近幾年探討存貨的文獻中，大多將前置時間視為已知的常數或隨機變數，是不可控制的。但事實上前置時間是可以縮短的。前置時間的縮減可以減少安全庫存量，增加客戶的滿意度，但相對而來的也可能增加採購成本。因此本論文結合碎型布朗運動與存貨模型，將赫斯特冪數應用於前置其間需求量，探討當前置時間為一變數且與採購成本相互影響之下與(s, Q)存貨模型的關係。研究目的為建立出一個適當模型來最小化總成本、決定最佳訂購量與最適前置時間，並幫助管理者做出更適合的存貨決策。

Most of the literature dealing with inventory problems assumes lead time as prescribed, whether deterministic or probabilistic. In certain cases, lead time can be reduced. A reduction in the inventory replenishment lead time allows reducing safety stock requirements and improving customer service. However, it might be accompanied by increased procurement costs because of premium charges imposed by suppliers, or higher transportation costs. This thesis focuses on the variable lead time inventory system characterized by fractional Brownian motion with lead time dependent to procurement cost. The objective is to formulate a model minimizing the expected value of approximate total annual cost and to help managers to make a correct inventory policy. The theoretical results obtained are illustrated with a numerical example.

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