A critical node identification method for supply chain networks

Abstract

The invention discloses a key node identification method applied to a supply chain network. First, a supply chain network is constructed; the initial node load is calculated according to the supply chain network and used as the initial importance index of the node in the supply chain network; for nodes in networks of different levels, a first importance evaluation index is obtained according to the influence between two nodes on a connection path and the initial importance index of the influencing node; for two nodes in a network of the same level, a second importance evaluation index is obtained through the importance of common neighbors, the connection strength between the nodes and the initial importance index of the influencing node; the values ​​of the first importance evaluation index and the second importance evaluation index are normalized; after the values ​​of the two indicators are normalized, the entropy weight method is used to obtain the weight coefficients of the two corresponding importance indicators respectively, and the two importance indicators are weighted and summed according to the weight coefficients to obtain the importance evaluation index of the node.

Description

Technical Field

[0001] The present invention relates to the technical field of complex networks, and in particular to a key node identification method applied to a supply chain network. Background Art

[0002] The supply chain network is a complex network in which the failure of a node will cause a cascading failure and paralyze the entire network. Accurately identifying the key nodes of the supply chain network is of great significance to ensuring the security of the supply chain. Traditional node importance methods for complex networks, such as degree centrality, betweenness centrality, and closeness centrality, only consider the structural characteristics of the network. Currently, there are few node importance methods used in supply chain networks, and none of them consider the impact of network structural characteristics and functional characteristics on node importance.

[0003] In the problem of identifying key nodes in complex networks, many methods have been proposed from multiple perspectives such as local properties, global properties and node positions of the network. For example, commonly used evaluation indicators such as degree centrality, betweenness centrality, closeness centrality and PageRank algorithm. However, these methods often do not fully consider the particularity of supply chain networks, and therefore may not be applicable when applied to supply chain networks. Existing key node identification methods for supply chain networks mostly focus on evaluating the impact of nodes on the overall network stability from the perspective of network disruption, thereby determining key nodes. However, these methods usually fail to simultaneously consider the structural and functional characteristics of supply chain networks. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention proposes a key node identification method applied to a supply chain network. For the supply chain network, the topological structure characteristics of the supply chain network and the supply relationship and competition relationship of the nodes in the supply chain network are considered, thereby effectively improving the accuracy of key node identification in the supply chain network.

[0005] In order to solve the above technical problems, the technical solution of the present invention is:

[0006] A key node identification method applied to a supply chain network comprises the following steps:

[0007] Step 1: Build a supply chain network. The supply chain network sets several network levels according to the supply type of the enterprise. Each network level has several nodes, and the nodes represent the enterprises in the network of the level. The enterprises between every two adjacent levels form directed edges, and the edges represent the supply relationship between the enterprises.

[0008] Step 2: Calculate the initial node load according to the supply chain network and use it as the initial importance index of the node in the supply chain network;

[0009] Step 3: Nodes in different layers of networks are connected by edges to obtain connection paths of nodes in different layers of networks, and a first importance evaluation index is obtained according to the influence between two nodes on the connection path and the initial importance index of the influencing node;

[0010] For two nodes in the same level network, the second importance evaluation index is obtained by the importance of common neighbors, the connection strength between nodes, and the initial importance index of the influencing node;

[0011] Step 4: normalize the values ​​of the first importance evaluation index and the second importance evaluation index;

[0012] Step 5: After normalizing the values ​​of the two indicators, use the entropy weight method to obtain the weight coefficients of the two corresponding importance indicators respectively, and perform weighted summation of the two importance indicators according to the weight coefficients to obtain the importance evaluation index of the node. The larger the value of the importance evaluation index, the more important the node is.

[0013] Preferably, the enterprise supply types include suppliers, manufacturers, distributors and retailers.

[0014] Preferably, in step 1, use Describe the supply chain network model, where Represents a node in the network; Represents the edges between nodes. and nodes When there is a directed link between ,otherwise ; Represents the node load; Represents the logistics volume between nodes.

[0015] Preferably, in step 1, when a new node is added, the supply chain network is grown to obtain a supply chain network growth model, and the supply chain network growth model is used as the latest supply chain network. The growth method of the supply chain network is:

[0016] At the initial moment, given a layer with Node The direction of the edges in this directed network is that the nodes in the first layer point to the nodes in the second layer, the nodes in the second layer point to the nodes in the third layer, and so on. The nodes in the layer point to the Nodes in a layer;

[0017] A new node is added at each time step , given a random number ,Depend on The value of determines the node Join hierarchical networks in the supply chain network;

[0018] Newly added node After confirming to join the hierarchy, a connection is established with the old nodes in the directed network.

