other nodes depend on. In the manufacturer network, a core manufacturer or minor core manufacturers show large market superiority and hold large market shares, which exert a significant effect on the property and the structure of supply chain network. Similarly, there are always one or several enterprises with competitive superiority in the levels of supplier and distributor agents, which occupy large market shares. According to the law of market competition, the enterprises with competitive superiority are chosen preferentially. Therefore, minor nodes in the supply chain show high degrees, which exhibits high-clustering characteristic of core enterprises. (5) High dynamics of network topology. Nodes in the network have independent judgment, behavior, adaption and learning capacities. During mutual competition, choosing, and being chosen, nodes follow the rule of survival of the fittest, that is, nodes with good adaptive and learning capacities grow. On the contrary, nodes with poor adaptation are eliminated or replaced by some new nodes. Therefore, the whole network topology exhibits a high dynamics. The distances, degrees and clustering coefficients of each node can be calculated by applying Pajek. Next, through data statistics and numerical fitting using Matlab, network characteristics of whole and local-worlds are obtained. Table 2 Average distances and clustering coefficients of nodes of the whole network and local area networks in each layer Whole network Distance
Clustering
Local world of manufacturers Distance
coefficient 3.89
0.00124
Clustering
Local world of suppliers Distance
coefficient 2.32339
0.414217823
Clustering
Local world of distributors Distance
coefficient 2.56147
0.277985165
Clustering coefficient
2.24063
0.429115
Table 2 displays the average distances and clustering coefficients of nodes. From Table 2, local-worlds in different layers all show short average distances and large clustering coefficients, which indicates that local area networks in each
layer of the system exhibit a small-world characteristic. The whole network contains numerous consumers and secondary suppliers while few connections between the both types of nodes, so the whole network shows small clustering coefficients and long average distances. 1.E+00
1.E-01
γ=3.319
1.E-02
Degree distribution 乘幂(度分布图)
度分布图
1.E-03
Fitting curve (power law)
拟合曲线（幂律）
1.E-04
1.E-05 1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
Figure 14 Degree distribution As shown in Figure 14, the network displays an overall distribution conforming to power-law distribution of f ( x) x and 3.319 can be obtained through simulation, which shows that the network has a typical characteristic of
scale-free networks on the whole. Numerous nodes in the network have a few connections while a few nodes (manufacturers 1-29, suppliers 30, 43, 45 and 50) have the majority of connections in the network. Due to this characteristic, when the nodes with high degrees are attacked, the whole network may be rapidly broken down. The nodes with high degrees play an important role in trouble-free running of the network, so they should be paid more attention in the maintenance. 4.3 Analysis from CAS The power spectra are drawn in Figures 15 based on inventories and orders of distributor 7, separately. No obvious peaks are observed, and the power spectral values are connected into one piece. Based on this, the system can be identified as a nonlinear one where its movement presents chaotic state. power /dB
power /dB
-15
40
-20
30 20
-25
10 -30 0 -35 -10 -40 -20 -45
-30
-50 -55
-40
0
100
200
300
400
500
600
700
800
900
1000
f/Hz
-50
0
100
200
300
400
500
600
700
800
900
1000
f/Hz
Figure 15 Power spectra drawn on the basis of the inventories and orders of distributor 7 The three-dimensional (3D) phase spaces obtained by combining the inventories, orders, and sales amount of manufacturer 21 and distributor 7 are shown Figures 16, separately. It can be seen from the figures that the 3D phase space charts are basically open and contain irregularly and disorderedly distributed helical curves. This suggests that the network is shown to move chaotically.
