network_ cpm dan pert
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NETWORK, CPM DAN PERT
Dr. Mohammad Abdul Mukhyi, SE., MM
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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?
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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
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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.
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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
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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.
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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
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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
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Work Breakdown Structure for Computer Order
Processin S stem Pro ect
Work Breakdown Structure for Computer Order
Processin S stem Pro ect
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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
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Untuk perencanaan.
Hubungan antara komponen dalam network danelemen dalam masalah riil
-Penerapan model network:Masalah transportasi
Masalah prosesing
erencanaan an pengen a an proyepenugasan
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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
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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
≥
===
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Untuk menentukan umlah dan lokasi titik an kutan
serta berguna untuk menentukan jumlah dan lokasititik angkutan secara optimal dengan meminimalkan
biaya angkutan antar lokasi.
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+ 1 truk
3
C23 C34
C36
6 7
C12
C24 C46 C67
5
- -
C25
54
C56
0 truk
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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
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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)
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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.
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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.
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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
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– Indicates only precedence relationships
– Does not require any time of effort
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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)
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in time
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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
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31 5
11btain financing
Order and receivematerials
Select paint
Select carpet
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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
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C
D
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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
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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 ?
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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".
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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
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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
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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
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CPM EXAMPLE
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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
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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
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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
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EXAMPLE
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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 ?
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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".
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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 ? “
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We shall see below how the network analysis diagram/picture we construct
helps us to answer this question.
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CRITICAL PATH TAKES 24 WEEKS FOR THE COMPLETION OF THE PROJECT
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Packages are available to determine the shortest path and
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Packages are available to determine the shortest path and
other relevant information.
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d
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Data entry window
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PERT
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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
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Variance: Vt =σ 2 = p - o
6
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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.
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Probability
Z
= tp Time
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PERT EXAMPLE
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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
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PERT EXAMPLE
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PERT Network
DD
A A EE HH JJ
CC
BB IIFF
GG
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PERT EXAMPLE
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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
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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 *
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PROJECT COST
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COST CONSIDERATION IN PROJECT
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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.
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PROJECT CRASHING
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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
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ACTIVITY CRASHING
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ACTIVITY CRASHING
Crashing activityCrash cost
Slope = crash cost per unit time
Normal ActivityNormal
cost
Normaltime
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Activity timeCrash time
TIME-COST RELATIONSHIP
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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
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time
PROJECT CRASHING EXAMPLE
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22
88
1212
77
1212
33 66
44
44 55
44
44
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TIME COST DATA
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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
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2
R500 R7000
4
Project duration = 36
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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
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BENEFITS OF CPM/PERT
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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
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the least cost?
LIMITATIONS TO CPM/PERT
Clearly defined, independent and stable activities
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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
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COMPUTER SOFTWARE
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Microsoft Project (Microsoft Corp.)
MacProject (Claris Corp.)
PowerPro ect ASTA Develo ment Inc.
Primavera Project Planner (Primavera)
. Project Workbench (ABT Corp.)
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PRACTICE EXAMPLE
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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
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.
duration.
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2
B
4
2
F
D
100 KM
40 KM 50 KM
1 6
F
A
5
3 E
A75 KM
3 E
C
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CONTOH 2
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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
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