本研究針對手術排程問題進行求解，當手術室數量相對於手術而言供不應求時，如何妥善安排手術執行的時間即成了一個重要的課題，安排手術時必須考慮各種資源的限制，不同狀況的發生也需要納入考量，而非僅專注於單一項績效，在本研究中考量了手術執行的時間、急診的需求、病患病情的緊急程度、手術室逾時狀況等因子建構模型，進行多台手術排入單間手術室的多天排程，決定每一台手術預定執行的日子。
而由於手術時間和急診的發生皆為隨機變數，造成此問題具有隨機目標式與多條隨機限制式，並不適用僅能求解確定性問題的數學規劃，而龐大的解空間也無法利用窮舉法來得到品質較佳的解甚至可行解；
因此本研究利用樣本平均近似法(Sample Average Approximation; SAA)的演算法進行求解，將問題的隨機性呈現於模型中；此外也會利用快速篩選法(Rapid Screening)做為另一種求解方法，加速候選解的搜尋，且在一定程度的統計保證下增加求解的效率；並將此兩種方法與其他啟發式解法進行比較，分析不同情境下的問題各種方法的優劣與適用性。
當手術耗時變異程度大時，結合SAA的快速篩選法會得到較佳的目標值，但其抽樣成本較其他方法多出許多；而SAA演算法則可以以明顯較低的抽樣成本來求得品質也不錯的解；而手術耗時變異小時，這兩種方法亦可以求得品質很好的解。
相較於此，啟發式排程方法僅能在手術耗時變異小的情況下求得較佳的解，當手術耗時變異大時，其求得的解品質皆與其他方式有落差。而在求解速度上，SAA演算法相較於快速篩選法則較為耗時。

Duration of surgeries and occurrence of emergency are important random factors in surgical scheduling problem. These factors cannot be known as deterministic values, so the surgical scheduling problem cannot be solved by mathematical programming methods. In our research, we use sample average approximation (SAA) algorithm and rapid screening (RS) to cope with these stochastic factors. In this way, surgical scheduling problem can be solved while its randomness is taken into account. Moreover, we solve surgical scheduling problem via several heuristic methods as well, and compare the results with the ones via SAA and RS.

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