臺灣博碩士論文加值系統

　　近年來，存貨管理在商業上已受到相當的重視，在存貨管理中的一項重要課題是如何決定最佳的產進料週期及控制生產貨品的存量，以往許多研究人員，依不同的研究假設，發展出多種的生產──存貨模式，K.S.park首先建立了一個具有指數退化性原料、批量生產及單一產品之生產──存貨系統模式，並求出了年平均總成本的函數，但他並未直接說明此一通式函數為凸函數(即唯一最小解)，他在引用了原料退化率(損耗率)非常小的假設之後,得到總成本函數的一個近似函數,從而證明此近似函數為凸函數，然而，在某些需要退化率高的單一產品上，此近似解將產生極大的誤差，而不適用。本文提供了一個直接以通式零誤差的求解方法。
　　本篇研究主要分為四部份來討論：首先我們簡述了本文的研究動機與目的；進而我們對K.S.Park的退化性原料之生產－存貨系統模式和求解方法加以探討；然後我們直接以數學方法證明此生產－存貨系統模式年平均總成本的通式函數為凸函數，最後以實例比較K.S.Park近似解與本文的差異。

　　Inventory management has received considerable attention from business in recent years. One of the important task of inventory management is to control the inventory quantity and determine the optimal order interval. Many researchers were devoted to the development of various inventory models. K.S.Park, however, developed the first production inventory model for deteriorationg raw materials and a single finished product. Equations for obtaining the exact average total cost function were then derived. K.S.Park couldn't prove that there is an unique optimal solution (ie. convex) for the exact average total cost function of his model. A modified special total cost function was obtained under the assumption of the raw materials with very small decaying rate. This sqecial total cost function was then proved to be convex.
　　In this paper, we have developed a mathematical method for proving that the Park's exact average total cost functionos is convex. A numerical example is used to illustrate the result.