在這經濟全球化的體系當中，使得企業競爭越來越激烈。企業為了增加其市場競爭優勢，必須提高顧客滿意度及減少製造成本。在企業上時間和成本是最主要的競爭因子。因此，決策者必須規劃適當生產計劃和安全存貨量，才能降低訂購成本、存貨成本、缺貨成本及趕工成本。然而，由於現今市場環境的快速變遷下，存貨管理對於企業的營運績效也越來越顯現出其重要性。所以如何有效的控制存貨水準已經變成企業管理者一個所必須要面對的議題。
本篇論文是連續盤查的存貨模式，其前置時間、訂購數量、安全因子和欠撥折扣為決策變數。每一個模型允許缺貨發生在缺貨期間考慮欠撥與銷售損失混合的情形。以往的學者所討論的缺貨模式之文獻，僅考量欠撥折扣對欠撥率的影響，或僅考量前置時間與欠撥率的關係。本篇論文同時考慮到欠撥折扣和前置時間皆會影響到欠撥率。
此外，我們認為不同的顧客會有不同的需求，不可能僅以常態需求分配來表示前置時間的需求量。因此，我們提出二個存貨模型，一為前置時間內需求量的機率分配服從常態的情形，並建立求問題最佳解的演算法；另一為前置時間內需求量的機率分配型式為未知，而僅已知其平均數與標準差的情形，並運用分配不拘大中取小準則來求得問題的最適解。對於所提出的每一個模型，我們均以數值範例說明。

In the system of this economic globalization, enterprises are fiercer and fiercer in competition. Enterprises must improve customer satisfaction and reduce the manufacturing cost in order to increase their market competition advantages. Time and cost are the most important competitive factors in business. Therefore, we must plan a suitable schedule of production and amount of safety stock. We could reduce the cost in ordering cost, holding cost, stock-out cost, and lead time crash cost. However, the inventory problem plays a more important role in production management. Therefore, how to efficiently control the inventory level becomes a very important issue.
In this paper, we develop a continuous review inventory model where the lead time, the order quantity, backorder discount, and safety factor are considered as the decision variables of a mixture of backorders and lost sales inventory model. A backorder rate is not only dependent on the price discount but also the length of lead time through the amount of shortages decision variable. Because the demands of different customers are not alike in the lead time, we cannot only use a single distribution such as a normal distribution to describe the demand of the lead time. Therefore, there are two inventory models proposed in the paper, one with normally distributed demand, and another with generally distributed demand.
We first assume that the lead time demand follows a normal distribution, and attempt to find the optimal solutions. Then, we next relax this assumption by only assuming that the first and second moments of the probability distribution of the lead time demand, and then solve this inventory model with the minimax distribution free approach. We develop an algorithmic procedure to find the order quantity, optimal lead time, optimal backorder discount, and optimal safety factor. We will give numerical examples to demonstrate solution procedure.

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