performance analysis in manufacturing systemmy.liuc.it/matsup/2017/n91328/lez 01 - little...
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Performance Analysis in
Manufacturing System–
Little’s Law
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Performance analysis
Performance analysis (or monitoring) related to a system composed of independent resources, (e.g. manufacturing system that produces a set of different pieces, each of them asking for system resources on the basis of its own cycle), is the analysis of the relationships among the differentperformance variables of the system, given the boundaries conditions.
Performance analysis is used both for making predictions on new systembehaviour, or for checking the performances for existing systems.
There are different performance analysis methods, depending on theircomplexity and approximation level. For example simulation is very precise and detailed, but very expensive to apply.
Little’s Law and Throughput Diagrams (or analysis) are two of the mostsimple methods.
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Performance analysis
Define the main performance of the system
By monitoring it is possible:
To obtain real-time information on the system
To make an analysis on system behaviour history
To compute and analyse the trand of performance index
3
Area i Area i+1
Production flow
Monitoring results
MONITORING
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Performance analysis
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b) Diagramma di Throughput
Ordini in arrivo
Ordini completati
a) Funnel model
Massima capacità Tasso di
output effettivo
Ordini in coda
(WIP)
Contenuto di lavoro
dell’ordine
[ ore standard ]
Tempo [ giorni a calendario ]
Curva di Output
Output
Input
WIP iniziale Tasso di output medio
Periodo di riferimento
Curva di Input
Tasso di carico (input) medio
WIP finale Funnel Model
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Base relationship
Critical WIP (WIP*): it is the WIP level
that allows to a manufacturing system to
reach the maximum throughput (THmax)
and the minimum lead time (LTmin)
WIP* = THmax x LTmin
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The Penny Fab
Characteristics:
4 identical machines (flow shop)
Manufacturing time equal to 2 h/penny for each machine
Fixed time
The pieces are loaded into the system in order to maintain a constant WIP level (CONWIP)
When a penny is released by the system, another one can be loaded
Parameters:
THcb = 0,5 penny/h
LTmin = 8 h
Critical WIP - WIP*= 0,5 penny/h x 8 h = 4 penny
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The Penny Fab
Factory Physics, Wallace J. Hopp and Mark L. Spearman, Irwin/McGraw-Hill, 1996
Penny Fab represents a simple production line that makes giant one-cent pieces used
extensively in Fourth of July parades
The line consists of four machines in sequence
The first machine is a punch press that cuts penny blanks, the second stamps Lincoln’s face on one
side and the Lincoln Memorial on the back, the third puts a rim on the penny, and the fourth cleans
away any burrs
After each penny is processed, it is moved immediately to the next machine
The line runs 24 hours per day, with breaks and lunches covered by spare operators
The market for giant pennies is assumed to be unlimited, so that all product made is sold;
thus, more throughput is unambiguously better for this system
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The Penny Fab (WIP=1)
Time = 0 hours
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The Penny Fab (WIP=1)
Time = 2 hours
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The Penny Fab (WIP=1)
Time = 4 hours
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The Penny Fab (WIP=1)
Time = 6 hours
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The Penny Fab (WIP=1)
Time = 8 hours
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The Penny Fab (WIP=1)
Time = 10 hours
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The Penny Fab (WIP=1)
Time = 12 hours
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The Penny Fab (WIP=1)
Time = 14 hours
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2
4
6
8
10
12
14
16
2 MONETE IN 16
MINUTI = 2/16 = 0,125
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Performance with WIP = 1
WIP[pz]
TH [pz/h]
LT[h]
THxLT[pz]
1 0,125 8 1
2
3
4
5
6
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The Penny Fab (WIP=2)
Time = 0 hours
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The Penny Fab (WIP=2)
Time = 2 hours
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The Penny Fab (WIP=2)
Time = 4 hours
