當多點災害發生且短時間內產生的傷患數量遠高於平時可用資源，稱為大規模傷亡事件（mass casualty incident, MCI），這導致對緊急醫療服務的需求激增，往往會壓倒當地緊急應變能力，也使救護車成為稀缺資源之一。在傳統的指派中，僅依靠決策者的經驗且通常順序紊亂，將造成更多人因延誤救醫而造成生命威脅，因此根據傷患優先順序分配緊急醫療資源和指派救護車路線以最大限度地提高傷患生存率至關重要。
本研究以地震災害發生後造成多地點湧出大量傷患的情境，且因地震造成道路損壞造成具有不確定運送時間下，提出二階段隨機混整數規劃模型（Two-Stage Stochastic Mixed Integer Programming），來求解大量傷患送醫順序、救護車派遣路線與傷患送醫院救治的最佳決策問題，同時也發展樣本平均近似法（Sample average approximation）將隨機參數透過隨機抽樣方式產生大量情境值（Scenarios），將隨機混整數規劃模型轉化為可求解的大型確定性混整數規劃模型，但該模型在有限時間和資源下無法用商用最佳化軟體（例如：CPLEX或Gurobi）求出最佳解，故本研究也提出結合樣本平均近似法與變數產生演算法（Column generation method），來有效率地求解此大型確定性混整數規劃模型。

This paper investigates the stochastic ambulance dispatching and routing (SADR) problem in a mass casualty incident under uncertainty of road vulnerability and traffic congestion caused by an earthquake. A two-stage stochastic mixed-integer nonlinear programing model is formulated to derive a robust ambulance scheduling decision for maximizing the expected total survival probability of all casualties. An integrated simulation optimization approach combining a travel time scenario generation algorithm, sample average approximation, and a column generation method is developed to efficiently solve this complicated two-stage SADR model with a nonlinear objective function and continuous travel time distributions. Collaborating with the National Science and Technology Center for Disaster Reduction (NCDR), an empirical study using a potential real-world earthquake scenario occurring in Taiwan is conducted to demonstrate the usefulness and superiority of our proposed model and solution approach compared to current-practice heuristics.

李洋寧、劉淑燕、李沁妍、吳佳容、鄧敏政、柯孝勳、李中生（2014）。大臺北地區大規模地震衝擊情境分析報告II ：道路系統、水電設施、重要設施、情境綜整。NCDR 102-T15。國家災害防救科技中心。
陳玥心、王晉元 (2013)。應用變數產生法求解電動公車車輛排程問題。國立交通大學運輸科技與管理學系碩士論文。
張偉德、王逸琳 (2016)。大量傷患緊急醫療救護之最佳救護車派遣數學模式研究。國立成功大學工業與資訊管理學系碩士論文。
陳禮仁（2020）。近年世界重大天然災害的回顧與省思。土木水利，47(2)，57–70。
Aslan, E. & Çelik, M. (2019). Pre-positioning of relief items under road/facility vulnerability with concurrent restoration and relief transportation. IISE Transactions, 51, 847–868
Benson, M., Koenig, K. L. & Schultz, C. H. (1996). Disaster Triage: Start, then Save: A New Method of Dynamic Triage for Victims of a Catastrophic Earthquake. Prehospital and Disaster Medicine, 11, 117–124
Bíl, M., Vodák, R., Kubeček, J., Bílová, M. & Sedoník, J. (2015). Evaluating road network damage caused by natural disasters in the Czech Republic between 1997 and 2010. Transportation Research Part A, 80, 90–103
Blackwell, T. H. & Kaufman, J. S. (2002). Response time effectiveness: comparison of response time and survival in an urban emergency medical services system. Acad Emerg Med, 9(4), 288–95
Budge, S., Ingolfsson, A. & Zerom, D. (2010). Empirical Analysis of Ambulance Travel Times：The Case of Calgary Emergency Medical Services. Empirical Analysis of Ambulance Travel Times Management Science, 56(4), 716–723
Burghout, W., Koutsopoulos, H. N., & Andreasson, I. (2006). A discrete-event mesoscopic traffic simulation model for hybrid traffic simulation. 2006 IEEE Intelligent Transportation Systems Conference, Toronto, Canada, 1102–1107
Chang, K. H., Hsiung, T. Y. and Chang, T. Y., (2022a). Multi-commodity distribution under uncertainty in disaster response phase: Model, solution method, and an empirical Study. European Journal of Operational Research, in press.
Chang, K. H., Wu, Y. Z. and Ke, S. S., (2022b). A simulation-based decision support tool for dynamic post-disaster pedestrian evacuation. Decision Support System, in press.
Chen, B. Y., Li, Q. & Lam, W. H.K. (2016). Finding the k reliable shortest paths under travel time uncertainty. Transportation Research Part B, 94, 189–203
Çoban, B., Scaparra, M. P. and O’Hanley, J. R., (2021). Use of OR in earthquake operations management: A review of the literature and roadmap for future research. International Journal of Disaster Risk Reduction, 65, 102539.
Dean, M. D. and Nair, S. K., (2014). Mass-casualty triage: Distribution of victims to multiple hospitals using the SAVE model. European Journal of Operational Research, 238(1), 363-373.
der Heide, E. A. (2006). The importance of evidence-based disaster planning. Ann Emerg Med, 47, 34–49
Farahani, R. Z., Lotfi, M. M., Baghaian, A., Ruiz, R. and Rezapour, S., (2020). Mass casualty management in disaster scene: A systematic review of OR&MS research in humanitarian operations. European Journal of Operational Research, 287(3), 787-819.
