A supply chain network optimization method and device based on risk grading propagation and dynamic recovery

Abstract

The application belongs to the technical field of supply chain management and risk control, and particularly relates to a supply chain network optimization method based on risk grading propagation and dynamic recovery. The method proposes a supply chain risk propagation and recovery model based on complex network theory and an optimization method thereof. A supply chain model based on a supply chain network topological structure is first constructed, a supply chain network topological structure G=(V, E) is composed of N nodes and E edges, each node represents an enterprise in the supply chain network, and each edge represents a supply chain business relationship between enterprises. Then, the risk of each enterprise in the supply chain is simulated by using the supply chain model, and based on the simulation result, the enterprises in the supply chain are optimized. The application is used for simulating the risk propagation dynamics between enterprises and optimizing the network structure, and improving the overall resilience and anti-risk ability of the supply chain network.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of supply chain management and risk control, and particularly relates to a supply chain network optimization method and equipment based on risk hierarchical propagation and dynamic recovery. BACKGROUND

[0002] As a complex system, the supply chain network is composed of enterprise nodes and their interconnections, with high interconnectivity and complexity. The main challenge it faces is the rapid propagation and spread of risks, which may lead to local failure evolving into systemic failure. Existing research usually uses epidemic models (such as SIR, SIS model) to simulate the propagation of supply chain risks, but has the following limitations: 1. Ignoring the heterogeneity of enterprise nodes: failing to fully consider the impact of enterprise size, risk resistance ability and other attributes on risk propagation; 2. Lack of multi-level risk classification: using only a single infection state, which is difficult to reflect the complexity of risk propagation; 3. Insufficient dynamic adjustment mechanism: lacking reasonable optimization for network reconnection strategy after disconnection. SUMMARY

[0003] To solve the above problems, the application aims to propose a multi-state risk propagation model combined with complex network theory, and introduce a dynamic adjustment strategy based on network topology attributes to enhance the anti-risk ability of the supply chain network, which can be used to simulate the dynamic propagation of risks between enterprises and optimize the network structure, and improve the overall resilience and anti-risk ability of the supply chain network.

[0004] The application provides a supply chain network optimization method based on risk hierarchical propagation and dynamic recovery, comprising the following steps:

[0005] S1. Constructing a supply chain model based on the topology structure of the supply chain network, comprising the following steps

[0006] Constructing a supply chain network topology structure G=(V, E) composed of N nodes and E edges, V being the node set and E being the edge set; wherein each node represents an enterprise in the supply chain network; each edge represents the existence of supply chain business relationship between enterprises;

[0007] Each of the nodes comprises the following states: normal state, denoted as S, initial risk state, denoted as I1, medium risk state, denoted as I2, high risk state, denoted as I3, immune state, denoted as R, and termination state, denoted as D;

[0008] Define the propagation probability α(n, f) = α0·n L / f;

[0009] Define the recovery probability μ(n, f, c) = μ0·e -n ·f / c;

[0010] The change of the state density of each node with time is set to meet the following dynamic equation set:

[0011] dS(t) / dt = -α1S(t)(I1(t) + I2(t) + I3(t)) + βR(t),

[0012] dI1(t) / dt = α1S(t)(I1(t) + I2(t) + I3(t)) - α2I1(t) - μ1I1(t),

[0013] dI2(t) / dt = α2I1(t) - α3I2(t) - μ2I2(t),

[0014] dI3(t) / dt = α3I2(t) - μ3I3(t) - γI3(t),

[0015] dR(t) / dt = μ1I1(t) + μ2I2(t) + μ3I3(t) - βR(t),

[0016] dD(t) / dt = γI3(t);

[0017] The dynamic equation set meets the following total constraint condition: S(t) + I1(t) + I2(t) + I3(t) + R(t) + D(t) = 1;

[0018] Wherein, n = 1, 2, 3, α0 is a preset basic transmission rate, μ0 is a preset basic recovery probability; L is an adjustment coefficient greater than 1, used for the nonlinear influence of the node risk level n on the transmission probability; α1, α2, α3 respectively represent the transmission probability of S to I1, I1 to I2, and I2 to I3 in α(n, f) when n = 1, 2, 3; μ1, μ2, μ3 respectively represent the recovery probability of I1 to R, I2 to R, and I3 to R in μ(n, f, c) when n = 1, 2, 3; f is the node anti-risk ability related to the enterprise scale, and c is the recovery cost related to the enterprise risk level and the working capital; γ is the probability of I3 to D, and β is the immune failure probability of R to S;

