由於自然災害的隨機性，這篇描述了如何制定兩階段數學模型的過程，此模型旨在於災前優化醫療資源和運輸資源的佈署，以因應地震。考量到台灣的地理環境，地震是必會發生，而本文的目的為減少此災害造成的損傷和經濟成本，和建構了新的不確定集合來表示隨機性。這集合相較以前可以同時表示不同情境發生的可能性和其他隨機變數的範圍。
本研究聚焦於災害的準備和反應階段，其中資源可以進一步劃分為兩種類型的資源：醫療資源，能直接緩解受難者的痛苦；運輸資源，雖然不能直接缓解，但能夠傳送其他資源至有需求的人們。為了展示情境的隨機性，本研究使用兩階段模型，而模型的第一階段對應到準備的緊急資源量，決定了將在第二階段能動用的資源。然後第二段是發生在地震後，所有未知的隨機變數都變成已知的確定變數，然後第決定是如何分配第一階段的資源，以最小化總經濟成本。
模型定義完後，透過運用分佈式穩健最佳化的模型和提供的不確定集合還有分解演算法，計算最佳解。總之，兩階段模型可以同時考慮醫療資源和相較新的運輸資源的配置。

In consideration of the stochasticity of natural disasters, we provide an in-depth description of formulating a two-stage mathematical model which optimizes both medical resources and transportation resource allocation in preparation for earthquakes. Given the geographic circumstances in Taiwan, the occurrence of earthquakes is almost certain, in which this paper aims prepare us for such event, and apply a novel method of expressing the randomness in ambiguity set, which contains the probabilities of different discrete events and the supports of random variables.
The research focuses on the preparation and response phase of disaster management, of which can be further divided into two types of resources medical, able to alleviating the victims’ suffering, and transportation, unable to relieve the suffering by itself but is required for delivering the other resources to those in need. To present the randomness of the situation, a two-stage model is used. Stage One of the model corresponds to the preparation phase and determines the amount of resources which would be available. Stage Two is for after the earthquake strikes, thereby all random variables become certain and distribute resources prepared at stage one to minimize the total economic cost.
With the model defined, the distributionally robust optimization (DRO) is utilized to gain for the optimal solution with the given the ambiguity set from a decomposition algorithm. To conclude, two-stage mathematical model can account for both medical resource allocation and the novel transportation resource allocation.

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