[0019] Preferably, in step 1, the strategy for a new node to join the hierarchical network in the supply chain network is:

[0020] when , it means that the newly added node is an enterprise node in the first layer, and it can only choose to establish a connection with the enterprise nodes in the second layer. Therefore, the node only has the downstream local world, that is, the enterprise nodes in the second layer;

[0021] when When , indicating that the newly added node is The enterprise node in the layer can choose Layer, Therefore, the node has the upstream local world, that is, the first The first layer of enterprise nodes and the downstream local world Layer enterprise node;

[0022] when , it indicates that the newly added node is The enterprise nodes in the layer can only select and Therefore, the node only has the upstream local world, i.e. Layer enterprise node.

[0023] Preferably, the method for establishing a connection between the newly added node and the old node in the supply chain network is:

[0024] Newly added node Is the first or The enterprise node in the layer, at this time, the node There is only a downstream local world or an upstream local world; this node forms a downstream local world or an upstream local world connection with nodes in the local world The probability of forming a connection is:

[0025]

[0026] in, For Node The degree, is the sum of the degrees of all nodes in the local world;

[0027] When a new node joins The second to third layers Nodes in the layer; at this time, nodes It has both an upstream local world and a downstream local world; the node must not only form a connection, and also form a connection with the nodes in the downstream local world The probability of forming a connection with a node in the upstream local world and a node in the downstream local world must satisfy the above formula.

[0028] Add nodes and edges to the network in the above manner until the number of nodes in the network reaches the desired number of network nodes , the supply chain network model is successfully constructed.

[0029] Preferably, the calculation method of the initial load of the node is:

[0030] Assume that the supply chain network has Layer, of which The total initial load of the nodes in the layer is known and is ,Will Assign the node to the The nodes in the layer, from which the initial load of the nodes in the layer can be obtained as:

[0031]

[0032] in For Node The degree, For the The sum of the node degrees of the layers;

[0033] According to The initial load of the nodes in the layer The initial load of the nodes in the layer is evenly distributed to the edge pointing to the node to form the initial logistics flow on this edge. Node in layer and Node in layer The initial logistics flow on all edges between is as follows:

[0034]

[0035] in, For Node The in-degree of . Layer and After the initial logistics flow on the edges between layer nodes, the first Node in layer The initial load is as follows:

[0036]

[0037] in is a set of nodes connected to the downstream nodes of the node, thus Node in layer Initial load As a node in the supply chain network The initial importance index .

[0038] Preferably, in step 3, the method for obtaining the first importance evaluation index is:

[0039] Assume that any two nodes in the unconnected hierarchical network and The node sequence contained in the path ,in ,node and The influence between them can be expressed as:

[0040]

[0041] in, Refers to the strength of the connection between two nodes;

[0042] According to the obtained influence degree and combined with the initial importance index of the influencing node, the node The first important evaluation index ,Right now

[0043] .

[0044] Preferably, the connection strength between the two nodes is calculated as follows:

[0045] Normalize the logistics volume of the edges in the supply chain network. The normalized result is As the connection strength between nodes, the expression is as follows:

[0046] .

[0047] Preferably, the method for obtaining the second importance evaluation index is:

[0048] Nodes in a hierarchical network From its upstream neighbor node The importance value obtained at each node depends on the connection strength between them. The ratio of the connection strength of all downstream neighbor nodes to , that is:

[0049]

[0050] in, Representation Node For Node The upstream neighbor of Representation Node For Node downstream neighbors;

[0051] Similarly, nodes in the network From its downstream neighbor node The importance value obtained at each node depends on the connection strength between them. The ratio of the connection strength of all upstream neighbor nodes, that is:

[0052]

[0053] Since the nodes in the first layer and the nodes in the Tth layer of the hierarchical supply chain network have only downstream nodes or upstream nodes, and the nodes in the middle layer have both upstream nodes and downstream nodes, the importance values ​​of the nodes in the middle layer obtained from the upstream neighbors and downstream neighbors are averaged to eliminate the error caused by the different layers of the nodes, and the node The second importance evaluation index :

[0054] .

