Brittleness Evolution Model of the Supply Chain Network Based on Adaptive Agent Graph Theory under the COVID-19 Pandemic
Abstract
:1. Introduction
- The evolution law of the vertex state of the uncertain supply chain under COVID-19 attack will be analyzed.
- The evolution law of brittleness entropy of the vertex in the supply chain will be solved.
- The evolution law of the global brittleness entropy of the uncertain supply chain will be demonstrated.
- The seasonal evolution law of the uncertain supply chain brittleness will be illustrated.
- The evolution law of the brittleness behavior of the uncertain supply chain will be solved.
- The model and algorithm of the vertex state and brittleness entropy of the vertex of the uncertain supply chain are established.
- The brittleness evolution model of the supply chain based on the adaptive agent graph is constructed.
- The simulation algorithm of the brittleness evolution of the uncertain supply chain based on the adaptive agent graph is designed.
2. Literature Review
2.1. Supply Chain Vulnerability
- The identification of vulnerability factors of the supply chain
- 2.
- Evaluation of supply chain vulnerability
- 3.
- Mechanism of correlation influence of supply chain vulnerability
- 4.
- Conceptual differences between supply chain vulnerability and supply chain brittleness
2.2. Brittleness Theory of Complex Systems
- Brittleness of complex systems based on catastrophe theory
- 2.
- Brittleness entropy of complex systems
- 3.
- Brittleness of complex systems based on the theory of self-organized criticality
- 4.
- Brittleness of complex systems based on graph theory
2.3. Research Summary
3. Study Description and Problem Definition
3.1. Study Description
3.2. The Adaptive Agent Graph of the Supply Chain Brittleness Network
- Vertexes: the suppliers, manufacturers, distributors, and end retailers of the supply chain are defined as the vertexes of the adaptive agent graph of the brittleness network.
- Arcs: The directed link a which connects the ordered vertex pairs i and j is defined as the arc of the adaptive agent graph of the supply chain brittleness network, denoted as a = <i, j>. Link a has both the meaning of directionality (vertex i and vertex j, respectively, represent the starting point and the ending point) and weight value.
- Adjacency relation: Whether there is a brittleness link between vertex i and vertex j is defined as the adjacency relation of the adaptive agent graph in this paper. If there is a brittleness link, rij = 1, rij ∈ R; otherwise, rij = 0. The mathematical expression is as follows:
- Topological structure: The weighted and directed graph D = <V,A,R> is defined as the topological structure of the adaptive agent graph, which is the graphic representation of the brittleness relationship of supply chain complex systems.Thereinto, V(i, j ∈ V) represents the vertex set of a supply chain brittleness network. A(a ∈ A) represents the directed link set of a brittleness network, and R(rij∈ R) represents the set of adjacency relations between vertex i and vertex j.
- The Flow of vertex: The entropy flow of supply chain nodes is defined as the flow of a vertex of an adaptive agent graph of a supply chain brittleness network. And the adjacency relationship would be obtained through the distribution results of the flow of vertex.
- The weight of adaptive agent graph: The proportion of the quantity of material flow supplied from vertex i to vertex j to total material flow of vertex i is defined as the weight ωij of the adaptive agent graph of the supply chain brittleness network.
- The interaction between vertexes: the transferring and exchanging of entropy flow between vertexes are defined as the interaction between vertexes in the adaptive agent graph of the supply chain brittleness network.
- The memory function of the vertex: the memory function is composed of the vertex state function and the entropy flow function of the vertex, which is used to store the state, the entropy flow, and brittleness evolution rules of each vertex.
- The global energy function: The global energy function reflects the disorder degree of the supply chain brittleness network and also reflects the superposition effect of the brittleness behavior of vertexes. In this study, the weighted sum of all brittleness entropy (the global brittleness entropy) of the supply chain brittleness network is defined as the global energy function of the adaptive agent graph.
