network_ cpm dan pert

8/13/2019 Network_ CPM Dan PERT

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NETWORK, CPM DAN PERT

Dr. Mohammad Abdul Mukhyi, SE., MM

1



PENDAHULUAN

Hal penting dalam manajemen proyek adalah :

Memilih manajer proyek yang tepat

as n egras an oor nas yang a

Diluar hal tsb diperlukan :

Apa yang akan dikerjakan

Bagaimana pengendaliannya?

2



LINGKUP PEKERJAAN

Perencanaan dan pengendalian :

Sebelum proyek dimulai

Selama proyek berlangsung

Koreksi pada saat terjadi perbedaan antara

rencana dan pelaksanaan

Ditujukan untuk mengurangi ketidakpastian tentang

apa yan a an as an ar pen er aan proye

3



ALAT ALAT PERENCANAAN

Banyak metoda yang digunakan dalam perencanaanantara lain:

Work breakdown structure (WBS) untukmenentukan pekerjaan pekerjaan yang ada dalam.

Matriks tanggungjawab untuk menentukan

organisasi proyek, orang orang kunci dan.

Gantt charts digunakan untuk menunjukkan jadwalinduk proyek, dan jadwal pekerjaan secara detail.

Jaringan kerja (network) untuk memperlihatkanurutan pekerjaan, kapan dimuiai, kapan selesai,ka an ro ek secara keseluruhan selesai.

4



PENDEFINISIAN PEKERJAAN

Utk proyek dalam skala besar diperlukan metode untukmenentukan elemen‐elemen proyek dalam bagian yanglebih detail.

Dapat diketahui keterkaian antar aktifitas, urutan waktudan personilnya.

Manfaat dari WBS : Dalam tahap analisis WBS dapat digunakan untuk

memastikan akurasi dan kelengkapan dari semuapersonil proyek

Dijadikan sebagai dasar penganggaran dan penjadwalan Sebagai alat kontrol pelaksanaan proyek

5



PROYEK

Suatu proyek adalah suatu usaha temporer yang

dihubungkan dengan sumber daya, yang dirancang

dan yang beroperasi di dalam waktu, biaya dan

batasan mutu dan sering digunakan untukmemperkenalkan perubahan.

6



CHARACTERISTIC OF A PROJECT

A unique, one-time operational activity or effort

Requires the completion of a large number ofinterrelated activities

Established to achieve specific objective

, ,

limited

yp ca y as s own mana emen s ruc ure Need leadership

7



PROJECT MANAGEMENT PROCESS Project planning Project scheduling Project control

made up of individuals from various areas and departments within

a company Matrix organization

a team structure with members from functional areas, dependingon s s requ re

Project Manager most important member of project team

Scope statement a document that provides an understanding, justification, and

expected result of a project Statement of work

written descri tion of ob ectives of a ro ect

Organizational Breakdown Structure a chart that shows which organizational units are responsible for

work items

shows who is responsible for work in a project

9



Work Breakdown Structure for Computer Order

Processin S stem Pro ect

Work Breakdown Structure for Computer Order

Processin S stem Pro ect

10



Gantt Chart

Graph or bar chart with a bar for each project activity that shows passage of time

Provides visual display of project scheduleProvides visual display of project schedule

13



Untuk perencanaan.

Hubungan antara komponen dalam network danelemen dalam masalah riil

-Penerapan model network:Masalah transportasi

Masalah prosesing

erencanaan an pengen a an proyepenugasan

14



BIAYA TRANSPORTASI DAN DISTRIBUSI BARANG

Tempat

pemasaran

pabrik

1 2 3 ……. MJumlah

persediaan

1 C11

X11

C12

X12

C13

X13

…….

C1M

X1M

S1

2C

21

X21

C22

X22

C23

X23

…….C

2M

X2M

S2

:

:

3

:

:

:

:

:

:…….

:

:

:

:

N CN1

XN1

CN2

XN2

CN3

XN3

……. CNM

XNM

SN

16

permintaanD

1D

2D

3……. M ΣD

J ≤ Σ S

J



Formulasi model transportasi

XC:Min

m

n

1iij

m

1 jij∑∑= = XC:Min

n

1i

ij

m

1 j

ij∑∑= =

n...,32,1, jdimana SX

m...,,,mana .

j

m

ij

i

1 j

ij

=≥

=

∑

= m...,32,1,idimana DX Sk.

m

i

m

1 j

ij ==∑=

jdanidimana0X ij

1 j

≥

=

jdanidimana0X

...,,,

ij

j

1 j

ij

≥

===

17



Untuk menentukan umlah dan lokasi titik an kutan

serta berguna untuk menentukan jumlah dan lokasititik angkutan secara optimal dengan meminimalkan

biaya angkutan antar lokasi.