[0055] The present invention has the following characteristics and beneficial effects:

[0056] The above technical scheme is adopted to comprehensively consider the structural characteristics and functional characteristics of the supply chain network. The initial load of the node is obtained by using the structural characteristics of the supply chain network as the initial importance index of the node, and two importance indexes are obtained by combining the two relationships in the supply chain network with the initial importance index. The node importance evaluation index in the supply chain network is obtained by weighted summing the two indexes. This method aims to simultaneously consider the influence of the structural characteristics and functional characteristics of the network on the identification of key nodes in the network, thereby improving the accuracy of key node identification in the supply chain network. In the simulation study, the method proposed in the present invention was compared with four traditional key node identification methods: degree centrality, betweenness centrality, closeness centrality, and PageRank algorithm. The results show that whether it is an attack on multiple nodes or an attack on a single node, the method proposed in this patent shows higher accuracy than the other four methods in identifying key nodes in the supply chain network. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0058] Figure 1 Schematic diagram of a flow chart of an embodiment of the present invention.

[0059] Figure 2 Schematic diagram of a supply chain network model in an embodiment of the present invention.

[0060] Figure 3 Schematic diagram of the results of the supply chain network theoretical model under multi-node attack.

[0061] Figure 4 Schematic diagram of the results of the supply chain network theoretical model under a single-node attack.

[0062] Figure 5 Schematic diagram of the results of a realistic supply chain network model under a multi-node attack mode.

[0063] Figure 6 Schematic diagram of the results of a real supply chain network model under a single-node attack. DETAILED DESCRIPTION

[0064] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0065] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0066] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0067] In the supply chain network, there are mainly two types of relationships between nodes: supply relationship and competition relationship. Supply relationship is usually reflected between nodes in different layers, while competition relationship exists between nodes in the same layer. These two relationships together constitute all the connections in the network. Therefore, this patent proposes a key node identification method for supply chain network based on the topological structure characteristics of the supply chain network and the supply relationship and competition relationship of nodes in the supply chain network. Figure 1 As shown, the following steps are included:

[0068] First, use Describe the supply chain network model. Represents a node in the network. Represents the edges between nodes. and nodes When there is a directed link between ,otherwise . Represents the node load. Represents the logistics volume between nodes.

[0069] Among them, Figure 2 As shown in the figure, the supply chain network sets up several network levels according to the enterprise supply type. Assume that the supply chain network has Layer, of which The total initial load of the nodes in the layer is known and is It can be understood that in this embodiment, the enterprise supply types generally include suppliers, manufacturers, distributors and retailers. Each network level has a number of nodes, and the nodes represent enterprises in the network of this level. Enterprises between every two adjacent levels form directed edges, and the edges represent the supply relationship between enterprises.

[0070] According to a further configuration of the present invention, when a new enterprise joins the supply chain network, the company usually prefers to cooperate with large enterprises in the supply chain network. Therefore, the supply chain network evolution model adopted in this embodiment is based on the local world evolution model. The newly added nodes are preferentially connected to the nodes with larger degrees in the local world, which is used as the growth model of the supply chain network. The specific algorithm is as follows:

[0071] At the initial moment, given a layer with Node The direction of the edges in this network is that the nodes in the first layer point to the nodes in the second layer, the nodes in the second layer point to the nodes in the third layer, and so on. The nodes in the layer point to the Nodes in a layer.

[0072] A new node is added at each time step . Given a random number ,Depend on The value of determines the node The levels added to the supply chain network are divided into the following three situations:

[0073] i.when , it means that the newly added node is an enterprise node in the first layer, and it can only choose to establish a connection with an enterprise node in the second layer. Therefore, the node has only a downstream local world, that is, a second-layer enterprise node.

[0074] ii. When , it indicates that the newly added node is The enterprise node in the layer can choose Layer, Therefore, this node has the upstream local world, that is, the first The first layer of enterprise nodes and the downstream local world Layer enterprise node.

[0075] iii. When , it indicates that the newly added node is The enterprise nodes in the layer can only select and Therefore, this node only has the upstream local world, i.e. Layer enterprise node.

[0076] Newly added node After confirming to join the hierarchy, a connection is established with the old nodes in the network. This connection is divided into the following two situations:

[0077] i. Newly added nodes Is the first or At this point, the node There is only a downstream local world or an upstream local world. This node forms a downstream local world or an upstream local world connection with nodes in the local world The probability of forming a connection is

[0078]

[0079] in, For Node The degree, is the sum of the degrees of all nodes in the local world.

