network, cpm dan pert - Official Site of MOHAMMAD ABDUL MUKHYI

NETWORK, CPM DAN PERT

Dr. Mohammad Abdul Mukhyi, SE., MM

1

PENDAHULUAN Hal penting dalam manajemen proyek adalah : ´ Ketepatan memilih bentuk organisasi (tim) ´ Memilih manajer proyek yang tepat ´ Aktifitas Aktifit integrasi i t i dan d koordinasi k di i yang baik b ik Diluar hal tsb diperlukan : ´ Apa yang akan dikerjakan ´ Bagaimana pengendaliannya?

2

LINGKUP PEKERJAAN Perencanaan dan pengendalian : ´ Sebelum S b l proyekk dimulai di l i ´ Selama proyek berlangsung ´ Koreksi pada saat terjadi perbedaan antara rencana dan ´ pelaksanaan l k Ditujukan untuk mengurangi ketidakpastian tentang apa yangg akan k dihasilkan dih ilk dari d i pengerjaan g j proyek k

3

ALAT ALAT PERENCANAAN Banyak metoda yang digunakan dalam perencanaan antara lain: ´ Work breakdown structure (WBS) untuk menentukan pekerjaan pekerjaan yang ada dalam proyek. proyek ´ Matriks tanggungjawab untuk menentukan organisasi proyek, orang orang kunci dan tanggungjawabnya. tanggungjawabnya ´ Gantt charts digunakan untuk menunjukkan jadwal induk proyek, dan jadwal pekerjaan secara detail. ´ Jaringan kerja (network) untuk memperlihatkan urutan pekerjaan, kapan dimuiai, kapan selesai, p p proyek y secara keseluruhan selesai. kapan 4

PENDEFINISIAN PEKERJAAN ´

´ ´

Utk proyek dalam skala besar diperlukan metode untuk menentukan elemen‐elemen proyek dalam bagian yang lebih detail. Dapat diketahui keterkaian antar aktifitas, urutan waktu dan personilnya. Work Breakdown Structure (WBS)

Manfaat dari WBS : ´ Dalam tahap analisis WBS dapat digunakan untuk memastikan akurasi dan kelengkapan dari semua personil proyek ´ Dijadikan sebagai dasar penganggaran dan penjadwalan ´ Sebagai alat kontrol pelaksanaan proyek

5

PROYEK Suatu proyek adalah suatu usaha temporer yang menyertakan suatu urutan aktivitas yang dihubungkan dengan sumber daya, yang dirancang untuk mencapai suatu hasil yang unik dan spesifik dan yang beroperasi di dalam waktu, biaya dan batasan mutu dan sering digunakan untuk memperkenalkan perubahan.

6

CHARACTERISTIC OF A PROJECT z z

z z

z z

A unique, one-time operational activity or effort Requires the completion of a large number of interrelated activities Established to achieve specific objective Resources such as time and/or money, Resources, money are limited T i ll has Typically h it its own management g t structure t t Need leadership 7

APA PROYEK MANAJEMEN? Aplikasi dari suatu koleksi teknik dan perkakas untuk mengarahkan penggunaan sumber daya yang berbeda b b d ke k arah h pemenuhan h dari d i suatu yang unik, kompleks, waktu, biaya dan batasan mutu. ´ Perang dunia II, manakala otoritas militer menggunakan teknik operasional research untuk t k merencanakan k jumlah j l h maksimum k i penggunaan sumber daya. ´ Salah satu teknik ini adalah penggunaan jaringan untuk menghadirkan suatu sistem dari aktivitas terkait ´

8

PROJECT MANAGEMENT PROCESS ´ ´ ´ ´

´

´ ´

´ ´

´

Project planning Project scheduling Project control Project team « made up of individuals from various areas and departments within a company Matrix organization « a team structure with members from functional areas, depending p g on skills kill required i d 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 description p of objectives j of a p project j Organizational Breakdown Structure « a chart that shows which organizational units are responsible for work items Responsibility Assignment Matrix « shows who is responsible for work in a project 9

Work Breakdown Structure for Computer Order Processing System Project

10

PROJECT PLANNING ´

Resource Availability and/or Limits « Due

date, date late penalties, penalties early completion incentives « Budget ´

Activity Information « Identify Id if

allll required i d activities i ii « Estimate the resources required (time) to complete l t each h activity ti it « Immediate predecessor(s) to each activity needed to create interrelationships 11

