# A Scheduling Algorithm for Multi-Workshop Production Based on BOM and Process Route
## 1 Introduction
[25] proposed an effective estimation of distribution algorithm (EDA) to solve the multi-objective flexible job-shop scheduling problem (MFJSP), and a probability model was built to generate the new individuals. [PERSON] et al. [26] proposed hybrid evolutionary algorithms (HEA) to solve a variety of single or multi-objective scheduling problems in manufacturing systems to obtain the best solution with the smallest computational time. Furthermore, ant colony optimization algorithms were proposed to solve complex scheduling problems. [PERSON] and [PERSON] [27] proposed a hybrid agent-based ant colony optimization-genetic algorithm for parallel two-sided assembly line balancing and model sequencing problems. [PERSON] et al. [28] studied a two-stage ant colony optimization algorithm, which can dynamically determine the actual process planning and scheduling according to the order details and the status of manufacturing system while considering the process planning and scheduling problems. [PERSON] et al. [29] studied two-stage permutation flow shop problems with batch processing machines, considering different job sizes and arbitrary arrival times, and proposed the quantum-inspired ant colony optimization (QIACO) algorithm to solve the problem. In addition to the above methods, many efficient methods were also developed to obtain optimal solutions. [PERSON] et al. [30] proposed an effective discrete artificial bee colony algorithm for solving the distributed lot-streaming flow shop scheduling problem with the objective of minimizing makespan. [PERSON], [PERSON], and [PERSON] [31] developed a hybrid sorting immune simulated annealing technique (HSISAT) to achieve multi-objective optimal scheduling by sorting the job through the isolation of critical machines, and the immune simulated annealing method was adopted to increase the convergence speed. [PERSON] and [PERSON] [32] studied the route selection and the sequencing sub-problems in the multiple-route job-shop scheduling problem (MRJSP) and proposed a two-phase algorithm that can generate high-quality schedules in a timely manner. [PERSON] et al. [33] built an assembly scheduling model by analyzing the characteristics of a complex product process flow and proposed an improved discrete krill herd (IDKH) algorithm. To solve the distributed two-stage hybrid flow shop scheduling problem (DTHFSP) in a multi-factory environment, [PERSON] and [PERSON] [34] proposed a shuffled frog-leaping algorithm with memeplex grouping (MGSFLA) to minimize makespan and the number of tardy jobs. To date, the research on scheduling problem has been mostly focused on single production processes, while research on the combination of machining and assembly processes is sparse, particularly research on the scheduling problem of complex products with complex processes. Scheduling problems for complex products in multi-workshop production are quite different from traditional job-shop scheduling problems. Traditionalscheduling problems generally consider specific job forms according to the characteristics of the products, and different job forms adopt different scheduling strategies. Scheduling for multi-workshop production needs to consider multiple job forms, as well as the constraints between products and the transfer between multiple workshops. In view of the scheduling problem of complex products in multi-workshop production, the research in this paper has the following characteristics: (1) the BOM structure of complex products is considered, including cross references between products; (2) the influence of the two-level process of the product in the process route and operation on the scheduling is considered. In addition, processing and assembly processes are considered simultaneously. In order to solve this complex problem, an improved particle swarm algorithm is developed and tested. This method has the potential to provide an effective solution for the multi-workshop scheduling problems involving complex products.