## 1 Introduction  
The optimization model for scheduling problems consists of boundary conditions, decision variables, constraints, and objective functions. In practice, it is difficult to adapt to changes in the selection of objective functions and weighting factors for multi-objective optimization problems when constructing an optimization model for production scheduling problems. Data-driven optimization is one of the decision-making methods based on quantitative data [1]. In the data-driven approach, the actions are determined after the data is collected, stored, and analyzed. This allows past information to be incorporated into future decision-making factors. The data-driven optimization approach has been widely used in various fields such as supply chain, transportation systems, and healthcare [2; 3; 4], and it is required for modeling complex production scheduling problems. Scheduling optimization has become an important issue in recent years. Many companies have interests to upgrade their industrial facilities to meet the Industry 4.0 paradigm. At the same time, they are required to optimally manage their production systems. In recent years, real-world scheduling problems have become complicated due to complex constraints and objective functions. Scheduling algorithms using the concepts of linear optimization and batch operation scheduling [5] and nonlinear optimization theory and batch scheduling [6] have been proposed and applied to a chemical industrial site. Methods for integrating multiple time scales to increase process efficiency have also been studied [7]. The application of game theoretical approaches to job scheduling has also been studied in the distributed scheduling methods. An autonomous decentralized scheduling [8; 9], non-cooperative game approach for scheduling [10], and evolutionary game theory approach [11] have been addressed. Recently, restaurant scheduling with resource allocation [12] has also been proposed. These approaches have been successfully applied to the job scheduling problems. It is also required to help decision-makers to build an optimization model from historical and real-time data for efficiency and flexibility of production systems. In online scheduling, algorithms have been proposed which take real-time data into account [13]. Scheduling problems with multiple objectives require mathematical models that reflect human operators' preferences based on multiple optimization criteria [14]. However, it is difficult to set the appropriate weighting factors for the objective function in a multi-objective scheduling problem [15]. Scheduling is a complex task that is often determined manually or by simulation. As a result, suboptimal solutions are derived [16]. If weighting factors that do not reflect the operator's intention are set, an undesired schedule will be generated. In that situation, human operators must manually fine-tune the schedule when the circumstances surrounding the production environment change. Thus, the weighting factors need to be modified iteratively in the multi-objective scheduling problem [17; 18]. The estimation of the weighting factors is required because the human operators can efficiently obtain the schedule originally desired. For example, when we automatically determine the weighting factors of the objective function, the input/output data is effectively used to quantify the evaluation criteria of the production schedules that had been already in operation. As a result, the weighting factor of the daily schedule result can be quantitatively analyzed. In this paper, we propose a machine learning method and an inverse optimization method to estimate weighting factors of the objective function for model identification of production scheduling problems. In machine learning, features for weighting factor estimation are selected using a wrapper method. In recent years, machine learning has grown rapidly with the increase in data and the development of computers performance.