3.3. The Problem Definition of Brittleness Evolution of the Supply Chain
4. Problem Formulation
4.1. The Brittleness Evolution Model of Adaptive Agent Graph of the Supply Chain
- AssumptionsAccording to Holland’s CAS (complex adaptive systems) theory [46], the evolutionary steps of vertexes of the adaptive agent graph of the supply chain are set as follows:
- (1)
- Each vertex senses the entropy flow from other agents and the increase of entropy caused by external environmental interference through the detector. And then, the entropy flow of the vertex is determined according to its own state value.
- (2)
- The memory function of the vertex is established to store its own state, the entropy flow, and other information into the memory, and the knowledge base is preliminarily constructed.
- (3)
- The vertex constantly learns from the knowledge base and establishes the control strategies. A series of IF/THEN rules are established to continuously learn memory functions, and the vertex state and vertex entropy flow are updated to update the knowledge base in the memory.
- (4)
- According to the interaction process of entropy flow, the vertex entropy flow is output through the reactor, and the vertex state is output through the flow function φ. The relationship between the vertex state value and the entropy flow value is determined by the IF/THEN rules in the actuator.
- (5)
- The updated flow of the vertex agent would be used as input to the actuator in times of t + 1.
- The brittleness evolution model of the vertex of the adaptive agent graph of the supply chain
- (1)
- When the adaptive behavior of the vertex is not considered, the entropy flow evolution model of the vertex is
- (2)
- When the adaptive behavior of the vertex is considered, the brittleness connection between vertexes is built through the distribution of entropy flow, and the evolution model of entropy flow of the vertex is
4.2. Model of Maximum/Minimum Brittleness Collapse Path of the Supply Chain
4.3. Calculation Model of Brittleness Evolution Parameters
- The collapse probability of vertex i under normal scenarios is
- 2.
- The probability of the brittleness event s of a supply chain is
- 3.
- The scheduling model of the brittleness network of the supply chain is [44]
- 4.
- When the brittleness event s occurs, the collapse probability of vertex i is
- 5.
- The state value of vertex i of the supply chain is
- 6.
- The entropy flow of vertex i of the supply chain is
- 7.
- The global brittleness entropy of each OD pair of the adaptive agent graph of the supply chain is as follows:
- 8.
- The global brittleness entropy of the adaptive agent graph of the supply chain is as follows:
4.4. Evolution Index Model of the Brittleness Behavior of the Supply Chain
5. Algorithm Design
Algorithm 1: Pseudocode of simulation algorithm of brittleness evolution of supply chain. |
Input: Parameters of integration scheduling of uncertainty supply chain |
Output: State value xi, entropy flow fi, the global brittleness entropy H(D,n) |
//Step 1. Compute the load value Ci and collapse probability Pi |
1: Compute scheduling results← Call scheduling model F = min [γf1 + (1 − γ)f2] |
2: Compute collapse probability Pi according to Pi = C(i)/Ck(i) |
//Step 2. Compute the state value and entropy flow fi |
3: Compute the state value xi according to |
4: Compute the entropy flow fi according to fi = −logxi |
//Step 3. Compute the weights ωmax, ωmin of brittleness collapse path |
5: Compute ωmax, ωmin according to Equations (15)–(18) via Lagrange relaxation algorithm |
//Step 4. Compute the brittleness entropy H(D) |
6: Compute H(D) of each OD pair according to |
//Step 5. Compute the global brittleness entropy H(D,n). |
7: Compute H(D,n) according to H(D,n) = ΣnH(D) |
//Step 6–7. Compute the results of brittleness evolution |
8: Update the value of xi and according to Equations (7)–(14) 9: If Then 10: Remove the vertex i 11: Call the scheduling model to compute the scheduling results 12: Compute Pi, xi, , ωmax, ωmin , H(D) and H(D,n) 13: End if 14: Else 15: Update the value of xi and fi according to Equations (10), (13) and (14) 16: Update H(D) and H(D,n) according to Equations (31) and (34) 17: While xi = 1 for all vertexs 18: End while 19: End |
6. Numerical Results and Discussion of Simulation Example
6.1. Case Description and Parameter Values
- Case description
- 2.