18



+ 1 truk

3

C23 C34

C36

6 7

C12

C24 C46 C67

5

- -

C25

54

C56

0 truk

19



Fungsi Linear Programing

8 X:

XCXCXCXCXCXCXCXCXCXC:Min

12

6767565654544646363634342525242423231212

=

+++++++++

sk

2- X-XX-X-

1 XX X-

0- XXXX-

54463424

363423

25242312

=+=++

=+++

4 X-

3- XX-X-X-

-

67

67564636

565425

−=

=+

=

ij

21



HISTORY OF CPM/PERT

Critical Path Method (CPM)

E I Du Pont de Nemours & Co. (1957) for construction of new

chemical plant and maintenance shut-down

Deterministic task times

- -

Repetitive nature of jobs

U S Navy (1958) for the POLARIS missile program

Multi le task time estimates robabilistic nature

Activity-on-arrow network construction

Non-repetitive jobs (R & D work)

22



Peker aan- eker aan dalam ro ek harus menandai

saat berakhirnya proyek. Pekerjaan-pekerjaan dapat dimulai, diakhiri dan

dilaksanakan secara terpisah dalam suatu rangkaian

tertentu. Pekerjaan-pekerjaan dapat diatur menurut suatu

rangkaian tertentu.

23



ATURAN

Setiap aktivitas ditujukan dengan suatu cabang tertentu, cabang ini

menunjukkan saat dimulainya dan diakhirinya suatu kejadian.

Antara suatu cabang dengan cabang lainnya hanya menunjukkan

hubungan antar aktivitas atau pekerjaan yang berbeda.

Bila se umlah aktivitas berakhir ada suatu ke adian maka ini

berarti bahwa kejadian ini tidak dapat dimulai sebelum aktivitas

yang berakhir pada kejadian ini selesai.

kejadian, bila antara suatu kejadian dan kejadian yang

mendahuluinya tidak dihubungkan dengan suatu aktivitas tertentu.

.

Setiap kejadian diberikan tanda angka, sedang setiap aktivitas

diberikan tanda angka menurut kejadian awal dan kejadian yang

mengakhiri.

24



PROJECT NETWORK

• Network analysis is the general name given to certain specific techniques which can

be used for the planning, management and control of projects

Use of nodes and arrows

Arrows An arrow leads from tail to head directionally Indicate ACTIVITY, a time consuming effort that is required to perform a

.

Nodes n A node is represented by a circle

- Indicate EVENT, a point in time where one or more activities start and/or

finish.

• Activity

– A task or a certain amount of work required in the project

– Requires time to complete– Represented by an arrow

• Dumm Activit

25

– Indicates only precedence relationships

– Does not require any time of effort



Project Network

Signals the beginning or ending of an activity

Designates a point in time

epresen e y a c rc e no e

Network Shows the sequential relationships among activities using

nodes and arrows

Activity-on-node (AON)

nodes represent activities, and arrows show precedence

Activity-on-arrow (AOA)

26

in time



AOA PROJECT NETWORK FOR HOUSE

3

3

2 0

11 2 4 6 7

3Lay foundation Dummy

Finish

work

Build

house

3

1 1

12 4 6 7

5

Design house

and obtainfinancing

Order and

receivematerials

Selectcarpet

Selectpaint

AON Project Network for House

22

43

7

Lay foundations Build house

Finish work

13

3 6

71tart

Design house and

27

31 5

11btain financing

Order and receivematerials

Select paint

Select carpet



SITUATIONS IN NETWORK DIAGRAM

B

C

A must finish before either B or C can start

B

C both A and B must finish before C can start

CA

both A and C must finish before either of B or D can

DB

B

Dummy

A must finish before B can start

both A and C must finish before D can start

28

C

D



CONCURRENT ACTIVITIES

2 3

Lay oundationLay oundation

DummyDummy

LayLay

foundationfoundation22 00

Order materialOrder material 42

Order materialOrder material

11

(a)(a) Incorrect precedenceIncorrect precedence

relationshiprelationship

(b)(b) Correct precedenceCorrect precedence

relationshiprelationship

29



NETWORK EXAMPLE us ra on o ne wor ana ys s o a m nor re es n o a pro uc an s assoc a e

packaging.

The key question is How long will it take to complete this project ?he key question is How long will it take to complete this project ?

30



For clarity, this list is kept to a minimum by specifying only immediate relationships,

that is relationships involving activities that "occur near to each other in time".