[0080] ii. Newly added nodes The second to third layers At this point, the nodes At the same time, it has an upstream local world and a downstream local world. This node must not only form a connection, and also form a connection with the nodes in the downstream local world The probability of forming a connection with a node in the upstream local world and a node in the downstream local world must satisfy the above formula.

[0081] Add nodes and edges to the network in the above manner until the number of nodes in the network reaches the desired number of network nodes . The supply chain network model is successfully constructed.

[0082] Further, Assign the node to the The nodes in the layer, from which the initial load of the nodes in the layer can be obtained as:

[0083]

[0084] in For Node The degree, For the The sum of the node degrees of the layer.

[0085] According to The initial load of the nodes in the layer The initial load of the nodes in the layer is evenly distributed to the edge pointing to the node to form the initial logistics flow on this edge. Node in layer and Node in layer The initial logistics flow on all edges between is as follows:

[0086]

[0087] in, For Node The in-degree of . Layer and After the initial logistics flow on the edges between layer nodes, the first Node in layer The initial load is as follows:

[0088]

[0089] in is a node set consisting of downstream nodes connected to the node. After the initial load of the layer node is calculated, the initial logistics volume and initial load calculation formula are used to calculate the first Layer nodes and The initial logistics flow on the edges between layer nodes and the The initial load of the layer nodes. Similarly, the initial logistics volume on all edges and the initial load of all nodes are calculated in sequence. The obtained logistics volume can satisfy the sum of the incoming flow of each node is equal to the sum of the outgoing flow, which is also equal to the initial load of the node, that is,

[0090]

[0091] in, is connected to the node This indicates that the demand and supply of the nodes are balanced, which meets the load definition.

[0092] The node load obtained in the above way reflects the structural characteristics of the supply chain network. Therefore, the calculated node initial load is used as the node load in the supply chain network. The initial importance index .

[0093] In the supply chain network, there is a supply relationship between two nodes with an edge, so there is mutual influence between the two nodes with an edge. Furthermore, it is believed that the degree of mutual influence between two enterprise nodes in the supply chain network is determined by the strength of the connection between them. The logistics volume of the edge in the supply chain network is normalized using the following formula. The normalized result is As the connection strength between nodes:

[0094] .

[0095] It can be understood that in the supply chain network, the relationship between nodes can be divided into two types. The first type is nodes at different levels, which are connected by edges. These connection paths show the supply relationship between nodes. The second type is nodes at the same level. Although there is no direct edge between these nodes, there is a competitive relationship between them due to the functional characteristics of the supply chain network. Based on these two connection relationships in the supply chain network and the connection strength between nodes, the following two importance evaluation indicators can be obtained:

[0096] For nodes at different levels of the network, if two nodes with a direct supply relationship have a direct impact on each other, then any two nodes that can form a connection path will also have an indirect impact on each other through the nodes in the path. The influence between two nodes that can form a path is the product of the connection strength on the path. Therefore, assuming that any two nodes in the network and The node sequence contained in the path ,in .node and The influence between them can be expressed as:

[0097]

[0098] In the supply chain network, the degree of influence of a node on other nodes is evaluated by the above method, and combined with the initial importance of these influencing nodes, the node The first importance evaluation indicator ,Right now

[0099] .

[0100] Nodes at the same level in the supply chain have a competitive relationship, which can be reflected by the importance of common neighbors and the strength of connections between nodes. In the supply chain, the more important a company node is, the less important the nodes with common neighbors will be. Therefore, the importance of two competitive company nodes can be reflected by their common neighbors and is related to the strength of connections between them and their common neighbors. From its upstream neighbor node The importance value obtained at each node depends on the connection strength between them. The ratio of the connection strength of all downstream neighbor nodes to , that is:

[0101]

[0102] in, Representation Node For Node The upstream neighbor of Representation Node For Node Similarly, nodes in the network From its downstream neighbor node The importance value obtained at each node depends on the connection strength between them. The ratio of the connection strength of all upstream neighbor nodes, that is:

[0103]

[0104] Since the nodes in the first layer and the Tth layer of the hierarchical supply chain network have only downstream nodes or upstream nodes, while the nodes in the middle layer have both upstream nodes and downstream nodes. Therefore, the importance values ​​of the nodes in the middle layer obtained from the upstream neighbors and downstream neighbors are averaged to eliminate the error caused by the different layers of the nodes. The second importance evaluation index :

