本研究提出能夠處理具有隨機目標式及單一隨機限制式的模擬最佳化(Simulation Optimization) 演算法，提供決策者在一般實務上可以實際運用的方法，許多商業軟體都具有能夠處理模擬最佳化的啟發式演算法 (例如 OptQuest)，但該類型演算法所需要的時間及耗費的抽樣成本龐大，且無法保證每次所找到的解為可行解。因此本研究運用實驗設計與超模型 (Metamodel) 中的反應曲面法 (Response Surface Methodology; RSM)，來降低模擬抽樣時所花費的成本，並以數學規劃求解該次迭代的最佳解，結合可行性驗證程序，使得演算法在求解過程中，能在 1-alpha 的情況下保證所找到的解為可行解，另外加入懲罰函數 (Penalty Function) 的概念發展出其他兩種演算法來建構超模型求解，最後以 Clean-Up 程序從可行解當中找到最佳解，將透過已知最佳解的隨機函數來驗證演算法的求解能力。本研究提出了三個演算法分別為使用可行性驗證的M演算法，以及配合懲罰函數的MP_I及MP_II演算法，根據實驗結果可以知道M演算法在限制式的容忍水準內有較佳的表現，MP_I及MP_II則可以在較少的樣本數下找到表現不錯的解，此外三種演算法實驗數值中無論是平均績效指標或是可行性上皆優於 OptQuest。

This study is intended to develop three heuristic algorithms for the purpose of solving a simulation optimization problem with a single stochastic constraint. The proposed algorithms employ metamodel to reduce the required simulation replications, mathematical programming to solve the optimization problem, feasibility check procedure to confirm the feasibility of the obtained solution under a specified confidence level, and clean-up procedure to select the best solution in terms of objective performance. The first heuristic is called the M algorithm, which is combined with the feasibility check procedure, and the other two heuristics, which are combined with the penalty method to fit the regression metamodel, are called MP_I and MP_II. The results show that MP_I and MP_{II perform well with a lower sampling budget, and M performs better in terms of finding a feasible solution within a given tolerance level. The heuristics are compared with OptQuest, which is commonly embedded in Arena, and the results also show that our heuristics outperform OptQuest in terms of objective values and the probability of finding feasible solutions.

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