A Method for Constructing an Underload Failure Propagation Model for Product Supply Chain Networks

Abstract

The present invention proposes a method for constructing an underload failure propagation model for a product supply chain network, and the steps are as follows: construct a complex network according to the business relationships between enterprises in the product supply chain network, and measure the intensity of supply-demand relationships according to global factors and local factors; define the initial load of nodes layer by layer according to the supply-demand relationship intensity of enterprises and the logistics balance constraint; calculate the lower limit of the load capacity of nodes from a non-linear perspective; the failure of nodes causes load loss, and the load loss propagates bidirectionally along the supply-demand direction; if new node failures are triggered during the propagation of load loss, continue according to the bidirectional load loss propagation mechanism until no more nodes in the entire network fail due to underload, and at this time the cascading failure ends. The present invention comprehensively considers the global factors and local factors of the network to measure the intensity of supply-demand relationships, defines the initial load according to the supply-demand relationship intensity of enterprises and the logistics balance constraint, and sets the lower limit of the load capacity according to the heterogeneity characteristics of enterprises, which is more in line with the actual situation.

Description

Technical Field

[0001] The present invention relates to the technical field of supply chain network modeling and analysis, and particularly relates to a method for constructing an underload failure propagation model for a product supply chain network triggered by the failure of node enterprises. Background Art

[0002] A supply chain is a functional chain-like structure that connects suppliers, manufacturers, distributors, and end-users into a whole, involving processes such as raw material procurement, processing of components and semi-finished products, and delivery of complete products. With the development of science and technology and the globalization of the economy, social division of labor has become increasingly refined, and the supply chain has gradually evolved into a complex network system that includes multiple levels of suppliers and manufacturers. The complexity of the supply chain network has exacerbated the uncertainty of the operating environment. At the same time, strategies such as lean production and business outsourcing have also made the supply chain network increasingly vulnerable. Under the dual pressure of the two, the phenomenon of the global collapse of the supply chain network caused by local failures occurs frequently, resulting in huge economic losses. For example, in July 2007, a magnitude 6.8 earthquake in central Japan severely damaged the equipment of the Institute of Physical and Chemical Research, forcing Toyota to close its 12 assembly plants in Japan, bringing huge losses to the entire automotive industry.

[0003] Modeling the above failure transfer effect and analyzing the failure transfer law of enterprises is an effective measure to improve the anti-interference ability of the supply chain network. Currently, there are mainly two types of models: overload failure propagation models and underload failure propagation models. The former is directly taken from infrastructure networks such as power grids, the Internet, and transportation networks, where nodes fail due to overload, belonging to overload failures. In contrast, the latter originates from real product supply chain networks and is more in line with reality. Specifically, in a product supply chain network, upstream enterprises provide raw materials or components for downstream enterprises, and there is a supply-demand relationship between upstream and downstream enterprises. An enterprise is both the demand side of upstream enterprises and the supply side of downstream enterprises. An enterprise will fail due to insufficient upstream raw material supply or decreased downstream product demand, belonging to underload failures. However, the existing underload failure propagation models still have some deficiencies in depicting the real situation. For example, the logistics balance constraints of enterprises are not considered when defining the initial load, the heterogeneity of enterprises is not considered when setting the upper and lower limits of capacity, and the impact of underloaded enterprises on neighboring enterprises is not considered when redistributing the load.

[0004] The invention patent with the application number 201910025801.6 discloses a method for constructing a cascading failure model of a supply chain network based on underloading, and the steps are as follows: abstract the supply chain network into a directed network pointing from upstream to downstream, use nodes to represent enterprises, and use an adjacency matrix to represent the directed network; define the initial load of nodes according to the degree of nodes in the supply chain network; define the load capacity according to the upper and lower limits of the load when the enterprise operates normally; calculate the business relationship strength between nodes through the degree of nodes, and redistribute the load after node failure according to the business relationship strength; update the enterprise load according to the losses suffered by the nodes and the protection measures taken; conduct a new round of failure judgment according to whether the enterprise is underloaded; measure the propagation scale of the cascading failure model according to the relative network efficiency. Compared with the overload cascading failure model, the invention can more profoundly reflect the propagation characteristics of cascading failures in the supply chain network and provide a useful reference for preventing and controlling cascading failures. However, the constructed cascading failure model does not consider the logistics balance constraint of enterprises when defining the initial load, does not consider the heterogeneity of enterprises when setting the upper and lower limits of capacity, and does not consider the impact of underloaded enterprises on neighboring enterprises when redistributing the load. Summary of the Invention

[0005] Aiming at the technical problem that the existing underloading failure propagation model considers incomplete when depicting the real situation, the present invention proposes a method for constructing an underloading failure propagation model for a product supply chain network, considering the initial load based on logistics balance constraints of global factors and local factors, the non-linear load capacity based on enterprise heterogeneity, and the global load distribution rule based on fixed allocation of failed enterprises and optimal allocation of underloaded enterprises, so as to be able to more accurately describe the failure propagation process of enterprises in the product supply chain network.

[0006] In order to achieve the above object, the technical solution of the present invention is realized as follows: A method for constructing an underloading failure propagation model for a product supply chain network, and the steps are as follows:

[0007] Step 1: Construct a complex network according to the business relationships between enterprises in the product supply chain network, map enterprises to nodes in the network, map the supply and demand relationships between enterprises to directed edges, map the supply and demand relationship strength to the weights of the directed edges, and measure the supply and demand relationship strength according to global factors and local factors;

[0008] Step 2: Regard logistics as the load flowing in the product supply chain network, and define the initial load of nodes layer by layer according to the supply and demand relationship strength of enterprises and the logistics balance constraint;

[0009] Step 3: Calculate the lower limit of the load capacity of nodes from a non-linear perspective according to the heterogeneity characteristics of enterprises;

[0010] Step 4: Use the scenario method to simulate that an enterprise in the product supply chain network encounters an unexpected event resulting in the failure of the corresponding node;

[0011] Step 5: Node failure causes load loss, which propagates in both directions along the supply and demand directions. The load loss propagates downward step by step to the last layer, and propagates upward step by step to the first layer. During the load loss propagation process, failed nodes distribute load according to the supply and demand relationship, and underloaded nodes distribute load according to the carrying capacity.

