臺灣博碩士論文加值系統

在典型的經濟生產數量（EPQ）模型通中常假設相關變數是會一直保持完美的狀態。然而，在現實生活中，一些庫存品會隨著時間的推移而劣化。劣化被定義為隨著時間的推移，產品因而損壞，變差，過時失去價值。這就是為什麼在開發EPQ模型時需要考慮劣化問題。在許多討論庫存模型的文獻，它是假設不允許缺貨發生的。然而，在許多實際情況下，由於各種不確定因性，缺貨情況變為無可避免。因而，庫存缺貨的發生是一個自然現象。但在既有的文獻中不多見有考慮到因庫存品劣化而導致缺貨的庫存模型。由於這種情況，本研究選擇了研究考慮因庫存品劣化而導致缺貨的庫存模型。
在這項研究中，開發了三個生產庫存模型。第一個模型提出了經濟生產週期（EPP）模型，考慮缺貨情境，但不考慮庫存品劣化因素。在這個模型中，我們通過尋找最佳化的補貨週期來取得總成本的最優化。第二個模型提出一個EPP模型，考慮困存品劣化所導致缺貨的情境。該模型在不使用串聯近似解以簡化與忽略劣化函數中θ項的第二或更高階的情況下找到總成本的最優解。第三個模型顯示了一個多庫存品劣化品所導致的缺貨EPP模型。此外，我們在這開發這個模式考慮到限制的存庫存量與限制的預算。
我們為多項庫存劣化所導致缺貨的問題開發了一個EPP庫存模式。這項研究的主要目標是減少總成本。庫存品的劣化的分佈遵循指數分佈。最佳庫存補貨週期和經濟生產週期是決策變量。由於這些數學模型是複雜的，因此不能推導出它們的閉合形式解。為簡化求解方法我們使用Maple 15版的來求解。
我們提供每個模型的數值範例來說明推論。通過呈現靈敏度分析證明了關鍵參數對生產時間和總成本的影響。

Classical economic production quantity (EPQ) models usually assume all the items will remain in perfect condition. However, in real life some items will deteriorate over time. Deterioration is defined as damage, decay, obsolescence, and loss of value in a product along time. That is why deterioration needs to be considering when developing EPQ model. Many literatures assume that shortages are not permitted to occur. Nevertheless, in many practical situations, stock out is unavoidable due to various uncertainties. Therefore, the occurrence of shortages in inventory is a natural phenomenon. But only a few inventory models for deteriorating item with considering allowable shortages have been found in the literature. Due to this condition, this research study inventory model dealing with deteriorating item and allowing shortage.
In this research, three production inventory models are developed. The first model presents an economic production period (EPP) model with shortage without deteriorating item. In this model, we get optimal solution of total cost by search the optimal cycle length. The second model gives an EPP model for deteriorating item with shortage. This model find the optimal solution of total cost without using series approximation to simplify and neglecting second or higher order of θ term in the deteriorate function. The third model shows an EPP model for multi-deteriorating items with shortage. Furthermore, we develop this model considering a limited storage capacity for item and a limited budget production.
In this study, we develop an EPP inventory model of deteriorating items for multi-items with shortage. The main objective of this research is to minimize the total cost. Distribution of the deterioration item follows the exponential distribution. The optimum inventory cycle and the economic production period are decision variables. Since these mathematical models are complex, their closed form solutions cannot be derived. We use the simple search method using Maple 15 software to solve the models.
We provide the numerical example for each model to illustrate the theorems. The effects of key parameters changes to production up time and total cost demonstrated by presenting sensitivity analysis.

Table of Contents

摘要 i
ABSTRACT ii
ACKNOWLEDGEMENTS iii
Table of Contents iv
List of Figures vi
List of Tables vii
CHAPTER 1 INTRODUCTION 1
1.1. Background 1
1.2. Research Problem 2
1.3. Research Goal 3
1.4. Research Framework 3
CHAPTER 2 LITERATURE REVIEW 6
2.1. EPQ model with shortage 6
2.2. Deteriorating Item Inventory Model 7
2.3. Research Methodology 9
2.4. State of The Art of Research 9
2.5. Research Contribution 10
CHAPTER 3 EPP MODEL ALLOWED SHORTAGE WITHOUT DETERIORATING ITEM 11
3.1. Notation 11
3.2. Model development 12
3.3. Numerical examples and sensitivity analysis 15
3.3.1. Warehouse capacity constraint 15
3.3.2. Warehouse capacity and budget constraint 18
CHAPTER 4 EPP MODEL FOR DETERIORATING ITEM WITH SHORTAGE 20
4.1. Notation 20
4.2. Model Development 20
4.3. Numerical example and sensitivity analysis 33
4.4. Warehouse capacity and budget constraint 34
4.4.1. Numerical example and sensitivity analysis 36
CHAPTER 5 EPP MODEL FOR MULTI DETERIORATING ITEM WITH SHORTAGE 40
5.1. Notation 40
5.2. Model Development 40
5.3. Numerical Example and Sensitivity Analysis 50
5.4. Warehouse capacity and budget constraint 51
5.4.1. Numerical example and sensitivity analysis 54
CHAPTER 6 CONCLUSION AND FUTURE RESEARCH 57
6.1. Summary of the Conducted Research 57
6.2. Conclusion 57
6.3. Future Research 58
REFERENCES 59

List of Figures
Figure 1.1 Research Frameworks 3
Figure 2.1 Research Methodology Flowchart 9
Figure 3.1 Inventory Cycle 11
Figure 3.2 The total cost sensitivity analysis 17
Figure 3.3 The total cost sensitivity analysis with 2 constraint 19
Figure 4.1 Inventory cycle 21
Figure 4.2 Total cost function convex 32
Figure 4.3 Variables sensitivity analysis for deterioration rate changes 34
Figure 4.4 Total cost sensitivity analysis 39
Figure 5.1 Inventory Cycle 41
Figure 5.2 Total cost function convex in terms of T21,T1 48
Figure 5.3 Total cost function convex in terms of T22, T1 48
Figure 5.4 Total cost function convex in terms of T21, T2 49
Figure 5.5 Total cost function convex in terms of T22, T2 49
Figure 5.6 Variable sensitivity analysis for deterioration rate θ1 changes 51
Figure 5.7. Variables sensitivity analysis for deterioration rate θ2 changes 51
Figure 5.8 Total cost sensitivity analysis 56
Figure 5.9 Total cost sensitivity analysis 56

List of Tables
Table 2.1 Research Position 10
Table 3.1 Sensitivity analysis of total cost 17
Table 3.2 Sensitivity analysis of total cost with 2 constraints 19
Table 4.1 Comparative result and Sensitivity of θ 33
Table 4.2 Sensitivity analysis of total cost 38
Table 5.1 The result and sensitivity of θi 50
Table 5.2 Sensitivity analysis of total cost 55

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