[0019] The following dynamic stability condition is set:

[0020] The time derivative of each state density is zero, dS(t) / dt = dI1(t) / dt = dI2(t) / dt = dI3(t) / dt = dR(t) / dt = dD(t) / dt = 0;

[0021] The transmission probability is less than the recovery probability, α(n, f) < μ(n, f, c).

[0022] The following dynamic disconnection and reconnection rules are set:

[0023] When a node enters the termination state D, all its connections are disconnected; the disconnected connections are reconnected to target nodes according to the following priority from front to back: 1. normal state S; 2. immune state R; 3. initial risk state I1; 4. medium risk state I2; 5. high risk state I3. If there is no target node meeting the conditions, the connection remains disconnected;

[0024] S2 simulates the risks of the enterprises in the supply chain using the supply chain model, and optimizes the enterprises in the supply chain based on the simulation results.

[0025] Preferably, step S2 specifically comprises the following steps:

[0026] Based on the risk situations of the enterprises in the supply chain, the initialization states of the nodes in the supply chain model are set;

[0027] γ and β are obtained; based on the enterprise scale and the enterprise working capital of the enterprises in the supply chain, the node risk resistance ability f and the recovery cost c of each enterprise are set;

[0028] The maximum simulation time T is set max , the maximum simulation time T max includes a plurality of time steps t; at each time step t, the state of each node is updated according to the propagation probability, the recovery probability, the probability from I3 to D, and the immune failure probability.

[0029] Preferably, step S2 further comprises the following steps:

[0030] When one of the following conditions is met, the simulation is terminated:

[0031] i. The number of nodes in each state in the network reaches dynamic balance;

[0032] ii. There is no I1, I2, I3 state node in the network;

[0033] iii. The simulation time reaches the maximum simulation time T max .

[0034] Preferably, step S2, based on the simulation results, optimizes the enterprises in the supply chain, specifically comprising:

[0035] When the number of nodes in each state in the network reaches dynamic balance or the simulation time reaches the maximum simulation time T max , the enterprises in the supply chain are adjusted as follows: the enterprises corresponding to the nodes in state D at the end of the simulation are deleted from the supply chain, replaced with other similar enterprises, and step S2 is re-executed.

[0036] Preferably, step S2, based on the simulation results, optimizes the enterprises in the supply chain, specifically comprising:

[0037] When the number of state nodes in the network reaches dynamic balance or the simulation time reaches the maximum simulation time T max When the number of state nodes in the network reaches dynamic balance or the simulation time reaches the maximum simulation time T

[0038] The application further provides a computer device, comprising a memory, a processor and computer instructions stored in the memory and running on the processor, and the processor implements the steps in the supply chain network optimization method based on risk classification propagation and dynamic recovery according to any one of claims 1-5 when running the computer instructions.

[0039] The application can simulate multi-level risk propagation, reveal risk diffusion law, propose dynamic disconnection and reconnection strategy, and optimize risk propagation path by accurately describing risk dynamics and optimizing network structure, thereby providing theoretical support and improving the overall resilience of the supply chain. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the specific embodiments of the application or the technical solutions in the prior art, the drawings needed in the specific embodiments or prior art description will be briefly introduced below, and some specific embodiments of the application will be described in detail below with reference to the drawings in an exemplary but non-limiting manner. The same reference signs in the drawings indicate the same or similar components or parts. Those skilled in the art should understand that these drawings are not necessarily drawn to scale. In the drawings:

[0041] Figure 1 The state transition diagram for supply chain risk propagation and recovery.