31



CPM CALCULATION

Path

A connected se uence of activities leadin from

the starting event to the ending event

The longest path (time); determines the project

duration

Critical Activities

33



CPM EXAMPLE:

CPM Network

f, 15f, 15f, 15f, 15

a, 6a, 6a, 6a, 6g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9

b, 8b, 8b, 8b, 8

,,,,

d, 13d, 13d, 13d, 13 j, 12 j, 12 j, 12 j, 12

c, 5c, 5c, 5c, 5e, 9e, 9e, 9e, 9

36



CPM EXAMPLE

ES and EF Timesf, 15f, 15f, 15f, 15

a, 6a, 6a, 6a, 6 g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9

b, 8b, 8b, 8b, 8

,,,,0 6

d, 13d, 13d, 13d, 13 j j, 12, 12 j j, 12, 120 8

c, 5c, 5c, 5c, 5

e, 9e, 9e, 9e, 90 5

37



CPM EXAMPLE



CPM EXAMPLE

ES and EF Times f f , 15, 15f f , 15, 15

a, 6a, 6a, 6a, 6 g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9

21 30

b, 8b, 8b, 8b, 8

,,,,0 6

23 29

d, 13d, 13d, 13d, 13 j, 12 j, 12 j, 12 j, 120 8

21 33c, 5c, 5c, 5c, 5

e, 9e, 9e, 9e, 90 5

Project’s EF = 33Project’s EF = 33

39

5 14



CPM EXAMPLE

LS and LF Timesf, 15f, 15f, 15f, 15

6 21

a, 6a, 6a, 6a, 6 g, 17g, 17g, 17g, 17

,,,,

21 30

24 33

b, 8b, 8b, 8b, 8

,,,,0 6

23 29

27 33

d, 13d, 13d, 13d, 13 j j, 12, 12 j j, 12, 120 8

8 2121 33

c, 5c, 5c, 5c, 5

e, 9e, 9e, 9e, 90 5

21 33

40

5 14



CPM EXAMPLE

Critical Pathf, 15f, 15f, 15f, 15

a, 6a, 6a, 6a, 6 g, 17g, 17g, 17g, 17 h, 9h, 9h, 9h, 9

b, 8b, 8b, 8b, 8

,,,,

d, 13d, 13d, 13d, 13 j, 12 j, 12 j, 12 j, 12

c, 5c, 5c, 5c, 5

e, 9e, 9e, 9e, 9

43

EXAMPLE



EXAMPLE

Illustration of network analysis of a minor redesign of a product and

its associated packaging.

The key question is: How long will it take to complete this project ?

44



For clarity, this list is kept to a minimum by specifying only

immediate relationships, that is relationships involving activitiesthat "occur near to each other in time".

45



Before starting any of the above activity, the questions

asked would be

•"What activities must be finished before this activity can start"

•could we complete this project in 30 weeks?

•

One answer could be, if we first do activity 1, then activity 2, then activity 3,

...., then activity 10, then activity 11 and the project would then take the sum

of the activity completion times, 30 weeks.

“What is the minimum possible time in which we can complete this project ? “

46



We shall see below how the network analysis diagram/picture we construct

helps us to answer this question.

47



CRITICAL PATH TAKES 24 WEEKS FOR THE COMPLETION OF THE PROJECT

48

Packages are available to determine the shortest path and



Packages are available to determine the shortest path and

other relevant information.

49

d



Data entry window

50



PERT



PERT ’

follows a probability distribution instead of being a singlevalue

Three time estimates are re uired to com ute theparameters of an activity’s duration distribution:

pessimistic time (tp ) - the time the activity would take ifthin s did not o well

most likely time (tm ) - the consensus best estimate of theactivity’s duration

o timistic time t - the time the activit would take ifthings did go well

t + 4 t + tean expec e me : e =

6

2

52

Variance: Vt =σ 2 = p - o

6



PERT ANALYSIS

Draw the network.

Analyze the paths through the network and find the critical

path.

The length of the critical path is the mean of the project

The standard deviation of the project duration probability

distribution is computed by adding the variances of the criticalactivities (all of the activities that make up the critical path) and

taking the square root of that sum

distribution table.

53



Probability

Z

= tp Time

55

PERT EXAMPLE



PERT EXAMPLE

Immed. Optimistic Most Likely Pessimistic

Activit Predec. Time Hr. Time Hr. Time Hr.

