In today’s time-based competition, the demand rate and the unit cost of a high-tech product are varying significantly over their short product life cycles. We build a generalized economic order quantity model with shortages for fluctuating demand and cost, and then we discuss the influences of both demand and cost over the length of the replenishment cycle. For the product that the demand rate and cost remains stable in the maturity stage of a product life cycle, we propose an easy-to-use and simple-to-understand method to solve the generalized EOQ model without taking derivatives. We also extend replenishment model for deteriorating items with partial backlogging and then compare four alternative inventory shortage models by using maximizing total profit as the objective. We also consider an appropriate EOQ model with trade credit financing, and then provide two different ways for the retailer to payoff the purchase cost. Finally, we propose a multi-item inventory system with capacity constraint. An iterative heuristic algorithm is proposed to determine the staggering times and order intervals of all items.

在今日以時迅競爭的時代，高科技產品在其短暫的生命週期中之需求率及零件成本有著劇烈的變化。因此，在傳統的經濟訂購量(EOQ)模式中，假設需求量及零件成本是不變的情況，已不能適用於今日的高科技產品。第一，我們放寬傳統的假設，在需求率以及單位成本隨時間變動下，導出演算法來尋求最佳的訂貨時間點及最佳的訂購次數，而後我們探討當需求率以及單位成本產生變化時，對訂購間隔時間以及訂購量、缺貨量等產生的影響。對於需求率與購買成本維持穩定的成熟期產品，我們捨棄複雜的微分模式，以簡化的代數方法來求出一般化EOQ模式之最佳訂購點及訂購量。第二，我們將擴充原來的存貨模式，從無腐壞性及不可缺貨到有腐壞性及可部分欠撥。而後我們依據存貨計畫週期的初始及最終時間是否能缺貨，分為四個不同的缺貨模式，探討在何種條件下，何種模式有最佳的獲利。第三，我們建立一個合宜的EOQ信用交易模式，而後提供兩個不同的途徑來償還其購買成本。最後，我們建立反覆的啟發式演算法，以交錯的訂購時間來訂購多樣化產品，以解決有限空間的限制。

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