4 precedence network final bgt 2
TRANSCRIPT
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IV
Ir. Rony Ardiansyah, MT, IP-U
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3.1 Penjadwalan Activity On Node
Penjadwalan dengan AON yang sudah dikenaladalah Precedence Diagram Methods (PDM).
Pada AOA/CPM kegiatan digambarkan padaArrow (anak panah) dan event/peristiwa/
kejadian pada node, sedang AON/PDMkegiatan digambarkan pada nodenya (biasanyadalam bentuk kotak) dan arrow (anak pana) nyamenggambarkan hubungannya.
Prinsip penggambarannya hampir sama dengan
AOA, didasarkan pada predecessor atausuccessor antar kegiatan.Karena kegiatan padanode maka kegiatan dummy pada CPM tidakada pada PDM.
CPM (critical path method)
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Penggambaran AON pada prinsipnya samadengan AOA. Berikut adalah beberapa
contoh penggamabaran karingan dari AOAke AON.
1) Kegiatan Predecessor
A -
B A
C B
A B C
AOA/CPM
AON/PDM
A B C
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2) Kegiatan Predecessor
A -
B AC A
AON/PDM
A
C
B
AOA/CPM
AB
C
3
4
21
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3) Kegiatan Predecessor
A -
B -C A, B
AON/PDM
A
C
B
AOA/CPM
A
B
C
3 4
2
1
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4)
AON/PDM
Kegiatan Predecessor
A -
B A
C AD B
E C
AOA/CPM
AB
C
3 5
21
64E
D
A
C
B
E
D
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5) Kegiatan Predecessor
A -
B A
C AD B
E B, C
AOA/CPM
AB
C
3 5
21
64E
D
X
AON/PDM
A
C
B
E
D
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6) Kegiatan Predecessor
A -
B A
C AD B, C
E B, C
3
AOA/CPMA
B
C
521
6
4 E
DX
A
C
B
E
DAON/PDM
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7)
AOA/CPM
A B
C5
321
64D
X
C
A
D
B
AON/PDM
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8)
AOA/CPM
B
D
C
3
65
1 42
E
X
F
A
AON/PDM
C
B
E
D
A F
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9)
AON/PDM
C
B
A D
AOA/CPM X
C
B
A D
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AON/PDM mempunyai hubungan logis ketergantunganyang bervariasi. Jika di AOA/CPM hanya terdapathubungan logis/konstrain FS = 0 dan SS = 0, maka pada
AON/PDM ada 4 macam hubungan logis/konstrain yangbervariasi, yaitu.
1) Finish to Finish (FF) yaitu hubungan yang menunjukkanbahwa selesainya (Finish) kegiatan berikutnya (Successor)
tergantung pada selesainya (Finish) kegiatan sebelumnya(Predecessor)
i
ji
j FFij = O
FFij =0, artinya selesainya
kegiatan i dan j secara bersamaan
FFij
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FFij = x, artinya kegiatan j selesainya setelah kegiatan i selesai.
i
j
FFij = -x, artinya kegiaan i selesainya x hari lebih dahulu dariselesainya kegiatan j
i
x
j
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2) Finish to Start (FS) yaitu hubungan yang menunjukkanbahwa mulainya (Start) kegiatan berikutnya (Successor)tergantung pada selesainya (Finish) kegiatan sebelumnya
(Predecessor)
i j
FS ij
FSij = 0, kegitan j dimulai langsung setelah kegiatan i selesai.
i
j
FS ij=0
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FSij = x kegiatan j dimulai setelah x hari kegiatan i selesai
Untuk kegiatan Finish to Finish (FF) dan Finish to Start (FS)tenggang waktu/waktu tunda untuk kegiatan berikutnya
disebut “Lag time”.
i
j
x
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3) Start to start (SS) yaitu hubungan yang menunjukkanbahwa mulainya (start) kegiatan berikutnya (Succesor)tergantung pada mulainya (Start) kegiatan sebelumnya
(Predecessor)
SSij = 0 Kegiatan i dan j dimulai (start) secara bersama-sama
i
jSSij
i
SSij = 0 j
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SSij = x kegiatan j dimulai setelah x hari kegiatan i dimulai.
