損耗性產品在允許缺貨下之最佳決策模式

The Optimal Decision Strategy of Deteriorating Item Models under Permitted Backlogging

黃天保(Tien-Pao Huang)

指導教授 ： 林賜德

中原大學/理學院/應用數學研究所/碩士(2004年)

https://doi.org/10.6840/cycu200400139

摘要

在傳統之存貨模式中，允許缺貨的數學模式較難用基本的分析方法求出最佳解。本研究主要是在探討G . Padmanabhan和Prem Vrat[9] 於1995年所提出的損耗性產品的訂購策略，作者依據各種不同的情況下，發展出三種存貨模式，第一種類型為不允許缺貨的模式，第二種類型為在允許缺貨下且可完全補貨模式，第三種類型為在允許缺貨下部分補貨模式。這些模式作者都是用數值方法以軟體搜尋最佳解，並由此來決定模式的最大利潤，但就理論基礎的推導中，似乎沒有證明其最佳值是否存在，只是假設其存在，再利用數值解。因此，本文利用分析的方法證明其最佳解之存在性。
此外，在Padmanabhan 和 Vrat[9]的論文中，根據第二種存貨模式，在允許缺貨下完全補貨的情形，其需求是以存貨為變數之線性函數，而缺貨是可以完全或部分回補。則可以發展一個有意義的存貨模式，並證明此存貨模式的最佳解(最小總成本)是存在的，並求其最佳訂購週期時間。

關鍵字

最佳解 ； 存貨 ； 損耗性 ； 缺貨

並列摘要

In classical stock model,The model with complete backlogging
is more difficult to find out the optimal solution. This paper mainly discusses G. Padmanabhan and Prem Vrat proposed a study of ordering strategy of the deterioration items. The authors developed three kinds of stock model based on different situations. First is the model that backlogging is not permitted. Second is the model that complete backlogging is permitted. Third is the model that partial backlogging is permitted. The authors seek the optimal solution and decide the maximum profit from these models with numerical methods. However, from the study of the theory, It can not prove if its optimal solution is existing. Therefore, this paper uses mathematical
analysis to prove the existence of the optimum.
Besides, our discussion in G. Padmanabhan and Prem Vrat dissertation, based on the second stock model with complete backlogging, the demand rate is the linear function which uses stock as variable, and stock can be completely or partially backlogging. In this way, we can develop a meaningful model, prove the optimum solution is existing. Meanwhile, we can determine the optimum order time by using the mathematical analysis.

並列關鍵字

Deteriorating ； Optimum solution ； Inventory ； Backlogging

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