存貨管制問題在企業上扮演著關鍵角色，因此本論文結合碎形布朗運動與存貨模型，將赫斯特冪數應用於前置期間需求量，探討在多產品(Q,r)存貨模型與投資限制式下相互影響的關係。研究的目的為建立出一個適當模型來最小化總成本、決定最佳訂購量並幫助管理者做出更合適的存貨決策。

Inventory control is a problem common to most organizations. For the problem of determining optimal policies for marginal shortage costs in an investment constrained multi-item (Q, r) inventory system with the fixed lead-time demand influenced by the “Hurst exponent” has not been explored. This thesis focuses on the application of fractional Brownian motion in the fixed lead-time demand. 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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