[0042] Figure 2 The reconnection strategy flowchart: when an enterprise cannot withstand the risk impact and becomes a D (elimination) state, all existing connections with associated enterprises are disconnected. In order to maintain the continuity of operation, the disconnected enterprise establishes new partnerships according to the risk level of potential partners in accordance with the defined priority order. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of the present application more clear, the present application will be further described in detail below in combination with the drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0044] State division and transition rules The enterprise nodes in the supply chain network are divided into six states:

[0045] Normal state, denoted by S: not affected by risk;

[0046] • Initial risk state, denoted as I1: slightly affected by risk;

[0047] • Moderate risk state, denoted as I2: risk aggravation;

[0048] • High risk state, denoted as I3: on the verge of failure;

[0049] • Immune state, denoted as R: complete recovery; enterprises in the immune state are neither contagious nor susceptible to infection;

[0050] • Termination state, denoted as D: eliminated from the network.

[0051] The transitions between states are controlled by dynamic probabilities, with the infection rate a and the recovery rate m defined as:

[0052] a(n, f) = a0- n L / f

[0053] m(n, f, c) = m0- e -n · f / c

[0054] where a0is the basic transmission rate and m0is the basic recovery probability, determined by experimental or empirical data. n (n = 1, 2, 3, corresponding to I1, I2, I3, respectively) is the risk level. The adjustment factor L (L > 1) describes the nonlinear effect of node risk level n on the transmission probability. f is the node's risk resistance (determined by enterprise size, supply network topology, etc.), and c is the recovery cost (constructed from enterprise working capital or characteristics related to risk resistance), used to control the dynamic process of risk transmission and recovery.

[0055] The infection probability a(n, f) is used to describe the ability of a node to transmit from state S to state I n .

[0056] The recovery probability m(n, f, c) is used to describe the ability of a node to recover from the risk state I n to the immune state R.

[0057] Immune failure probability b: for nodes in the immune state R, they may lose immunity and enter state S.

[0058] Elimination probability g: for nodes in the high-risk state I3, they may fail to recover and enter the failure state D, with an elimination probability of g.

[0059] All formulas are defined by a parameterized method, which facilitates flexible adjustment to adapt to different supply chain network application scenarios.

[0060] Dynamic equation description:

[0061] In the supply chain network, the density of each state node changes over time and is described by the following dynamic equation:

[0062] dS(t) / dt=-α1S(t)(I1(t)+I2(t)+I3(t))+βR(t),

[0063] dI1(t) / dt=α1S(t)(I1(t)+I2(t)+I3(t))-α2I1(t)-μ1I1(t),

[0064] dI2(t) / dt=α2I1(t)-α3I2(t)-μ2I2(t),

[0065] dI3(t) / dt=α3I2(t)-μ3I3(t)-γI3(t),

[0066] dR(t) / dt=μ1I1(t)+μ2I2(t)+μ3I3(t)-βR(t),

[0067] dD(t) / dt=γI3(t)。

[0068] α1,α2,α3 respectively represent the corresponding propagation probability in α(n,f) when n=1,2,3, representing the infection probability of different risk levels;

[0069] μ1,μ2,μ3 respectively represent the recovery probability in μ(n,f,c) when n=1,2,3, representing the recovery probability of different risk levels;

[0070] γ is the probability of high-risk state (I3) entering the termination state (D);

[0071] β is the probability of immune failure of the recovery state (R) returning to the normal state (S).

[0072] γ and β are determined values, limited between [0,1], and the present application directly obtains the γ and β values of each enterprise.

[0073] The size of γ is usually directly related to the following attributes of the enterprise:

[0074] 1. Enterprise asset-liability ratio, if the enterprise asset-liability ratio is high (such as close to or even more than 100%), the possibility of its bankruptcy is greater, so the value of γ is higher. 2. Liquidity, the short-term debt servicing ability of the enterprise determines its ability to cope with crisis. Enterprises with low liquidity (such as liquidity ratio <1) are more likely to go bankrupt, resulting in an increase in γ. 3. Enterprise industry risk coefficient, some industries (such as catering, retail, etc.) are more vulnerable to external environmental changes. 4. Risk event frequency, the frequency of risk events (such as default, supply chain rupture) in the history of the enterprise is higher, and the failure probability γ of the enterprise is also increased accordingly.

[0075] The size of β is mainly related to the risk resistance of the enterprise and the effectiveness of resource allocation after recovery.

