允許缺貨並考慮延遲付款的非瞬間退化物品之經濟訂購量存貨模式

An EOQ inventory model for non-instantaneous deteriorating items with shortages under permissible delay in payments.

陳浩榮(Hao-Rong Chen)

指導教授 ： 歐陽良裕

淡江大學/管理學院/管理科學研究所碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00932

摘要

存貨問題已成為現今各行各業中最基本，也是最重要的課題之一，許多企業都希望擬定一個最適且最有效的存貨策略來達成最大的經濟效益。近年來，關於延遲付款這類的議題常被提出來討論，其原因在於實際的市場交易行為中，供應商往往會提供延遲付款的優惠給零售商，零售商在延遲付款期限中可利用已出售物品的收入，做為短期資金的來源。再者，供應商所提供的延遲付款期限長度也常與零售商的訂購數量有關，即訂購量越多，可以享有更長的付款期限優惠。

此外，對於生鮮蔬果、酒精類、化學製品和科技類等的產品，它們會隨著時間、溫度等環境的變化而逐漸發生退化、變質、揮發、腐敗或是損壞的現象。由於這些物品會產生額外的成本，因此將物品的退化性納入存貨模式中考量是必要的。再者，有時候企業為了減少存貨成本，在期初時會訂購較少的數量，而在期末容易產生缺貨的情形。一旦發生缺貨，顧客只好選擇等候補貨或是放棄購買；然而近幾年來，在全球化與完全競爭市場日漸普及的情況下，在市場中因為同質性產品多且顧客忠誠度低而流失所造成的銷售損失成本也逐漸被企業所重視。

本文主要探討允許缺貨並考慮延遲付款下的非瞬間退化物品之存貨系統，全文包括了兩個存貨模式，第二章為一個需求率固定且考慮延遲付款的非瞬間退化物品之存貨模式，模式中允許缺貨發生且缺貨期間的缺貨數量為完全欠撥。第三章則是延續第二章的研究，假設延遲付款期限長度與訂購數量有關，缺貨期間的缺貨數量為部份欠撥，並有一隨機的欠撥率。兩個模式皆以單位時間存貨相關總成本有最小值為目標，利用數學分析方法中的最佳化原理，證明最適解存在且為唯一。由於模式的複雜性，分別建立演算法輔助找出最適解；接著，舉數值範例說明求解過程並做主要參數值的敏感度分析。最後，第四章提出本研究的結論及未來研究的方向。

關鍵字

存貨 ； 非瞬間退化 ； 延遲付款 ； 完全欠撥 ； 隨機欠撥率

並列摘要

Nowadays, inventory problem has become one of the most basic and important topics in every walk of life. Many enterprises hope to draw up the optimal and the most effective inventory strategy in order to achieve the maximal economic benefits. In recent years, the topics about delay in payment have been proposed and discussed extensively. Since in real life, the supplier often offers the retailer an indulgence with delay in payment. In this situation, the retailer can gain sales revenue of items which is treated as short-term funds within the deadline of delay in payment. Moreover, the length of delay in payment which the supplier offers often is depend on the retailer’s ordering quantity. That is, the more quantities the retailer orders, the longer the length of delay in payment will be.

Besides, products such as fresh vegetables and fruits, alcohol, chemical products, technical products and so on will be deteriorated, denaturalized, evaporated, decayed or damaged gradually with the environment changes of time and temperature and others. Due to these types of items could produce additional costs, it is essential to consider the deterioration of items into inventory models. Furthermore, enterprises sometimes order fewer quantity at the initial period to reduce inventory costs but the shortages occur easily at the terminal period. Once the shortages occur, customers are only forced to wait for backorder or give up. In recent years, under the situations of globalization and complete competition market popularizes day after day, the issue of sales loss cost which is owing to high homogeneous products and low customers’ loyalties also has been respected by enterprises gradually.

In this thesis, two inventory models are developed for non-instantaneous deteriorating items with shortages under permissible delay in payments. In chapter 2, we establish an inventory model for non-instantaneous deteriorating items with constant demand rate and permissible delay in payment. In the model, shortages are allowed and the shortage quantities are completely backlogging. In chapter 3, we extend the model in chapter 2, it is assumed that the length of delay in payment depends on the ordering quantities and partially backlogging with a random backlogging rate. The objective is to find the minimum inventory relevant total cost per unit time for the two models. In mathematical analysis, we prove that the optimal solutions exist and are unique for the two models. Due to the complexity of the models, we establish algorithms to assist and find the optimal solution, respectively. Then, numerical examples are provided to illustrate the solution process and sensitivity analysis for primary parameters is carried out. Finally, concluding remarks and future research directions are proposed in chapter 4.

並列關鍵字

Inventory ； Non-instantaneous Deterioration ； Delay in Payment ； Complete Backlogging ； Random Backlogging Rate

參考文獻

[1] 楊志德 (2007)。考慮非即時退化性物品的一些確定性存貨模式之研究，淡江大學管理科學研究所博士學位論文。

[2] 吳興漢 (2007)。變動需求下考慮允許缺貨且部份欠撥之非瞬間退化物品的存貨模式，淡江大學管理科學研究所碩士學位論文。

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