[0012] Step 6: If the load loss propagation process causes new node failures, then continue back to step 5 and follow the load loss bidirectional propagation mechanism until no node in the entire network fails due to underload, at which point the cascading failure ends.

[0013] Preferably, the complex network is G = {V, A, E, W}, where V = {v1, v2, ..., v n} represents a node set, n is the number of nodes; A=(a ij ) n×n Represents the adjacency matrix. If the node v i With node v j If there is a directed edge between them, then element a ij =1, otherwise element a ij =0; E = {e ij |a ij =1} represents a directed edge set, e ij Represents node v i With node v j Directed edges between; W = {w ij |a ij =1} represents the weight set of directed edges, w ij For directed edge e ij The weight of .

[0014] Preferably, the global factor - edge betweenness and the local factor - node degree are used to calculate the directed edge e ij The initial weight w ij (0)=(B ij k i k j ) α ;in, For directed edge e ij The betweenness, P(v b ,v c ) represents node v b With node v c The number of shortest paths between b ,v c ,e ij ) represents node v b With node v c The shortest path between ij The number of shortest paths; is the degree of node v i , where is the in-degree and is equal to the sum of the elements in the i-th column of the adjacency matrix A. The corresponding nodes form the set U of upstream neighbor nodes of node v i ; i ; is the out-degree and is equal to the sum of the elements in the i-th row of the adjacency matrix A. The corresponding nodes form the set D of downstream neighbor nodes of node v i ; k i is the degree of node v j ; α is an adjustable parameter that controls the weight of the directed edge. j ; α is an adjustable parameter that controls the weight of the directed edge.

[0015] Preferably, the method for determining the initial load in step 2 is as follows:

[0016] The product supply chain network has a total of T layers. Randomly assign an initial load of L z (0) to the node v z in the T-th layer; Calculate the initial logistics on the directed edge between the nodes in the (T - 1)-th layer and the T-th layer according to the supply-demand relationship strength: For the node v z in the T-th layer and its upstream neighbor node v x in the (T - 1)-th layer, the initial logistics on the directed edge e xz is:

[0017]

[0018] where w xz (0) and w uz (0) are the initial weights of the directed edge e xz and the directed edge e uz respectively. U z is the set of upstream neighbor nodes of node v z ; The node v uz on the directed edge e u represents the node in the set U of upstream neighbor nodes z ;

[0019] Then the initial logistics flowing out of the upstream neighbor node v x is:

[0020] where m xy (0) is the initial logistics on the directed edge e xy , and D x is the set of downstream neighbor nodes of node v x ;

[0021] According to the logistics balance constraint, the initial logistics flowing into the node v x is:

[0022] Among them, λ x is the material list coefficient of node v x , indicating that v x flows into λ x units of materials to obtain one unit of material output;

[0023] Then the initial load of node v x on the (T - 1)-th layer is In this way, the initial loads of all nodes on the (T - 1)-th layer are obtained;

[0024] Similarly, according to the strength of the supply-demand relationship, the initial logistics on the directed edges between the nodes on the (T - 2)-th layer and the (T - 1)-th layer are calculated, and the initial loads of all nodes on the (T - 2)-th layer are obtained; in this way, the initial loads of the nodes on each layer are gradually obtained forward, and the initial load of the nodes on the first layer is the initial logistics flowing out of it.

[0025] Preferably, the calculation method of the lower limit of the load capacity of the node is:

[0026] The lower limit of the load capacity of node v x is

[0027]

[0028] Among them, L max (0) is the maximum initial load of n nodes, β is a tolerance parameter and 0 < β ≤ 1, γ is a capacity adjustable parameter and γ ≥ 0; L x (0) is the initial load of node v x .

[0029] Preferably, the load loss in step 5 propagates bidirectionally along the supply-demand direction and is a global behavior of gradual propagation. After a node fails, the load loss of the upstream neighbor node is manifested as a decrease in its logistics demand, and the decrease in demand upstream is transmitted all the way to the first layer. The load loss of the downstream neighbor node is manifested as a decrease in its logistics supply, and the decrease in supply downstream is transmitted all the way to the last layer; the propagation of load loss upstream and the propagation of load loss downstream are similar.

[0030] Preferably, the propagation of the load loss downstream is a gradual propagation, and the method is: Node v g suffers a loss at time t and propagates the loss to the downstream neighbor node v o at time t + 1; after node v o suffers a loss at time t + 1, it propagates the loss to its downstream neighbor node v q at time t + 2. In this process, the update of node load and state and the update of logistics and weight on the directed edges between nodes are also involved.

[0031] Preferably, it is assumed that an emergency causes losses to node v at time t g resulting in losses making node v g fail at time t + 1. Node v g starts to gradually spread the load loss to downstream neighbor nodes from time t + 1, that is, allocates the load to downstream neighbor nodes. The steps are as follows:

[0032] Step 1: The failed node v g transmits the loss to downstream neighbor nodes according to the supply - demand relationship at time t + 1. The total transmitted loss is where λ g is the material list coefficient of node v g , L g (t) is the load of node v g at time t; the loss received by node v o is w go (t) is the weight on the directed edge e go at time t, D g is the set of downstream neighbor nodes of node v g , w gp (t) is the weight on the directed edge e gp at time t; the logistics on the directed edge e go is updated to m go (t + 1)=0, and the weight on the directed edge e oq is updated to w go (t + 1)=0;

[0033] Step 2: The load of node v o at time t + 2 is updated to If L o (t + 2)≥C o , then node v o is under - loaded; if L o (t + 2)<C o , then node v o fails, and the load is further updated to L o (t + 2)=0; where C o represents the lower limit of the load capacity of node v o ;

[0034] Step 3: ① When node v o is under - loaded, it transmits the loss to downstream neighbor nodes according to the bearing capacity;

[0035] ② When node v o fails, it transmits the loss to downstream neighbor nodes according to the supply - demand relationship;

[0036] Step 4: Repeat Step 2 and Step 3 until the load loss is transmitted to the neighbor nodes of the last layer.