PROJECT SCHEDULING AND CONTROL TECHNIQUES Gantt Chart Critical Path Method (CPM) Program Evaluation and Review Technique (PERT)

12

Gantt Chart ŠGraph or bar chart with a bar for each project activity that shows passage of time ŠProvides visual display of project schedule

13

NETWORK ™ ™

p Untuk perencanaan. Hubungan antara komponen dalam network dan elemen dalam masalah riil

-Penerapan

model network: Masalah transportasi Masalah prosesing P Perencanaan d pengendalian dan d li proyek k penugasan 14

Masalah Transportasi: PABRIK

TEMPAT PEMASARAN

A1

A2

A3

= suplly

B1

B2

B3

= demand

15

BIAYA TRANSPORTASI DAN DISTRIBUSI BARANG Tempat pemasaran pabrik

1

2

3

1

C11 X11

C12 X12

2

C21 X21

: : 3

…….

M

Jumlah persediaan

C13 X13

…….

C1M X1M

S1

C22 X22

C23 X23

…….

C2M X2M

S2

: :

: :

: :

…….

: :

: :

N

CN1 XN1

CN2 XN2

CN3 XN3

…….

CNM XNM

SN

Jumlah permintaan

D1

D2

D3

…….

DM

ΣDJ ≤ Σ SJ 16

Formulasi model transportasi m

n

Min : ∑∑ CijX ij i =1 j =1

∑X j =1

ij

j =1

Min : ∑∑ CijX ij

≤ Di dimana di i = 1, 1 2, 2 3 ..., m

m

Sk.

∑X j =1

m

∑X

m

i =1 j =1

m

Sk Sk.

n

ij

≥ S j dimana j = 1, 2, 3 ..., n

X ij ≥ 0 dimana i dan j

ij

= Di dimana i = 1, 2, 3 ..., m

ij

= S j dimana j = 1, 1 2, 2 3 ..., n

m

∑X j =1

X ij ≥ 0 dimana i dan j

17

Masalah Transhipment g Untuk menentukan jjumlah dan lokasi titik angkutan serta berguna untuk menentukan jumlah dan lokasi titik angkutan secara optimal dengan meminimalkan biaya angkutan antar lokasi.

18

+ 1 truk 3 C23 C12 1 + 8 truk

C36 C34

C24

2 0 truk C25

4

6 - 3 truk

C54 5

C46

C67

7 - 4 truk

C56

0 truk

19

Rute Pengiriman X34

X36

X54

X56

X63

X67

Kapasi tas Barang

0

0

0

0

0

0

0

+8

+1

+1

0

0

0

0

0

0

0

-1

0

0

+1

+1

0

0

-1

0

+1

0

0

-1

0

-1

0

-1

0

0

0

-2

5

0

0

0

-1

0

0

+1

+1

0

0

0

6

0

0

0

0

0

-1

0

+1

+1

-3

7

0

0

0

0

0

0

0

0

-1 1

-4 4

Lokasi

X12

X23

X24

1

+1

0

0

2

-1

+1

3

0

4

X25

-1 0

20

Fungsi Linear Programing Min : C12 X12 + C 23 X 23 + C 24 X 24 + C 25 X 25 + C34 X 34 + C36 X 36 + C 46 X 46 + C54 X 54 + C56 X 56 + C 67 X 67 =8

sk : X12 - X12 + X 23 + X 24 + X 25 + X 34 + X 36

- X 23

= -0 =1

- X 24 - X 34 + X 46 - X 54

=-2

- X 25 + X 54 + X 56

=0

- X 36 - X 46 - X 56 + X 67

= -3

- X 67

= −4

X ij ≥ 0 untuk semua i dan j

21

HISTORY OF CPM/PERT ´

Critical Path Method (CPM) «

« « «

´

E I Du Pont de Nemours & Co. (1957) for construction of new chemical and shut-down h i l plant l d maintenance i h d Deterministic task times Activity on node network construction Activity-on-node Repetitive nature of jobs

Project Evaluation and Review Technique (PERT) « « « «

U S Navy (1958) for the POLARIS missile program Multiple p task time estimates (p (probabilistic nature)) Activity-on-arrow network construction Non-repetitive jobs (R & D work) 22

