## 4 Results
### Layout, Tests, and Results of the Production System  
AGV systems are widely used in automobile production plants. A case study was considered in a body department of an automobile production plant that uses a low-cost AGV system. The layout of the analyzed case is shown in Figure 3. Ten AGV circuits exist in the system and 17 AGVs are in use to satisfy the production requirements. Due to the implementation constraint, only 12 parking stations can be found in the layout. If an AGV circuit does not employ the pool methodology, its production station is utilized as a parking station. Thus, there were twenty-two parking stations, and ten parking stations were specific to an AGV circuit. AGV circuits, parts that are transported, their hourly consumption,  
In the first stage, AGV circuit combinations with parking stations were calculated. \(I\) = 22 and \(S\) = 10, and at the end, 2\({}^{10}\)\(\times\) 22 = 22,528 (\(GP_{ij}\)) values were calculated by the algorithm [50]. The next stage was about the selection of the optimum AGV fleet size with the GA. Genes reflect the parking station to which the AGV circuits are assigned. The population size was 300. Chromosomes are selected randomly such as 1-13-13-15-5-6-13-18-9-22. First, the AGV circuit was assigned to the first parking station. AGV circuits 2, 3, and 6 were used as an AGV pool in parking station 13. The fitness function is the sum of \(GP_{ij}\), which indicates the required AGV number to fulfill production demands. GA solutions are given in Table 6. Tables 6 and 7 are the solutions for the best chromosomes of the genetic algorithm, showing which AGV circuits will be assigned to which parking stations. As a second objective, the AGV service time is included. With this approach, the minimum required AGVs that satisfy the minimum AGV investment and minimum service time lead to the minimum energy consumption, because AGVs use the minimum energy in waiting but moving on the ground increases the energy consumption. The pool combination that satisfies the minimum required AGVs with the minimum service time was computed as the optimal solution. The objective of the first fitness function was the required number of AGVs; then, the AGV service time was added as a second target to avoid unnecessary parking station assignments. To add this second objective, a new fitness function was defined by using coefficients separating the AGV number from the service time as follows,  
\[\text{Fitness function}=1000\times\text{Required AGV number}+\text{Service time}/1000\]  
The GA solutions with the new fitness function are given in Table 7.  
According to the results, some circuits were repeatedly assigned to the original parking stations; for example, AGV circuit 1 is usually assigned to the parking (production) station. The second observation was regarding the sharing of parking stations. When certain circuits do not share parking stations with other circuits, they use their own parking (production) station as the desired state. As a result, the suggested solution is 1-2-3-4-16-15-7-8-16-15. According to this solution, two pool systems should be created. The first pool should be at parking station 16, and AGV circuits 5 and 9 should use this pool. A second pool should be created at parking station 15, and AGV circuits 6 and 10 should use this pool. Other AGV circuits should use the production stations as parking stations. It was shown that the proposed approach provides a fleet size which requires five fewer AGVs, with a 29% reduction in the number of AGVs.