# A Study on Operator Allocation in Consideration of Fatigue in Cell Manufacturing System +
## 1 Introduction  
The manufacturing industry is transitioning from high-volume, low-volume production to high-mix, low-volume production (HMLV) [1; 2; 3; 4] as consumer needs diversify. This transition requires more flexibility in the manufacturing process. Manual assembly operators remain essential in many manufacturing industries [5] and they provide flexibility to the assembly line that is not possible with automated systems [6]. Manual handling is essential, especially in situations where flexibility is important.  
Cell production systems are attracting attention as a form of production suitable for high-mix, low-volume production. In this system, operators are responsible for a wide range of tasks, and their skills have a significant impact on quality and productivity. Therefore, in cell production systems, it is important to accurately identify the skills of operators and effectively train them accordingly.  
In recent years, the use of virtual reality (VR) and augmented virtual reality (AVR) technology has been reported as a training method to improve operators' skills [7]. [PERSON] et al. (2024) [8] study how to design VR systems to reduce cognitive load. Immersion in a virtual environment (VE) allows operators to experience the same emotions and sensations during training as they experience, such as the same anxiety, fear, and concern [7]. This is especially important in operations where a minor mistake can result in a serious accident [9]. Since this study targets simple assembly tasks, VR technology is not considered.  
In the manufacturing industry, a skill management chart called a \"skill map\" is generally used to clarify the skills required for a task and to confirm and visualize the current skills of the operators. We proposed the \"skill index\", which classifies operators' skills based on the time required for a task, as a notation method for skill maps [10]. Operators become more proficient by repeating the same task, and the time required decreases. Theskill index updates the skill level by estimating the time required to complete a task by simulating proficiency. However, in actual workplaces, it has been found that factors affecting assembly time are related to proficiency and other factors related to operator ability and the work environment [11; 12]. These factors include age and experience, work design, and the effects of forgetting due to differences in the length of breaks separating work cycles [13; 14; 15]. Furthermore, human factors, such as fatigue, affect the change in proficiency rate [16]. There are several learning models that incorporate fatigue parameters, which have been proposed by [PERSON] et al. (2021) [17], [PERSON] et al. (2014) [18], [PERSON] et al. (2009) [19], [PERSON] (1974) [20], and [PERSON] (2018) [21], among others. In previous studies, these models were applied to datasets, and it was reported that the model by [PERSON] et al. (2021) was the most effective [17].  
In this study, we focus on the effect of fatigue among various human factors to simulate more realistically a task-division-type multi-person cell production system. [PERSON] et al.'s method [10] is used as the conventional method, and the method of [PERSON] et al. [17] is incorporated into the conventional method to propose an operator allocation method that considers the effects of fatigue. Therefore, the structure of this thesis is as follows: Section 2 describes the methodology used in the paper. Next, in Section 3, we design a specific mathematical model for the subject. In Section 4, we conduct computer experiments to verify the mathematical model's properties; in Section 5, we conduct assembly experiments, which are important, to validate the model with the mathematical model. To ensure the fairness of the comparison of the two experiments, the computer experiments are conducted again in Section 5 under the same conditions as the assembly experiments. The final chapter, Section 6, summarizes this study.