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 Graph or bar chart with a bar for each project activity that shows passage of time Provides 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
Activity-on-node A i i d (AON) nodes represent activities, and arrows show precedence relationships Activity-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
Latest Start Time (LS) Latest time an activity can start without delaying critical path time LS= LF - t Latest 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
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