[0037] Preferably, the method of transmitting the loss to the downstream neighbor nodes according to the bearing capacity in Step 3 is: the total transmitted loss is λ o is the material unit coefficient of node v o ; the loss received by node v q is R q (t + 1) = L q (t) - C q is the bearing capacity of node v q at time t + 1, L q (t) is the load of node v q at time t, C q is the lower limit of the load capacity of node v q , D o is the set of downstream neighbor nodes of node v o , R r (t + 1) is the bearing capacity of node v r at time t + 1; if the loss received by node v q is then let and still allocate the load for the remaining loss according to the bearing capacity of the remaining nodes; the logistics on the directed edge e oq is updated to the logistics on the directed edge e oq is updated to m oq (t + 1) represents the logistics on the directed edge e oq at time t + 1, D o is the set of downstream neighbor nodes of node v o ;

[0038] The method of transmitting the loss to the downstream neighbor nodes according to the supply and demand relationship in Step 3 is: the total transmitted loss is λ o is the material unit coefficient of node v o , where the loss received by node v q is w oq (t + 1) is the weight on the directed edge e oq at time t + 1, D o is the set of downstream neighbor nodes of node v o , w or (t + 1) is the weight on the directed edge e orThe weight on; the directed edge e oq The logistics on is updated to m oq (t + 2) = 0, the directed edge e oq The weight on is updated to w oq (t + 2) = 0.

[0039] Preferably, the operation efficiency is used to measure the impact of load loss propagation on the product supply chain network, and the operation efficiency at time t is where L l (0) and L l (t) respectively represent the initial load and the load at time t of the node v l of.

[0040] Compared with the prior art, the beneficial effects of the present invention are:

[0041] (1) The present invention comprehensively considers the global and local factors of the network to measure the intensity of the supply-demand relationship, defines the initial load according to the supply-demand relationship intensity of the enterprise and the logistics balance constraint, and sets the lower limit of the load capacity according to the heterogeneity characteristics of the enterprise. It is more in line with the actual situation in these three aspects, enabling managers to accurately and objectively evaluate the potential cascading failure propagation risk of the product supply chain network, and thus formulate effective management prevention measures, with high application value.

[0042] (2) The present invention reveals the impact of network parameters on cascading failure propagation from a more realistic perspective: increasing the heterogeneity of the supply-demand relationship can improve the robustness of the network to cascading failures; reducing the heterogeneity of the lower limit of the load capacity can improve the robustness of the network to cascading failures; the loss caused by allocating the load according to the bearing capacity can improve the robustness of the network to cascading failures; enhancing the core competitiveness of enterprises is always an effective means to improve the robustness of the network to cascading failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0044] Figure 1 is the flowchart of the present invention.

[0045] Figure 2 is a schematic diagram of the "layer" in the product supply chain network.

[0046] Figure 3 is the schematic diagram I of the global step-by-step load loss propagation downstream.

[0047] Figure 4 Schematic diagram II of the global step-by-step load loss propagation to the downstream

[0048] Figure 5 Schematic diagram III of the global step-by-step load loss propagation to the downstream

[0049] Figure 6 Simulation diagram of the influence of the weight adjustable parameter α of the present invention on cascading failure

[0050] Figure 7 Simulation diagram of the influence of the tolerance parameter β of the present invention on cascading failure

[0051] Figure 8 Simulation diagram of the influence of the capacity adjustable parameter γ of the present invention on cascading failure

[0052] Figure 9 Comparison diagram of the global load distribution of the failed nodes and the nearest neighbor load distribution of the present invention

[0053] Figure 10 Comparison diagram of the load distribution of the underloaded nodes according to the bearing capacity and the load distribution according to the service relationship of the present invention Detailed implementation manners

[0054] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0055] As Figure 1 shown, a method for constructing an underload failure propagation model for a product supply chain network includes the following steps:

[0056] Step 1: Construct a complex network according to the business relationships between enterprises in the product supply chain network, map the enterprises to the nodes in the network, map the supply and demand relationships between enterprises to directed edges, and map the intensity of the supply and demand relationships to the weights of the directed edges. Measure the intensity of the supply and demand relationships according to global factors and local factors.

[0057] Describe the product supply chain network with the complex network G = {V, A, E, W}, where V = {v1, v2,..., v n} represents the node set, and n is the number of nodes; A = (a ij ) n×n represents the adjacency matrix. If there is a directed edge between node v i and node v j , then the element a ij = 1; otherwise, the element a ij= 0; E = {e ij | a ij = 1} represents the set of directed edges, and e ij represents the node v i and the node v j between the directed edge; W = {w ij | a ij = 1} represents the set of weights of the directed edges, and w ij is the weight of the directed edge e ij .

[0058] The initial weight w of the directed edge e is calculated by using the global factor - edge betweenness and the local factor - node degree ij (0) = (B ij k ij K i ) j . Here, α is the betweenness of the directed edge e , where P(v ij , v b ) represents the number of shortest paths between the node v c and the node v b , and P(v c , v b , e c ) represents the number of shortest paths passing through the directed edge e ij among the shortest paths between the node v b and the node v c . ij is the degree of the node v i , where, is the in - degree and is equal to the sum of the elements in the i - th column of the adjacency matrix A, and the corresponding nodes form the set U i of the upstream neighbor nodes of the node v i ; is the out - degree and is equal to the sum of the elements in the i - th row of the adjacency matrix A, and the corresponding nodes form the set D i of the downstream neighbor nodes of the node v i ; k j is the degree of the node v j ; α is an adjustable parameter for controlling the weight of the directed edge.

[0059] The degree is a local index of the network. The initial weight w ij (0) = (k i k j ) α that only considers the degrees of neighbor nodes cannot take into account the edges of important nodes with small degrees. The betweenness is a global index of the network. The larger the edge betweenness, the more important the position of the edge in the network. The edges connected to important nodes usually play important roles in network transmission, wij (0) = (B ij k i k j ) α can make up for the deficiency of w ij (0) = (B ij k i k j ) α . In addition, w ij (0) = (B ij k i k j ) α combines the global and local factors of the network, which is more comprehensive.

[0060] Step 2: Take logistics as the load flowing in the product supply chain network, and define the initial load of nodes layer by layer according to the intensity of the supply-demand relationship of the enterprise and the logistics balance constraint.

