## 2 Literature Review  
Analytic Hierarchy Process (AHP) is one of the traditional decision-making methods for estimating weighting factors for multi-criteria decision-making [21]. Evaluation is performed by pairwise comparison for multiple evaluation criteria and alternatives. The pairwise comparison determines the importance of evaluation criteria and alternatives. Itis effective in rationalizing complicated decision-making. Since it is a simple method, it is used in various situations. For example, the AHP model is used to evaluate the components of a machining center so that the manufacturer can purchase the most suitable machining center [22]. However, when there are so many evaluation criteria and alternative options, it is too complicated to set appropriate pairwise comparisons for multiple evaluation criteria. In general, the methods for solving multi-objective optimization problems are classified into the following three methods depending on the situation in which the decision-maker involves the process [23]. 1. A priori methods: The decision maker specifies the preferred objective function before executing the solution process. 2. Interactive methods: Phases of interaction between decision-makers and the solution process are iteratively conducted. 3. Posteriori or generation methods: After the solutions are generated by the weighting method or \(\epsilon\)-constraint method, the decision-maker selects the preferred solution. In this study, the a priori method is used to solve the scheduling problems. However, the aim of this study is to estimate the weighting factor of a scheduling problem instead of solving it. A previous study on the identification of the objective function was conducted to read the operator's intentions from the input/output data of a scheduling problem [24]. In the single-objective scheduling problem, the objective function used was estimated from historical data in the literature. This was conducted for only one objective function. However, in an actual factory, there are multiple objective functions to be optimized in many cases. The methods for solving multi-objective optimization problems have been extensively studied in the literature. A decomposition-based evolutionary multi-objective optimization algorithm is used, which transforms a multi-objective optimization problem into several single objective optimization problems and optimizes them simultaneously [25]. For the three-objective scheduling problem, a three-phase decision-making method is constructed, and finally, a data envelopment analysis technique is applied to determine the preferred schedule [26]. Dynamic scheduling is proposed to solve the optimization problem of selecting the next job for each schedule [27]. In multi-objective flow shop scheduling, optimization algorithms are used which consider changes in material requirements, inventory control, and delivery dates [23]. To solve the multi-objective scheduling problems, there is a method of setting a weighting factor for each objective function to create a single objective function. To reflect the operator's intentions from the past schedule, it is necessary to estimate the weighting factors of the objective function. Previous studies on weighting factor estimation are described. The inverse problem using linear programming was used to estimate the weighting factors after the range of weighting factor that derives a preferred solution is derived when a person in the field makes decisions [18]. However, this method has not been applied to the actual scheduling problem in the literature. In reference [28], a method for estimating the weighting factors from past scheduling data has been proposed for small-scale scheduling problems. However, the scale of production processes in the conventional study is not so large because the exact optimal solutions are used to find the weighting factors by using commercial solvers. It becomes intractable to utilize exact algorithms for large scale problems.