臺灣博碩士論文加值系統

摘要
產品庫存是公司的資產，並與公司的財務方面有密切的相關。因此，若無妥善的管理，庫存將會降低利潤。此後，存貨模式總是被用來設定為使總成本達到最小化。而且總成本為影響存貨模式之一重要參數。本研究提出一個EOQ存貨模式考慮到變動的訂購成本及持有成本使模式更符合現實情況。且本EOQ模式使用考慮缺貨 (允許缺貨補貨) 及不考慮缺貨(不允許缺貨補貨)兩種情況。主要目的為使總成本(TC)達到最小化。然而，此存貨模式以最佳存貨週期、經濟訂購量、及缺貨量為決策變數。
典型的最佳化方式是透過傳統的微積分求得目標函數之極大(小)值。因此，本研究透過微積分求解此存貨模式下的最佳存貨週期、經濟訂購量、及缺貨量之表示式並證明其存貨模式之凸性(convexity)。之後，透過一個數值範例說明此存貨模式之有效性及實用性，以及考量不同的訂購成本(α)及持有成本(β)下對於目標函數之敏感度分析，並用圖解與數值結果呈現參數改變對目標函數之影響。

Inventory is an important asset of a company, and its policy greatly influences the financial success of a company. Therefore, a company’s profit may decline due to inappropriately inventory management. Hence, inventory model should aim to minimize the total relevant inventory cost. Consequently, the total inventory cost becomes an important consideration and it affects the performance of a company. In this research, we propose a more practical EOQ models where the ordering cost and the holding cost are an increasing function of the ordering cycle length. Two EOQ models are developed. One considers no shortage environment and the other allows for shortage and backorder. The main objective of this research is to minimize the total inventory related costs. The optimum inventory cycle, the economic order quantity, and backorder size are the decision variables in this study. The classical optimization techniques using calculus technique with first-order and second-order derivatives have been performed to determine the optimum lot size, and to prove its convexity. To demonstrate the utility of the formulated models, and study the effect of the ordering cost (α)shape parameter and the holding cost (β) shape parameter on the optimal solution, numerical examples considering different value of α and β are given. Sensitivity analyses are also performed. They are presented graphically and numerically to illustrate the behavior of the models, and to determine the effects of the parameters changes. The numerical results show that our proposed models give smaller annual total costs than the traditional EOQ model. Finally, the results of the sensitivity analysis show that only the ordering cost parameter has a significant effect on the optimal total cost in both models.