[0061] Logistics is a general term for the material flow of raw materials, parts, semi-finished products, finished products, etc. of products. Then, what is transmitted in the product supply chain network is logistics. The starting point of the network corresponds to the raw material supplier, and the logistics flowing out of it is taken as the load; the end point of the network corresponds to the user, and the logistics flowing into it is taken as the load; the intermediate nodes in the network receive the upstream logistics, and after processing and manufacturing, they are transmitted to the downstream, and the logistics flowing into it is taken as the load. For the intermediate node v d , the inflowing logistics is the outflowing logistics is Then the two satisfy the logistics balance constraint where λ d is the material list coefficient of node v d , indicating that one unit of material output is obtained when λ d units of materials flow into v d .

[0062] Define the initial load of nodes based on the concept of "layer". Nodes with the same function in the network (enterprises corresponding to the same business) are called "layers" of the network. As Figure 2 shown, the product supply chain network contains a total of T layers, and there is also a supply-demand relationship between adjacent layers. Assume that the product supply chain network adopts a pull production method, that is, the demand for products by users in the T-th layer is known, and the product supply chain network manufactures products according to market demand.

[0063] Randomly assign the initial load of nodes in the T-th layer. For example, the initial load of node v z is L z (0). Calculate the initial logistics on the directed edge between nodes in the (T - 1)-th layer and the T-th layer according to the intensity of the supply-demand relationship. For the node v z in the T-th layer and its upstream neighbor node v in the (T - 1)-th layerx , the initial logistics on the directed edge e xz is:

[0064]

[0065] Among them, w xz (0) and w uz (0) are the initial weights of the directed edges e xz and the directed edge e uz respectively. U z is the set of upstream neighbor nodes of the node v z . The node v uz on the directed edge e u represents the node in the set of upstream neighbor nodes U z .

[0066] Then the initial logistics flowing out of the upstream neighbor node v x is:

[0067]

[0068] Among them, m xy (0) is the initial logistics on the directed edge e xy . D x is the set of downstream neighbor nodes of the node v x . The logistics flowing out of the node v x is equal to the sum of the logistics on each of its out-going edges. y ∈ D x represents any point in the set of downstream neighbor nodes of the node v x .

[0069] From Figure 2 , it is known that assuming the initial loads of the last layer v y and v z etc. are known, according to the weights on the directed edges, the logistics m xy (0), m xz (0) and m uz (0) etc. can be obtained. Then the logistics flowing out of the node v x in the T - 1 layer is equal to the sum of the logistics on each of its out-going edges. Then, according to the bill of materials coefficient, the logistics flowing into the node v x can be obtained, that is, the initial load of v x . In this way, the initial loads of the nodes in each layer are gradually obtained forward.

[0070] According to the logistics balance constraint, the initial logistics flowing into the node v x is:

[0071]

[0072] Among them, λx For node v x The material list coefficient of, indicating v x Flows into λ x When λ units of materials flow in, one unit of material output is obtained.

[0073] Finally, the initial load of node v x is In this way, the initial loads of all nodes in the (T - 1)-th layer are obtained.

[0074] Similarly, according to the strength of the supply - demand relationship, the initial logistics on the directed edges between the nodes in the (T - 2)-th layer and the (T - 1)-th layer are calculated, and the initial loads of all nodes in the (T - 2)-th layer are obtained. In this way, the initial loads of the nodes in each layer are gradually obtained forward. The initial load of the nodes in the first layer is the initial logistics flowing out of them.

[0075] In the actual product supply chain network, assume that enterprise J has two supplier enterprises I and K. If the supply of enterprise I to enterprise J is M, then after enterprise I fails, the supply loss of enterprise J is M (at this time, enterprise J still has the supply from enterprise K). Conversely, after enterprise J fails, the demand loss of enterprise I is also M.

[0076] The initial load defined based on the node degree has the following problems in the process of failure load redistribution because it does not consider the strength of the supply - demand relationship of enterprises and the logistics balance constraint: After node v i fails, the load assigned to the neighbor node v j is not equal to the load assigned to v j after v i fails, and the load assigned to v i after v j fails is greater than the total load of v j in some cases. The method designed in the present invention can solve these problems and be consistent with the actual situation.

[0077] Step 3: According to the heterogeneous characteristics of enterprises, calculate the lower limit of the load capacity of nodes from a non - linear perspective.

[0078] In the actual product supply chain network, the production of enterprises is restricted by fixed costs (such as equipment depreciation, house rent, and employee salaries). If the supply or demand of an enterprise is too small to cover the fixed costs, the enterprise will be in a loss-making state and may choose to shut down. Therefore, when an enterprise operates normally, its load should be higher than a certain limit, which is called the lower limit of load capacity. If it is lower than this limit, it will fail. For the sake of simplicity, it is generally assumed that the lower limit of the load capacity of a node is proportional to the initial load, but this assumption does not conform to the actual situation, which is manifested as follows: Enterprises have heterogeneity in terms of production scale, business relationships, etc. Enterprises with a large production scale and extensive business relationships usually have advanced mechanical equipment, skilled labor, higher management and scheduling capabilities, etc., thus forming economies of scale and enabling them to have lower costs. That is, the lower limit of the load capacity of a node and the initial load should be a non-linear relationship, and linearity is a special case of non-linearity.

[0079] For node v x , its lower limit of load capacity is

[0080]

[0081] where L max (0) is the maximum initial load of n nodes, β (0 < β ≤ 1) is the tolerance parameter, and γ (γ ≥ 0) is the capacity adjustable parameter. When γ = 1, the relationship between the lower limit of the load capacity and the initial load degenerates into a linear relationship.

[0082] Step 4: Use the scenario method to simulate that enterprises in the product supply chain network encounter emergencies, resulting in the failure of corresponding nodes.

[0083] Suppose enterprises encounter random or deliberate emergencies such as fires, earthquakes, and terrorist attacks, which prevent them from normal production. Specifically, assume that several nodes encounter emergencies at time t and fail at time t + 1. Losses occur at time t, and the load is updated at time t + 1, which can clearly represent the "gradual propagation behavior of load losses".

[0084] Step 5: The failure of nodes causes load losses, and the losses propagate bidirectionally along the supply and demand directions; among them, they propagate step by step downward until the last layer and step by step upward until the first layer; during the propagation of load losses, the failed nodes distribute the load according to the supply and demand relationship, and the underloaded nodes distribute the load according to their bearing capacity.

