因大血管阻塞(large vessel occlusion, LVO)的缺血性中風患者可以得益於盡快地接受血管取栓術(endovascular treatment, EVT)；另一方面，對於那些非大血管阻塞的病患而言，盡早地施打血栓溶解劑(intravenous tissue-type plasminogen activator, IV-tPA)，將會使病患在施打後能有較大的機會恢復到中風前的狀態。由前面這些事實，可以得知這兩種治療方式有其時效性。然而，實際上，一位疑似中風病患的血管狀態是無法在沒有詳細檢查下得知的，所以急救人員需要在現場使用院前中風嚴重程度量表(prehospital stroke severity scale, PSSS)來辨別出這位病患的中風嚴重程度，然後再決定將此病患送至只有提供施打血栓溶解劑診療方案的基本中風病患醫院(primary stroke center, PSC)或者提供血管取栓術及血栓溶解劑的中風病患醫學中心(comprehensive stroke center, CSC)。我們想要處理的問題為建立一個數學規劃模型給急救人員一個建議的醫院來運送病患。

在先前的研究中，兩種接受中風病患的醫院，其院內時間流程是假設為一定值，而這是不實際的。為了解決這個議題，我們考慮院內時間不確定性。也就是把這些時間視為一個機率分布。因此，在此篇論文中我們建立三個基於這種想法的數學規劃模型。藉由模擬在數次的試驗下，我們所提出的模型相較於以往所提出的，大部分都有較佳的表現。我們所使用的資料為台灣台北市中風病患的資訊以及十間位於台北市的醫院，以及由Google Map所估得的病患至這十間醫院的車行時間。

An acute ischemic stroke (AIS) patient with large vessel occlusion (LVO) can benefit from the endovascular treatment (EVT) as soon as possible, and on the other hand, a patient without LVO will have a better outcome when receive the intravenous tissue-type plasminogen activator (IV-tPA) early. Therefore, these facts indicate that both of the treatments are time-sensitive. Nevertheless, in reality, the vessel status of a suspected stroke patient is unknown without a sophisticated inspection, so the Emergency Medical Technicians (EMTs) need to use prehospital stroke severity scale (PSSS) to identify the severity of this stroke patient on the spot and then determine to transport either to primary stroke centers (PSCs), which offer the IV-tPA only, or to comprehensive stroke centers (CSCs), which provide both of the IV-tPA and EVT. The problem we want to handle is to build a mathematical programming model that give a recommended hospital for EMTs to transport the patients.

In the prior research, the in-hospital workflow time in the stroke centers (both PSCs and CSCs) is assumed to be a deterministic value. However, it is not realistic. To address this issue, we take the uncertainty of the workflow time of the hospitals into consideration. That is, we model these intervals of time into a distribution. Thus, in this thesis, we build three mathematical programming models based on this concept to transport patients. We then show that the result of our proposed models is better than the previously proposed strategies in the total number of patients receiving the definitive treatment within a given time by simulating on the numerous number of trials. The data we used is based on the off-peak transport time in the real world from Google Map, the historical performance of the workflow time of ten hospitals, and the real patient’s profiles including the geographic locations, response time, on-scene time and prehospital stroke severity scale scores in the Taipei City, Taiwan.

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