[0105]

[0106] Therefore, the importance index can be obtained through the topological structure of the supply chain network and the unique supply relationship and competition relationship between nodes in the supply chain network. and Among them, the importance index It reflects the importance of nodes in the supply chain network in the supply relationship between nodes at different levels. It reflects the importance of nodes in the supply chain network in the competitive relationship between nodes at the same level. These two indicators jointly describe the role of each node in the supply chain network. Therefore, the two importance index values ​​of the node are obtained. and After that, the values ​​of the two indicators are normalized and the entropy weight method is used to obtain the weights of the two importance indicators: , , add the two importance indicators according to the weights to get the node Importance evaluation indicators:

[0107]

[0108] The larger the index is, the more important the node is.

[0109] Comparative Example:

[0110] The simulation uses a supply chain network theory model containing 200 nodes and a real supply chain network containing 271 nodes. The initial load of each node in the network and the initial logistics volume between the nodes are calculated. The importance evaluation index value proposed in this embodiment of each node is obtained by using the initial load and initial logistics volume, and the nodes in the network are ranked by importance.

[0111] In this embodiment, cascading failures in the supply chain network will lead to node load loss in the network. Therefore, the network load loss ratio is used as an evaluation index to judge the accuracy of the key node identification method of the supply chain network. The load loss after the cascading failure of the supply chain network accounts for the proportion of the entire network load, and the calculation formula is as follows:

[0112]

[0113] in, represents the sum of the initial loads of all nodes in the network, It represents the sum of the loads of all nodes after the network cascade failure ends.

[0114] In addition, the degree centrality, betweenness centrality, closeness centrality and PageRank value of each node in the network are calculated and ranked. According to the rankings obtained by the five methods, two methods, multi-node attack and single-node attack, are used to cause underload cascading failure in the network, and the proportion of load loss after cascading failure is compared, so as to compare the accuracy of the five methods in identifying key nodes in the supply chain network.

[0115] The underload cascading failure process is as follows. In the constructed supply chain network, the node With initial load , even edge With initial flow In terms of load constraints, it is assumed that the node Load lower limit With initial load Proportional to:

[0116]

[0117] in is the lower limit parameter, .

[0118] A node in the network In time If a node fails, the node is regarded as the initial failed node, and the load of the node is set to 0. At the same time, due to the failure of the node, it can neither receive supply from upstream neighbors nor provide supply to downstream neighbors. Therefore, the logistics volume of the node's incoming and outgoing edges is set to 0. The loss of its upstream neighbor nodes and downstream neighbor nodes caused by the failure of satisfies the following formula:

[0119] in, Representation Node The sum of the logistics flows between all its upstream neighbor nodes at the steady state moment before the failure occurs, Representation Node The sum of the logistics flows between the node and all its downstream neighbor nodes at the steady state moment before the failure occurs. Failed node , its load loss is ,node Upstream neighbor node The load loss is ,node The load is reduced to ,node With Node The logistics volume between ,node Downstream neighbor nodes The load loss is ,node The load is reduced to ,node With Node The logistics volume between .node The impact on network cascading failure can be divided into two cases:

[0120] (1) When the node An upstream neighbor node or downstream neighbor node When the load of the node is lower than the lower limit. or Node The load of is set to 0, and the logistics flow of the node's incoming and outgoing edges is also set to 0. At this time, the node is completely failed, and the impact of this failure on its upstream and downstream neighbor nodes is the same as in formula (15).

[0121] (2) When the node Upstream neighbor node or downstream neighbor node When the load of the node does not drop to the lower limit, or Node The load of the node has dropped but it has not completely failed. Nodes that cause The load reduction will cause the incoming The load of its upstream neighbor nodes is reduced. However, this change does not affect the slave nodes. The outgoing logistics volume and the load of its downstream neighbor nodes. To its upstream neighbor node The load and incoming The impact of the logistics volume satisfies the following formula:

[0122] in, Representation Node The sum of the load reductions caused by all its downstream neighbor nodes. Nodes that cause The load reduction will cause The outgoing volume of logistics has decreased and The load on the downstream neighbor nodes decreases. However, this change does not affect the incoming nodes. The logistics volume of nodes and the load of their upstream neighbor nodes. To its downstream neighbor nodes The load and The impact of the outgoing logistics volume satisfies the following formula:

[0123] in, Representation Node The sum of the load reductions caused by all its upstream neighbor nodes.

