Supply chain network optimization method and equipment based on risk hierarchical propagation and dynamic recovery

Abstract

The invention belongs to the technical field of supply chain management and risk control, particularly relates to a supply chain network optimization method based on risk hierarchical propagation and dynamic recovery, and provides a supply chain risk propagation and recovery model based on a complex network theory and an optimization method thereof. Firstly, a supply chain model based on a supply chain network topology structure is constructed, the supply chain network topology structure G = (V, E) is formed by N nodes and E edges, and each node represents an enterprise in the supply chain network; each edge represents a supply chain business relationship between enterprises; and simulating the risk of each enterprise in the supply chain by using the supply chain model, and optimizing the enterprises in the supply chain based on a simulation result. The method is used for simulating the risk propagation dynamic state between enterprises and optimizing the network structure, and the overall toughness and the anti-risk capability of the supply chain network are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of supply chain management and risk control, and specifically relates to a supply chain network optimization method and device based on risk classification propagation and dynamic recovery. Background Art

[0002] As a complex system, the supply chain network is composed of enterprise nodes and their interconnected relationships, with high interconnectivity and complexity. The main challenge it faces is the rapid spread and spread of risks, which may cause local failures to evolve into systemic failures. Existing studies usually use epidemic models (such as SIR and SIS models) to simulate the spread of supply chain risks, but they have the following limitations: 1. Ignoring the heterogeneity of enterprise nodes: failing to fully consider the impact of attributes such as enterprise scale and risk resistance on risk propagation; 2. Lack of multi-level risk classification: using only a single infection state, it is difficult to reflect the complexity of risk propagation; 3. Insufficient dynamic adjustment mechanism: lack of reasonable optimization of the network reconnection strategy after disconnection. Summary of the invention

[0003] In order to solve the above problems, the present invention 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 risk resistance of the supply chain network. It can be used to simulate the risk propagation dynamics between enterprises and optimize the network structure, thereby improving the overall resilience and risk resistance of the supply chain network.

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

[0005] S1 builds a supply chain model based on the supply chain network topology structure, including the following steps

[0006] Construct a supply chain network topology structure 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; each edge represents the supply chain business relationship between enterprises;

[0007] 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;

[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 state density of each node is set to change with time, which conforms to the following dynamic equations:

[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 equations satisfy the following total constraint conditions: S(t)+I1(t)+I2(t)+I3(t)+R(t)+D(t)=1;

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

[0019] The following dynamic stability conditions are 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 propagation probability is less than the recovery probability, α(n,f)<μ(n,f,c).

[0022] Set the following dynamic disconnection and reconnection rules:

[0023] When a node enters the terminal state D, all its connections are disconnected; the disconnected connections are reconnected to the target node according to the following priorities 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;

[0024] 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.

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

[0026] Based on the risk situation of each enterprise in the supply chain, set the initialization status of each node in the supply chain model;

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

[0028] 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, probability of I3 to D and probability of immune failure.

[0029] Preferably, step S2 also includes the following steps:

[0030] The simulation terminates when one of the following conditions is met:

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

[0032] ii. There are no nodes in the I1, I2, or I3 states in the network;

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

[0034] Preferably, the optimization of enterprises in the supply chain based on the simulation results described in step S2 specifically includes:

[0035] 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 manner: the enterprise corresponding to the node with the state D when the simulation ends is deleted from the supply chain, replaced with other similar enterprises, and step S2 is re-executed.

[0036] Preferably, the optimization of enterprises in the supply chain based on the simulation results described in step S2 specifically includes:

[0037] 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 manner: the enterprises corresponding to the nodes whose initialization states are not S are deleted from the supply chain, replaced by other similar enterprises, and step S2 is re-executed.

[0038] The present invention also provides a computer device, comprising a memory, a processor, and computer instructions stored in the memory and running on the processor, characterized in that when the processor runs the computer instructions, it implements the steps in the supply chain network optimization method based on risk grading propagation and dynamic recovery as described in any one of claims 1 to 5.

[0039] By accurately describing risk dynamics and optimizing network structure, the present invention can: 1. simulate multi-level risk propagation and reveal the law of risk diffusion; 2. propose dynamic disconnection and reconnection strategies to optimize risk propagation paths; 3. provide theoretical support to enhance the overall resilience of the supply chain. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the specific implementation of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the specific implementation or the prior art description. Some specific embodiments of the present invention will be described in detail in an exemplary but not restrictive manner with reference to the drawings. The same reference numerals 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 This is the supply chain risk propagation and recovery state transition diagram.