[0076] The values of γ and β vary depending on factors such as the financial health of the enterprise, operational efficiency, industry risk, etc. By combining enterprise-specific data (such as asset-liability ratio, management efficiency, resource utilization rate, etc.), more realistic dynamic parameter values can be set.

[0077] The adjustment coefficient L (L>1) describes the non-linear impact of node risk level n on the transmission probability. In actual supply chain networks, the value of parameter L is closely related to the following factors:

[0078] 1. Risk sensitivity: L describes the degree of non-linear impact of risk level n changes on transmission probability or recovery probability. For highly dependent industries or enterprises, a small increase in risk level may lead to a significant increase in transmission probability, thus showing a larger L value.

[0079] 2. Industry characteristics: Different industries have different risk transmission characteristics. For example, in high-risk industries (such as pharmaceutical or high-tech industries), the supply chain has a fast risk transmission speed or a wide impact range, so L is usually high; while in more stable industries (such as food industry), it may show a lower L value.

[0080] 3. Network structure: The topological characteristics of the supply chain network will affect the value of L. For example, in a highly centralized network, the non-linear propagation characteristics of core node risk are more pronounced, which may lead to a higher L; while in a decentralized network, the non-linear impact of risk propagation may be weaker.

[0081] 4. Enterprise adaptability: The recovery ability and resource allocation efficiency of the enterprise have a significant impact on L. Enterprises with strong adaptability can quickly adjust when facing risks, thus weakening the impact of risk level and leading to a lower L.

[0082] The above system of equations satisfies the following total constraint condition: S(t) + I1(t) + I2(t) + I3(t) + R(t) + D(t) = 1

[0083] Dynamic stability condition:

[0084] The conditions for the system to tend towards dynamic stability include:

[0085] 1. The time derivative of each state density is zero:

[0086] dS(t) / dt = dI1(t) / dt = dI2(t) / dt = dI3(t) / dt = dR(t) / dt = dD(t) / dt = 0.

[0087] 2. The transmission rate of each risk state is less than the recovery rate:

[0088] α(n,f) < μ(n,f,c).

[0089] Dynamic disconnect and reconnect strategy:

[0090] Disconnect rule: When a node enters the termination state (D), all its connections are disconnected.

[0091] Reconnect rule: The disconnected connections are reconnected to target nodes according to the following priority: 1. Normal state (S); 2. Immune state (R); 3. Initial risk state (I1); 4. Moderate risk state (I2); 5. High risk state (I3).

[0092] Random link probability: Among the set of target nodes meeting the priority, a target node is selected as the reconnect object in a uniform random manner. The link probability formula is: where, represents the set of candidate target nodes in the current priority range, and its value is the number of nodes in the set.

[0093] No historical connection restriction: The target node and the disconnected node must meet the "no historical connection" condition before reconnecting, i.e., where (i,j) represents the connection relationship between the disconnected node i and the candidate target node j, E 历史 represents the existing edge set in the current network.

[0094] Cannot connect: If no node meeting the "no historical connection" condition is found among all priority target nodes, the disconnected connection remains disconnected.

[0095] Implementation steps:

[0096] 1. Model initialization:

[0097] (a) Construct a supply chain network topology G = (V, E) consisting of N nodes and E edges, where V is the node set and E is the edge set.

[0098] (b) Set the initial state of all nodes to S (normal state).

[0099] (c) Randomly select m nodes as seed nodes and set their state to I1 (initial risk state).

[0100] (d) Define infection probability α(n,f), recovery probability μ(n,f,c), and immune failure probability β, and determine the simulation time step T and the maximum simulation time T max .

[0101] 2. Risk propagation:

[0102] (a) At each time step t, update the state of each node sequentially.

[0103] (b) For a node in state I1, infect its neighbor nodes with probability a(1,f), and the neighbor nodes change their state to I1.

[0104] (c) After a node in state I1 is infected, it upgrades to state I2 (medium-risk state) with probability a(2,f).

[0105] (d) After a node in state I2 is infected, it upgrades to state I3 (high-risk state) with probability a(3,f).

[0106] (e) After a node in state I3 is infected, it transitions to state D (failure state) with probability γ, i.e., the enterprise exits the network.