[0124] The load failure of a node is propagated in the above manner, and this propagation process will gradually spread to the entire network. moment, a node At the same time, its upstream neighbors and downstream neighbors The impact of this node The amount of load reduction is determined by the neighboring nodes that have a greater impact on it, i.e.

[0125]

[0126] The propagation process continues until no more nodes in the network experience a drop in load.

[0127] In this comparative example, two different methods are used to attack the network. The first is a multi-node attack method, which simultaneously attacks the top k nodes in the supply chain network obtained by the five key node identification methods to make them invalid, and obtains the load loss ratio after cascading failure. The results of the supply chain network theoretical model are shown in Figure 3 As shown in Figure 2, the results of the real supply chain network are as follows: Figure 5 As shown. The results show that compared with other methods, the method proposed in this patent causes more serious damage to the supply chain network when attacking multiple nodes in order of importance. This shows that removing multiple nodes in the order of key node ranking determined by the method proposed in this patent is the most harmful to the supply chain network. The second is a single node attack method, which attacks the k-ranked node in the supply chain network obtained by the five key node identification methods in turn to make it invalid, and obtain the load loss ratio after cascading failure. The results of the supply chain network theoretical model are shown in Figure 4 As shown in Figure 2, the results of the real supply chain network are as follows: Figure 6 The results show that when the node importance ranking is the same, the key nodes found by the method proposed in this patent cause greater network load loss and are more destructive to the supply chain network.

[0128] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments including components are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. A key node identification method applied to a supply chain network, characterized in that: The steps include: Step 1: Build a supply chain network. The supply chain network sets several network levels according to the supply type of the enterprise. Each network level has several nodes, and the nodes represent the enterprises in the network of the level. The enterprises between every two adjacent levels form directed edges, and the edges represent the supply relationship between the enterprises. Step 2: Calculate the initial node load based on the supply chain network and use it as the initial importance indicator of the node in the supply chain network; Step 3: Nodes in different layers of networks are connected by edges to obtain connection paths of nodes in different layers of networks, and a first importance evaluation index is obtained according to the influence between two nodes on the connection path and the initial importance index of the influencing node; The method for obtaining the first importance evaluation index is: Assume that any two nodes v in different layers of the network i and v j The node sequence contained in the path where k1=i,k n =j, node v i and v j The influence between them can be expressed as: in, Refers to the connection strength between two nodes, which refers to the normalized result of the logistics volume of the edge in the supply chain network; According to the obtained influence degree and combined with the initial importance index of the influencing node, the node v is obtained. i The first importance evaluation index I2(i), that is, For two nodes in the same level network, the second importance evaluation index is obtained by the importance of common neighbors, the connection strength between nodes, and the initial importance index of the influencing node; The method for obtaining the second importance evaluation index is: Node v in the hierarchical network i From its upstream neighbor node v m The importance value obtained at each node depends on the connection strength between them. m The ratio of the connection strength of all downstream neighbor nodes to , that is: Where m∈Γ i U Represents node v m For node v i The upstream neighbor of Represents node v n For node v m downstream neighbors; Similarly, the node v in the network i From its downstream neighbor node v p The importance value obtained at each node depends on the connection strength between them. p The ratio of the connection strength of all upstream neighbor nodes, that is: Since the nodes in the first layer and the Tth layer of the hierarchical supply chain network have only downstream nodes or upstream nodes, and the nodes in the middle layer have both upstream nodes and downstream nodes, the importance values ​​of the nodes in the middle layer obtained from the upstream neighbors and downstream neighbors are averaged to eliminate the error caused by the different layers of the nodes, and the node v is obtained. i The second importance evaluation indicator I3(i): Step 4: normalize the values ​​of the first importance evaluation index and the second importance evaluation index; Step 5: After normalizing the values ​​of the two indicators, use the entropy weight method to obtain the weight coefficients of the two corresponding importance indicators respectively, and perform weighted summation of the two importance indicators according to the weight coefficients to obtain the importance evaluation index of the node. The larger the value of the importance evaluation index, the more important the node is.

2. A key node identification method applied to a supply chain network according to claim 1, characterized in that: The business supply types include suppliers, manufacturers, distributors and retailers.