[0085] The load loss propagates bidirectionally along the supply-demand direction and is a global behavior of gradual propagation. After a node fails, the load loss of its upstream neighbor nodes is manifested as a reduction in its logistics demand, and the load loss of its downstream neighbor nodes is manifested as a reduction in its logistics supply. The reduction in demand upstream is transmitted all the way to the first layer, and the reduction in supply downstream is transmitted all the way to the last layer. The load loss propagation upstream is similar to that downstream. Taking the load loss propagation downstream as an example, as Figure 3 shown, its gradual propagation is manifested as follows: Node v g suffers a loss at time t and propagates the loss to its downstream neighbor node v o at time t + 1; After node v o suffers a loss at time t + 1, it propagates the loss to its downstream neighbor node v q at time t + 2. In this process, it also involves the update of node load and status, as well as the update of logistics and weights on the directed edges between nodes.

[0086] Assume that an emergency causes a loss g to node v at time t, causing node v g to fail at time t + 1. Node v g starts to gradually propagate the load loss to its downstream neighbor nodes from time t + 1, that is, allocates the load to the downstream neighbor nodes. As Figure 4 shown, the steps are as follows:

[0087] Step 1: The failed node v g transmits the loss to its downstream neighbor nodes according to the supply-demand relationship at time t + 1, and the total loss transmitted is where λ g is the bill of materials coefficient of node v g , L g (t) is the load of node v g at time t; The loss suffered by node v o is w go (t) is the weight on the directed edge e go at time t, D g is the set of downstream neighbor nodes of node v g , w gp (t) is the weight on the directed edge e gp at time t, and the logistics on the directed edge e go is updated to m go (t + 1) = 0, and the weight is updated to w go (t + 1) = 0.

[0088] Step 2: The load of node v o at time t + 2 is updated to If Lo (t + 2) ≥ C o , then node v o is underloaded; if L o (t + 2) < C o , then node v o fails, and the load is further updated to L o (t + 2) = 0; where C o represents the lower limit of the load capacity of node v o .

[0089] Step 3: ① When node v o is underloaded, it transfers the loss to its downstream neighbor nodes according to the bearing capacity. The total loss transferred is λ o is the material list coefficient of node v o ; the loss suffered by node v q is R q (t + 1) = L q (t) - C q is the bearing capacity of node v q at time t + 1, that is, the maximum loss that can be tolerated to maintain operation; D o is the set of downstream neighbor nodes of node v o . If , then let and the remaining loss is still distributed according to the bearing capacity of the remaining nodes; the logistics on the directed edge e oq is updated to and the weight is updated to m oq (t + 1) represents the logistics on the directed edge e oq at time t + 1, and D o is the set of downstream neighbor nodes of node v o .

[0090] ② When node v o fails, it transfers the loss to its downstream neighbor nodes according to the supply and demand relationship. The total loss transferred is λ o is the material list coefficient of node v o , where the loss suffered by node v q is w oq (t + 1) is the weight on the directed edge e oq at time t + 1, and D o is the set of downstream neighbor nodes of node v o ; the logistics on the directed edge e oq is updated to m oq(t + 2) = 0, and the weight is updated to w oq (t + 2) = 0.

[0091] Step 4: Repeat Step 2 and Step 3 until the loss is propagated to the neighbor nodes of the last layer.

[0092] The existing load reallocation, i.e., load loss propagation, is mainly divided into two categories: nearest neighbor allocation and global allocation.

[0093] When using the nearest neighbor allocation, only the failed node and its neighbor nodes are considered. That is, the failed node propagates the loss to the neighbor nodes according to the supply-demand relationship. If the neighbor node fails, the propagation continues; otherwise, it stops. This does not conform to the actual situation. In fact, the load loss is propagated globally. That is, after a neighbor node suffers a loss, it will continue to propagate the loss to its neighbor nodes. For example Figure 3 in, node v g propagates the loss to the downstream neighbor node v o After node v o suffers a loss, it will continue to propagate the loss to its downstream neighbor node v q More importantly, there is a situation where node v o is damaged but not failed while node v q is damaged and failed. This situation cannot be described by the nearest neighbor allocation.

[0094] When using global allocation, the load loss spreads throughout the network at the same time, which is an instantaneous propagation behavior, which is inconsistent with Figure 3 the described real step-by-step propagation behavior. In addition, when using global allocation, the loss is propagated to the neighbor nodes according to the supply-demand relationship, without considering the situation where the underloaded node can flexibly propagate the loss. For example Figure 5 as shown, the numerical value on the directed edge represents the logistics on the edge; assume that the material list coefficient λ o of node v o = 1, then the logistics flowing into node v o and the logistics flowing out are both 70; if node v g fails, then the lost logistics of node v o is 40; assume that at this time node v o is not failed, i.e., underloaded, then node v o can flexibly propagate the loss to node v q and node v r such as propagating 15 and 25, 10 and 30, etc. The maximum loss that an enterprise can bear to maintain operation is called the carrying capacity of the node. Then, preferentially transmitting the loss to the neighbor nodes according to the carrying capacity can protect the neighbor nodes to the greatest extent.

[0095] Figure 3 and Figure 4The described global step-by-step load redistribution can make up for the deficiencies of the existing load redistribution mentioned above.

[0096] The impact of load loss propagation on the product supply chain network is measured using operational efficiency. The operational efficiency at time t is defined as where L l (0) and L l (t) represent the initial load and the load at time t of node v l respectively.