[0107] (f) For a node in state D, its connections with other nodes in the network will be disconnected, and the disconnected connections will be randomly reconnected to target nodes according to the priority S > R > I1 > I2 > I3.

[0108] 3. Recovery strategy:

[0109] (a) For nodes in states I1, I2, and I3, recover to immune state R with probabilities μ(1,f,c), μ(2,f,c), and μ(3,f,c), respectively.

[0110] (b) For a node in state R, recover to susceptible state S with probability β and participate in risk propagation again.

[0111] 4. State update and simulation termination:

[0112] (a) At each time step t, update the state of all nodes according to the risk propagation and recovery strategies.

[0113] (b) Record the number of nodes in each state at the current time, including S (normal state), I1 (initial risk state), I2 (medium-risk state), I3 (high-risk state), R (recovery state), and D (failure state).

[0114] (c) Terminate the simulation when one of the following conditions is met:

[0115] i. The number of nodes in each state in the network reaches a dynamic equilibrium, i.e., the state density no longer changes over time.

[0116] ii. There are no nodes in states I1, I2, and I3 in the network.

[0117] iii. The simulation time reaches the maximum simulation time T max .

[0118] 5. Performance evaluation:

[0119] (a) By adjusting parameters a(n,f), μ(n,f,c), β and γ, analyze the influence on the risk propagation range and recovery ability.

[0120] (b) Compare the applicability and performance of the model under different network topologies.

[0121] Using the model evaluated as a supply chain model based on the supply chain network topology, using the supply chain model to simulate the risks of each enterprise in the supply chain, and based on the simulation results, optimizing the enterprises in the supply chain.

[0122] Based on the risk situation of each enterprise in the supply chain, set the initialization state of each node in the supply chain model;

[0123] Obtain γ, β; based on the enterprise size and enterprise working capital of each enterprise in the supply chain, set the node risk resistance ability f and recovery cost c of each enterprise;

[0124] Set the maximum simulation time T max , the maximum simulation time T max includes a plurality of time steps t; at each time step t, according to the propagation probability, recovery probability, I3 to D probability and immune failure probability, reconnect strategy, update the state of each node.

[0125] When one of the following conditions is met, terminate the simulation:

[0126] i. The number of state nodes in the network reaches dynamic balance;

[0127] ii. There is no I1, I2, I3 state node in the network;

[0128] iii. The simulation time reaches the maximum simulation time T max .

[0129] When the number of state nodes in the network reaches dynamic balance or the simulation time reaches the maximum simulation time T max , adjust the enterprises in the supply chain in the following way to realize the optimization of the enterprises in the supply chain: delete the enterprise corresponding to the node in state D at the end of simulation from the supply chain, replace it with other similar enterprises, and then re-simulate. The enterprise corresponding to the node whose initialization state is not S can also be deleted from the supply chain and replaced with other similar enterprises.

