確定性需求下補貨政策最佳化方法—二方程模式

Abstract

傳統的經濟訂購量模式在使用時受到相當多的限制，例如需求率必須為常數、不考慮庫存損耗等。但在實際的存貨系統中，產品的需求率通常是時間的函數，而且對於許多存貨系統，例如食品、軟片、化學藥品、電子零件及放射性物質等，存貨的損耗對存貨系統的影響是無法被忽略的。由於傳統的經濟訂購量模式過於簡化，無法完全滿足許多實際存貨系統的需求，因此有許多研究提出不同的最佳化方法，以最佳化一些比較接近實際情況之存貨系統的補貨政策。但就這些方法整體來看，因受限於補貨政策問題的複雜性，除了極少數的方法在問題定義很完美的情況下能得到解析解之外，絕大多數的方法都是近似方法，僅能得到近似的最佳解。 基於上述之背景，本研究首先針對不考慮缺貨而需求率為具有對數凹性（log-concave）特性之補貨政策最佳化問題，提出一個稱為“二方程模式”之補貨政策最佳化方法。接著，本研究將二方程模式分別應用到不考慮缺貨而需求率為非線性之補貨政策問題，及不考慮缺貨但考慮存貨的損耗而需求率為線性之補貨政策問題，以探討二方程模式對於比較接近實際情況之補貨問題的適用性與發展潛力。此外，在本研究中，對於二方程模式最佳解的存在性與唯一性亦加以證明。

Many constraints such as constant demand, without deterioration, etc., must be considered when applying the conventional EOQ model. But in an actual situation, the demand rate of a product usually is a function of time and in many actual inventory systems such as food items, photo films, chemicals, electronics components and radioactive substances, the effect of deterioration is not negligible. Since the simplicity of the EOQ model, it can not completely satisfy the needs in some practical inventory systems, therefore, many approaches have been proposed to optimize the replenishment policy for some more realistic inventory system. But as a whole, due to the complexity of the replenishment problem, most of these approaches belong to approximate approaches, only few approaches could provide the analytical solution under a well-defined situation. Under the background, the main objective of this research is to develop a new optimization method, called “Two Equations Model”, for replenishment policy under deterministic demand. This research firstly focuses on the no-shortage replenishment problem with a log-concave demand to develop such an optimization method. In addition, this research applies the Two Equations Model to a no-shortage replenishment problem with a non-linear trend in demand, and a no-shortage replenishment problem for deteriorating items with a linear trend in demand to verify the expandable potentiality of the Two Equations Model. The optimality of the Two Equations Model is also proved in this research for each problem of replenishment policy.