本研究考量一旦發生地震將會在短時間內造成大量傷患，同時橋樑斷裂或是通行道路的損壞也會增加救援上的困難，而傷患的救援行動相當急迫，必須迅速將傷患移轉至醫院進行救治。為了有效的將醫療資源保留給真正需要醫療資源的傷患，在送往醫院前會在災區的附近設置臨時的檢傷站集合傷患，透過檢傷站將傷患分類並且進行緊急處理後送醫，災害管理團隊須根據傷患優先順序分配緊急醫療資源和指派救護車路線，以最大限度地降低檢傷站開設成本以及傷患的剝奪成本。
本研究針對地震後災難管理過程的整備與應變階段，考慮道路損壞造成運送時間不確定與需求不確定下，提出二階段隨機混整數規劃模型，來求解檢傷站開設位置、災區傷患指派決策、大量傷患送醫順序與救護車派遣規劃，本研究透過快速篩選法（Rapid Screening Procedure）快速找出存活的檢傷站開設解與災區指派解，結合最佳資源分配法（Optimal Computing Budget Allocation, OCBA）以節省運算成本，並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，並利用啟發式列生成法（Column-generation-based Heuristic）求解大量傷患送醫順序與救護車派遣規劃。最後本研究與國家災害防救科技中心合作，透過山腳斷層規模6.5之地震情境來證實演算法在結果上相較於其他演算法有93%的改善，並表明二階之決策最佳化能有效影響一階決策，同時針對參數進行分析，觀察參數之影響並給予決策者建議。

A mass casualty incident（MCI） describes an incident in which emergency medical services resources are overwhelmed by the number and severity of casualties. To make sure the rescue can be carried out smoothly, comprehensive strategy is essential and necessary. Finding a system to arrange the medical resources properly and dispatch the ambulances efficiently is important before MCI taken place. In this study, we developed an algorithm from several models and thanks to the algorithm, we will be able to lower the deprivation cost and shorten the time to send the injured to the hospital. In this research, we propose a two-stage stochastic programming model in which the first stage optimizes the location of Casualty Collection Point（CCP） as well as the patient allocated to the CCP for triage, while the second stage determines the patient prioritization, hospital selection and ambulation dispatching and routing planning decisions after the random factors（the severity of damage to the road network and the number of patients in disaster region） associated with the disaster are revealed.
We use Rapid screening to find the survival solution of first stage efficiently, and through Optimal Computing Budget Allocation（OCBA） to determine the proper simulation time of the second stage. After the stochastic MIP model is transferred into the deterministic MIP model, we apply the Column generation to solve the second stage to get the solution of ambulance deployment and redeployment. This study also collaborates with the National Science and Technology Center for Disaster Reduction (NCDR) and utilizes a realistic earthquake scenario in Taiwan to illustrate the superior efficiency of our model and methodology compared to traditional approaches.

致謝 I
摘要 II
Abstract III
目錄 IV
圖目錄 VI
表目錄 VII
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 論文架構 3
第二章 文獻回顧 5
第三章 數學模型 12
3.1 問題定義 12
3.2 符號定義 15
3.3 數學模型 17
第四章 研究方法 20
4.1 ORSA演算法（OCBA based rapid screening algorithm） 22
4.1.1 初始化階段之方法（起始解產生） 25
4.1.2 可行性評估階段之方法 26
4.1.3 目標篩選階段之方法 26
4.1.4 停止階段之方法（候選解產生之方法） 30
4.1.5 選擇階段之方法 33
4.2 情境生成演算法（Scenario Generation algorithm） 37
4.2.1 需求生成演算法（Demand generation algorithm） 37
4.2.2 道路旅行時間生成演算法(Travel time scenario generation algorithm) 38
4.3 啟發式列生成法（Column-Generation-based Heuristic, CGH） 42
第五章 數值實驗 49
5.1 實驗區域 49
5.2 大安區路網與演算法參數設定 51
5.3 大安區最佳化結果 52
第六章 演算法比較與數值分析 55
6.1 演算法比較結果 55
6.2 環境因子對模型之影響 57
6.3 醫療資源之敏感度分析 60
6.3.1 檢傷站的最大開設數對目標值與最佳解之影響 61
6.3.2 醫院可用資源對目標值與最佳解之影響 62
6.3.3 可用救護車數目對目標值與最佳解之影響 64
6.4 檢傷站開設成本與剝奪成本之敏感度分析 65
第七章 結論與未來研究 68
參考文獻 70

