performance analysis in manufacturing systemmy.liuc.it/matsup/2017/n91328/lez 01 - little...

1

Performance Analysis in

Manufacturing System–

Little’s Law

2

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.


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


4

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

5

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

6

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

7

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

8

The Penny Fab (WIP=1)

Time = 0 hours

9


Time = 2 hours

10


Time = 4 hours

11


Time = 6 hours

12


Time = 8 hours

13


Time = 10 hours

14


Time = 12 hours

15


Time = 14 hours

16

2

4

6

8

10

12

14

16

2 MONETE IN 16

MINUTI = 2/16 = 0,125

17

Performance with WIP = 1

WIP[pz]

TH [pz/h]

LT[h]

THxLT[pz]

1 0,125 8 1

2

3

4

5

6

18


Time = 0 hours

19


Time = 2 hours

20


Time = 4 hours

21


Time = 6 hours

22


Time = 8 hours

23


Time = 10 hours

24


Time = 12 hours

25


Time = 14 hours

26

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

27


WIP[pz]

TH [pz/h]

LT[h]

THxLT[pz]

1 0,125 8 1

2 0,250 8 2

3

4

5

6

28


Time = 0 hours

29


Time = 2 hours

30


Time = 4 hours

31


Time = 6 hours

32


Time = 8 hours

33


Time = 10 hours

34


Time = 12 hours

35

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

36


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

37


Time = 0 hours

38


Time = 2 hours

39


Time = 4 hours

40


Time = 6 hours

41


Time = 8 hours

42


Time = 10 hours

43


Time = 12 hours

44


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

45


Time = 0 hours

46


Time = 2 hours

47


Time = 4 hours

48


Time = 6 hours

49


Time = 8 hours

50


Time = 10 hours

51


Time = 12 hours

52


Time = 14 hours

53


Time = 16 hours

54


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

55


Time = 0 hours

56


Time = 2 hours

57


Time = 4 hours

58


Time = 6 hours

59


Time = 8 hours

60


Time = 10 hours

61


Time = 12 hours

62


Time = 14 hours

63


Time = 16 hours

64


Time = 18 hours

65


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

66

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

67

LT vs. WIP

02468

101214161820222426

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

LT

LTmin

WIP*

1/THcb

68

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)

69

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

70

Little’s Law

The main relationship among WIP, LT and

Th is

LT = WIP/TH

LTTHWIP hh

pcspcs

71

Penny Fab Two

10 h

2 h

5 h 3 h

72

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

73

Penny Fab Two Simulation

(Time=0)

10 hr

2 hr

5 hr 3 hr

2

74


(Time=2)

10 hr

2 hr

5 hr 3 hr

4

7

75


(Time=4)

10 hr

2 hr

5 hr 3 hr

6

7

9

76


(Time=6)

10 hr

2 hr

5 hr 3 hr

8

7

9

77


(Time=7)

10 hr

2 hr

5 hr 3 hr

8

12

9

17

78


(Time=8)

10 hr

2 hr

5 hr 3 hr

10

12

9

17

79


(Time=9)

10 hr

2 hr

5 hr 3 hr

10

12

14

17

19

80


(Time=10)

10 hr

2 hr

5 hr 3 hr

12

12

14

17

19

81


(Time=12)

10 hr

2 hr

5 hr 3 hr

14

17

14

17

19

22

82


(Time=14)

10 hr

2 hr

5 hr 3 hr

16

17

19

17

19

22

24

83


(Time=16)

10 hr

2 hr

5 hr 3 hr

17

19

17

19

22

24

84


(Time=17)

10 hr

2 hr

5 hr 3 hr

22

19

27

19

22

24

20

85


(Time=19)

10 hr

2 hr

5 hr 3 hr

22

24

27

29

22

24

20

22

86


(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

87


(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

88


(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)

89

tgb

tga

I/LTmin

I/THmax

Little’s diagram

LTmin

LT

LT

Wip*

THmax

TH

TH

THmin

1Wip

Real form

90

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.

performance analysis in manufacturing systemmy.liuc.it/matsup/2017/n91328/lez 01 - little...

Documents