[0130] The above is only part of the specific embodiments of the present application, but the protection scope of the present application is not limited to this, any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A supply chain network optimization method based on risk hierarchical propagation and dynamic recovery, characterized by: The following steps are involved: S1 builds a supply chain model based on the supply chain network topology, including the following steps: Construct a supply chain network topology G = (V, E) consisting of N nodes and E edges, where V is the node set and E is the edge set. Each node represents an enterprise in the supply chain network, and each edge represents the supply chain business relationship between enterprises. Each of the nodes includes the following states: normal state, denoted as S, initial risk state, denoted as I1, medium risk state, denoted as I2, high risk state, denoted as I3, immune state, denoted as R, and termination state, denoted as D; Define the propagation probability α(n,f) = α0·n L / f; Define the recovery probability μ(n,f,c)=μ0·e -n f / c; Assume that the state density of each node changes with time, which conforms to the following dynamic equations: dS(t) / dt=-α1S(t)(I1(t)+I2(t)+I3(t))+βR(t), dI1(t) / dt=α1S(t)(I1(t)+I2(t)+I3(t))-α2I1(t)-μ1I1(t), dI2(t) / dt=α2I1(t)-α3I2(t)-μ2I2(t), dI3(t) / dt=α3I2(t)-μ3I3(t)-γI3(t), dR(t) / dt=μ1I1(t)+μ2I2(t)+μ3I3(t)-βR(t), dD(t) / dt=γI3(t); The dynamic equations satisfy the following total constraint conditions: S(t)+I1(t)+I2(t)+I3(t)+R(t)+D(t)=1; Where n = 1, 2, 3; α0 is the preset basic transmission rate, μ0 is the preset basic recovery probability; α1, α2, and α3 represent the propagation probabilities from S to I1, I1 to I2, and I2 to I3 when n = 1, 2, and 3 in α(n, f), respectively; μ1, μ2, and μ3 represent the recovery probabilities of I1 to R, I2 to R, and I3 to R when n = 1, 2, and 3 in μ(n, f, c), respectively; f is the node risk resistance capacity related to the enterprise size, c is the recovery cost related to the enterprise risk level and liquidity; L is an adjustment coefficient greater than 1, which is used for the nonlinear effect of node risk level n on the propagation probability; γ is the probability of I3 to D, β is the probability of immune failure from R to S; The following dynamic stability conditions are set: The time derivative of each state density is zero, dS(t) / dt=dI1(t) / dt=dI2(t) / dt=dI3(t) / dt=dR(t) / dt=dD(t) / dt=0; The propagation probability is less than the recovery probability, α(n,f)<μ(n,f,c). Set the following dynamic disconnection and reconnection rules: When a node enters the terminal state D, all its connections are disconnected. Disconnected connections are reconnected to the target node according to the following priority from front to back:

1. Normal state S; 2. Immune state R; 3. Initial risk state I1; 4. Medium risk state I2; 5. High risk state I3. If there is no target node that meets the conditions, the connection remains disconnected. S2 uses the supply chain model to simulate the risks of each enterprise in the supply chain and optimizes the enterprises in the supply chain based on the simulation results.

2. A supply chain network optimization method based on risk hierarchical propagation and dynamic recovery as claimed in claim 1, characterized in that: Step S2 specifically includes the following steps: Based on the risk situation of each enterprise in the supply chain, set the initialization status of each node in the supply chain model; Obtain γ and β; based on the enterprise scale and liquidity of each enterprise in the supply chain, set the node risk resistance f and recovery cost c of each enterprise; Set the maximum simulation time T max , the maximum simulation time T max It includes several time steps t; at each time step t, the state of each node is updated according to the propagation probability, recovery probability, I3 to D probability and immunity failure probability.

3. A supply chain network optimization method based on risk hierarchical propagation and dynamic recovery as claimed in claim 2, characterized in that: Step S2 also includes the following steps: The simulation terminates when one of the following conditions is met: i. The number of nodes in each state in the network reaches a dynamic balance; ii. There are no nodes in the I1, I2, or I3 states in the network; iii. The simulation time reaches the maximum simulation time T max .

4. A supply chain network optimization method based on risk hierarchical propagation and dynamic recovery as claimed in claim 3, characterized in that: In step S2, based on the simulation results, the enterprises in the supply chain are optimized, specifically including: When the number of nodes in each state in the network reaches a dynamic equilibrium or the simulation time reaches the maximum simulation time T max When , the enterprises in the supply chain are adjusted in the following way: the enterprise corresponding to the node with status D at the end of the simulation is deleted from the supply chain, replaced with other similar enterprises, and step S2 is executed again.

5. The supply chain network optimization method based on risk hierarchical propagation and dynamic recovery according to claim 3, characterized in that: In step S2, based on the simulation results, the enterprises in the supply chain are optimized, specifically including: When the number of nodes in each state in the network reaches a dynamic equilibrium or the simulation time reaches the maximum simulation time T max When , the enterprises in the supply chain are adjusted in the following way: the enterprises corresponding to the nodes whose simulation initialization state is not S are deleted from the supply chain, replaced by other similar enterprises, and step S2 is executed again.

6. A computer device comprising a memory, a processor, and computer instructions stored in the memory and executed on the processor, wherein: When the processor executes the computer instructions, the steps of the supply chain network optimization method based on risk hierarchical propagation and dynamic recovery as described in any one of claims 1 to 5 are implemented.

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