本研究探討兩階層存貨問題包含一個外部供應商、一個中心倉庫與多個零售商，供應鏈皆採用定期盤點制，中心倉庫負責下游所有零售商的補貨訂單，倉庫也定期盤點存貨並向外部供應商下訂單，需求發生於零售商端且與訂單前置期一樣為隨機變數。過往多數研究存貨問題的文獻為了分析上的可行或方便皆採用遇缺補貨假設居多，我們認為銷售損失假設更能反映真實零售市場的環境。而績效指標除了單位時間的成本外還包含存貨問題中最常見的服務水準。本研究接著指出許多文獻中用分析方法求解銷售損失假設下的存貨問題所遭遇的困境，並點出以模擬最佳化方法求解能打破許多非必要的假設限制等優勢。

本研究將以回溯最佳化求解以下三個問題：(1)多重服務水準限制式之整數存貨問題、(2)單一服務水準限制式之整數存貨問題、(3)單一服務水準限制式之混整數存貨問題，找到一組滿足服務水準式下讓成本最小化的存貨策略。cgR-SPLINE為以梯度為基礎之離散型模擬最佳化方法，適合求解高維度且離散型決策變數的問題，以內外圈迭代的設計下，在廣大的解空間中有效率地朝品質佳的解前進，同時顧及演算法效率以及解的品質。但cgR-SPLINE的線性插值搜尋法在迭代解靠近可行解域邊界時，無法估計梯度向量，影響求解效率，因此本研究提出兩個方法來改善cgR-SPLINE。SFB方法是利用最佳解位於可行解域邊界的特性，繼續在邊界搜尋品質更佳的解，SPF則是利用懲罰函數將原問題轉換為無隨機限制式的問題，而實驗結果也顯示兩種方法對cgR-SPLINE皆有一定程度的改善，但SFB的改善效果比SPF更明顯。

本研究繼續推展SFB的方法使其適用於單一服務水準限制式的混整數存貨問題，實驗結果顯示其求解效率要比OptQuest方法好，而目前文獻中沒有能處理具有隨機限制式的混整數模擬最佳化方法，本研究也在未來研究方向提出幾個具有發展潛力的方法。

We consider a time-base inventory control policy for a two-echelon inventory system consisting of an external supplier, a central warehouse, and some retailers. The objective in the discrete optimization problem is to determine the order-up-to-levels at the warehouse and retailer locations and the replenishment interval at the warehouse that minimize a cost function, defined in terms of both holding cost and fixed ordering cost, subject to the service levels.

In contrast to previous research, the two-echelon inventory system considered in our study with a lost-sales assumption and stochastic lead time is more realistic in many retail environments than its counterparts. There are few applications that consider lost-sales. One of the major reasons for this is that inventory models that include lost sales are more difficult to analyze and to perform computations on compared to backorder models. Simulation optimization is a potentially powerful and flexible tool for solving complex optimization problems, without the need to make restrictive assumptions.

We use the cgR-SPLINE algorithm to solve the problems, and propose two new approaches based on this algorithm. First, the SFB algorithm takes advantage of the problem structure by searching around a feasibility boundary to find more quality solutions. Second, SPF transfers stochastic constraints into an objective function by using a penalty function. The empirical results show that both SFB and SPF are more efficient than cgR-SPLINE. We then extend the concept from SFB to the MISO algorithm, which can be used to solve the mixed-integer inventory problem with a single service level constraint.

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