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.

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 3
1.3論文架構 5
第二章　文獻回顧 7
2.1大規模傷亡事件（MCI） 7
2.2救護車派遣 8
第三章　數學模型 12
3.1問題定義 12
3.2符號定義 13
3.3數學模型 15
第四章　研究方法 20
4.1道路損壞下旅行時間生成演算法（Travel time scenario generation algorithm, TTSGA） 21
4.2樣本平均近似法（Sample average approximation） 26
4.3變數產生法（Column generation） 29
第五章　個案實驗 37
5.1實驗區域 37
5.2數值設定 39
5.3案例結果 40
第六章　參數分析 45
6.1各生存率(樂觀、中等和悲觀)下，本模型與現行策略之差異 45
6.2二水準部份因子實驗設計 49
第七章　結論與未來研究 53
參考文獻 55

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