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. Introduction to the study ............................................................................................. 1
1.2. Research Problem ...................................................................................................... 4
1.3. Research Goals............................................................................................................ 5
1.4. Research Scope ........................................................................................................... 5
1.5. Research Framework .................................................................................................. 5
1.6. Research Contribution ................................................................................................ 8
CHAPTER 2 LITERATURE REVIEW .................................................................................... 8
2.1. Inventory Management ................................................................................................. 10
2.1.1. Inventory and The Flow of Material ...................................................................... 10
2.1.2. Inventory Costs ...................................................................................................... 11
2.1.2.1. Item Costs ............................................................................................................ 12
2.1.2.2. Holding Costs ...................................................................................................... 12
2.1.2.3. Ordering Costs .................................................................................................... 12
2.1.2.4. Stockout/Shortage Costs ..................................................................................... 13
2.2. EOQ Model ................................................................................................................... 13
2.2.1. EOQ Model Without Backorders/Shortages .......................................................... 14
2.2.1.1. Model Formulation .............................................................................................. 15
2.2.2. EOQ Model With Backordering/Shortages............................................................ 16
2.2.2.1. Model Formulation .............................................................................................. 17
2.3. Some Inventory Models ................................................................................................ 19
2.3.1. EPQ Models with Varying Setup Cost ................................................................... 19
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2.3.1.1. Determination of the model assumptions and notation ....................................... 20
2.3.1.2. Development of models ...................................................................................... 20
2.3.1.3. Result and Summary .......................................................................................... 23
2.3.2. EOQ Model With Varying Holding Cost ............................................................... 25
2.3.2.1. Problem Description ............................................................................................ 25
2.3.2.2. Models Development .......................................................................................... 26
2.3.2.3. Conclusion and Suggestions ............................................................................... 27
CHAPTER 3 MODEL DEVELOPMENT .............................................................................. 29
3.1. Assumptions .............................................................................................................. 29
3.2. Notations ................................................................................................................... 30
3.3. The Models ............................................................................................................... 30
3.3.1. Model I: EOQ Model without Shortages ............................................................... 31
3.3.1.1. Model Formulation .............................................................................................. 31
3.3.1.2. Optimal Solution ................................................................................................. 32
3.3.1.3. Convexity of the Total Cost Function ................................................................. 33
3.3.1.4. Numerical Example ............................................................................................. 34
3.3.2. Model II: EOQ Model with Shortages ................................................................... 41
3.3.2.1. Model Formulation .............................................................................................. 41
3.3.2.2. Optimal Solution ................................................................................................. 42
3.3.2.3. Convexity of the Total Cost Function ................................................................. 42
3.3.2.4. Numerical Example ............................................................................................. 45
CHAPTER 4 SENSITIVITY ANALYSIS .............................................................................. 52
4.1. Sensitivity Analysis for Model I (EOQ Model without Shortages) .............................. 52
4.2. Sensitivity Analysis for Model II (EOQ Model with Shortages) ................................. 59
CHAPTER 5 CONCLUSION AND FURTHER RESEARCH .............................................. 70
REFERENCES ........................................................................................................................ 71
APPENDIX ............................................................................................................................. 73
vi
LIST OF FIGURES
Figure 1.1. Flowchart Framework .............................................................................................. 6
Figure 2.1. Inventories and the flow of materials .................................................................... 11
Figure 2.2 A typical EOQ inventory model without backorders .............................................. 15
Figure 2.3 A typical EOQ inventory model with backorder .................................................... 17
Figure 2.4 Setup Cost Against Production Run Length for Different Values of ε ................... 21
Figure 2.5 Setup Cost Against Production Run Length for Different Values of ε ................... 22
Figure 3.1 Total Cost Versus Cycle Length for α=0.1 and β=0.1 ............................................ 33
Figure 3.2 Optimal lot size’s behavior in varying α for Model I ............................................. 34
Figure 3.3 Optimal lot size’s behavior in varying β for Model I ............................................. 35
Figure 3.4 Optimal total cost’s behavior in varying α for Model I .......................................... 35
Figure 3.5 Optimal total cost’s behavior in varying β for Model I .......................................... 36
Figure 3.6 Total cost Vs cycle length and backorder size for α=0.1 and β=0.1 ...................... 44
Figure 3.7 Optimal lot size’s behavior in varying α for Model II ............................................ 45
Figure 3.8 Optimal lot size’s behavior in varying β for Model II ............................................ 46
Figure 3.9 Optimal total cost’s behavior in varying α for Model II ......................................... 46
Figure 3.10 Optimal total cost’s behavior in varying β for Model II………………… ……...47
Figure 4.1 Effects of the parameter changes to the optimal lot size for Model I… ................. 53
Figure 4.2 Effects of the parameter changes to the total cost for Model I……………...… .... 53
Figure 4.3 Effects of the parameter changes to the optimal lot size for Model II………… .... 59
Figure 4.4 Effects of the parameter changes to the backorder size for Model II………… ..... 60
Figure 4.5 Effects of the parameter changes to the total cost for Model II………….…… .... .60
Figure 4.6 Sensitivity analysis of total cost in Model II with varying C when α=0.9 .............. 69
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LIST OF TABLES
Table 1.1 Research Position Related to the Prior Research .................................................................... 9
Table 3.1 The notations uded in the models ...........................................................................................30
Table 3.2 Optimal Solution for different values of β when α= 0 and α= 0.1 for Model I .....................37
Table 3.3 Optimal Solution for different values of β when α= 0.5 and α= 0.9 for Model I ...................38
Table 3.4 Optimal Solution for different values of α when β = 0 and β = 0.1 for Model I ....................39
Table 3.5 Optimal Solution for different values of α when β = 0.5, β = 0.9, and β = 1.0 for Model I ...40
Table 3.6 Optimal Solution for different values of β when α= 0 and α= 0.1 for Model II ....................48
Table 3.7 Optimal Solution for different values of β when α= 0.5 and α= 0.9 for Model II..................49
Table 3.8 Optimal Solution for different values of α when β = 0 and β = 0.1 for Model II ..................50
Table 3.9 Optimal Solution for different values of α when β = 0.5, β = 0.9, and β = 1.0 for Model II .51
Table 4.1 Summary of values for the sensitivity analysis for Model I ...................................................52
Table 4.2 The resulting values for Q* and TC* with varying R for Model I when α= 0.9 ....................54
Table 4.3 The resulting values for Q* and TC* with varying C for Model I when α= 0.9 ....................56
Table 4.4 The resulting values for Q* and TC* with varying H for Model I when α= 0.9 ....................58
Table 4.5 Summary of values for the sensitivity analysis for Model II .................................................59
Table 4.6 The resulting values for B*, Q*, and TC* with varying R for Model II when α= 0.9 ...........61
Table 4.7 The resulting values for B*, Q*, and TC* with varying C for Model II when α= 0.9 ..........63
Table 4.8 The resulting values for B*, Q*, and TC* with varying H for Model II when α= 0.9 ...........65
Table 4.9 The resulting values for B*, Q*, and TC* with varying π for Model II when α= 0.9 ...........67

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