- Parameter values
6.2. Brittleness Evolution Simulation When Vertex Adaptability Is Not Considered
6.3. Brittleness Evolution Simulation When Vertex Adaptability Is Considered
6.4. Evolution Simulation Considered Characteristics of Seasonal Demand of the Supply Chain
6.5. The Evolution Simulation of Brittleness Behavior
7. Conclusions and Future Research
- Brittleness evolution law based on the vertex adaptability of the supply chain
- (1)
- When the vertex adaptability is not considered, the supply chain system does not collapse immediately when the vertex of the brittleness source is failed but takes a certain period of time, which reflects the feature of delay of the supply chain’s brittleness.
- (2)
- When the vertex adaptability is considered, the vertex which has a close brittleness link with the brittleness source does not immediately collapse. This is because the adaptive behavior of the vertex agent resists the brittleness evolution of the supply chain to collapse.
- Seasonal evolution law of supply chain brittleness based on demand characteristics
- 3.
- The evolution law of brittleness behavior of the supply chain
- The model constructed in this paper is only considered the characteristics of the vertex within the supply chain system, based on which the brittleness evolution of the supply chain is compared and analyzed. The COVID-19 pandemic outside the supply chain system has attacked and disrupted the supply chain to varying degrees; therefore, the attack of the COVID-19 pandemic can be modeled and quantified to study its impact on the brittleness evolution of the supply chain in the future.
- The characteristics of the seasonal demand of brittleness evolution of the supply chain are compared and analyzed in this paper. In the future, more cluster analysis of demand characteristics can be conducted to study the relationship between brittleness evolution and more demand characteristics.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Cpit 1 | 1 | 21 | 25 | 28 | 24 | 23 | 19 | 30 | 15 | 17 |
2 | 20 | 26 | 28 | 25 | 22 | 19 | 28 | 15 | 16 | |
3 | 21 | 25 | 27 | 23 | 23 | 18 | 29 | 14 | 16 | |
4 | 21 | 25 | 27 | 24 | 22 | 18 | 30 | 13 | 17 | |
fli 2 | 0.6 | 0.40 | 0.30 | 0.45 | 0.55 | 0.63 | 0.20 | 0.7 | 0.65 |
t | J1 | J2 | J3 | |
---|---|---|---|---|
cdjt 1 | 1 | 5 | 12 | 7 |
2 | 6 | 11 | 8 | |
3 | 4 | 12 | 7 | |
4 | 5 | 13 | 6 |
K1 | K2 | K3 | K4 | K5 | K6 | K7 | K8 | K9 | K10 | K11 | K12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
dk 1 | 6 | 8 | 6 | 7 | 7 | 6 | 7 | 9 | 6 | 7 | 6 | 6 |
gk 2 | 2.4 | 1.7 | 2.2 | 2.1 | 1.7 | 2.4 | 2.1 | 1.7 | 1.8 | 1.7 | 2.4 | 1.9 |
hk 3 | 5.1 | 3.8 | 4.0 | 4.6 | 3.9 | 4.8 | 4.0 | 4.9 | 4.2 | 3.8 | 3.6 | 3.8 |
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Cao, W.; Wang, X. Brittleness Evolution Model of the Supply Chain Network Based on Adaptive Agent Graph Theory under the COVID-19 Pandemic. Sustainability 2022, 14, 12211. https://doi.org/10.3390/su141912211
Cao W, Wang X. Brittleness Evolution Model of the Supply Chain Network Based on Adaptive Agent Graph Theory under the COVID-19 Pandemic. Sustainability. 2022; 14(19):12211. https://doi.org/10.3390/su141912211
Chicago/Turabian StyleCao, Wei, and Xifu Wang. 2022. "Brittleness Evolution Model of the Supply Chain Network Based on Adaptive Agent Graph Theory under the COVID-19 Pandemic" Sustainability 14, no. 19: 12211. https://doi.org/10.3390/su141912211