# A Scheduling Algorithm for Multi-Workshop Production Based on BOM and Process Route
## 7 A Case Study  
In order to verify the feasibility and performance of the model and algorithm proposed in this paper, the product in Figure 3 is taken as an example. In this example, this case study consists of 12 products/workpieces, 61 processes, and 4 workshops. The parameters of PSO are set as follows: \(T=100\), \(N=15\), \(c1=2\), \(c2=2\). The fluctuation range of \(\omega\) is (0.8, 1.2), the particle velocity range is in (\(-\)0.8, 0.8), and the particle position is limited in the range of the workpiece serial number. The calculation results of the model are shown in the figure below. Figure 9 shows the fitness evolution curve of the optimized scheduling of each round of iteration, Figure 10a illustrates the initial scheduling sequence, and Figure 10b shows the optimized scheduling sequence after 100 iterations. In order to confirm the effectiveness of the algorithm, the algorithm in this paper is compared with the ant colony algorithm and genetic algorithm. After analyzing the convergence and stability of different algorithms, the experimental data obtained by comparison are shown in Figure 11. The parameters of the genetic algorithm are as follows: the number of populations is 10, the crossover probability is 0.4, the mutation probability is 0.2, and the normalized elimination acceleration index is 1.5. The parameters of ant colony algorithm are set as follows: number of ant colonies is 15, heuristic factor is 3, expected heuristic factor is 3, information intensity is 20, pheromone evaporation factor is 0.5, and the iterations of the three algorithms are 100. Figure 11a shows the comparison of the scheduling optimization results of the three algorithms for 30 products and 107 processes, and Figure 11b shows the comparison of the scheduling optimization results for 70 products and 225 processes. It can be seen from the results in the figure that, in the two examples, the improved particle swarm optimization algorithm used in this paper has achieved good results. In order to evaluate the performance of different algorithms, this paper further tests six cases with different  
Figure 8: Implementation of the path search rescheduling strategy. Through the analysis of Table 3, we can find that the algorithm and GA algorithm can obtain better scheduling results for case 1 and 2 with fewer products; for case 3 and 4, the algorithm in this paper is similar to the other two algorithms, but it is still better than the other two algorithms; in case 5 and 6, with the increase in the product number, the optimal value of this algorithm is still better than the other algorithms. This shows that the algorithm can not only obtain a better solution but also has strong stability, which is not random or accidental. Figure 12a shows the scheduling result analysis when the product quantity and process route remain unchanged and the product complexity increases. The three curves respectively correspond to the worst value, the best value, and the average value of the scheduling result. It can be seen that the product complexity has a positive relationship with the scheduling result. Figure 12b shows the scheduling result analysis when the product quantity and product complexity remain the same while the process route increases. It can be seen that the process route is in a reverse relationship with the scheduling result at the beginning, and then tends to be synchronous. Figure 12c shows the scheduling result analysis when the complexity of process route and product remains unchanged while the number of products increases. It can be seen that there is a positive relationship between product quantity and scheduling results. Figure 13 is a comparison of the scheduling results for 100 products and 291 processes. From the computation results of the above case study, it can be seen that, under the premise of satisfying the constraints of product structure and process route, the op  
Figure 12: Influence of product complexity, process route, and product quantity on scheduling results.