[0097] Step 6: If new node failures are triggered during the load loss propagation process, continue to return to Step 5 and propagate the loss according to the above mechanism until no more nodes in the entire network fail due to underloading, at which point the cascading failure ends. The present invention actually proposes an underloading failure propagation model, which mainly includes three parts: initial load, capacity limit, and load redistribution, corresponding to Step 2, Step 3, and Step 5 respectively. Specific embodiment:

[0099] Considering that the product supply chain network has a scale-free property, a scale-free network is used as an example to further illustrate the present invention. The specific implementation steps of a method for constructing an underloading failure propagation model for a product supply chain network are as follows:

[0100] Step 1: Construct a scale-free product supply chain network

[0101] Construct a scale-free network G = {V, A, E, W} with 10 layers, where V contains 300 nodes; E contains 1000 directed edges; the adjacency matrix A is a 300×300 square matrix. If there is a directed edge from node v i to v j , then a ij = 1, otherwise a ij = 0; W represents the set of weights of the directed edges. If a ij = 1, then the corresponding initial weight w ij (0) = (B ij k i k j ). Here α . Here is the betweenness of the directed edge e ij . Among them, P(v b , v c ) represents the number of shortest paths between node v b and v c , and P(v b , v c , e ij ) represents the number of shortest paths passing through the directed edge e ij among the above paths. is the degree of node vi The degree of is the in-degree and is equal to the sum of the elements in the \(i\)-th column of \(A\). The corresponding nodes form \(v\)'s i set of upstream neighbor nodes \(U\) i ; is the out-degree and is equal to the sum of the elements in the \(i\)-th row of \(A\). The corresponding nodes form \(v\)'s i set of downstream neighbor nodes \(D\) i ; \(k\) j is the degree of node \(v\) j ; \(\alpha\) is an adjustable parameter that controls the weight of the directed edge.

[0102] Step 2: Calculate the initial load of the nodes.

[0103] Randomly assign the initial load to the nodes in the 10th layer. For example, the initial load of node \(v\) z is \(L\) z (0). Calculate the initial logistics on the directed edge between the nodes in the 10th layer and the 9th layer according to the supply-demand relationship strength. For node \(v\) z in the 10th layer and its upstream neighbor node \(v\) x in the 9th layer, the initial logistics on the directed edge \(e\) xz is

[0104]

[0105] where \(w\) xz (0) and \(w\) uz (0) are the initial weights of the directed edges \(e\) xz and \(e\) uz respectively, and \(U\) z is the set of upstream neighbor nodes of \(v\) z .

[0106] Then the initial logistics flowing out of node \(v\) x is

[0107]

[0108] where \(m\) xy (0) is the initial logistics on the directed edge \(e\) xy , and \(D\) x is the set of downstream neighbor nodes of \(v\) x .

[0109] According to the logistics balance constraint, the initial logistics flowing into node \(v\) x is

[0110]

[0111] where \(\lambda\) x is the bill of materials coefficient of node \(v\) x , indicating \(v\)x Inflow λ x Receiving λ units of material to obtain one unit of material output, where λ is a number greater than zero. It can be an integer or a decimal, and the value does not affect the result of loss propagation.

[0112] Finally, the initial load of node v x is In this way, the initial loads of all nodes in the 9th layer are obtained.

[0113] Similarly, according to the strength of the supply-demand relationship, calculate the initial logistics on the directed edges between the nodes in the 9th layer and the 8th layer, and obtain the initial loads of all nodes in the 8th layer. In this way, the initial loads of nodes in each layer are gradually obtained forward. The initial load of the nodes in the 1st layer is the initial logistics flowing out of them.

[0114] Step 3: Calculate the lower limit of the load capacity of the nodes.

[0115] For node v x , its lower limit of the load capacity is

[0116]

[0117] where L max (0) is the maximum initial load of 300 nodes, β (0 < β ≤ 1) is the tolerance parameter, and γ (γ ≥ 0) is the capacity adjustable parameter.

[0118] Step 4: Use the scenario method to simulate node failures

[0119] At time t = 1, attack the top 10 nodes with the largest loads in the network, causing them to fail at time t = 2.

[0120] Step 5: The load loss caused by node failures propagates bidirectionally along the supply-demand direction.

[0121] Combined with Figure 4 , taking the load loss propagation downstream as an example for illustration. Suppose node v g is attacked at time t = 1 and fails at time t = 2, and starts to gradually propagate the load loss to the downstream neighbor nodes. The steps are as follows:

[0122] Step 1: Node v g transmits the loss to the downstream neighbor nodes according to the supply-demand relationship at time t = 2, and the total transmitted loss is (λ g is the bill of materials coefficient of node v g ), where the loss received by node v o is w go (1) is the directed edge e at time t = 1 goThe weight on D g is the set of downstream neighbor nodes of node v g , and the logistics on the directed edge e go is updated to m go (2) = 0, and the weight is updated to w go (2) = 0.

[0123] Step 2: The load of node v o at time t = 3 is updated to If L o (3) ≥ C o , then node v o is underloaded; if L o (3) < C o , then node v o fails, and the load is further updated to L o (3) = 0.

[0124] Step 3: ① When node v o is underloaded, it transfers the loss to the downstream neighbor nodes according to its carrying capacity, and the total transferred loss is (λ o is the bill of materials coefficient of node v o ), where the loss suffered by node v q is R q (2) = L q (1) - C q is the carrying capacity of node v q at time t = 2, that is, the maximum loss that can be tolerated to maintain operation; if then let and the remaining loss is still distributed according to the carrying capacity of the remaining nodes; the logistics on the directed edge e oq is updated to and the weight is updated to

[0125] ② When node v o fails, it transfers the loss to the downstream neighbor nodes according to the supply-demand relationship, and the total transferred loss is (λ o is the bill of materials coefficient of node v o ), where the loss suffered by node v q is w oq (2) is the weight on the directed edge e oq at time t = 2, D o is the set of downstream neighbor nodes of node v o ; the logistics on the directed edge e oq is updated to moq (3) = 0, the weight is updated to w oq (3) = 0.

[0126] Step 4: Repeat Step 2 and Step 3 until the loss is propagated to the neighbor nodes of the 10th layer.

[0127] The impact of load loss propagation on the product supply chain network is measured by operational efficiency. The operational efficiency at time t is defined as

[0128] Step 6: If new node failures are triggered during the load loss propagation process, continue to propagate the loss according to the above mechanism until no more nodes in the entire network fail due to underloading, at which point the cascading failure ends. The evolution of the operational efficiency F(t) during this period can reflect the changes in the state of the product supply chain network. The following is a further explanation in combination with Figures 6 - 10 for further illustration.

