• 製造系統管理作業分享(3)-Chapter 7 Factory Dynamics
  • 前言:
  • 正文
    • 1. (Chapter7. Study Question5) Can the critical WIP level W_0 ever exceed the number of machines in the line?
    • 2. (Chapter7. Problem 5) Consider a four-station line in-which all stations consist of single machines. Station 2 has average processing times of 2 hours per job, while the remaining stations have average processing time of 1 hour per job. Answer the following, under the assumption that process times are deterministic (as in the best case)
    • 3. (Chapter7. Study Question6) Repeat Problem 6 under the assumption that all jobs are processed at a station before moving (as in the worst case).

tags: Manufacturing Manamagement 製造系統管理 Factory Physics Factory Dynamics Little's Law

製造系統管理作業分享(3)-Chapter 7 Factory Dynamics

前言:

本篇會分享2017年修製造系統管理這門課時候的作業，依照慣例，每一題的題號，前面都是代表在Factory Physics這本教科書的原本題目出處。
之所以分享是因為，這些題目蠻多都能夠將該章節的一些精華、重點進行規劃，或者透過題目的方式複習課堂所學，因此，在此提供個人的見解給大家。
同時一併感謝當時與我同組的組員-王行寬同學，與我一起完成作業。

正文

1. (Chapter7. Study Question5) Can the critical WIP level W_0 ever exceed the number of machines in the line?

Ans:
$Critical\ WIP\ =\ W_0\ =\ r_b\ * T_0\ =\ r_b\ * \sum_{i=1}^{n}t_i -(1)$

根據Factory Physics對於Critical WIP的定義，如上式子(1)所示。其中 $r_b$ 代表的是瓶頸的產出速率， $T_0$ 代表整條生產線的加工時間的加總，因此我們用 $t_i$ 來表示在生產線的第i站的加工時間，故$T_0= \sum_{i=1}^{n}t_i$。

剛據此式子，我們可以討論兩種情況，
一是當每個工作站的產能是相同的時候，我們可以稱作是平衡系統，如下:

圖一 平衡系統範例

此時每個機台都是兩小時產出一件，因此每個機台的產能都是0.5件/小時，此時的Critical WIP剛好會等於系統的機台數量。

二是當並非平衡的系統，系統內每個工作站的平均產出不一，瓶頸機台就會是其中產能最低的，此時Critical WIP會小於系統的機台數量。由這兩種情況的討論，我們可以知道Critical WIP level是不會超出機台的數量的。

若用公式證明，則我們知道在瓶頸站的產出速率

$r_b\ =\ N_b/t_b -(2)$

此處的N_b代表是在瓶頸工作站的機台數量，而t_b是該站的加工時間；而對於其他非瓶頸工作站而言，我們可以知道他的產出速率一定大於等於瓶頸工作站，故可以列出下式子:

$r_b\ <=\ r_i\ =N_i/t_i-(3)$

$N_i$、$t_i$則分別代表非瓶頸工作站的第i站所對應的機台數量與加工時間。將式子(3)同乘$t_i$並進行加總，可以得到下式子(4)，

$Critical WIP=W_0=r_b*T_0= \sum_{i=1}^{n}r_bt_i<=\sum_{i=1}^{n}r_it_i=\ \sum_{i=1}^{n}N_i-(4)$

所以我們可以知道Critical WIP是不會超過生產線上機台的數量，而Critical WIP要等於生產線上機台數量，只會發生在生產線為平衡的情況下。

2. (Chapter7. Problem 5) Consider a four-station line in-which all stations consist of single machines. Station 2 has average processing times of 2 hours per job, while the remaining stations have average processing time of 1 hour per job. Answer the following, under the assumption that process times are deterministic (as in the best case)

Translation:
考量一個有四個站的生產線，其中各站都有一台機器。第二站平均加工時間是$2\ hours/job$，而其餘的工作站則是平均加工時間為$1\ hours/job$。在假設加工時間為決定性的(也就是最佳情況下)，回答下列問題

Ans:
將題意繪製如下圖:

圖二 非平衡系統範例

(a)What are $r_b$ and $T_0$ for this line?
從上圖可知道瓶頸站為第二站，其

$r_b\ =\ \dfrac{1}{2}\ =\ 0.5(piece/h)$
$T_0\ =\ 1+2+1+1=5(h)$

(b)How do $r_b$ and $T_0$ change if a second identical machine is added to station 2? What effects will this have on performance?
在第二站加入相同(等效)機台時候，生產線變成如下所示:

圖三 瓶頸站加入等效機台

Station Number	No. of machines	Station Capacity (pieces/per hour)
1	1	1
2	2	1
3	1	1
4	1	1

$r_b\ =\ 1\ (piece/h)$
$T_0\ =\ 1+2+1+1\ =\ 5\ (h)$

當第二站的瓶頸站，增加第二台等效機台，使第二站機台增加至兩台，產能提升兩倍，系統CT降低、產出提升。

(c) How do $r_b$ and $T_0$ change if the machine at station 2 is speeded up to have average processing times of 1 hour? What effects will this have on performance?