TEKNIK CPM ´

´

´

j p j y harus menandai Pekerjaan-pekerjaan dalam p proyek saat berakhirnya proyek. Pekerjaan-pekerjaan j p j dapat p 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 a seju sejumlah a a aktivitas t tas be berakhir a pada suatu kejadian, ejad a , maka a a ini berarti bahwa kejadian ini tidak dapat dimulai sebelum aktivitas yang berakhir pada kejadian ini selesai. Aktivitas dummy digunakan untuk menggabungkan dua buah kejadian, bila antara suatu kejadian dan kejadian yang mendahuluinya tidak dihubungkan dengan suatu aktivitas tertentu. Aktivitas dummy ini tidak mempunyai biaya dan waktu. waktu 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 Î An arrow leads from tail to head directionally « Indicate ACTIVITY, a time consuming effort that is required to perform a part of the work. work 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 • Dummyy Activityy – Indicates only precedence relationships – Does not require any time of effort

25

Project Network

´

´

Event « Signals the beginning or ending of an activity « Designates a point in time « Represented R t d by b a circle i l (node) ( d ) Network « Shows the sequential relationships among activities using nodes and arrows

ŠActivity-on-node A i i d (AON) nodes represent activities, and arrows show precedence relationships ŠActivity-on-arrow (AOA) arrows represent activities and nodes are events for points in time 26

AOA PROJECT NETWORK FOR HOUSE 3

Lay foundation 2

1

3 Design house and obtain financing

2

Dummy 0

1 Order and receive materials

4 Select paint

Build house

Finish work

6

3 1

1

5

7

1

Select carpet

AON Project Network for House Lay foundations

Build house

4 3

2 2 Start

Finish work

7 1

1 3

Design house and obtain financing

3 1 Order and receive materials

5 1 Select paint

6 1 Select carpet 27

SITUATIONS IN NETWORK DIAGRAM B

A

A must finish before either B or C can start C

A C

both A and B must finish before C can start

B A

C

B A

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

D B

A must finish before B can start both A and C must finish before D can start

Dummy C D

28

CONCURRENT ACTIVITIES

Lay foundation f

2

3 Lay foundation

3

Order material

(a) Incorrect precedence relationship

2

Dummy 2

0 1

4

Order material (b) Correct precedence relationship

29

NETWORK EXAMPLE Illustration Ill t ti off network t k analysis l i off a minor i redesign d ig off a product d t and d its it associated i t d packaging. The 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

QUESTIONS TO PREPARE ACTIVITY NETWORK ´ ´ ´ ´ ´

Is this a Start Activity? I this Is thi a Finish Fi i h A Activity? ti it ? What Activity Precedes this? What Activity Follows this? What Activity is Concurrent with this?

32

CPM CALCULATION ´

Path q connected sequence of activities leadingg from the starting event to the ending event

«A

´

Critical Path « The

longest path (time); determines the project duration

´

Critical Activities « All

of the activities that make up the critical path

33

FORWARD PASS ´

´

Earliest Start Time (ES) « earliest time an activity can start « ES = maximum EF of immediate predecessors Earliest finish time (EF) « earliest time an activity can finish « earliest start time plus activity time EF= ES + t

Backward Pass

ŠLatest Start Time (LS) Latest time an activity can start without delaying critical path time LS= LF - t ŠLatest finish time (LF) latest time an activity can be completed without delaying critical path time LS = minimum LS of immediate predecessors

34

CPM ANALYSIS ´ ´ ´

´

´

Draw the CPM network Analyze the paths through the network Determine the float for each activity « Compute the activity’s float float = LS - ES = LF - EF « Float is the maximum amount of time that this activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the project Find the critical path is that the sequence of activities and events where there is no “slack” slack i.e.. i e Zero slack « Longest path through a network Find the p project j duration is minimum p project j completion p time 35