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。
Alizadeh, M., Amiri-Aref, M., Mustafee, N., & Matilal, S. (2019). A robust stochastic Casualty Collection Points location problem. European Journal of Operational Research, 279(3), 965-983.
Ankrah, R., Lacroix, B., McCall, J., Hardwick, A., Conway, A., & Owusu, G. (2020, July). Racing Strategy for the Dynamic-Customer Location-Allocation Problem. In 2020 IEEE Congress on Evolutionary Computation (CEC) (p. 1-8). IEEE.
Aydin, N. (2016). A stochastic mathematical model to locate field hospitals under disruption uncertainty for large-scale disaster preparedness. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 6(2), 85-102.
Baluja, S. (1994). Population-based incremental learning. a method for integrating genetic search based function optimization and competitive learning. Carnegie-Mellon Univ Pittsburgh Pa Dept Of Computer Science.
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(2), 117-124.
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations research, 52(1), 35-53.
Burghout, W., Koutsopoulos, H. N., & Andreasson, I. (2006, September). A discrete-event mesoscopic traffic simulation model for hybrid traffic simulation. In 2006 IEEE intelligent transportation systems conference (p. 1102-1107). IEEE.
Cantillo, V., Serrano, I., Macea, L. F., & Holguín-Veras, J. (2018). Discrete choice approach for assessing deprivation cost in humanitarian relief operations. Socio-Economic Planning Sciences, 63, 33-46.
Caunhye, A. M., Nie, X., & Pokharel, S. (2012). Optimization models in emergency logistics: A literature review. Socio-Economic Planning Sciences, 46(1), 4-13.
Chang, K.-H., Chen, T.-L., Yang, F.-H., & Chang, T.-Y. (2023). Simulation optimization for stochastic casualty collection point location and resource allocation problem in a mass casualty incident. European Journal of Operational Research, 309(3), 1237-1262.
Chen, C.-H., He, D., Fu, M., & Lee, L. H. (2008). Efficient simulation budget allocation for selecting an optimal subset. INFORMS Journal on Computing, 20(4), 579-595.
Chen, C.-H., Lin, J., Yücesan, E., & Chick, S. E. (2000). Simulation budget allocation for further enhancing the efficiency of ordinal optimization. Discrete Event Dynamic Systems, 10, 251-270.
Drezner, T. (2004). Location of casualty collection points. Environment and Planning C: Government and Policy, 22(6), 899-912.
Drezner, T., Drezner, Z., & Salhi, S. (2006). A multi-objective heuristic approach for the casualty collection points location problem. Journal of the Operational Research Society, 57(6), 727-734.
Farahani, R. Z., Lotfi, M., Baghaian, A., Ruiz, R., & 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.
Gharib, M., Fatemi Ghomi, S. M. T., & Jolai, F. (2021). A dynamic dispatching problem to allocate relief vehicles after a disaster. Engineering Optimization, 53(11), 1999-2016.
Gupta, S., Starr, M. K., Farahani, R. Z., & Matinrad, N. (2016). Disaster management from a POM perspective: Mapping a new domain. Production and Operations Management, 25(10), 1611-1637.
Holguín-Veras, J., Amaya-Leal, J., Cantillo, V., Van Wassenhove, L. N., Aros-Vera, F., & Jaller, M. (2016). Econometric estimation of deprivation cost functions: A contingent valuation experiment. Journal of Operations Management, 45, 44-56.
Holguín-Veras, J., Pérez, N., Jaller, M., Van Wassenhove, L. N., & Aros-Vera, F. (2013). On the appropriate objective function for post-disaster humanitarian logistics models. Journal of Operations Management, 31(5), 262-280.
Jabbarzadeh, A., Fahimnia, B., & Seuring, S. (2014). Dynamic supply chain network design for the supply of blood in disasters: A robust model with real world application. Transportation research part E: logistics and transportation review, 70, 225-244.
Jain, A., & Dubes, R. (1988). Algorithms for Clustering Data. Prentice-Hall, Inc..
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, 2(3), 129-147.
Klibi, W., & Martel, A. (2013). The design of robust value-creating supply chain networks. OR spectrum, 35(4), 867-903.
Kou, G., Xiao, H., Cao, M., & Lee, L. H. (2021). Optimal computing budget allocation for the vector evaluated genetic algorithm in multi-objective simulation optimization. Automatica, 129, 109599.
Liu, Y., Cui, N., & Zhang, J. (2019). Integrated temporary facility location and casualty allocation planning for post-disaster humanitarian medical service. Transportation research part E: logistics and transportation review, 128, 1-16.
May, A., & Keller, H. (1967). Non-integer car-following models, Highway Res. Rec, 199, 19-32.
McLoughlin, D. (1985). A framework for integrated emergency management. Public administration review, 45, 165-172.
Memari, P., Tavakkoli-Moghaddam, R., Navazi, F., & Jolai, F. (2020). Air and ground ambulance location-allocation-routing problem for designing a temporary emergency management system after a disaster. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of engineering in medicine, 234(8), 812-828.
Mousavi, S., Sajadi, S. M., AlemTabriz, A., & Najafi, S. E. (2022). Location and hierarchical allocation disaster with combined ε-constraint and simulation-based optimization approach. Simulation, 98(5), 407-432.
Oksuz, M. K., & Satoglu, S. I. (2020). A two-stage stochastic model for location planning of temporary medical centers for disaster response. International Journal of Disaster Risk Reduction, 44, 101426.
Sun, H., Li, J., Wang, T., & Xue, Y. (2022). A novel scenario-based robust bi-objective optimization model for humanitarian logistics network under risk of disruptions. Transportation research part E: logistics and transportation review, 157, 102578.
Sun, H., Wang, Y., Zhang, J., & Cao, W. (2021). A robust optimization model for location-transportation problem of disaster casualties with triage and uncertainty. Expert Systems with Applications, 175, 114867.
Sung, I., & 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.
Tsai, S. C. (2013). Rapid screening procedures for zero-one optimization via simulation. INFORMS Journal on Computing, 25(2), 317-331.
Ulmi, M. (2014). Hazus-MH 2.1 Canada, User and Technical Manual: Earthquake Module (p. 245). Ottawa, ON, Canada: Natural Resources Canada.
Yuan, Y., Cattaruzza, D., Ogier, M., Semet, F., & Vigo, D. (2021). A column generation based heuristic for the generalized vehicle routing problem with time windows. Transportation research part E: logistics and transportation review, 152, 102391.
Zhu, L., Gong, Y., Xu, Y., & Gu, J. (2019). Emergency relief routing models for injured victims considering equity and priority. Annals of Operations Research, 283, 1573-1606.