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The Penny Fab (WIP=2)
Time = 6 hours
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The Penny Fab (WIP=2)
Time = 8 hours
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The Penny Fab (WIP=2)
Time = 10 hours
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The Penny Fab (WIP=2)
Time = 12 hours
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The Penny Fab (WIP=2)
Time = 14 hours
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2
4
6
8
10
12
14
16
Dopo la fase di transitorio
(riempimento del
sistema)
2 MONETE IN 8 MINUTI
= 2/8 = 0,250
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Performance with WIP = 2
WIP[pz]
TH [pz/h]
LT[h]
THxLT[pz]
1 0,125 8 1
2 0,250 8 2
3
4
5
6
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The Penny Fab (WIP=3)
Time = 0 hours
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The Penny Fab (WIP=3)
Time = 2 hours
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The Penny Fab (WIP=3)
Time = 4 hours
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The Penny Fab (WIP=3)
Time = 6 hours
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The Penny Fab (WIP=3)
Time = 8 hours
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The Penny Fab (WIP=3)
Time = 10 hours
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The Penny Fab (WIP=3)
Time = 12 hours
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2
4
6
8
10
12
14
16
Dopo la fase di transitorio
(riempimento del
sistema)
3 MONETE IN 8 MINUTI
= 3/8 = 0,375
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Performance with WIP = 3
WIP[pz]
TH [pz/h]
LT[h]
THxLT[pz]
1 0,125 8 1
2 0,250 8 2
3 0,375 8 3
4
5
6
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The Penny Fab (WIP=4)
Time = 0 hours
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The Penny Fab (WIP=4)
Time = 2 hours
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The Penny Fab (WIP=4)
Time = 4 hours
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The Penny Fab (WIP=4)
Time = 6 hours
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The Penny Fab (WIP=4)
Time = 8 hours
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The Penny Fab (WIP=4)
Time = 10 hours
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The Penny Fab (WIP=4)
Time = 12 hours
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Performance with WIP = 4
WIP[pz]
TH [pz/h]
LT[h]
THxLT[pz]
1 0,125 8 1
2 0,250 8 2
3 0,375 8 3
4 0,500 8 4
5
6
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The Penny Fab (WIP=5)
Time = 0 hours
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The Penny Fab (WIP=5)
Time = 2 hours
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The Penny Fab (WIP=5)
Time = 4 hours
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The Penny Fab (WIP=5)
Time = 6 hours
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The Penny Fab (WIP=5)
Time = 8 hours
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The Penny Fab (WIP=5)
Time = 10 hours
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The Penny Fab (WIP=5)
Time = 12 hours
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The Penny Fab (WIP=5)
Time = 14 hours
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The Penny Fab (WIP=5)
Time = 16 hours
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Performance with WIP = 5
WIP[pz]
TH [pz/h]
LT[h]
THxLT[pz]
1 0,125 8 1
2 0,250 8 2
3 0,375 8 3
4 0,500 8 4
5 0,500 10 5
6
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The Penny Fab (WIP=6)
Time = 0 hours
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The Penny Fab (WIP=6)
Time = 2 hours
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The Penny Fab (WIP=6)
Time = 4 hours
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The Penny Fab (WIP=6)
Time = 6 hours
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The Penny Fab (WIP=6)
Time = 8 hours
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The Penny Fab (WIP=6)
Time = 10 hours
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The Penny Fab (WIP=6)
Time = 12 hours
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The Penny Fab (WIP=6)
Time = 14 hours
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The Penny Fab (WIP=6)
Time = 16 hours
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The Penny Fab (WIP=6)
Time = 18 hours
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Performance with WIP = 6
WIP[pz]
TH [pz/h]
LT[h]
THxLT[pz]
1 0,125 8 1
2 0,250 8 2
3 0,375 8 3
4 0,500 8 4
5 0,500 10 5
6 0,500 12 6
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TH vs. WIP
0
0,1
0,2
0,3
0,4
0,5
0,6
0 1 2 3 4 5 6 7 8 9 10 11 12
