鐵路系統是一種高效率的運輸系統，具有高度之計劃性，必須在運轉前規劃時刻表及諸多計劃。其中時刻表對於鐵路系統運轉相關之績效具有關鍵性影響。對於鐵路系統的乘客而言，列車是否準點依照時刻表運轉，是一個關鍵的績效指標。在時刻表中適當排入寬裕時間或緩衝時間，可以有效降低晚點的發生與傳播，但亦同時降低運轉效率；但如何適當分配寬裕時間與緩衝時間是一個困難的課題。本研究為此提出結合系統模擬與線性規劃模式之演算法以調整各列車之寬裕時間與緩衝時間，同時控制系統的平均晚點量以及運轉效率。利用此演算法，本研究以臺鐵真實時刻表為例，解得其效率與穩定間之關係曲線，同時找到對乘客總旅行時間最有利之平衡點，以提供營運單位參考。
實務上規劃時刻表多僅考慮乘客需求、列車編組與人力資源等因素，較少考慮執行時刻表所需之能耗，過往文獻亦多聚焦於極小化單一列車的能耗。為此本研究提出有系統之方法，在維持列車既有順序的前提下調整時刻表，以降低整體能耗。本研究首先使用多目標最短路徑模式求得列車的能量曲線，再以線性迴歸歸納能耗與行駛時間之關係式，據以利用線性規劃模式調整時刻表。以臺鐵真實時刻表測試結果顯示，微幅增加列車運行時間，可有效降低整體系統能耗，顯示本研究成果具有實務運用價值。

Railway is an efficient transportation system. Timetable has critical effect on the operational performance of railway system. For a railway system passenger, timetable adherence and punctuality are important performance indicators. Appropriate slack time and buffer time in the timetable can effectively reduce delays as well as their propagation, at the cost of reduced efficiency. In this study, we integrate simulation and linear programming to develop a heuristic that adjusts the slack time and buffer time in a given timetable, that controls both delay and efficiency. With a numerical case derived from Taiwan Railway Administration timetable, we quantify the relationship between timetable efficiency and robustness with the heuristic, and demonstrate that one can find the ideal balance between passenger total travel times and robustness.
In practice, timetables typically take passenger demand, rolling stock and human resource into consideration, but energy consumption is less concerned. This study proposes an approach to optimize the system-wide energy consumption by adjusting a given timetable while preserving the order the trains go through stations. The model first uses a multi-objective shortest path problem to derive the energy-time curve of trains, then establishes numerically the relationship between energy consumption and running time. Finally, a linear program adjusts the given timetable to minimize total energy consumption. With a numerical case based on Taiwan Railways Administration system data, we demonstrate the ability of the model to reduce overall energy consumption by slightly increasing the trains’ running times.

Albrecht, T. (2004). "Reducing power peaks and energy consumption in rail transit systems by simultaneous train running time control." Advances in Transport 15: 885-894.

Brännlund, U., P. O. Lindberg, A. Nou and J.-E. Nilsson (1998). "Railway timetabling using Lagrangian relaxation." Transportation science 32(4): 358-369.

Carey, M. and I. Crawford (2007). "Scheduling trains on a network of busy complex stations." Transportation research part B: Methodological 41(2): 159-178.

Carey, M. and D. Lockwood (1995). "A model, algorithms and strategy for train pathing." Journal of the Operational Research Society 46(8): 988-1005.

Conte, C. and A. Schöbel (2007). Identifying dependencies among delays. IAROR Hannover, Germany.

Delorme, X., X. Gandibleux and J. Rodriguez (2009). "Stability evaluation of a railway timetable at station level." European Journal of Operational Research 195(3): 780-790.

Dingler, M., A. Koenig, S. Sogin and C. P. Barkan (2010). Determining the causes of train delay. Annual Conference of the American Railway Orlando, Florida.

Dingler, M. H., Y.-C. Lai and C. P. L. Barkan (2009). "Impact of Train Type Heterogeneity on Single-Track Railway Capacity." Transportation Research Record 2117(1): 41-49.

Domínguez, M., A. Fernández, A. Cucala and P. Lukaszewicz (2011). "Optimal design of metro automatic train operation speed profiles for reducing energy consumption." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail Rapid Transit 225(5): 463-474.

Fischetti, M. and M. Monaci (2009). Light robustness. Robust and online large-scale optimization, Springer: 61-84.