[0129] Figure 6 is the simulation diagram of the impact on cascading failure when the adjustable parameter α of the weight takes different values. From Figure 6 it can be seen that the operational efficiency of the network increases with the increase of the adjustable parameter α. The larger the adjustable parameter α, the stronger the heterogeneity of the supply-demand relationship intensity, indicating that increasing the heterogeneity of the supply-demand relationship can improve the robustness of the network to cascading failure.

[0130] Figure 7 is the simulation diagram of the impact on cascading failure when the tolerance parameter β takes different values. From Figure 7 it can be seen that the operational efficiency of the network increases with the increase of the tolerance parameter β. The larger the tolerance parameter β, the smaller the lower limit of the load capacity, and the less likely the enterprise is to fail. At the same time, the larger the tolerance parameter β, the stronger the core competitiveness of the enterprise.

[0131] Figure 8 is the simulation diagram of the impact on cascading failure when the capacity adjustable parameter γ takes different values. From Figure 8 it can be seen that the operational efficiency of the network decreases with the increase of the capacity adjustable parameter γ. The larger the capacity adjustable parameter γ, the stronger the heterogeneity of the lower limit of the load capacity, indicating that reducing the heterogeneity of the lower limit of the load capacity can improve the robustness of the network to cascading failure.

[0132] Figure 9 is the comparison diagram of the global load distribution of the failed nodes proposed by the present invention and the nearest neighbor load distribution in the prior art. From Figure 9 it can be seen that under the same initial conditions, the loss caused by the nearest neighbor load distribution is smaller, because it ignores the situation that the neighbor nodes of the failed nodes may further trigger failures, which will mislead the decision-making of enterprise managers.

[0133] Figure 10This is a comparison chart of load distribution of underloaded nodes according to bearing capacity proposed by the present invention and load distribution according to business relationships in the prior art. From Figure 10 It can be seen that under the same initial conditions, the loss caused by load distribution according to bearing capacity is smaller, which helps to improve the robustness of the network to cascading failures.

[0134] The present invention constructs a complex network based on the business relationships between enterprises in the product supply chain network, where nodes represent enterprises, directed edges represent the supply-demand relationships between enterprises, and the intensity of the supply-demand relationship, i.e., the weight of the directed edge, is comprehensively measured through the global factors and local factors of the network; defines the initial load of the nodes according to the intensity of the supply-demand relationship between enterprises and the logistics balance constraint; sets the lower limit of the load capacity of the nodes according to the heterogeneity characteristics of the enterprises; uses the scenario method to simulate that enterprises in the product supply chain network encounter emergencies resulting in the failure of the corresponding nodes; the failure of the nodes causes load loss and propagates the loss bidirectionally along the supply-demand direction to the whole, and in this process, the failed nodes distribute the load according to the supply-demand relationship, and the underloaded nodes distribute the load according to the bearing capacity; if new node failures are triggered during the propagation of the load loss, the loss continues to be gradually propagated to the whole until no node in the whole network fails due to underloading, and the cascading failure ends. Compared with the prior art, the present invention has clear logic and is closer to the actual situation, and can provide better decision-making for the supply chain management of enterprises.

[0135] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for constructing an underload failure propagation model for a product supply chain network, characterized in that The steps are as follows: Step 1: Construct a complex network based on the business relationships among enterprises in the product supply chain network. Map enterprises to nodes in the network, map the supply-demand relationships among enterprises to directed edges, and map the intensity of the supply-demand relationships to the weights of the directed edges. Measure the intensity of the supply-demand relationships according to global factors and local factors. Step 2: Regard logistics as the load flowing in the product supply chain network, and define the initial load of nodes layer by layer according to the intensity of the supply-demand relationships of enterprises and the logistics balance constraint. Step 3: Calculate the lower limit of the load capacity of nodes from a non-linear perspective according to the heterogeneous characteristics of enterprises. Step 4: Use the scenario method to simulate the failure of corresponding nodes in the product supply chain network due to emergencies encountered by enterprises. Step 5: The node failure causes load loss, and the load loss propagates bidirectionally along the supply-demand direction; among them, it propagates layer by layer downward until the last layer, and propagates layer by layer upward until the first layer; during the propagation of the load loss, the failed nodes distribute the load according to the supply-demand relationship, and the underloaded nodes distribute the load according to the bearing capacity. Step 6: If new node failures are triggered during the propagation of the load loss, then return to Step 5 again, and according to the bidirectional propagation mechanism of the load loss, until no more nodes in the entire network fail due to underloading, and at this time the cascading failure ends.

2. The method for constructing an underload failure propagation model for a product supply chain network according to claim 1, wherein The complex network is \(G = \{V, A, E, W\}\), where \(V=\{v_1, v_2, \ldots, v\) n \} represents the set of nodes, and \(n\) is the number of nodes; \(A=(a\) ij ) n×n represents the adjacency matrix. If there is a directed edge between node \(v\) i and node \(v\) j , then the element \(a\) ij = 1; otherwise, the element \(a\) ij = 0; \(E = \{e\) ij |a ij = 1\} represents the set of directed edges, and \(e\) ij represents the directed edge between node \(v\) i and node \(v\) j ; \(W = \{w\) ij |a ij = 1\} represents the set of weights of directed edges, and \(w\) ij is the weight of the directed edge \(e\) ij .

3. The method for constructing an underload failure propagation model for a product supply chain network according to claim 2, wherein, Calculate the initial weight w of the directed edge e using the global factor - betweenness centrality and the local factor - node degree ij of ij (0)=(B ij k i k j ) α ; where is the betweenness centrality of the directed edge e ij , P(v b , v c ) represents the number of shortest paths between node v b and node v c , and P(v b , v c , e ij ) represents the number of shortest paths passing through the directed edge e b in the shortest paths between node v c and node v ij ; is the degree of node v i , where is the in - degree and is equal to the sum of the elements in the i - th column of the adjacency matrix A, and the corresponding nodes form the set U i of the upstream neighbor nodes of node v i ; is the out - degree and is equal to the sum of the elements in the i - th row of the adjacency matrix A, and the corresponding nodes form the set D i of the downstream neighbor nodes of node v i ; k j is the degree of node v j ; α is an adjustable parameter that controls the weight of the directed edge.

