## 5 Applicability on Various Technologies
### Holonic Manufacturing System for Distribution Systems  
The last study deals with mail distribution centers of the French national postal service, La Poste [53]. Every day, human operators need to handle about 30,000 containers full of mail per center (about 12 kg each) to distribute them to the right carts before they are placed in trucks. One of the objectives of the digital transformation of the company was to robotize this task in order to decrease its impact on operator health. To be efficient, it is therefore necessary to optimize the distribution of containers and carts towards the robots in order to maximize the load no longer handled by the operators [54]. **Step II:** The major problem facing the distribution centers is the unpredictability of mail arrival. It is customary to say that the centers suffer the arrival of mail rather than control it. Even if some patterns can be identified, the variability between two \"similar\" days is too important. The lever identified here is the variability in the demand. In addition, many disturbances appear all along the year, which have a similar impact on disorganizing the distribution process (traffic problems, weather variability, etc.). **Step I2:** The paradigm that was identified here is the multi-agent paradigm, and holonic manufacturing systems in particular. The notion of an agent is very well suited for adapting to the variability of an input, but the emerging behavior makes the guarantee of performance difficult to evaluate; thus, the difficulty of introducing this notion in industry. **Step I3:** The ultimate objective of the digital transformation of the distribution centers is to implement this paradigm in the whole center, interconnecting all the sub-systems. This study started with the implementation of the \"Flexibac\" system, i.e., a pick and place robotic system aiming at handling mail containers. Therefore, the study only focuses on the integration of this system on the main transitic loop, in parallel with the conveyors occupied by the operators. **Step P4:** The KPIs of this study are related to the number of containers handled by Flexibac. In parallel, the filling rate of the carts is measured, as it is connected to the number of cart movements made by the operators. These KPIs were evaluated in the execution over several days, chosen by the experts as typical days. The input of each scenario contains a timestamp of arrival for each container in the system to be handled. **Step P5:** The evaluation of the lower bound of the performance was made in the simulation of a virtual implementation of Flexibac. In this model, the knowledge of the experts was formalized in order to determine the best organization currently implementable with the available computer infrastructure. It was designed as an evolution of the daily plans that are currently in use in those centers. **Step P6:** The upper bound was made using operational research techniques. The objective was to determine the optimal schedule of carts and containers to send to Flexible in order to optimize the KPI. The results that were obtained necessitated adding several hypotheses to simplify the problem, which included the necessity to suppress the input variability: the scheduler needed the knowledge of the incoming containers of the whole day to really be able to optimize the distribution [54]. The schedule was tested on simulations of different days and showed low results, which confirmed the impossibility of implementing this solution. However, the level of the KPI (about four times better than the lower bound) provides a clear upper bound that will be almost unreachable for any other solution. **Step S7:** The solutions that were designed were based on heuristics. The experts of the system were interviewed to gather their opinions about a first version of the optimal behavior they imagined. Based on their answers, a rule-based behavior of the system was designed.