3. The key node identification method applied to the supply chain network according to claim 1 is characterized in that: In step 1, G = (V, E, L, F) is used to describe the supply chain network model, where V = (v1, v2, ..., v n ) represents the nodes in the network; E = {(v i ,v j )|e ij =1or0} represents the edge between nodes, and node v i and node v j When there is a directed link between ij =1, otherwise e ij =0; L = {L1, L2, ..., L n } represents the node load; F = F ij Represents the logistics volume between nodes.

4. The key node identification method applied to the supply chain network according to claim 3 is characterized in that: In step 1, when a new node is added, the supply chain network is grown to obtain a supply chain network growth model, and the supply chain network growth model is used as the latest supply chain network. The growth method of the supply chain network is: At the initial moment, given a T-layer directed network with m0 nodes in each layer, the direction of the edges in the directed network is that the nodes in the first layer point to the nodes in the second layer, the nodes in the second layer point to the nodes in the third layer, and so on, the nodes in the T-1th layer point to the nodes in the Tth layer; A new node v is added at each time step j , given a random number r∈(0,1], the value of r determines the node v j Join hierarchical networks in the supply chain network; Newly added node v j After confirming to join the hierarchy, a connection is established with the old nodes in the directed network.

5. The key node identification method applied to the supply chain network according to claim 4 is characterized in that: In step 1, the strategy for a new node to join the hierarchical network in the supply chain network is: when , it means that the newly added node is an enterprise node in the first layer, and it can only choose to establish a connection with the enterprise nodes in the second layer. Therefore, the node only has the downstream local world, that is, the enterprise nodes in the second layer; when When 1<i<T, it means that the newly added node is an enterprise node in the i-th layer, and it can choose to establish connections with enterprise nodes in the i-1th layer and the i+1th layer; therefore, the node has an upstream local world, i.e., an enterprise node in the i-1th layer, and a downstream local world, i.e., an enterprise node in the i+1th layer; when , it means that the newly added node is an enterprise node in the Tth layer, and it can only choose to establish a connection with the enterprise nodes in the T-1th layer; therefore, the node only has the upstream local world, that is, the T-1th layer enterprise node.

6. A key node identification method applied to a supply chain network according to claim 5, characterized in that: The method for establishing a connection between the newly added node and the old node in the supply chain network is: Newly added node v j is an enterprise node in the first or Tth layer. At this time, node v j There is only a downstream local world or an upstream local world; this node forms M connections with the downstream local world or the upstream local world, and with the node v in the local world i The probability of forming a connection is: Among them, d i For node v i The degree, is the sum of the degrees of all nodes in the local world; When a new node v j are the nodes in the second to T-1th layers; at this time, node v j It has both an upstream local world and a downstream local world. The node must not only form M connections with nodes in the upstream local world, but also form M connections with nodes in the downstream local world. The probability of forming connections with nodes in the upstream local world and with nodes in the downstream local world must satisfy the above formula. By adding nodes and edges to the network in the above manner until the number of nodes in the network reaches the desired number of network nodes n, the supply chain network model is successfully constructed.

7. A key node identification method applied to a supply chain network according to any one of claims 3 to 6, characterized in that: The calculation method of the initial load of the node is: Assume that the supply chain network has T layers, where the total initial load of the nodes in the Tth layer is known and is Q. Q is distributed to the nodes in the Tth layer according to the degree of the nodes, so the initial load of the nodes in the Tth layer can be obtained as: where d j For node v j The degree, is the sum of the node degrees of the Tth layer; According to the initial load of the nodes in the Tth layer, the initial load of the nodes in the Tth layer is evenly distributed to the edge pointing to the node to form the initial logistics flow on this edge, and the initial load of the node v in the T-1th layer is calculated. i and node v in layer T j The initial logistics flow on all edges between is as follows: in, For node v j After obtaining the initial logistics flow on the edge between the T-1th layer and the Tth layer node, we can infer the node v in the T-1th layer. i The initial load is as follows: in is a set of nodes connected to the downstream nodes of the node, so that the node v in the T-1th layer i The initial load L i As a node in the supply chain network i The initial importance index I1(i).

8. The key node identification method applied to a supply chain network according to claim 1, characterized in that: The connection strength between the two nodes is calculated as follows: Normalize the logistics volume of the edges in the supply chain network, and the normalized result W ij As the connection strength between nodes, the expression is as follows:

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