4. The method for constructing an underload failure propagation model for a product-oriented supply chain network according to claim 2 or 3, characterized in that, The method for determining the initial load in Step 2 is: The product supply chain network consists of a total of T layers. Randomly assign the initial load of node v at the T-th layer as L(0). Calculate the initial logistics on the directed edge between the nodes at the (T - 1)-th layer and the T-th layer according to the strength of the supply-demand relationship: For node v at the T-th layer and its upstream neighbor node v at the (T - 1)-th layer, the initial logistics on the directed edge e between them is: z z (0); z x xz ​​​​ where, w xz (0) and w uz (0) are the initial weights of the directed edges e xz and the directed edge e uz respectively, U z is the set of upstream neighbor nodes of the node v z ; the node v uz on the directed edge e u represents the node in the set of upstream neighbor nodes U z ; Then the initial logistics flowing out of the upstream neighbor node v x is as follows: where m xy (0) is the initial logistics on the directed edge e xy , D x is the set of downstream neighbor nodes of the node v x ; According to the logistics balance constraint, the initial logistics flowing into node v x is as follows: Among them, λ x is the material list coefficient of node v x , indicating that when v x flows into λ x units of materials, one unit of material output is obtained; Then the initial load of the node v at the (T - 1)-th layer x is In this way, the initial loads of all nodes at the (T - 1)-th layer are obtained; Similarly, calculate the initial logistics on the directed edge between the nodes of the (T - 2)-th layer and the (T - 1)-th layer according to the intensity of the supply-demand relationship, and obtain the initial load of all nodes in the (T - 2)-th layer; thus, gradually obtain the initial load of nodes in each layer forward, and the initial load of the nodes in the first layer is the initial logistics flowing out of it.

5. The method for constructing an underload failure propagation model for a product supply chain network according to claim 2 or 4, characterized in that, The calculation method for the lower limit of the load capacity of the nodes is: Node v x has a lower limit of load capacity of Among them, L max (0) is the maximum initial load of n nodes, β is the tolerance parameter and 0 < β ≤ 1, γ is the capacity adjustable parameter and γ ≥ 0; L x (0) is the initial load of node v x of.

6. The method for constructing an underload failure propagation model for a product supply chain network according to claim 5, characterized in that In Step 5, the load loss propagates bidirectionally along the supply-demand direction. After the node fails, the load loss of the upstream neighbor node is manifested as a decrease in the logistics demand for it, and the decrease in the demand upstream is transmitted all the way to the first layer. The load loss of the downstream neighbor node is manifested as a decrease in the logistics supply for it, and the decrease in the supply downstream is transmitted all the way to the last layer.

7. The method for constructing an underload failure propagation model for a product supply chain network according to claim 6, characterized in that The downstream load loss propagation is a step-by-step propagation, and the method is as follows: Node v g suffers a loss at time t and propagates the loss to its downstream neighbor node v o at time t + 1; After node v o suffers a loss at time t + 1, it propagates the loss to its downstream neighbor node v q at time t + 2. During this process, updates of node loads and states, as well as updates of logistics and weights on the directed edges between nodes, are also involved.

8. The method for constructing an underload failure propagation model for a product supply chain network according to claim 7, wherein Suppose that an emergency causes node v to suffer losses at time t g suffer losses causes node v g to fail at time t + 1. Node v g starts to gradually spread the load loss to its downstream neighbor nodes from time t + 1, that is, allocates the load to its downstream neighbor nodes. The steps are as follows: Step 1: The failed node v g At time t+1, transfer the loss to the downstream neighbor nodes according to the supply-demand relationship. The total transferred loss is where λ g is the material list coefficient of node v g , L g (t) is the load of node v g at time t; the loss received by node v o is w go (t) is the weight on the directed edge e go at time t, D g is the set of downstream neighbor nodes of node v g , w gp (t) is the weight on the directed edge e gp at time t; the logistics on the directed edge e go is updated to m go (t+1) = 0, and the weight on the directed edge e oq is updated to w go (t+1) = 0; Step 2: Node v o The load at time t + 2 is updated to If L o (t + 2) ≥ C o , then node v o is underloaded; if L o (t + 2) < C o , then node v o fails, and the load is further updated to L o (t + 2) = 0; where C o represents the lower limit of the load capacity of node v o . Step 3: ① When node v o is underloaded, transfer the loss to downstream neighbor nodes according to the bearing capacity; ②When node v o fails, the loss is passed to the downstream neighbor nodes according to the supply-demand relationship; Step 4: Repeat Step 2 and Step 3 until the load loss reaches the neighbor nodes of the last layer.

9. The method for constructing an underload failure propagation model for a product supply chain network according to claim 8, wherein The method of transmitting losses to downstream neighbor nodes according to the carrying capacity in Step 3 is as follows: The total transmitted loss is λ o which is the material list coefficient of node v o ; the loss suffered by node v q is R q (t + 1) = L q (t) - C q where R q (t + 1) is the carrying capacity of node v at time t + 1, L q (t) is the load of node v q at time t, C q is the lower limit of the load capacity of node v q , D o is the set of downstream neighbor nodes of node v o , R r (t + 1) is the carrying capacity of node v r at time t + 1; if the loss suffered by node v q is then let and still distribute the remaining load according to the carrying capacity of the remaining nodes; the logistics on the directed edge e oq is updated to The logistics on the directed edge e oq and the weight on it are updated to m oq (t + 1) represents the logistics on the directed edge e oq at time t + 1, D o is the set of downstream neighbor nodes of node v o ; The method of transmitting losses to downstream neighbor nodes according to the supply-demand relationship in Step 3 is as follows: The total loss to be transmitted is λ o which is the bill of materials coefficient of node v o , where the loss suffered by node v q is w oq (t + 1) is the weight on the directed edge e oq at time t + 1, D o is the set of downstream neighbor nodes of node v o , w or (t + 1) is the weight on the directed edge e or at time t + 1; the logistics on the directed edge e oq is updated to m oq (t + 2) = 0, and the weight on the directed edge e oq is updated to w oq (t + 2) = 0.

10. The method for constructing an underload failure propagation model for a product supply chain network according to claim 9, wherein Use the operation efficiency to measure the impact of the load loss propagation on the product supply chain network. The operation efficiency at time t is Among them, L l (0) and L l (t) respectively represent the initial load and the load at time t of node v l .

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