[0042] Figure 2 Reconnection strategy flow chart: When an enterprise fails to withstand the risk impact and becomes D (eliminated), all its existing connections with related enterprises are cut off. In order to maintain operational continuity, the disconnected enterprises establish new partnerships according to the defined priority based on the risk level of potential partners. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0044] State division and transfer rules Enterprise nodes in the supply chain network are divided into six states:

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

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

[0047] Medium risk status, denoted as I2: increased risk;

[0048] High-risk state, denoted as I3: imminent failure;

[0049] Immune state, denoted as R: Complete recovery; enterprises in the immune state are neither contagious nor infected by risks;

[0050] The terminal state, denoted as D: is eliminated from the network.

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

[0052] α(n,f)=α0·n L / f

[0053] μ(n,f,c)=μ0·e -n f / c

[0054] Where α0 is the basic transmission rate and μ0 is the basic recovery probability, which are determined by experimental or empirical data. n (n = 1, 2, 3, corresponding to I1, I2, I3 respectively) is the risk level. The adjustment coefficient L (L>1) describes the nonlinear effect of the node risk level n on the transmission probability. f is the node's risk resistance (determined by the enterprise scale, supply network topology, etc.), and c is the recovery cost (constructed by the enterprise's working capital, or characteristics related to risk resistance), which is used to control the dynamic process of risk transmission and recovery.

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

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

[0057] Immune failure probability β: For a node in immune state R, it may enter state S due to loss of immunity.

[0058] Elimination probability γ: For nodes in high-risk state I3, they may enter the failed state D due to inability to recover, and the elimination probability is γ.

[0059] All formulas are defined through parameterized methods, which can be flexibly adjusted to suit different application scenarios of supply chain networks.

[0060] Dynamic equation description:

[0061] In the supply chain network, the density of each state node changes over time 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, and α3 represent the corresponding transmission probabilities when n = 1, 2, and 3 in α(n, f), respectively, indicating the probability of infection at different risk levels;

[0069] μ1, μ2, and μ3 represent the corresponding recovery probabilities when n=1, 2, and 3 in μ(n, f, c), respectively, indicating the recovery probabilities at different risk levels;

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

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

[0072] γ and β are determined values, limited to [0, 1]. The present invention 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. The debt-to-asset ratio of the enterprise. If the debt-to-asset ratio of the enterprise is high (such as close to or even exceeding 100%), it is more likely to go bankrupt, so the γ value is higher. 2. Liquidity of funds. The short-term debt repayment ability of the enterprise determines its ability to cope with crises. Enterprises with low liquidity (such as current ratio <1) are more likely to go bankrupt, resulting in an increase in γ. 3. The risk coefficient of the enterprise industry. Some industries (such as catering, retail, etc.) are more vulnerable to shocks due to changes in the external environment (such as economic downturns, policy changes). 4. The frequency of risk events. The higher the frequency of risk events (such as defaults, supply chain disruptions) that have occurred in the company's history, the higher the probability of failure γ will be.

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

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

[0077] The adjustment coefficient L (L>1) describes the nonlinear effect of the node risk level n on the probability of infection. In the actual supply chain network, the value of parameter L is closely related to the following factors:

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

[0079] 2. Industry characteristics: Risk propagation characteristics vary greatly between industries. For example, in the supply chain of high-risk industries (such as pharmaceuticals or high-tech industries), L is usually higher due to the rapid spread of risks or the wide range of impact; while more stable industries (such as the food industry) may show lower L values.

[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 nonlinear propagation characteristics of core node risks are more significant, which may lead to a higher L; while in a decentralized network, the nonlinear impact of risk propagation may be weaker.

[0081] 4. Enterprise adaptability: The enterprise's resilience and resource allocation efficiency have a significant impact on L. Enterprises with strong adaptability can adjust more quickly when facing risks, thereby weakening the impact of risk levels and resulting in lower L.

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

[0083] Dynamic stability conditions:

[0084] The conditions for the system to tend to 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 infection rate of each risk state is less than the recovery rate:

[0088] α(n,f)<μ(n,f,c).

