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。

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.

目錄
頁次
目錄	I
表目錄	III
圖目錄	IV
使用符號一覽表	V
基本假設	VI
第一章  緒論	1
1.1 研究動機與目的	1
1.2 文獻探討	3
1.2.1 物品的退化	3
1.2.2 缺貨數量欠撥	5
1.2.3 延遲付款	6
1.3 研究方法	8
1.4 研究架構	8
第二章  完全欠撥且考慮延遲付款的非瞬間退化物品之經濟訂購量存貨模式	10
2.1 前言	10
2.2 符號與假設	11
2.3 模式的建立	11
2.4 模式的求解	20
2.5 數值範例	37
第三章  延遲付款期限與訂購量有關且具隨機欠撥率的非瞬間退化物品之經濟訂購量存貨模式	44
3.1 前言	44
3.2 符號與假設	45
3.3 模式的建立	46
3.4 模式的求解	57
3.5 數值範例	82
第四章 結論及後續研究方向	86
4.1 主要研究成果	86
4.2 未來研究方向	90
參考文獻	92
附錄一(A) 第二章系2.1與系2.2之證明	98
附錄一(B) 第三章系3.1與系3.2之證明  101

表目錄
頁次
表2.1  例題2.1的最適解表	38
表2.2  存貨模式中不同參數值變動下的敏感度分析(%)	40
表3.1  不同訂購數量下的付款期限	82
表3.2  例題3.1的求解過程	83
表3.3  存貨模式中主要參數值的變動對最適解的影響	84

圖目錄
頁次
圖2.1  完全欠撥之存貨水準與時間的關係圖	12
圖2.2  完全欠撥時Case 1的存貨水準與時間關係示意圖	15
圖2.3  完全欠撥時Case 2的存貨水準與時間關係示意圖	16
圖2.4  完全欠撥時Case 3的存貨水準與時間關係示意圖	17
圖2.5  完全欠撥時Case 4的存貨水準與時間關係示意圖	18
圖3.1  隨機欠撥率之存貨水準與時間的關係圖	47
圖3.2  隨機欠撥率時Case 1的存貨水準與時間關係示意圖	50
圖3.3  隨機欠撥率時Case 2的存貨水準與時間關係示意圖	51
圖3.4  隨機欠撥率時Case 3的存貨水準與時間關係示意圖	52
圖3.5  隨機欠撥率時Case 4的存貨水準與時間關係示意圖	53

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