Gaddam, H. K., & Rao, K. R. (2019). Speed-density functional relationship for heterogeneous traffic data: a statistical and theoretical investigation. Journal of Modern Transportation, 27(1), 61–74
Gharib, M., Ghomi, S. M. T. F. & Jolai, F. (2021). A dynamic dispatching problem to allocate relief vehicles after a disaster. Engineering Optimization, 53, 1999–2016
Gong, Q. and Batta, R., (2007). Allocation and reallocation of ambulances to casualty clusters in a disaster relief operation. IIE Transactions, 39(1), 27-39.
Gormez, N., Koksalan, M. and Salman, F. S., (2011). Locating disaster response facilities in Istanbul. Journal of the Operational Research Society, 62(7), 1239-1252.
Jayakrishnan, R., Mahmassani, H. S., & Hu, T. Y. (1994). An evaluation tool for advanced traffic information and management systems in urban networks. Transportation Research Part C: Emerging Technologies, 3(2), 129–147
Jotshi, A., Gong, Q. and Batta, R., (2009). Dispatching and routing of emergency vehicles in disaster mitigation using data fusion. Socio-Economic Planning Sciences, 43(1), 1-24.
Kleywegt, A. J., Shapiro, A. and Homem-De-Mello, T., (2001). The sample average approximation method for stochastic discrete optimization. SIAM Journal on Optimization,12, 479–502.
Lee, Y. C., Chen, Y. S. and Chen, A. Y., (2022). Lagrangian dual decomposition for the ambulance relocation and routing considering stochastic demand with the truncated Poisson. Transportation Research Part B: Methodological, 157, 1-23.
Lei, C., Lin, W. H. and Miao, L., (2014). A stochastic emergency vehicle redeployment model for an effective response to traffic incidents. IEEE Transactions on Intelligent Transportation Systems, 16(2), 898-909.
May A. D. Jr., & Keller H. E. M. (1967). Non-integer car-following models. Highway Research Record, 199, 19–32.
Miller, A. F., Argon, N. T. and Ziya, S., (2013). Resource-based patient prioritization in Mass–Casualty incidents. Manufacturing & Service Operations Management, 15(3), 361-377.
Mills, A. F. Argon, N. T. and Ziya, S., (2018). Dynamic distribution of patients to medical facilities in the aftermath of a disaster. Operations Research, 66(3), 597-892.
Mills, A. F.,Argon, N. T. & Ziya, S. (2014). Resource-based patient prioritization in mass-casualty incidents. Manufacturing & Service Operations Management, 15, 361–377
Naoum-Sawaya, J. and Elhedhli, S., (2013). A stochastic optimization model for real-time ambulance redeployment. Computers & Operations Research, 40(8), 1972-1978.
Park, J. O. (2010). Epidemiological characteristics and resource utilization of mass casualty incidents (MCI) and disaster in Korea, Ewha Womans University
Repoussis, P. P., Paraskevopoulos, D. C., Vazacopoulos, A. and Hupert, N., (2016). Optimizing emergency preparedness and resource utilization in mass-casualty incidents. European Journal of Operational Research, 255(2), 531-544.
Rocha, P., Ravetti, M., Mateus, G. & Pardalos P. (2008). Exact algorithms for a sche-duling problem with unrelated parallel machines and sequence and machine-dependent setup times. Computers & Operations Research, 35, 1250–1264
Sanci E. & Daskin M. S. (2019). Integrating location and network restoration decisions in relief networks under uncertainty. European Journal of Operational Research, 279, 335–350
Santoso, T., Ahmed S., Goetschalckx M. & Shapiro A. (2005). A stochastic programming approach for supply chain network design under uncertainty. European Journal of Operational Research, 167, 96–115
Shin, K. and Lee, T., (2020). Emergency medical service resource allocation in a mass casualty incident by integrating patient prioritization and hospital selection problems. IISE Transactions, 52(10), 1141-1155.
Sung, I. and Lee, T., (2016). Optimal allocation of emergency medical resources in a mass casualty incident: Patient prioritization by column generation. European Journal of Operational Research, 252(2), 623-634.
Talarico, L., Meisel, F. and Sörensen, K., (2015). Ambulance routing for disaster response with patient groups. Computers & Operations Research, 56, 120-133.
Tayfur, E. & Taaffe, K. (2009). A model for allocating resources during hospital evacuations. Computers & Industrial Engineering, 57, 1313–1323
Wang, Q. & Nie, X. (2019). A Stochastic Programming Model for Emergency Supply Planning Considering Traffic Congestion. IISE Transactions, 51, 910–920
Wei, K., Gao, Y., Zhang, W. & Lin, S. (2019). A Modified Dijkstra's Algorithm for Solving the Problem of Finding the Maximum Load Path. International Conference on Information and Computer Technologies, 14–17
Wilson, D. T., Hawe, G. I., Coates, G. and Crouch, R. S., (2012). A multi-objective combinatorial model of casualty processing in major incident response. European Journal of Operational Research, 230(3), 643-655.
Zhen, L., Sun, Q., Zhang, W., Wang, K. & Yi, W. (2020). Column generation for low carbon berth allocation under uncertainty. Journal of the Operational Research Society, 72, 2225–2240