CPM EXAMPLE: ´

CPM Network f, 15 h, 9

g, 17 a, 6 i, 6 b, 8 d, 13

j, 12

c, 5 e, 9

36

CPM EXAMPLE ´

ES and EF Times

h, 9

g, 17

a, 6 0

f, 15

i, 6

6 b, 8 0

8

d, 13

j, 12

c, 5 0

5

e, 9

37

CPM EXAMPLE ´

ES and EF Times

f, 15 6

h, 9

g, 17

a, 6 0

21

6

6

23

i, 6

b, 8 0

d, 13

8

8

c, 5 0

5

j, 12

21

e, 9 5

14 38

CPM EXAMPLE ´

ES and EF Times

f, 15 6

h, 9

g, 17

a, 6 0

21

6

6

21 30

23

i, 6 23

29

b, 8 0

d, 13

8

8

c, 5 0

5

21

j, 12 21 33

e, 9 Project’s EF = 33 5

14 39

CPM EXAMPLE ´

LS and LF Times

f, 15 6

a, 6 0

21

h, h 9 21 30

g, 17 6

6 b, 8 0

d, 13

8

8

21

c, 5 0

5

24 33

i, 6

23

23

29

27

33 j, 12 21

33

21

33

e, 9 5

14 40

CPM EXAMPLE ´

LS and LF Times

f, 15 6

21

h, h 9

18 24 a, 6

21 30

g, 17

0

6

6

4

10

10 27

24 33

i, 6

23

b, 8 0

8

d, 13

0

8

8

21

c, 5

8

21

0

5

e, 9

7

12

5

14

12

21

23

29

27

33 j, 12 21

33

21

33

41

CPM EXAMPLE ´

Fl t Float

f, 15 3 a, 6

3

6

21

9

24

g, 17

0

6

3

9

4

6

7

3

10 27 4

0

8

0

8

d, 13 8

0

8

0

5

e, 9

7

12

7

23

29

27

33 j, 12

21

c, 5

21 30 24 33

i, 6

23

b, 8 0

h, h 9

21

5

14

12

21

0

21

33

21

33

42

CPM EXAMPLE ´

Critical Path

f, 15

h, 9

g, 17

a, 6

i, 6 b, 8 d, 13

j, 12

c, 5 e, 9

43

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 activities that "occur near to each other in time".

45

Before starting any of the above activity, the questions asked as ed would be •"What activities must be finished before this activity can start" •could we complete this project in 30 weeks? •could could we complete this project in 2 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 other relevant information.

49

Data entry window

50

Output of the package

51

PERT ´

´

PERT is based on the assumption that an activity activity’ss duration follows a probability distribution instead of being a single value q p Three time estimates are required to compute the parameters of an activity’s duration distribution: « pessimistic time (tp ) - the time the activity would take if things g did not ggo well « most likely time (tm ) - the consensus best estimate of the activity’s duration « optimistic time (to ) - the time the activity would take if things did go well M Mean ((expected t d titime): )

te =

Variance: Vt =σ 2 =

tp + 4 tm + to 6

tp - to

2

6 52

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 duration probability distribution which is assumed to be normal The standard deviation of the project duration probability distribution is computed by adding the variances of the critical activities (all of the activities that make up the critical path) and taking the square root of that sum Probability computations can now be made using the normal distribution table.

53

PROBABILITY COMPUTATION Determine probability that project is completed within specified time Z=

x-µ σ

where µ = tp = project mean time σ = project standard mean time x = (proposed ) specified time

54

NORMAL DISTRIBUTION OF PROJECT TIME Probability

Zσ

µ = tp

x

Time

55

PERT EXAMPLE Immed. Optimistic Most Likely Pessimistic Activity Predec. Time (Hr.) Time (Hr.) Time (Hr.) A -4 6 8 B -1 4.5 5 C A 3 3 3 D A 4 5 6 E A 05 0.5 1 1.5 15 F B,C 3 4 5 G B,C 1 1.5 5 H E,F EF 5 6 7 I E,F 2 5 8 J D,H 2.5 2.75 4.5 K G,I 3 5 7 56

PERT EXAMPLE PERT Network D

A

E

H

J

C B

I F

K

G

57

PERT EXAMPLE

Activity A B C D E F G H I J K

Expected Time 6 4 3 5 1 4 2 6 5 3 5

Variance 4/9 4/9 0 1/9 1/36 1/9 4/9 1/9 1 1/9 4/9 58

PERT EXAMPLE Activity

ES

A B C D E F G H I J K

0 0 6 6 6 9 9 13 13 19 18

EF 6 4 9 11 7 13 11 19 18 22 23

LS 0 5 6 15 12 9 16 14 13 20 18

LF 6 9 9 20 13 13 18 20 18 23 23

Slack 0 *critical 5 0* 9 6 0* 7 1 0* 1 0* 59

PERT EXAMPLE Vpath = VA + VC + VF + VI + VK = 4/9 + 0 + 1/9 + 1 + 4/9 = 2 σpath = 1.414 z = (24 - 23)/σ = (24-23)/1.414 (24 23)/1 414 = .71 71 From the Standard Normal Distribution table: P(z < .71) = .5 + .2612 = .7612