x
j
i
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4) Start to Finish (SF) yaitu hubungan yang menunjukkanbahwa selesainya (Finish) kegiatan berikutnya
(Successor) tergantung pada mulainya (Start) kegiatansebelumnya (Predecessor)
SF = x kegiatan j selesai setelah x hari kegiatan Idimulai
i
j
SFij
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j
x
i
Untuk kegiatan Start to Start (SS) dan Start to
Finish (SF), waktu tenggang/waktu tunda untuk
kegiatan berikutnya disebut “ lead time “
Dengan adanya hubungan logis/ketergantungan
yang bervariasi dari AON maka penjadwalan
dengan network diagram yang kegiatannya
overlapping dapat menggunakan AON/PDM
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Kotak Node yang lengkap yang biasa digunakan dalamDiagram PDM antara lain:
Act
No
ESActivity
DiscriptionDuration
EF
LS LF
ES Duration EF
Activity NumberActivity Discription
LS TF LF
1
2
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3
4
Activity Number TF
Activity
Discription
OD
RD
ES EF
OD = Original DurationRD = Remaining Duration
ActivityNumber
Dur TF
Activity Discription
ES EF
LS LF
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3.2 Perhitungan PDM
Pada dasarnya perhitungan PDM samadengan CPM, yaitu menggunakanperhitungan ke muka (forward pass) untukmenentukan Earlies Start(ES) dan EarliestFinish (EF). Dan menggunakanperhitungan ke belakang (backward pass)untuk menentukan Latest Finish (LF) danLatest Start (LS) berdasarkan hubungan
logis/ketergantungan yang ada antarkegiatan
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3.2.1 Perhitungan ke Muka (Forward Pass)
Untuk AON/PDM kegiatan awal (start) merupakansuatu aktifitas dalam bentuk node yangdurasinya =0 dan ES, EF, LS dan LF nya juga sama dengan nol
ES D EF
kegiatan
LS TF LF
0 0 0
Start
0
A
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1. Hubungan Kegiatan Finish to Finish (FF)
EFi
i
ESj Dj EFj
j
EF j = EF i + FF ij ES j = EF j - Dj
FFij
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5 10 15
A12 8 20
B
EF B = EF A + FF AB = 15 + 5 = 20ES B = EF B – DB = 20 - 8 =12
FF = 5
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Jika lebih dari satu kegiatan Predecessor (yang mendahului):
A
1468
P
22814B
15510
C
16106
FF 3
FF 5
FF6
EFP = max EF A+FF AP = 14+3 =17
EFB+FFBP = 15+5 =20EFC+FFCP = 16+6 = 22
ESP = EFPmax- DP
=22 – 8 =14
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EFi
iESj Dj
EFi
j
5 10 15
A
EF B = EF A + FS AB = 15 + 2 = 17
ES B = EF B + DB = 17 + 8 = 25
17 8 25
B
2. Hubungan Kegiatan Finish to Start (FS)
ES j = EF i + FS ij EF j = ES j + D j
FS2
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9 6 15
A
6
10
16
C
10 5 15
B
19 8 27
P
Jika lebih dari satu kegiatan Predecessor
ESP = max EF A+FS AP = 15+4 =19
EFB+FSBP = 15+2 =17EFC+FSCP = 16+3 =19
EFP = ESPmax+ DP
=19 + 8 =27
FS4
FS2
FS3
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3. Hubungan Kegiatan Start to Start (SS)
ESi Dj EFj
i
9 8 17
B
5 10 15
B
ESi Dj EFj
j
SS4
ESB = ES A + SS AB = 5 + 4 = 9EFB = ESB + DB = 9 +8 = 17
ES j = ESi + SSijEF j = ES j + D j
SSij
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8 6 14
A
6 10 16
C
10 5 15
B 15 8 23P
Jika lebih dari satu kegiatan Predecessor
ES = max ES A+SS AP = 8 +4 =12
ESB+SSBP = 10+5 =15ESC+SSCP = 6 +6 =12
ESP = ESPmax+ DP =15 + 8 =23
SS4
SS5
SS6
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4. Hubungan Kegiatan Start to Finish (SF)
ESi D j EF j
j
4 8 12
B
5 10 15
A
ESi Dj
i
SF7
EFB = ES A + SF AB = 5 + 7 = 12ESB = EFB - DB = 12 - 8 = 4
EF j = ESi + SSijES j = ES j - D j
SFij
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8 6 14
A
6 10 16
C
10 5 15
B
9 8 17
P
Jika lebih dari satu kegiatan Predecessor
