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研究生:許桀瑋
研究生(外文):Jye-Wei Hsu
論文名稱:產品壽命為混合分配且具有可控制的欠撥率之存貨模式研究
論文名稱(外文):The research of inventory model with controllable backorder rate for product life with mixtures of distribution.
指導教授:吳忠武吳忠武引用關係
指導教授(外文):Jong-Wuu Wu
學位類別:碩士
校院名稱:淡江大學
系所名稱:統計學系
學門:商業及管理學門
學類:會計學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:212
中文關鍵詞:存貨模式混合分配混合指數分配混合韋伯分配混合伽瑪分配退化率可控制欠撥率服務水準
外文關鍵詞:Inventory modelMixtures of DistributionMixtures of Exponential DistributionMixtures of Weibull DistributionMixtures of Gamma DistributionDeteriorated RateControllable Backorder RateService Level
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在諸多產品中,退化是一種非常普遍的現象,所謂退化即產品因衰退或腐敗後而不能執行其原有的功能,例如:食物、水果、藥品、電子零件與放射性物質等,使得存貨數量除了因為需求的耗用而減少外,也因為產品的退化而降低;因此,在探討此類產品時,因產品退化所造成的損失是不能被忽略的。關於退化性產品的存貨系統模式之探討,最早是由Ghare和Schrader在1963年提出來的,他們建立了一個退化率與需求率為常數的存貨模式。後來,許多專家學者探討不同退化率的退化性商品,而他們建立的退化性存貨模式,都是假設產品退化率為單一分配,但是有很多因素會造成產品退化,如果每一因素皆假設一分配來考慮,則產品的退化率將會服從於混合型分配,而不是單一分配所能涵蓋。
因此,基於上述理由,本研究考慮在有限的計劃期間內,分別建立產品退化率服從於混合指數分配、混合韋伯分配與混合伽瑪分配的存貨模式。雖然,此模式很難直接求解,但是,在有限的計劃期間內,我們推導出其對應之訂購週期的上限,對於求解很有幫助。依此,並透過求解的程序,可以求得最適的訂購週期以及服務水準。
此外,在傳統的EOQ存貨模式中,我們經常假設需求率為固定已知的常數。然而在日常生活中,我們可以觀察到需求率通常為任一已知的連續時間函數,且隨時間遞增物價指數呈現上揚的趨勢,訂購成本與持有成本皆為非負的線性遞增時間函數。另外,在缺貨發生時,有一些顧客不願意等候欠撥,但有些顧客願意等候欠撥,因此,等候廠商補貨所需要時間的長短,往往成為消費者是否願意接受欠撥的主要關鍵。
最後,本文將分別建立三個含有訂購成本、持有成本、退化成本、缺貨成本與機會損失成本的退化性存貨模式。並且針對每一個模式所適用的不同情境,分別以實例來說明求解的過程。而且,根據實例所做的敏感度分析,以提供企業界管理存貨的參考。
In many products, the effect of deterioration is very important. Deterioration is defined as decay, change or spoilage that prevents the item from being used for its original purpose (e.g. food, fruit, drugs, electrical components, radioactive substances, etc.). First, Ghare and Schrader (1963) suggest an inventory model for deteriorating items with fixed deteriorated rate and demand rate. Many Scholars discuss different deteriorated rate of deteriorating items, and they build deteriorated model assumed that all product life from a single distribution, but many factors that will make items deteriorated. If every factor assumes a single distribution, then product life will follow mixtures of distribution.
So, in this thesis we will consider product life with the mixtures of exponential distribution, mixtures of weibull distribution and mixtures of gamma distribution over a fixed planning horizon, respectively. Since it is difficult to solve the problem directly, we derived the upper bound of replenishment number for a specific planning horizon, and found the solution of service level under a given number of replenishment. Afterwards, the optimal solutions were determined.
In the present paper, the holding cost and ordering cost is assumed to be constant. In practice, the holding cost and ordering cost may not always be constant because the price index may increase with time. Therefore, we also assume that the holding cost and ordering cost per unit per unit time is a continuous, non-negative and non-decreasing function of time. Moreover, we also consider that the demand rate usually assumed to be continuous function of time.
In addition, during the shortage period, the backorder rate is variable and is dependent on the length of the waiting time for the length replenishment. The longer the waiting time is, the proportion of customers who should like to accept backorder at time t is decreasing with the waiting time ( t j - t ) waiting for the next replenishment, where sj≦t≦t j, sj is the time at which the inventory in the jth cycle drops to zero, j=1,2,…,n,t j is the time of the (j+1)th replenishment, j=0,1,…,n-1,with t0=0.
Finally, we give some numerical examples are proposed that illustrate three
inventory models with ordering cost, holding cost, deteriorating cost, shortage cost ,
opportunity cost and solution procedure. The sensitivity analysis of the major
parameters of the model is also performed.
目錄……………………………………………………………………….I
圖目錄…………………………………………………………………..III
表目錄…………………………………………………………………...IV
第一章 緒論…...……………………………………………………...1
1-1 研究動機與目的……………………………………………..1
1-2 相關文獻探討………………………………………………..4
1-3 研究流程……………………………………………………..7
1-4 研究架構………………………………….……………...…9
第二章 有限計劃期間內產品壽命服從於混合指數分配的存貨模
式………...…………………………………….………………10
2-1 符號說明與假設……………………………………....……11
2-2 模式建立……………………………………..………..……14
2-2-1 欠撥率為線性遞減函數之存貨模式……..…………14
2-2-2 欠撥率為指數遞減函數之存貨模式………..………22
2-3 模式的求解過程…………………………….………..…….28
2-4 數值範例……………………………………….…………….30
2-5 敏感度分析……...………………………………….………55
第三章 有限計劃期間內產品壽命服從於混合韋伯分配的存貨模
式….…………………………………….…….…………….…73
3-1 符號說明與假設……………………………..………..……73
3-2 模式建立……………………………………..………………77
3-2-1 欠撥率為線性遞減函數之存貨模式……………..…77
3-2-2 欠撥率為指數遞減函數之存貨模式…………………85
3-3 模式的求解過程…………………………….……………….90
3-4 數值範例……………………………………………………..92
3-5 敏感度分析……...………………………………….………114
第四章 有限計劃期間內產品壽命服從於混合伽瑪分配的存貨模
式…...………………………………………….………..……132
4-1 符號說明與假設……………………………………....…..132
4-2 模式建立……………………………………..……………. 136
4-2-1 欠撥率為線性遞減函數之存貨模式……………..…136
4-2-2 欠撥率為指數遞減函數之存貨模式…..…..………145
4-3 模式的求解過程……………………………..……………..150
4-4 數值範例…………………………………….……………...152
4-5 敏感度分析……………………………………….…….....175
第五章 結論與未來研究方向………………………………...……….185
5-1 結論………………………………….…………...………..185
5-2 未來研究方向…………………………………….………….188
參考文獻………………………………………………………………...190
附錄一…………………………………………………………………...197
附錄二….……………………………………………………………....202
附錄三…….………………………………………………………………207
中文部分
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[3]陳志輝,2000,「服從珈瑪分配的退化性商品在允許缺貨、
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