# A Scheduling Algorithm for Multi-Workshop Production Based on BOM and Process Route
## 1 Introduction  
The job scheduling problem is generally considered to study the problem of the order-oriented task arrangement, and the product's process route is in a single workshop, while the scheduling takes place at the internal process level of the workshop. However, in actual production, the production of complex products is often involved. These products are complex in structure and have long process routes, and they often need to be completed by going through multiple workshops--that is, multi-workshop production. For the scheduling of complex products in multi-workshop production, it is necessary to consider not only the dependence on different products and their components, but the scheduling between workshops and the job scheduling for each workshop should also be considered. In addition, for some products, the manufacturer also needs to consider the issue of the delivery cycle. Therefore, it is necessary to study the scheduling problem of complex products in multi-workshop production environments to meet the actual production and manufacturing needs. To date, researchers have carried out a great deal of research on complex scheduling problems. These research studies mainly focused on multi-objective job shop scheduling, distributed job scheduling, and flexible job shop scheduling. For the modeling of complex scheduling problems, some researchers proposed modeling methods based on the analysis of process planning. [PERSON] et al. [1] proposed a mathematical model of the multi-objective job-shop scheduling problem with alternative process plans and unrelated parallel machines. Then, the problem was divided into two sub-problems: flexible processing route decision and task sorting. [PERSON] [2] studied the scheduling problem with complex correlations between processes. The scheduling was decomposed into two nested sub-problems, namely arranging processes and machine arrangement, and the complex scheduling problem wasrealized by a nested optimization method with the inclusion of ant colony optimization (ACO). [PERSON] et al. [3] analyzed the characteristics of the energy consumption composition of the workpiece machining and proposed a batch splitting flexible job shop scheduling model based on alternative process plans for the optimization objectives of minimizing energy consumption and makespan. To solve the flexible job-shop scheduling problem with multiple process plans (FJSP-MPP), [PERSON] et al. [4] built a mathematical model by using a four-tuple-based mathematical scheme (FTMS) and developed an integrated scheduling algorithm based on ant colony optimization. The method of mixed-integer linear programming was used for the modeling of complex scheduling problems. [PERSON] and [PERSON] [5] used a mixed-integer linear programming model to solve the distributed job shop scheduling problem and proposed a new simulated annealing algorithm using advanced mobile operators. [PERSON], [PERSON], and [PERSON] [6] proposed a mixed-integer linear programming (MILP) model for the simultaneous batching and scheduling of multi-site multi-product batch plants with non-identical parallel units. [PERSON], [PERSON], and [PERSON] [7] studied the multi-model assembly line balancing problem, in which several products were produced in separate batches on a single assembly line, and proposed a multi-objective mixed-integer linear programming model. [PERSON], [PERSON], and [PERSON] [8] investigated a complex two-stage hybrid flow shop scheduling problem and proposed a discrete-time mixed-integer linear programming model. To solve the large instances of the problem, a genetic algorithm (GA) with a novel crossover operator was developed. Aiming at the many-objective scheduling problem, [PERSON] et al. [9] proposed a fitness evaluation mechanism based on fuzzy correlation entropy (FCE), and, on the basis of FCE and clustering methods, an environmental selection mechanism (ESM) was proposed to balance the convergence and diversity of solutions. In view of the flexible job shop scheduling problem (FJSP), [PERSON] et al.