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研究生:石仲哲
研究生(外文):Shin Chung Che
論文名稱:多批量下料問題在中斷式幾何分配及機台當機下之研究
論文名稱(外文):The Study of Multiple Lotsizing in Production to Order with Interrupted Geometric Yield Distribution and Machine Failure
指導教授:阮約翰阮約翰引用關係
指導教授(外文):John Yuan
學位類別:碩士
校院名稱:國立清華大學
系所名稱:工業工程與工程管理學系
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:64
中文關鍵詞:多批量中斷式幾何分配Alternating renewal process
外文關鍵詞:Multiple lotsizingInterrupted GeometricAlternating renewal process
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對於訂單式生產而言,如何去決定滿足需求D之最佳的生產批量,是相當重要的課題。本文改善傳統之多次批量問題,另增加對機台發生當機且符合指數分配的考量, 在機台運轉時產品良率為中斷式幾何分配下決定滿足需求D之最佳的生產批量之研究。良品數的多寡,只有在批量生產完畢後經檢驗決定;當良品數不夠時,必須再次批量生產,直到總良品數已滿足需求。每一批量的生產,必須付出固定成本及單位成本;而每當機一次,也必須付出修復成本。批量如果過大,可能會造成過多的材料浪費;而批量過小,可能會造成多次設置成本;修復成本的大小,亦會影響的最佳批量的選擇。本研究先以Em-plant模擬軟體求出良品機率,並以此良品機率,再以S-PLUS統計軟體求得需求為D時,第一次最佳生產批量ND。得知 Ⅰ.相同需求下,越容易當機,ND越大;Ⅱ.一旦發生當機,固定成本越大,越容易發生當機,會使得ND不具有(ND不大於需求D)之性質;Ⅲ.修復成本越大,ND會越小。

How to determine the optimal lot-size for D good items in a job shop is quite important problem. We extend the study on the multiple lotsizing in production to order to the case that machine is in an alternating renewal process (i.e. alternates between operating and failed) with both up and down times are exponential. The numeral solution & procedure is carried out in the case that yield distribution when the machine is operating is the so-called Interrupted Geometric. The number of good items in a lot can be accurately determined only after completing production of that lot. If the number of good items falls short of the outstanding order, the other production will be required until the total good items produced is at least D. Processing each lot entails fixed, per-unit production costs and machine repair cost. The tradeoff is between running large lots which entails potentially costly overproduction, and small lots which may necessitate multiple production runs and their associated setups. The value of repair cost will also affect the optimal lot-size. In this article, first we derive the yield probability by the simulation software “Em-plant”, and then through the probability, we get the optimal lot-sizing ND with demand D by the statistic software “S-plus”. We provide Ⅰ.Under the same demand, the more failure frequency causes the larger ND. Ⅱ. Once the machine has failure, the more setup cost and more failure frequency will make ND have not the property “ND is no more than D”. Ⅲ. The increasing repair cost causes the decreasing ND.

目錄
第一章 問題說明 1
1.1問題研究背景及動機 1
1.2研究問題及目的 2
1.3研究流程 3
1.4論文架構 4
第二章 MLPO問題或模型文獻探討 5
2.1固定需求量D及產品良率為離散均等分配(discrete uniform)環境下 5
2.1.1數學模式 5
2.1.2演算法 6
2.1.3最佳生產批量ND之特性 7
2.2固定需求量及產品良率為二項分配(Binomial)環境下 7
2.2.1數學模式 7
2.2.2最佳生產批量ND之特性 9
2.3固定需求量及產品良率為中斷式幾何分配(interrupted geometric)環境下 10
2.3.1數學模式 10
2.3.2最佳生產批量ND之特性 11
2.4固定需求量及產品良率為隨機比例(stochastically proportional) 12
2.4.1數學模式 12
2.4.2給定參數r下之明確解 14
第三章 改善後之MLPO模型 16
3.1假設及目的 16
3.2符號說明 16
3.3模式建立 17
3.3.1推導 公式 18
第四章 改善後之MLPO模型之實例應用及比較 23
4.1模擬產生P'(y,N) 23
4.2求解 25
4.2.1α=1,β=1.c=1,θ=0.97 26
4.2.2固定β=1.c=1,θ=0.97 ,變動α值 27
4.2.3固定α=1,β=1,θ=0.97 ,變動c值 30
第五章 結論及未來研究的方向 33
5.1研究結果 33
5.2建議 34
5.3未來研究方向 35
附錄A-1模擬產生之 (N=1~20,λ=1/40000 ,θ =0.97) 36
附錄A-2求解ND程式(S-PLUS) 40
附錄B-1(α=1,β=1.c=1,θ=0.97 ) 41
附錄C-1(β=1.c=1,θ=0.97, λ=1/2 ) 43
附錄C-2(β=1.c=1,θ=0.97, λ=1/5 ) 45
附錄C-3(β=1.c=1,θ=0.97, λ=1/10 ) 47
附錄C-4(β=1.c=1,θ=0.97, λ=1/20 ) 49
附錄C-5(β=1.c=1,θ=0.97, λ=1/40 ) 51
附錄D-1(α=1,β=1,θ=0.97 λ=1/2) 53
附錄D-2(α=1,β=1,θ=0.97 λ=1/5) 55
附錄D-3(α=1,β=1,θ=0.97 λ=1/10 ) 57
附錄D-4(α=1,β=1,θ=0.97 λ=1/20 ) 59
附錄D-5(α=1,β=1,θ=0.97 λ=1/40 ) 61
參考文獻 63

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