# Reducing Nervousness in Master Production Planning:
## 3 Proposed PDS
### PDS Architecture  
The system architecture contains physical and virtual layers, each with three levels (configuration, interactions, and results), as shown in Figure 1. An agent represents each product in the virtual layer, transforming the information into valuable data for decision making. The configuration of the virtual layer represents the results generated by the optimization model as data for communication and decision making by each agent. Thus, the physical layer of the system interacts with other physical entities, and its virtual layer interacts with the environment for production control and management. Decision making  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(k/t\) & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline
**1** & \(Q_{i1}^{1}\) & \(Q_{i2}^{1}\) & \(Q_{i3}^{1}\) & \(Q_{i4}^{1}\) & & & & \\ \hline
**2** & & \(Q_{i2}^{2}\) & \(Q_{i3}^{2}\) & \(Q_{i4}^{2}\) & \(Q_{i5}^{2}\) & & & \\ \hline
**3** & & & \(Q_{i3}^{3 and communication among agents are distributed on the same hierarchical scale. The intelligence function of the agents considers decision rules for obtaining a global objective considering all of the system's entities. Such decision rules are known and applied by all of the agents of the system through internal and inter-agent communication. This information is processed and stored in the physical part of the components. At the results level, the model outputs correspond to the production planning, virtually and physically representing the planning. The virtual layer in Figure 1 contemplates an intelligence function that evaluates individual and collective performance, looking for system stability with a sustained cost increase. To this end, the intelligence function measures the nervousness of each agent using Equation (8). Each agent complies with the characteristics of an intelligent product defined by [PERSON] et al. [43], i.e., they have a unique identifier and can communicate with the surrounding agents of the same product type. Agent communication occurs within the system's virtual layer, where each product corresponds to an individual agent (Figure 1). This communication converts information into data. Each agent collects and processes data on its current state, production requirements, and resource needs. Interaction between agents occurs through a question-and-answer system. In addition, communication between agents eventually involves transferring data through the system optimization model, including results derived from production planning, capacity, and constraint information and recommendations to support decision making. Figure 2 depicts the communication process among agents representing various product types within the system. These agents engage in virtual interactions, inquiring about the required production quantity for each period and cycle. Furthermore, when the daily production capacity is exceeded, agents reach out to agents representing other product types. Such interactions constitute internal communication among agents of the same type and external communication between agents of different types. For instance, an agent positioned in the production plan's second cycle and second period would query the production quantities for future periods pertaining to the product it represents. Additionally, this agent would refer to the quantities produced in previous cycles to ensure production stability. This continuous communication facilitates the coordination of production activi  
Figure 1: Model characterization matrix. ties and enables informed decision making that aligns with each product's specific needs and capacities. Figure 3 shows the sequence of actions of the proposed architecture. First, the algorithm solves the mathematical model and generates the optimal production. Then, the agents evaluate the nervousness and the planning cost to determine the required production that minimizes the increase in production cost. The objective function of the lot-sizing model (Equation (1)) is the basis of such calculation.