零售商考慮損耗性商品在允許缺貨下最佳利潤的訂購策略

The Ordering Strategy for Porfit Maximization of Retailer On Deteriorating Item under Permitted Backlogging

許又元(You-Yuan Hsu)

指導教授 ： 林賜德

中原大學/商學院/企業管理研究所/碩士(2016年)

https://doi.org/10.6840/cycu201600810

摘要

傳統的存貨模型中，允許缺貨的數學模型可以用分析的方法求出最佳解。本研究主要是在探討損耗性產品允許缺貨部分待補的存貨模式。Padmanabhan和PremVrat分別於1995及1987年所提出具有損耗性質商品的訂購策略，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，第二種類型為在可允許缺貨之下完全補貨模式，第三種類型為在可允許缺貨之下部分補貨模式。本研究不僅探討這些模式，並嚴謹的證明這些解的存在性並可以搜索最佳解答，求此模式最大利潤的最佳週期時間及最佳訂購量，本研究利用分析的最佳化理論證明最佳解的存在。在Padmanabhan和PremVrat於1995及1987年的論文中，根據第二種存貨模型，在可允許缺貨且完全補貨的情形，需求率是固定的值，現在本研究將第二種模型的假設條件做部分的調整，也就是說假設需求率是一個隨存貨線性函數的需求時，在最大利潤需求下，求最佳的補貨量及最佳的週期時間。而補貨率是在缺貨時間內，需求率為固定值α乘上一個介於0到1的常數K等於0時，即為不允許缺貨，K等於1時表示缺貨時可以完全待補，推廣出另一個有意義的模型，再利用數學證明的方式來探討其最佳總利潤是存在的。

關鍵字

損耗性，存貨，最佳化

並列摘要

In traditional theory of inventory, the optimization solutions can be obtained by the analytic method to solve the permissible model problem. This study was to explore the inventory model of production. In 1987 and 1995, Padmanabhan and Prem Vrat published the papers concerning the different perishable ordering strategy. They developed three kinds of inventory strategies. The first is not permissible shortage model, the second is the full replenishment under permissible shortage model, and the third is partial replenishment under permissible shortage model. In this paper, we prove the existence of solutions and solve the optimal cycle time and economic order quantity by mathematical skills. By two papers of Padmanabhan and Prem Vrat we mention above, they assume that the demand rate is a fixed constant in the second inventory model. Recently, in this paper, we assume that the demand rate is a linear function of the inventory level to explore the optimal profit. In 1987 and 1995, Padmanabhan and Prem Vrat published their papers according to the second inventory model, that is allowable backlogging and replenishment needs perfectly. In this paper, we made some adjustments in assumptions condition. In other words, we assume that demand is a linear function of the inventory level and to find the maximum profit, optimal replenishment time and horizon cycle time. In the paper, we also mention the demand rate for fixed α multiplied by the constant value k between 0 and 1 in the period of backlogging time, which is not allowable stock shortage as the value k equal to 0 and stock shortage is permitted backlogging when k equal to 1. This is a generalization of an meaningful model, and we use mathematical method to prove the existence of its optimal profit.

並列關鍵字

Backlogging，Inventory，Optimal

參考文獻

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