存貨管理在製造業上是個很重要的議題，如何訂購最佳的訂購量並減少成本以得到最大獲利，一直都是此議題必須努力改善實現的目標。因此，本研究假設製造業上的需求屬於碎形布朗運動並驗證之，並根據碎形布朗運動的特性結合存貨模型，將赫斯特幂數應用於前置期間需求量，進行(Q, r)存貨模型的修正。最後利用碎形布朗運動產生不同赫斯特幂數的需求數列，發展存貨政策，與假設獨立的存貨模型作數值比較，發現本存貨模型改善後的效能更優於獨立模型，可獲得較小的總成本，因此可提供管理者進行生產決策或預測規劃。

Inventory management is an important issue in the manufacture. The target of developing these inventory models is to determine optimal order quantity and gain the maximum profit. Hence, in this thesis, we assume the demand in the manufacture is under fractional Brownian motion. We also use fractional Brownian motion by Hurst exponent in the fixed lead-time demand to modify (Q, r) inventory model. Finally, we simulated fBm process by different H values for the lead time demand to develop inventory policy. We compare result with independent model. We could find out our model is better than assumed independent model. We hope that could provide managers to make a correct decision.

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