## 5 Numerical Experiment
### Parameters Setting
#### 5.2.2 After Applying a Mathematical Model  
Unlike a staff schedule before applying a mathematical model, a derived staff schedule is more efficient. As shown in Figure 4, all constraints regarding work in the daytime are satisfied. For example, 45 employees are scheduled to work if looking at Day 1. In addition, job assignments are met as well. Continuing looking at Day 1, more than 15 employees are assigned on each floor and two of the employees conduct Job 2 as equipment supervisors. Furthermore, more than one manager is assigned on each floor to supervise other regular and irregular employees as well. Moreover, over two of the employees work at open storage and a manager works in an office. That is, the failure of employees' assignments caused by a manager's random employee assignment does not happen. Other days, as well as Day 1 meet all constraints for job assignments. Along with this, the 52-h workweek policy is well applied in the mathematical model as the result shows. There are no employees who come to work for more than five days a week. All employees have a day off on Sunday. Furthermore, the purpose of the developed mathematical model is to minimize the total labor cost of regular and irregular employees. This means that the result in the numerical experiment is for a company that has a priority of saving the total labor cost. Therefore, if looking at the result in Figure 4, as many irregular employees as possible are scheduled on each workday even though the average percent of irregular employee absence is considered. It is more advantageous for a company to minimize the total labor costs by using as many irregular employees as possible out of 22 irregular employees due to relatively low labor costs. However, it is seen that as many irregular employees as possible are not used. This is because there are rules on conducting jobs for a company and there are jobs that can be conducted by regular employees. A company allocates overtime work by assigning only regular employees to jobs for consideration for regular employees as well. To conduct overtime work, regular employees should work during the daytime. Thus, the result in Figure 4 is derived, even though a company has enough irregular employees that can cover more jobs. Figure 3: A staff schedule before applying a mathematical model. Comparing a staff schedule before and after applying a mathematical model, the following things can be found. First, there is a difference in the number of employees who come to work per day on average. Consequently, about 1.6 employees come to work less than before after applying a mathematical model every day. Second, a developed mathematical model prevents situations where employees come to work more or less than the number of employees a company needs a day. This can aid in the improvement of human resource management. Third, a company can save total labor costs even though the company has the same number of employees as before. It was USD 143,525 before applying a mathematical model and it is USD 138,335 after applying a mathematical model. That is, a company can save a total labor cost of USD 5190. Lastly, the different employee work pattern is found due to consideration of the change in labor policy. Some employees came to work more than 6 days a week before applying a developed model. However, it is constrained by a mathematical model at the moment because a company should follow the change of labor policy, which is each employee should work less than 5 days a week. Figure 4: Optimal staff schedule during daytime. The number of days regular employees come to work is constrained after applying a mathematical model due to the change in labor policy and high labor costs. Some regular employees come to work 4 days a week. This could be shown not to allow them to work more. However, it indirectly proved that a company that did not efficiently manage human resources has several employees more than the number they need to have.