60

PROJECT COST

61

COST CONSIDERATION IN PROJECT ´ ´ ´ ´

´ ´ ´

Project managers may have the option or requirement to crash the project, 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 activityy requires q the expenditure p of an amount of moneyy to reduce its duration by one unit of time, then the project manager selects 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 p path, each of the critical p paths must be reduced. If the length of the project needs to be reduced further, the process is repeated. 62

PROJECT CRASHING ´

´

´

´

Crashing « reducing project time by expending additional resources Crash time « an amount of time an activity y is reduced Crash cost « cost of reducing activity time G l Goal « reduce project duration at minimum cost

63

ACTIVITY CRASHING

Crash cost

Crashing activity Slope = crash cost per unit time

Normal Activity

Normal cost

Normal time Crash time

Activity time 64

TIME-COST RELATIONSHIP ƒ ƒ ƒ

Crashing costs increase as project duration decreases Indirect costs increase as project duration increases Reduce project length as long as crashing costs are less than indirect costs

Time-Cost Tradeoff Min total cost = optimal project time

Total project cost Indirect cost

Direct cost

time 65

PROJECT CRASHING EXAMPLE

4

2 8

12

7 4

1 12

3 4

5 4

6 4

66

TIME COST DATA

Activity Normal time ti 1 12 2 8 3 4 4 12 5 4 6 4 7 4

Normal costt Rs R 3000 2000 4000 50000 500 500 1500 75000

Crash time ti 7 5 3 9 1 1 3

Crash costt Rs R 5000 3500 7000 71000 1100 1100 22000 110700

Allowable crashh time ti 5 3 1 3 3 3 1

slope 400 500 3000 7000 200 200 7000

67

R7000

R500

Project duration = 36

4

2 8

R700

12

From…..

7 4

1 12

R400

3 4

6 4

5 4

R3000

R200

R200 R7000

R500

4

2 8

To…..

R700

12

7 4

1 7

Project duration = 31 Additional cost = R2000

R400

3 4 R3000

5 4

6 4 R200

R200 68

BENEFITS OF CPM/PERT ´ ´ ´ ´ ´

Useful at many stages of project management Mathematically simple Give critical path and slack time Provide project documentation Useful in monitoring costs

CPM/PERT can answer the following important questions: •How long will the entire project take to be completed? What are the risks involved? Which are the critical activities or tasks in the project which could delay the entire •Which 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 the least cost? ? 69

LIMITATIONS TO CPM/PERT ´ ´ ´ ´ ´ ´ ´

Clearly defined, independent and stable activities Specified precedence relationships Over emphasis on critical paths Deterministic CPM model 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 consistentlyy underestimates the expected p p project j completion time due to alternate paths becoming critical

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

70

COMPUTER SOFTWARE FOR PROJECT MANAGEMENT ´ ´ ´ ´ ´ ´

Microsoft Project (Microsoft Corp.) MacProject (Claris Corp.) PowerProject j ((ASTA Development p Inc.)) Primavera Project Planner (Primavera) Project Scheduler (Scitor Corp.) Project Workbench (ABT Corp.)

71

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

Activity A ti it Description D i ti

Duration D ti

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

Draw network diagram and show the critical path path. Calculate project duration. 72

PRACTICE PROBLEM Activityy Description p

Duration

1-2 1-3 3-4 2-4 3-5 4-5

5w 12w 5w 14w 15w 4w

Social work team to live in village Social research team to do survey Analyse results of survey Establish mother & child health program Establish rural credit programme Carry out immunization of under fives 4

2 1

5 3 73

CONTOH 1: B 2 100 KM

60 KM 40 KM

D 4

50 KM

1 A

F 6

55 KM

75 KM

25 KM 5

3

E

C

74

CONTOH 2 AKTIVITAS

URAIAN

AKTIVITAS PENDAHULUAN

WAKTU PENYELESAIAN (HARI

A

Desain daftar pertanyaan

-

4

B

Desain sampling

-

5

C

Testing daftar pertanyaan dan perbaikan

A

4

D

Memilih calon intervierwer

B

1

E

Melatih interviewer

D, A

2

F

Membagi wilayah kepada interviewer

B

4

G

Pelaksanaan interview

C, E, F

10

H

Evaluasi hasil riset

G

15 75