## Problem Description  
The DRCFJSP can be applied in various industries including automobile industry, equipment industry [6] and electromechanical industry [17]. We consider DRCFJSP with an MLPS to deal with the scheduling problem of manufacturing systems with assembly lines. There is a set of orders, \(O=\{O_{1},O_{2},...,O_{n}\}\); a set of final products \(F=\{F_{1},F_{2},...,F_{t}\}\); a set of machines \(M=\{M_{1},M_{2},...,M_{m}\}\); and a set of workers \(W=\{W_{1},W_{2},...,W_{k}\}\). An order, \(O_{i}\), denotes a production request for the final products, \(F_{a}\), within the due date, \(DD_{i}\). MLPS is a hierarchical tree that expresses the BOM structure for a final product and subcomponents. To produce each upper element, various types of child components are required. In Figure 1, the numbers on the arcs connecting each node represent the number of child components required to produce the parent node. Figure 1 illustrates an example of the MLPS for a final product, F1, in [PERSON] et al. [9]. F1 is produced by assembling one component S1 and two C1s, and C3 requires three successive processes, namely, P1, P2, and P3. When more than one process is required to produce a component, the process name is written along with the component name in the node. For example, in Figure 1, C3P1, C3P2, and C3P3 imply that the component C3 is processed in P1, P2, and P3, respectively.  
Several constraints are considered for an environment of DRCFJSP with MLPS. First, MLPS must be considered to determine the schedule, i.e., a sequence of operations according to MLPS. For example, in Figure 1, the operations for C1 and C2 must be executed before S1. Second, each item and subitem can be processed only in the designated machines, and each worker can work on all machines. The processing time of an item depends on the assigned machine and the skill level of the worker.  
Figure 1: Example of multilevel product structure ([PERSON] et al. [9]).  
Third, each machine and worker cannot simultaneously perform more than two operations. The same type of item cannot be worked on machines at the same time. Finally, the production quantity is determined based on the lot size and the total demand. It must be greater than the demand and must be an integer multiple of the lot size.  
In addition to the constraints, the following assumptions are made for the parameter values.  
* The raw materials required for the operation of the items are sufficient.
* The operation setup time is small enough to be ignored.
* The lot-size of each operation is fixed.
* There is a difference in the skill level of each worker according to the machine; however, the improvement in the worker's skill level because of the learning effect is small enough to ignore.  
This study aims to minimize the lateness, makespan, and maximum deviation of the workload in the machines. Among these objective functions, lateness minimization has the highest priority, followed by makespan minimization and workload balance; the function with the highest priority is the most preferred. Equation (1) represents the objective function for lateness. Delays in delivery are one of the most important factors in the manufacturing environment, because frequent delivery violations and lateness cause financial damage by lowering the corporate trust and resulting in long-term declines in orders. Equation (2) minimizes the makespan, which is used in many scheduling studies as a measure of process productivity. Equation (3) represents the objective function for minimizing the deviation of workload between machines, and is used to prevent the imbalance of workload between machines. The notations used in this paper are summarized in Table 11  
\[(G1)\ \min\sum_{i=1}^{n}(DD_{i}-\left[\frac{C_{i}}{CA}\right]) \tag{1}\]  
\[(G2)\ \min\left(\max C_{i}\right) \tag{2}\]  
\[(G3)\ \min\left(\max WT_{j}-\min WT_{j}\right) \tag{3}\]