在將第二站加速到有平均生產的時間為1小時，生產線變成如下所示:

圖四 瓶頸站機台加速

$r_b\ =\ 1\ (piece/h)$
$T_0\ =\ 1+1+1+1\ =\ 4\ (h)$

第二站原本是瓶頸機台，現在第二站的機台速率提升兩倍，產能提升兩倍，系統CT降低、產出提升。

(d) How do $r_b$ and $T_0$ change if a second identical machine is added to station 1? What effects will this have on performance?
在將第一站加入相同(等效)機台時候，生產線變成如下所示:

圖五 非瓶頸站增加機台

Station Number	No. of machines	Station Capacity (pieces/per hour)
1	2	2
2	1	0.5
3	1	1
4	1	1

$r_b\ =\ 0.5\ (piece/h)$
$T_0\ =\ 1+2+1+1\ =\ 5\ (h)$

非瓶頸機台增加為兩台，對瓶頸機台產能無影響，系統週期時間、產出依舊不變。

(e)How do $r_b$ and $T_0$ change if the machine at station 1 is speeded up to have average processing times of 1/2 hour? What effects will this have on performance? Do your results agree or disagree with the statement “An hour saved at a nonbottleneck is a mirage(ie.e, of no value)”?

當地一站的機器的平均加工時間加速變為$\dfrac{1}{2}$小時，則會對於績效有什麼影響。你會同意或不同意以下的論述:“在非瓶頸站節省一小時是徒勞無功的(沒有價值)”

當第一站的平均加工時間變為0.5小時，則生產線如下:

圖六 非瓶頸站機台加速

Station Number	No. of machines	Station Capacity (pieces/per hour)
1	1	2
2	1	0.5
3	1	1
4	1	1

$r_b\ =\ 0.5\ (piece/h)$
$T_0\ =\ 0.5+2+1+1\ =\ 4.5\ (h)$

非瓶頸機台生產速率變為兩倍，週期時間下降，但對於瓶頸機台產能無影響，系統產出依舊不變。

3. (Chapter7. Study Question6) Repeat Problem 6 under the assumption that all jobs are processed at a station before moving (as in the worst case).

Translation:
重複第六題的假設，在移動前所有被加工的工件都會在工作站中(意即是最差的情況下)。

Ans:
在最差的情況下，$CT = wT_0$ , $TH = \dfrac{1}{T_0}$。
(a)
$r_b= 0.5 \ (件/h)$
$T_0 = 1 + 2 + 1 + 1 = 5\ (h)$

(b)
$r_b = 1 \ (件/h)$
$T_0 = 1 + 2 + 1 + 1 = 5\ (h)$
在最差的情況下，由公式可知，$r_b$的增加並不影響系統的產出及週期時間

(c)
$r_b = 1 \ (件/h)$
$T_0 = 1 + 1 + 1 + 1 = 4\ (h)$
$T_0$下降，對於不同的WIP level來說，系統週期時間下降、產出提升。

(d)
$r_b = 0.5 \ (件/h)$
$T_0 = 1 + 2 + 1 + 1 = 5\ (h)$
由於$T_0$不變，系統績效不變

(e)
$r_b = 0.5 \ (件/h)$
$T_0 = 0.5 + 2 + 1 + 1 = 4.5\ (h)$
$T_0$下降，系統週期時間下降、產出提升

• 製造系統管理作業分享(3)-Chapter 7 Factory Dynamics
  • 前言:
  • 正文
    • 1. (Chapter7. Study Question5) Can the critical WIP level W_0 ever exceed the number of machines in the line?
    • 2. (Chapter7. Problem 5) Consider a four-station line in-which all stations consist of single machines. Station 2 has average processing times of 2 hours per job, while the remaining stations have average processing time of 1 hour per job. Answer the following, under the assumption that process times are deterministic (as in the best case)
    • 3. (Chapter7. Study Question6) Repeat Problem 6 under the assumption that all jobs are processed at a station before moving (as in the worst case).
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• 製造系統管理作業分享(3)-Chapter 7 Factory Dynamics
  • 前言:
  • 正文
    • 1. (Chapter7. Study Question5) Can the critical WIP level W_0 ever exceed the number of machines in the line?
    • 2. (Chapter7. Problem 5) Consider a four-station line in-which all stations consist of single machines. Station 2 has average processing times of 2 hours per job, while the remaining stations have average processing time of 1 hour per job. Answer the following, under the assumption that process times are deterministic (as in the best case)
    • 3. (Chapter7. Study Question6) Repeat Problem 6 under the assumption that all jobs are processed at a station before moving (as in the worst case).

全部展開回到頂部移至底部