A -- 4 6 8B -- 1 4.5 5C A 3 3 3D A 4 5 6

. .F B,C 3 4 5G B,C 1 1.5 5

,I E,F 2 5 8

K G,I 3 5 7

56

PERT EXAMPLE



PERT Network

DD

A A EE HH JJ

CC

BB IIFF

GG

57

PERT EXAMPLE



Activity Expected Time Variance

B 4 4/9

D 5 1/9

E 1 1/36F 4 1/9

G 2 4/9

I 5 1

K 5 4/958



PERT EXAMPLE

Activity ES EF LS LF Slack

B 0 4 5 9 5C 6 9 6 9 0 *

D 6 11 15 20 9

E 6 7 12 13 6

F 9 13 9 13 0 * G 9 11 16 18 7

H 13 19 14 20 1

J 19 22 20 23 1

K 18 23 18 23 0 *

59



PROJECT COST

61

COST CONSIDERATION IN PROJECT



Project managers may have the option or requirement to crash theproject, or accelerate the completion of the project.

This is accomplished by reducing the length of the critical path(s).

The length of the critical path is reduced by reducing the duration of

the activities on the critical path. If each activit re uires the ex enditure of an amount of mone to

reduce its duration by one unit of time, then the project managerselects the least cost critical activity, reduces it by one time unit, and

traces that change through the remainder of the network. As a result of a reduction in an activity’s time, a new critical path

may be created.

When there is more than one critical path, each of the critical pathsmust be reduced.

If the length of the project needs to be reduced further, the processis repeated.

62

PROJECT CRASHING



PROJECT CRASHING

Crashing

reducing project time by expending additionalresources

Crash time an amount of time an activit is reduced

Crash cost

cost of reducing activity time

Goal

reduce project duration at minimum cost

63

ACTIVITY CRASHING



ACTIVITY CRASHING

Crashing activityCrash cost

Slope = crash cost per unit time

Normal ActivityNormal

cost

Normaltime

64

Activity timeCrash time

TIME-COST RELATIONSHIP



Crashing costs increase as project duration decreases

Indirect costs increase as project duration increases

Time-Cost TradeoffMin total cost =

Indirect cost

optimal project time

Direct cost

65

time

PROJECT CRASHING EXAMPLE



22

88

1212

77

1212

33 66

44

44 55

44

44

66

TIME COST DATA



Activity Normal Normal Crash Crash Allowable slope

me cos s me cos s cras me

1 12 3000 7 5000 5 400

3

4

4

12

4000

50000

3

9

7000

71000

1

3

3000

70005

6

4

4

500

500

1

1

1100

1100

3

3

200

200

7 4 1500 3 22000 1 700075000 110700

67

2

R500 R7000

4

Project duration = 36



1

12

7

4From…..

3

4 54

6

4

R400

R200

R200

R500 R7000

4

To…..1

8

7

4

R70012

3

4 5

6

4R400Project

duration = 31

R3000R200

R200Additional cost =

R2000

68

BENEFITS OF CPM/PERT



Useful at many stages of project management

Mathematically simple

Provide project documentation

Useful in monitoring costs

CPM/PERT can answer the following important

i n :

•How long will the entire project take to be completed? What are the risks involved?

•

project if they were not completed on time?•Is the project on schedule, behind schedule or ahead of schedule?

•If the project has to be finished earlier than planned, what is the best way to do this at

69

the least cost?

LIMITATIONS TO CPM/PERT

Clearly defined, independent and stable activities



y p

Specified precedence relationships Over emphasis on critical paths

Activity time estimates are subjective and depend on judgment

PERT assumes a beta distribution for these time estimates,but the actual distribution may be different

PERT consistentl underestimates the ex ected ro ectcompletion time due to alternate paths becoming critical

To overcome the limitation, Monte Carlo simulations can be performed on thenetwork to eliminate the optimistic bias

70

COMPUTER SOFTWARE



Microsoft Project (Microsoft Corp.)

MacProject (Claris Corp.)

PowerPro ect ASTA Develo ment Inc.

Primavera Project Planner (Primavera)

. Project Workbench (ABT Corp.)

71

PRACTICE EXAMPLE



A social project manager is faced with a project with the following activities:

c v y escr p on ura on

Social work team to live in village 5w

Social research team to do survey 12w

Analyse results of survey 5w

Establish mother & child health program 14w

Establish rural credit programme 15w

Carry out immunization of under fives 4w

72

.

duration.



2

B

4

2

F

D

100 KM

40 KM 50 KM

1 6

F

A

5

3 E

A75 KM

3 E

C

74

CONTOH 2



AKTIVITAS URAIAN AKTIVITAS

PENDAHULUAN

WAKTU

PENYELESAIAN

HARIHARI

A Desain daftar pertanyaan - 4

B Desain sampling - 5

C Testing daftar pertanyaan dan

perbaikan

A 4

D Memilih calon intervierwer B 1E Melatih interviewer D, A 2

F Membagi wilayah kepada B 4

G Pelaksanaan interview C, E, F 10

75

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