Fischetti, M., D. Salvagnin and A. Zanette (2009). "Fast approaches to improve the robustness of a railway timetable." Transportation science 43(3): 321-335.

Frank, O. (1966). "Two-way traffic on a single line of railway." Operations Research 14(5): 801-811.

Ghoseiri, K., F. Szidarovszky and M. J. Asgharpour (2004). "A multi-objective train scheduling model and solution." Transportation research part B: Methodological 38(10): 927-952.

Higgins, A., E. Kozan and L. Ferreira (1996). "Optimal scheduling of trains on a single line track." Transportation research part B: Methodological 30(2): 147-161.

Howlett, P. (1996). "Optimal strategies for the control of a train." Automatica 32(4): 519-532.

Howlett, P., I. Milroy and P. Pudney (1994). "Energy-efficient train control." Control Engineering Practice 2(2): 193-200.

Jovanović, D. and P. T. Harker (1991). "Tactical scheduling of rail operations: the SCAN I system." Transportation science 25(1): 46-64.

Kliewer, N. and L. Suhl (2011). "A note on the online nature of the railway delay management problem." Networks 57(1): 28-37.

Kraay, D. R. and P. T. Harker (1995). "Real-time scheduling of freight railroads." Transportation research part B: Methodological 29(3): 213-229.

Kroon, L., G. Maróti, M. R. Helmrich, M. Vromans and R. Dekker (2008). "Stochastic improvement of cyclic railway timetables." Transportation research part B: Methodological 42(6): 553-570.

Krueger, H. (1999). Parametric modeling in rail capacity planning. Winter Simulation Conference, Phoenix,Arizona.

Lechelle, S. A. and Z. S. Mouneimne (2010). OptiDrive: A practical approach for the calculation of energy-optimised operating speed profiles. IET Conference on Railway Traction Systems (RTS 2010), Birmingham, UK.

Lee, Y. and C.-Y. Chen (2009). "A heuristic for the train pathing and timetabling problem." Transportation Research Part B: Methodological 43(8): 837-851.

Liu, S. Q. and E. Kozan (2009). "Scheduling trains as a blocking parallel-machine job shop scheduling problem." Computers Operations Research 36(10): 2840-2852.

Olsson, N. O. and H. Haugland (2004). "Influencing factors on train punctuality—results from some Norwegian studies." Transport policy 11(4): 387-397.

Pachl, J. (2015). Railway Operation and Control, VTD Rail Publishing.

Peña-Alcaraz, M., A. Fernández, A. P. Cucala, A. Ramos and R. R. Pecharromán (2012). "Optimal underground timetable design based on power flow for maximizing the use of regenerative-braking energy." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail Rapid Transit 226(4): 397-408.

Sicre, C., P. Cucala, A. Fernández, J. Jiménez, I. Ribera and A. Serrano (2010). "A method to optimise train energy consumption combining manual energy efficient driving and scheduling." WIT Transactions on The Built Environment 114: 549-560.

Wang, P. and R. M. P. Goverde (2016). "Multiple-phase train trajectory optimization with signalling and operational constraints." Transportation Research Part C: Emerging Technologies 69: 255-275.

Wang, Y., B. De Schutter, T. J. J. van den Boom and B. Ning (2014). "Optimal trajectory planning for trains under fixed and moving signaling systems using mixed integer linear programming." Control Engineering Practice 22: 44-56.

Yang, L., K. Li, Z. Gao and X. Li (2012). "Optimizing trains movement on a railway network." Omega 40(5): 619-633.

Ye, H. and R. Liu (2016). "A multiphase optimal control method for multi-train control and scheduling on railway lines." Transportation research part B: Methodological 93: 377-393.

Zhou, X. and M. Zhong (2007). "Single-track train timetabling with guaranteed optimality: Branch-and-bound algorithms with enhanced lower bounds." Transportation research part B: Methodological 41(3): 320-341.

曾乙申 (2002). "「捷運與輕軌供電系統電腦化模擬(上)—列車運行模擬」." 捷運技術半年刊 27: 161-184.

張有恆 (2010). 現代運輸學, 華泰文化.

李治綱、陳鑑康 (1995). "列車運行績效之模擬分析." 運輸計劃季刊 24(1): 1-15.

林宜勝、陳雙源 (2000). "軌道列車曲線阻力和坡度阻力之探討." 台鐵資料季刊 304: 93-95.