本研究探討台灣高鐵服勤員排班問題,利用數學規劃法建構符合政府法規及公司規定之數學規劃模型,其目標式為最小化違反服勤員班表偏好。本研究可分為三階段:第一階段中,依照高鐵13位服勤員之周排班,利用數學規劃法建構符合其硬限制及軟限制的數學規劃模型,再運用IBM ILOG CPLEX Optimization Studio求解服勤員之周班表;第二階段中,將周班表擴增至月班表,求解服勤員排班問題;第三階段中,增加每位服勤員執勤每個班別(早班、中班、晚班)至少6天與至多8天之軟限制,求解服勤員之月班表。再者,本研究以敏感度分析討論服勤員人數從15位遞減至12位對目標式之影響。其數值結果顯示:數學規劃法能有效率求解台灣高鐵服勤員排班問題,並產生最大滿足服勤員偏好之班表。因此,本研究之方法論可提供排班人員做參考。
This research studies Taiwan high speed rail staff scheduling problem, and applies mathematical programming to construct a mathematical model which complies with government regulations and company's rules. The objective function of the model is to minimize the violations of staff preferences. This study contains three phases: in the first phase, this study applies mathematical programming to construct a hard- and soft-constraint mathematical staff scheduling model based on Taiwan high speed rail company's 13 staff weekly schedules, and uses IBM ILOG CPLEX Optimization Studio to solve the corresponding problem. In the second phase, this study extends the weekly to monthly schedule, and solves the corresponding problem. In the third phase, this study adds two soft constraints, each staff should have at least 6 working shifts on the day, afternoon, and night shifts and each staff should have at most 8 working shifts on the day, afternoon, and night shifts during the entire scheduling periods. Then, this study solves the modified problem in order to obtain an optimal staff monthly schedule for 13 employees. Furthermore, this research adopts the sensitivity analysis to investigate the impact of the number of staff (reducing from 15 to 12 employees) on the objective function. The numerical results show that mathematical programming can efficiently solve the proposed Taiwan high speed rail staff scheduling problem and can generate a maximal satisfactory staff schedule. Therefore, the proposed methodology of this study can provide schedulers for a reference.