## 2 Literature Review on Solution Strategies  
The possible solution strategies for the ISLP problem can be classified into three categories, as shown in Figure 2.  
Figure 1: Relations between FJSSP and MRWLP.  
For the sequential method, the integrated problem is decomposed into two subproblems: one is the upper-level subproblem to determine scheduling schemes; the other is the lower-level subproblem to design corresponding layout schemes. The upper-level decisions are used as inputs for the lower-level subproblem. It is noted that the flow of information is only from the upper-level problem toward the lower-level problem. The sequential method is widely applied because of its simplicity, but it often results in a sub-optimal solution for the entire production process [27]. The sequential nature of the traditional approach prevents the scheduling model from considering detailed workshop layout information because the layout problem is not solved in the scheduling phase, which may lead to the scheduling scheme becoming inefficient and less practical. For example, a scheduling model often includes a parameter to denote the time required to process a job, but the actual completion time is highly dependent on the layout scheme, which influences the performance of the scheduling scheme.  
In the simultaneous method, the layout model is simply appended to the scheduling model as constraints [10; 15; 16; 17], which leads to the layout scheme lacking autonomy. Without its own objectives, the layout model is optimized to purse the objectives of the scheduling model. Nevertheless, in addition to considering the objectives of the scheduling problem, the layout problem also needs to achieve some objectives, such as the material handling cost, closeness rating score, space utilization ratio, and so on, to ensure the performance of the layout scheme. For the monolithic model only including scheduling objectives, it is difficult to consider the interaction of scheduling and layout planning. For example, if only the makespan of the scheduling problem is optimized, a scheduling scheme with minimum makespan may be executed difficultly in an unreasonable layout, resulting in frequent delays, interruptions, or failures in the operation process.  
For the bi-level method, it can be regarded as a compromise between the sequential method and simultaneous method. Similar to the simultaneous method, it optimizes the scheduling and layout problems simultaneously as an integrated problem. Meanwhile, this method grants a degree of autonomy to the layout problems, so it has its own objectives. More importantly, the method enables collaboration between the scheduling problem and the layout problem by a feedback loop. Though the method outperforms the sequential and simultaneous methods in terms of the solution quality, the method encounters severe computational complexity [28]. Therefore, it is necessary to develop efficient algorithms to achieve this method.  
In the proposed MEIFM problem, different from the previous literature [11; 13; 19], this paper considers flexible processing routes of jobs and unequal-area machines concurrently, which embodies a strong interaction between FJSSP and MRWLP. In addition, both FJSSP and MRWLP have independent objectives. Based on the characteristics of this problem and the description of the above three methods, it can be found that the bi-level method is a very efficient technique to tackle this MEIFM problem. In this method, the FJSSP and MRWLP represent two levels, with autonomy and independent objectives. More importantly, the bi-level method is flexible enough to consider the interaction of the FJSSP and  
Figure 2: Structures of three methods for solving the ISLP problem.  
MRWLP by the feedback loop. Therefore, the motivation of this study is using the hierarchical interaction characteristic of the FJSSP and MRWLP to search for a more effective model and solution for solving the complex integrated problem. In the next section, an MOBLP model for the proposed MEIFM problem is presented.