本研究針對兩階層存貨系統問題發展演算法，此存貨系統包含一個外部供應商、一個中心倉庫與多個零售商，當需求發生時，零售商扮演服務顧客的角色，提供商品給顧客，並根據存貨策略向中心倉庫及時下訂單進行補貨。中心倉庫具有供應產品功能，負責滿足各個零售商的需求。當中心倉庫開始缺貨後(亦即存貨量降為零)，此時由外部供應商提供存貨來滿足各分倉的補貨訂單需求，由外部供應商提供存貨時顧客等候時間會較由中心倉庫提供存貨時較長。在此存貨系統中，顧客需求的間隔時間、顧客需求的數量和補貨前置期長度皆為隨機性的變數，因此為高度複雜性的問題。
本研究之兩階層存貨系統採用連續補貨策略(S-1,S)，將顧客等候時間當作服務績效，而顧客等候時間為顧客向各零售商提出需求時至顧客需求被滿足的間隔時間，期望在最小化總成本且顧客等候時間低於門檻值下，求得最佳的存貨初始存貨水準。此系統具有一個隨機目標式和多條隨機限制式且擁有龐大的解空間，無法透過傳統數學模式進行有效率的求解。此外，為了更符合真實情境的隨機性，本研究將發展一個模擬最佳化演算法，結合樣本平均近似法(Sample Average Approximation)、切面法(Cutting Plane Method)和可行性檢查程序(Feasible Check Procedure)求解問題。

We address a two-echelon inventory system consisting of an external supplier, a central warehouse and some retailers. The objective is to determine an (S-1, S) pair that minimizes a cost function, defined in terms of both holding costs and shortage costs, subject to the constraint that the average response time to each customer is below a specified threshold level. The problem we formulate has a large solution space; however, traditional mathematical model can not solve these problems efficiently, so we propose an algorithm based on simulation. The Ranking and Selection (R&S) procedure can be used to solve simulation optimization problems for which the number of feasible solutions is small, and thus we propose a simulation algorithm which combines the sample average approximation, the cutting plane method and the feasibility check procedure.

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