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研究生:洪正興
研究生(外文):Hung, Cheng Hsing
論文名稱:考慮損耗性商品的一些確定性存貨模式之研究
論文名稱(外文):A Study of Several Deterministic Inventory Models with Deteriorating Items
指導教授:張紘炬張紘炬引用關係
指導教授(外文):Chang, Horng Jinh
學位類別:博士
校院名稱:淡江大學
系所名稱:管理科學學系
學門:商業及管理學門
學類:企業管理學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:英文
論文頁數:84
中文關鍵詞:存貨損耗性商品允許延遲付款與時間有關的需求部分欠撥
外文關鍵詞:InventoryDeteriorationPermissible Delay in PaymentTime-varying DemandPartial Backlogging
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傳統的經濟訂購量模式(EOQ)和文獻上大部分的存貨模式通常都假設所販賣的物品可以無限期儲存來滿足未來的需求。然而,很多產品例如藥品、揮發性液體、血庫以及蔬果食物等在正常的儲存過程中可能因為退化(蒸發、毀壞、損耗等)而使得數量減少。如果未將退化的因素加以考量的話將會使存貨模式的成本結構產生偏差。因此,在探討此類產品的存貨模式時,因產品退化所造成的損失就不能被忽視。
本論文中,我們在考量退化性商品的假設下建構了三個確定性存貨模式。
傳統的經濟訂購量模式假設當供應商將貨品送至零售商時,零售商需將款項立即交付給供應商。然而,這樣的假設通常與實務上並不相符,在現實社會中,我們可以發現供應商往往為了刺激市場需求、提高市場佔有率或降低本身的存貨壓力而會給與零售商一段固定的付款期限,在此一延遲付款的條件下,我們於第二章和第三章中分別建構了一個確定性存貨模式。第二章我們首先建構了一個供應商提供零售商延遲付款期間下,需求率為與時間有關的線性遞增函數的單一退化性商品存貨模式。在第三章中,我們提出一個有限計畫期間下,同時考慮延遲付款條件及貨幣時間價值的退化性商品存貨模式。
此外,在缺貨期間,等候廠商補貨所需時間的長短往往成為消費者是否願意接受欠撥的主要關鍵。等候欠撥的時間愈長,則願意接受欠撥的比率也就愈小。由此可知,缺貨期間內的欠撥率應該是變動的,而且與等候廠商下次補貨時間長短有關。近來許多學者開始探討與顧客等候時間長短有關的欠撥率,然而大部分都限定於指數或線性遞減形式。因此,在第四章中提出了一個有限計畫期間下同時考慮與時間有關的需求和部分欠撥的退化商品存貨模式,與之前學者所研究不同的是,缺貨不是假設為完全欠撥也不是完全不補,而是將欠撥率假設為等候廠商下次補貨所需時間的一般化函數。最後,以上所建立的數理存貨模式均以數值範例來展示其求解過程,並分別列於相關章節之後。
The classical Economic Order Quantity (EOQ) model and most of the existing inventory models in the literature assume that items can be stored indefinitely to meet future demands. However, it is well known that certain products such as medicine, volatile liquids, blood bank and foodstuff, etc., decrease under deterioration (vaporization, damage, spoilage, etc.) during their normal storage period. Without taking deterioration into consideration will cause deviations of cost structure for an inventory model. Therefore, the impact of deterioration cannot be ignored on modeling an inventory system.
In this dissertation, three deterministic inventory models for deteriorating items have been formulated.
In EOQ models, it is often assumed that payment will be made to the vendor for the goods immediately after receiving the consignment. Such assumption is usually not fulfilled in many practical situations. In practice, it is observed that suppliers sometimes offer a fixed credit period to stimulate demand, boost market share or decrease inventories of certain items. Base on the condition of permissible delay in payment, two deterministic inventory models are proposed in Chapter 2 and Chapter 3, respectively. In Chapter 2, we first deal with inventory problems for a single deteriorating item with linear trend in demand while the suppliers offer some credit periods to the retailers. In Chapter 3, a finite time horizon inventory model with deterioration and time-value of money under the conditions of permissible delay in payments is discussed.
As a physical phenomenon, some customers would like to wait for backlogging during the shortage period, while others would not. Recently, many studies have modified inventory policies by considering the time-proportional partial backlogging rate. Accordingly, the length of the period becomes the dominant factor when considering accepting the backlogging. The longer the waiting time is, the lower the backlogging rate would be. However, their theory is limited only to the exponential or linear classes of backlogging rate. Hence, a finite time horizon EOQ model for deteriorating items with time varying demand and partial backlogging is proposed in Chapter 4. In particular, the backlogging rate is assumed to be a general function of customers’ waiting time to the next replenishment.
Additionally, in all mathematical inventory models, some numerical examples are also provided to illustrate the proposed models.
Contents
List of Tables iv
List of Figures v
1. Introduction 1
1.1 Motivation and purpose 1
1.2 Literature review 4
1.3 Framework 9
2. An Inventory Model for Deteriorating Items with Linear Trend Demand Under the Condition of Permissible Delay in Payments 10
2.1 Exordium 10
2.2 Assumptions and notations 11
2.2.1 Assumptions 11
2.2.2 Notations 12
2.3 Model formulation 13
2.3.1 Case 1: 13
2.3.2 Case 2: 15
2.4 Special case 18
2.5 Numerical examples 20
3. A Finite Time Horizon Inventory Model with Deterioration and Time-value of Money Under the Conditions of Permissible Delay in Payments 23
3.1 Exordium 23
3.2 Assumptions and notations 24
3.2.1 Assumptions 24
3.2.2 Notations 25
3.3 Model formulation 26
3.3.1 Case 1: 29
3.3.2 Case 2: 30
3.3.3 Case 3: 33
3.4 Special case 35
3.5 Numerical examples 39
3.5.1 Example 1: Weibull deterioration rate 39
3.5.2 Example 2: Exponential deterioration rate 39
4. A Finite Time Horizon Inventory Model with Deteriorating Items, Time-varying Demand, Linear Replenishment Cost, and General Time-proportional Partially Backlogging 44
4.1 Exordium 44
4.2 Assumptions and notations 46
4.2.1 Assumptions 46
4.2.2 Notations 47
4.3 Model formulation 48
4.3.1 Exact solution procedure 50
4.3.2 Adjusted solution procedure 52
4.4 Special cases 53
4.4.1 Linear time-proportional backlogging pattern 53
4.4.2 Exponential time-proportional backlogging pattern 53
4.4.3 Weighted time-proportional backlogging pattern: 54
4.5 Numerical example 54
4.5.1 Exact solution procedure 55
4.5.2 Adjusted solutions procedure 55
5. Conclusion 58
5.1 Results of the study 58
5.2 Future studies 61
BIBLIOGRAPHY 64
Appendix A 72
Appendix B 74
Appendix C 75
Appendix D 80
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