臺灣博碩士論文加值系統

在存貨系統中，大多數的物品於持有過程中都會有退化的現象產生，然而並非所有退化性物品都在一開始即發生退化，通常會有一段能保持新鮮或維持原有品質的期間，亦即在這一段期間內，物品不會立即發生退化。我們將這種現象定義為「非即時退化」；而這類型的物品稱為「非即時性退化物品」。
再者，物品的需求率並非固定不變，在現實的日常生活中可以觀察到一種現象（尤其在超級市場或大型量販店）：一些量販業者會儘量將貨架上的物品擺滿，藉此刺激顧客的需求。對於這類型的物品，其需求通常與貨架上的存貨數量有關。其次，在市場消費行為裡，顧客對於流行的商品、時髦的服飾與產品生命週期短的高科技產品來說，若零售商發生缺貨，顧客在缺貨期間願意等候補貨的比例常與等候補貨時間的長度呈反比；亦即，等候時間愈長，欠撥的比例愈小。
而在一般的商業交易行為中，我們也發現到：供應商基於某些原因如欲刺激零售商購買或買賣雙方訂定的供應鏈合約，會嘗試提供零售商數量折扣或延遲付款等的優惠。
本文係探討一些非即時退化性物品的存貨系統，全文包括了三個存貨模式，第二章考慮一個需求率與存貨水準有關的非即時退化性物品的存貨問題。系統中允許缺貨發生且部分欠撥，並假設欠撥率與等到下一次補貨的時間長度有關。第三章延續第二章的研究，亦假設物品的需求率與存貨水準有關，並考慮在供應商提供數量折扣下探討非即時退化性物品的存貨問題。存貨系統中允許缺貨發生且為部分欠撥，而欠撥率為一隨機變數。第四章則考慮在允許延遲付款下的非即時退化性物品之存貨問題。進一步，我們利用數理方法分別得到所提三種存貨模式最適解存在的充分且必要條件，並分別舉例說明其求解過程，再透過敏感度分析，以瞭解參數值改變對於最適解所造成的影響。最後，第五章則提出本研究的結論及未來的研究方向。

In the inventory system, most of goods will have a phenomenon that deteriorates during the course of stock holding. However, the deterioration always does not occur as soon as the retailer receives the commodities. In real life, most goods would have a span of maintaining quality or original condition, namely, during that period, there is no deterioration occurring. We term the phenomenon as “non-instantaneous deterioration” and this type of item as “non-instantaneous deteriorating item”.
Besides, the assumption of constant demand is not always applicable to real situations. For instance, it is usually observed in the supermarket that display of the consumer goods in large quantities attracts more customers and generates higher demand. Furthermore, when the shortages occur, some customers are willing to wait for backorder and others would turn to buy from other sellers. In some inventory systems, such as fashionable commodities, the length of the waiting time for the next replenishment would determine whether the backlogging will be accepted or not. Therefore, the backlogging rate is variable and dependent on the waiting time for the next replenishment.
In business dealing, for encouraging the retailer to buy more, the supplier offers a price discount or allows a certain fixed period for settling the account but doesn’t charge any interest from the retailer on the amount owed during this period.
This thesis mainly focuses on some deterministic inventory models with non-instantaneous deteriorating items. There are three inventory models including this study. In Chapter 2, we first consider a problem of determining the optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand. In the model, shortages are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment. In Chapter 3, we extend Chapter 2’s model when supplier offers the quantity discount. In this model, shortages are also allowed but the backorder rate is considered as a random variable. In Chapter 4, an attempt is made to develop an appropriate inventory model for non-instantaneous deteriorating items when the supplier provides a permissible delay in payments. The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions for the three models are shown. Numerical examples are added to illustrate the results, and the sensitivity analyses of the optimal solution with respect to parameters of the systems are also carried out for understanding how parameter changes influence the optimal solution. Finally, concluding remarks are made in Chapter 5 and future research directions are proposed.

目錄
頁次
第一章 緒論 1
1.1. 研究動機與目的 1
1.2. 相關文獻探討 3
1.2.1. 退化性物品 3
1.2.2. 需求型態 6
1.2.3. 數量折扣 7
1.2.4. 延遲付款 8
1.3. 本文結構 10
第二章 需求與存貨水準有關且部分欠撥之非即時退化性物品的存貨模式 13
2.1. 前言 13
2.2. 符號與假設說明 15
2.3. 模式建立 17
2.4. 模式求解 22
2.5. 一些特殊情況與比較 25
2.6. 敏感度分析 28
2.7. 數值範例 30
2.8. 小結 34
第三章 考慮數量折扣下需求與存貨水準有關且隨機欠撥率之非即時退化性物品的存貨模式 36
3.1. 前言 36
3.2. 符號與假設 37
3.3. 模式建立 39
3.4. 模式求解 43
3.5. 數值範例 47
3.6. 敏感性分析 51
3.7. 小結 53
第四章 考慮延遲付款下之非即時退化物品的存貨模式 55
4.1. 前言 55
4.2. 符號與假設 57
4.3. 模式建立 58
4.4. 模式求解 66
4.5. 數值範例與敏感度分析 75
4.6. 小結 80
第五章 結論與後續研究 81
5.1. 主要研究成果 81
5.2. 未來研究方向 85
參考文獻 87
附錄 A. 定理2.1之證明 96
附錄 B. 定理2.2之證明 98
附錄 C. 定理2.3之證明 100
附錄 D. 定理3.1之證明 101
附錄 E. 定理3.2之證明 103
附錄 F. 引理4.1的證明 105
附錄 G. 引理4.2的證明 106
附錄 H. 引理4.3的證明 107

圖目錄
頁次
圖1.1 本文研究架構流程圖 12
圖2.1 部分欠撥且欠撥率與等候時間有關之非即時退化物品存貨系統 18
圖3.1 部分欠撥且隨機欠撥率之非即時退化物品存貨系統 40
圖4.1 情況1的存貨系統（M≦td） 63
圖4.2 情況2的存貨系統（M＞td） 64




表目錄
頁次
表2.1 不同的參數值變動對於最適解的影響 32
表2.2 不同情況存貨模式最適解 34
表3.1 數量折扣相關資訊 48
表3.2 範例3.1的求解過程 48
表3.3 不同td與θ值下最適解 49
表3.4 不同a值下之最適解 (其中b=1) 50
表3.5 不同參數變動下對最適解之影響 52
表4.1 範例4.1不同訂購成本A下之最適解 75
表4.2 範例4.2不同訂購成本A下之最適解 76
表4.3 不同M、td與θ值下之最適解彙整表 78

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