[0089] Dynamic disconnection and reconnection strategy:

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

[0091] Reconnection rules: The disconnected connection reconnects to the target node according to the following priorities: 1. Normal state (S); 2. Immune state (R); 3. Initial risk state (I1); 4. Medium risk state (I2); 5. High risk state (I3).

[0092] Random link probability: In the target node set that meets the priority, a target node is selected as the reconnection object in a uniformly random manner. The link probability formula is: in, Represents the set of candidate target nodes within 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, that is: Among them, (i, j) represents the disconnection relationship between node i and candidate target node j, E 历史 Represents the edge set that already exists in the current network.

[0094] Unable to connect: If no node that satisfies "no historical connection" is found among the target nodes of all priorities, the disconnected connection remains disconnected.

[0095] Implementation steps:

[0096] 1. Model initialization:

[0097] (a) Construct a supply chain network topology structure 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 states to I1 (initial risk state).

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

[0101] 2. Risk Communication:

[0102] (a) At each time step t, the state of each node is updated in turn.

[0103] (b) For a node in state I1, it infects its neighbor node with probability α(1,f), and the state of the neighbor node changes to I1.

[0104] (c) After node I1 is infected, it is upgraded to I2 (medium risk state) with probability α(2,f).

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

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

[0107] (f) For nodes in state D, their connections with other nodes in the network will be disconnected, and the disconnected connections will select target nodes for random reconnection according to the priority S>R>I1>I2>I3.

[0108] 3. Recovery strategy:

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

[0110] (b) For nodes that have recovered to state R, they recover to the susceptible state S with probability β and participate in risk propagation again.

[0111] 4. Status update and simulation termination:

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

[0113] (b) Record the number of nodes in each state at the current moment, 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) The simulation is terminated when one of the following conditions is met:

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

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

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

[0118] 5. Performance evaluation:

[0119] (a) By adjusting the parameters α(n,f), μ(n,f,c), β and γ, we analyze their impact on the risk spread and recovery capacity.

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

[0121] The evaluated model is used as a supply chain model based on the supply chain network topology structure, the supply chain model is used to simulate the risks of each enterprise in the supply chain, and based on the simulation results, the enterprises in the supply chain are optimized.

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

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

[0124] 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, probability of I3 to D and immune failure probability, and reconnection strategy.

[0125] The simulation terminates when one of the following conditions is met:

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

[0127] ii. There are no nodes in the I1, I2, or I3 states in the network;

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

[0129] 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 simulation is terminated, the enterprises in the supply chain are adjusted in the following way to optimize the enterprises in the supply chain: the enterprises corresponding to the nodes whose state is D at the end of the simulation are deleted from the supply chain, replaced with other similar enterprises, and then the simulation is repeated. The enterprises corresponding to the nodes whose initial state is not S can also be deleted from the supply chain and replaced with other similar enterprises.

[0130] The above descriptions are only some specific implementation methods of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any person familiar with the art within the technical scope disclosed in the present invention should be covered within the protection scope of the present invention.

Claims

1. A supply chain network optimization method based on risk hierarchical propagation and dynamic recovery, characterized in that: The following steps are involved: S1 builds a supply chain model based on the supply chain network topology structure, including the following steps: Construct a supply chain network topology structure 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; 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; The state density of each node is set to change 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, 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 scale, c is the recovery cost related to the enterprise risk level and working capital; 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; the disconnected connections are reconnected to the target node according to the following priorities 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 working capital 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, probability of I3 to D and probability of immune failure.

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: The optimization of enterprises in the supply chain based on the simulation results described in step S2 specifically includes: 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 manner: the enterprise corresponding to the node with the state D when the simulation ends is deleted from the supply chain, replaced with other similar enterprises, and step S2 is re-executed.

5. A supply chain network optimization method based on risk hierarchical propagation and dynamic recovery as claimed in claim 3, characterized in that: The optimization of enterprises in the supply chain based on the simulation results described in step S2 specifically includes: 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 manner: the enterprises corresponding to the nodes whose simulation initialization states are not S are deleted from the supply chain, replaced by other similar enterprises, and step S2 is re-executed.

6. A computer device comprising a memory, a processor, and computer instructions stored in the memory and executed on the processor, characterized in that: When the processor runs the computer instructions, it implements the steps in the supply chain network optimization method based on risk classification propagation and dynamic recovery as described in any one of claims 1 to 5.

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