Z: sale volume
Z: sale volume 250
150
200
100
150
100 50
50
0
0
250
150
200
250
150 100
150
200 100
X: orders
100
150 100 50
50 0
0
Y: inventory
X: orders
50 50
0
Y: i n v e n t o r y
0
Figure 16 Phase spaces of manufacturer 21 and distributor 7 After calculating the Lyapunov index with the application of WOLF algorithm, the maximum values of these data are normalized. Thereinto, inventories, orders, and sale volumes show the maximum Lyapunov exponents of 0.00104, 0.00152, and 0.00086, respectively. As these maximum exponents are larger than zero, it suggests that the system is in chaotic state. Besides, it has CAS’s nonlinear characteristics. 5 Conclusions (1) The simulation system is constructed using hybrid modeling method (integrating ABM and discrete event modeling). It presents the operation process of all agents microscopically, which preferably reflects the business process of supply chain. Also, the model shows the overall evolutionary characteristic of automobile supply chain network in the macroscopic level. The modeling idea provides bases for establishing evolutionary mechanism of supply chain and studying bottom-up emergence mechanisms. (2) As for model verification, the changes and relationships of various parameters of all agents including the orders, sales amount, transportation inventory, factory inventory and WIP are analyzed. On this basis, the authors simulate parameter changes during business process of automobile supply chain and verify the correctness and rationality of the model (3) In terms of analysis, the system is comprehensive studied in terms of the CAS and the complex network. Moreover, the authors explore the system macrocosmically and microcosmically. With regard to the analysis of complex network, the relationships of nodes in the supply chain network are analyzed. In this way, it can be obtained that the nodes of all local area networks in the supply chain have short average distances, large average clustering coefficients, and specific features of small-world networks. In addition, supply chain network exhibits scale-free characteristic on the whole and the degree distribution accords with power-law distribution. Besides, the supply chain it proved to show chaotic motion by analyzing the power spectra, Lyapunov exponents, and phase spaces. Furthermore, the system has CAS’s nonlinear characteristics. (4) Future works are supposed to be conducted from the following aspects: it is necessary to introduce learning system for agents [9] and develop a proper intelligent algorithm. In addition, the emergence and clustering characteristics of the supply chain network need to be studied from the CASs and the complex networks. Acknowledgements The work was supported by NSFC (No. 51275407, No. 11072192). Reference [1] Souad Benomrane, Zied Sellami, Mounir Ben Ayed. An ontologist feedback driven ontology evolution with an adaptive multi-agentsystem. Advanced Engineering Informatics, 2016, 30(3): 337-353. [2] Sun Jun-yan, Wang Wen, Fu wei-ping, Yao Dan. Evolution of car supply chain complex adaptive system. Computer Integrated Manufacturing Systems, 2016, 22(8):2011-2022 (in Chinese). [3] Nicolas Couellan, Sophie Jan, Tom Jorquera, Jean-Pierre Georgé. Self-adaptive Support Vector Machine: A multi-agent optimization perspective. Expert Systems with Applications, 2015, 42(9):4284-4298. [4] R Axelrod . Advancing the art of simulation in the social sciences. Complexity , 1997 , 3(2) : 16-22 . [5] Songjing Wang, Lifeng Xi, Hui Xu, Lihong Wang. Scale-free and small-world properties of Sierpinski networks. Physica A: Statistical Mechanics and its Applications, 2017, 465(1): 690-700. [6] Paul Kim, Sangwook Kim. Detecting community structure in complex networks using an interaction optimization
process. Physica A: Statistical Mechanics and its Applications, 2017, 465(1): 525-542. [7] Zhou He, Shouyang Wang, T.C.E. Cheng. Competition and evolution in multi-product supply chains: An agent-based retailer model [J].International Journal of Production Economics, 2013, 146(1): 325-336. [8] Georg Weichhart, Wided Guédria, Yannick Naudet. Supporting interoperability in complex adaptive enterprise systems: A domain specific language approach. Data & Knowledge Engineering, 2016, 105(9): 90-106. [9] Tao You, Hui-Min Cheng, Yi-Zi Ning, Ben-Chang Shia, Zhong-Yuan Zhang. Community detection in complex networks using density-based clustering algorithm and manifold learning. Physica A: Statistical Mechanics and its Applications, 2016, 464(15): 221-230.
Highlights
The model construction and simulation of the system by means of combining CAS theory and complex networks The hybrid modeling method (integrating ABM and discrete event modeling). The modeling method based on GIS. The macroscopically illustrates and microcosmically reflect of the system. The local area networks have typical characteristics of small-world networks. The whole network exhibits scale-free characteristic and accords with power-law distribution. The supply chain show chaotic motion and has CAS’s nonlinear characteristics.