WIP
TH
THmax
= THcb
WIP*
1/LTmin
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LT vs. WIP
02468
101214161820222426
0 1 2 3 4 5 6 7 8 9 10 11 12
WIP
LT
LTmin
WIP*
1/THcb
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THmax and LTmin
Minimum LT (LTmin) given the WIP level
is
Maximum throughput (THmax) given the
level WIP is
otherwise
* if
,/
,LT
max
min
WIPwip
THwip
Tprocess
otherwise
* if
,
,/TH
min
max
WIPwip
TH
LTwip
bn
LTmin is the sum of effort
(time) for each machine in
order to realize a single
penny
THmax is the TH of
the system
bottleneck (the
slowest resource)
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THmax and LTmin
Penny Fab, THcb = 0.5 and LTmin = 8
WIP* = 0.5 8 = 4,
otherwise
4 if
,2
,8LTmin
wip
wip
otherwise
4 if
,5.0
,8/THmax
wipwip
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Little’s Law
The main relationship among WIP, LT and
Th is
LT = WIP/TH
LTTHWIP hh
pcspcs
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Penny Fab Two
10 h
2 h
5 h 3 h
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Penny Fab Two
DepartmentNumber ot
machinesWork time [h]
Department TH
[job/h]
1 1 2 0,5
2 2 5 0,4
3 6 10 0,6
4 2 3 0,67
THcb = LTmin = WIP* = 0.4 p/h 20 h 8 penny
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Penny Fab Two Simulation
(Time=0)
10 hr
2 hr
5 hr 3 hr
2
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Penny Fab Two Simulation
(Time=2)
10 hr
2 hr
5 hr 3 hr
4
7
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Penny Fab Two Simulation
(Time=4)
10 hr
2 hr
5 hr 3 hr
6
7
9
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Penny Fab Two Simulation
(Time=6)
10 hr
2 hr
5 hr 3 hr
8
7
9
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Penny Fab Two Simulation
(Time=7)
10 hr
2 hr
5 hr 3 hr
8
12
9
17
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Penny Fab Two Simulation
(Time=8)
10 hr
2 hr
5 hr 3 hr
10
12
9
17
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Penny Fab Two Simulation
(Time=9)
10 hr
2 hr
5 hr 3 hr
10
12
14
17
19
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Penny Fab Two Simulation
(Time=10)
10 hr
2 hr
5 hr 3 hr
12
12
14
17
19
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Penny Fab Two Simulation
(Time=12)
10 hr
2 hr
5 hr 3 hr
14
17
14
17
19
22
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Penny Fab Two Simulation
(Time=14)
10 hr
2 hr
5 hr 3 hr
16
17
19
17
19
22
24
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Penny Fab Two Simulation
(Time=16)
10 hr
2 hr
5 hr 3 hr
17
19
17
19
22
24
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Penny Fab Two Simulation
(Time=17)
10 hr
2 hr
5 hr 3 hr
22
19
27
19
22
24
20
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Penny Fab Two Simulation
(Time=19)
10 hr
2 hr
5 hr 3 hr
22
24
27
29
22
24
20
22
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Penny Fab Two Simulation
(Time=20)
10 hr
2 hr
5 hr 3 hr
22
24
27
29
22
24 22
22
Note: the job will arrive to the
bottleneck just in time to avoid
starvation
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Penny Fab Two Simulation
(Time=22)
10 hr
2 hr
5 hr 3 hr
27
24
27
29
32
24
25
24
Note: the job will arrive to the
bottleneck just in time to avoid
starvation
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Penny Fab Two Simulation
(Time=24)
10 hr
2 hr
5 hr 3 hr
27
29
27
29
32
34
25
27
And so on… The bottleneck will
be always busy, while the other
resources will have idle periods
(starvation)
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tgb
tga
I/LTmin
I/THmax
Little’s diagram
LTmin
LT
LT
Wip*
THmax
TH
TH
THmin
1Wip
Real form
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Conclusions In real cases, also for low level of WIP, the different pieces concurr in order to obtain
system resources (not only machines, but also operators, transporters, tools) and, for this reason, the real form of the LT and TH diagrams is not exactly the one describedby Little’s Law.
Penny Fab is only an ideal case with fixed time and balanced line
Wip* is equal to stations number and TH grows to the maximum value with LT = LTmin; from that point on LT grows without advantages.
In a non-ideal case (not balanced line) Wip* is less than stations number (e.g. Penny FabTwo).
Also for balaced line, in case of non-fixed times, a wating time can occurr
In all these cases, the specific form of diagrams should be evaluated case by case, for example with simulation
On the basis of Little’s Law, in order to reduce the LT of a system the Wip valueshould be reduced in order to mantain a constant TH
For this reason, if a system is characterized by the presence of queues, it should be possibleto reduce LT and WIP.