Effects of a Trust Mechanism on Complex Adaptive Supply Networks: An Agent-Based Social Simulation Study
Journal of Artificial Societies and Social Simulation
12 (3) 4
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Received: 31-Jan-2009 Accepted: 16-May-2009 Published: 30-Jun-2009
|Trust kj, tm = MAX[Trust kj, t m-1, ρ Orderkj, tm-s-o + (1- ρ) Trust kj, t m-1]||(3.1)|
Negative experience: Shipmentjk, tm-s < Orderkj, tm-s-o
|Trust kj, tm = MIN[Trust kj, t m-1, ρ Shipmentjk, tm-s + (1- ρ) Trust kj, t m-1]||(3.2)|
where MAX and MIN functions are used for the self-reinforcing mechanism which induces positive feedbacks. That is, in the case of positive experience, the trust value never goes down, and in the case of negative experience, the trust value never goes up. Moreover, this self-reinforcing mechanism corresponds to an argument by Ring and Van de Ven (1994) that the more frequently the parties have successfully transacted, the more likely they will bring higher levels of trust to subsequent transactions.
|Trust ki, tm = MAX[Trust ki, t m-1, ρ Shipmentki, tm-s-o + (1- ρ) Trust ki, t m-1]||(3.3)|
Negative experience: Orderik, tm-o < Shipmentki, tm-s-o
|Trust ki, tm = MIN[Trust ki, t m-1, ρ Orderik, tm-o + (1- ρ) Trust ki, t m-1]||(3.4)|
The equations of (3.1), (3.2), (3.3) and (3.4) show that within each pair of agents, trust levels may differ, implying the possibility of asymmetrical trust relationships
|Shipment ki,tm = Total_Shipment k,tm * [ Backorder ki,tm / ∑ i Backorder ki,tm ]||(3.5)|
Order Allocation Rule:
|Order kj ,tm = Total_Order k,tm * [ (1/Backorder jk,tm) / ∑ j (1/Backorder jk,tm) ]||(3.6)|
|Shipment ki,tm = Total_Shipment k,tm * [ Trust ki,tm / ∑ i Trust ki,tm]||(3.7)|
Order Allocation Rule:
|Order kj,tm = Total_Order k,tm * [ Trust kj,tm / ∑ j Trust kj,tm ]||(3.8)|
|Shipment ki,tm = Total_Shipment k,tm * [(1-γ)Backorder ki,tm+γTrust ki,tm] / [(1-γ)∑ i Backorder ki,tm+γ∑ i Trust ki,tm]||(3.9)|
Order Allocation Rule:
|Order kj,tm = Total_Order k,tm * [(1-γ)(1/Backorder jk,tm)+γTrust kj,tm] / [(1-γ)∑ j (1/Backorder jk,tm)+γ∑ j Trust kj,tm]||(3.10)|
where γ has a value in (0,1) and represents the relative weight on the trust level compared to the backorder level in the above allocation decisions.
|Figure 1. A supply network with L=5 and N=3|
|Total_Order k,tm||= ∑iExpected_Demand ik,tm + Stock_Adjustment k,tm + Pipeline_Adjustment k,tm|
|= θ ∑ i Order ik,t m-1 + (1- θ) ∑ i Expected_Demand ik,t m-1 + aS (Desired_Inventoryk - Inventory k,tm) + aPL (Desired_Pipelinek - Pipeline k,tm)|
|= θ ∑ i Order ik,t m-1 + (1- θ) ∑ i Expected_Demand ik,t m-1 + aS (Qk - Inventory k,tm -βPipeline k,tm)||(4.1)|
where θ : adaptation parameter controlling the rate at which demand expectations are updated aS : stock adjustment parameter (fraction of the discrepancy between the desired and the actual inventory) (=α) aPL: pipeline adjustment parameter (fraction of the discrepancy between the desired and the actual pipeline) β= aPL/aS & Qk = Desired_Inventoryk + β Desired_Pipelinek
|Figure 2. The simulation model structure with a case of L=5 and N=3|
|Figure 3. A simulation output with the backorder-based heuristic algorithms|
|Figure 4. Trust levels of 4 sample agents with the backorder-based heuristic algorithms|
|Figure 5. A simulation output with the trust-based heuristic algorithms|
|Figure 6. Trust levels of 4 neighboring agents and their trust relationships with the trust-based heuristic algorithms|
|Figure 7. The emergent structure of collaboration patterns with the trust-based heuristic algorithms|
|Figure 8. Inventory levels of all agents with the combined algorithms and γ = 0.2|
|Figure 9. Inventory levels of all agents with the combined algorithms and γ = 0.5|
|Figure 10. Inventory levels of all agents with the combined algorithms and γ = 0.8|
|Figure 11. Inventory levels of Distributors with the combined algorithms and γ = 0.2|
|Figure 12. Inventory levels of Distributors with the combined algorithms and γ = 0.5|
|Figure 13. Inventory levels of Distributors with the combined algorithms and γ = 0.8|
For tm = t1 to tT, // T is total simulation time steps. For i=0 to L-1, For j=0 to N-1, Call agent [i][j]. step(tm); // Execute each agent's step()method.
2 Multi-Agent Simulation (MAS) is a simulation method similar to ABSS. MAS is a well-established research and applied branch of Artificial Intelligence (AI). Since MAS is more related with AI, logic-based and cognitive science, it can be defined as the study of societies of autonomous “artificial agents.” In contrast, ABSS can be defined as the study of “artificial societies” of autonomous agents (Conte et al. 1998).
3 The pipeline consists of orders placed but not received.
4 The sequence of supply chain stages from factory to final customer is termed “downstream,” and the sequence of supply chain stages from final customer to factory is termed “upstream.”
5 Backorders, also called backlog of orders, refer to previously unmet demands.
6 The shipment can exceed the order due to the previously unmet demand which is called backorder.
7 The homogeneous agents in the simulation model will produce symmetric simulation results, from which some valuable insights may not be gained.
8 The steep ramp-up is comparable to that used in the simulation experiments of Akkermans (2001) in which business cycles are introduced and a supply network model is tested under severe stress.
9 Eclipse is an open source community whose projects are focused on building an open development platform comprised of extensible frameworks, tools and runtimes for building, deploying and managing software across the lifecycle ( source: http://www.eclipse.org). It provides a Java IDE (Integrated Development Environment) including convenient user interface and other useful tools.
10 The simulations were run for 500 time periods ( t1 ~ t500), but the graph shows the simulation results only up to 80 time periods ( t80). Even after that time, the inventory levels repeat the same pattern, so I chose to show the results only up to that time.
11 The simulation results of symmetrical trust levels coincide with the argument by Anderson and Weitz (1992) that the trust levels in the mutual relationship become symmetrical in the long run, through repeated cyclical interactions between two firms.
12 The argument assumes that preference in their models corresponds to trust in my model.
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