SF5
SF7
SF8
EFP = max ES A+SF AP = 8 + 5 =13
ESB+SFBP = 10+7 =17ESC+SSCP = 6 +8 =14
ESP = ESPmax- DP = 17 - 8 =9
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3.2.2 Perhitungan ke Belakang (Backward Pass)
D j
j
LS j LF j
12 8 20
B40
5 10 15
A25 35
Dj
i
LSi LFi
FF=5
LF A = LFB - FFBA = 40 – 5 = 35LSB = LFB - D A = 35 - 10 = 25
LF j = LSi - FFij
LS j = LS j - D j
FFij
1. Hubungan Kegiatan Start to Finish (SF)
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Jika lebih dari satu kegiatan yang mengikuti (successor)
8
P
40
10
R
38
7
Q
42
6
M
26 32
FF5
FF4
FF6
LFM = min LFP - FFPM = 40 - 5 = 35
LFQ - FFQM = 42 - 4 = 38LFR - FFRM = 38 - 6 = 32
LSM = LFMmiN- DM = 32 - 6 = 26
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Jika lebih dari kegiatan Successornya
2. Hubungan Finish to Start (FS)
jLS j
8
B
32 40
6
A
21 27
Dj
i
LSi LFi
FS5
LFi = LSi - FSij
LSi = LF j - D j
FSij
LF A = LFB - FFBA = 32 – 5 = 27
LS A = LF A - D A = 27 - 6 = 21
LFM = min LSP - FSPM
LSQ - FFQM
LSR - FSRM LSM = LFMmiN- DN
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Jika lebih dari kegiatan Successor
3. Hubungan Kegiatan Start to Start (SS)
jLS j
8
B
32 40
6
A
28 34
Dj
i
LSi LFi
SS4
LSi = LSi - FSij
LFi = LF j + D j
SSij
LS A = LSB - SSBA = 32 – 4 = 28LF A = LS A+ D A = 28 +6 = 34
LSM = min LSP - SSPM
LSQ - SSQM
LSR - SSRM LFM = LSMmiN+ DM
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Jika lebih dari kegiatan Successor
4. Hubungan Kegiatan Start to Finish (FS)
jLF j
8
B
32 40
6
A
30 36
Dj
i
LSi
SF10
LSi = LF j - SFij
LFi = LSi + Di
SFij
LS A = LFB - SFBA = 40 – 10 = 30LF A = LS A - D A = 30 + 6 = 36
LSM = min LFP - SSPM
LFQ - SSQM
LFR - SSRM LFM = LSMmiN+ D A
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Jika pada perhitungan ke muka ada lebih satu
kegiatan Predecessor yang hubuunganketergantungan (konstrain) berlainan (FF;FS;SS;SF)maka ES dan EF di ambil yang maksimum
Jika pada perhitungan ke belakang ada lebihkegiatan Successor yang hubungan ketergantungan(konstrain) berlainan, maka LS dan EF diambil yangminimum.
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1
17
2
19
3
14
4
19 11 30
SS34 = 3
FS24 = 0
FS14 = 1
181917
293028
HITUNGAN KE MUKA
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j
817
23 31
319
31
4
30
2
19
35
SS14 = 2
FS13 = 0
FS14 = 1
3134
HITUNGAN KE BELAKANG
28
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Contoh:
No Kegiatan Durasi D Predecessor Hubungan/konstrain Lag/Lead
1 A 5 - - -
2 B 6 A FF 4
3 C 4 A FS 2
4 D 4 B SS 2
5 E 9 B SS 3
6 F 6 B, C FS, FF 0;2
7 G 3 D SF 4
8 H 6 E, F SS, SF 1;4
9 I 4 G, H FF, SS 5,2
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9 6 15
F
10 16
0 5 5
A
0 5
3 6 9
B
3 9
7 6 13
H
8 14
10 4 14
I10 14
6 3 9
G
6 9
7 4 11
C
10 14
6 9 15
E
7 16
5 4 9
D
5 9
FS2
SS3
SS2 SF4
SS1
SF4
FF5
SS2
FF2
FS0
FF4
Hitungan ke Muka
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Hitungan ke MukaTitik A:ESA = 0EFA = 0 + 5 = 5
Titik B:EFB = EFA + FFAB = 5+4 = 9ESB = EFB – DB = 9-6 = 3
Titik CESC = EFA + FSA = 5 +2 = 7EFC = ESC + DC = 7 + 4 = 11
Titik DESD = ESB + SSBD = 3 + 2 = 5EFD = ESD + DD = 5 + 4 = 9
Titik EESE = ESB + SSBE = 3 + 3 = 5EFE = ESE + DE = 6 + 9 = 15
Titik FDari C EFF = EFC + FFCF = 11 + 2 = 13
ESF = EEF + DF = 13 - 6 = 7Dari B ESF = EFB + FSBF = 9 + 0 = 9
EFF = ESF + DF = 9 + 6 = 15
Yang menentukan dari B ESF = 9
EFF = 15
Hitungan ke Muka (lanjutan)
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Hitungan ke Muka (lanjutan)
Titik G:ESG = ESD + SFDG = 5 + 4 = 9EFG = EFG - DG = 9 - 3 = 6
Titik H:Dari E ESH = ESE + SSEH = 6 + 1 = 7
FH = EEF + DF = 7 + 6 = 13
Dari F EFH = ESH + ESFH = 9 + 4 = 13
EFH = ESH + DH = 13 - 6 = 7
Yang menentukan dari ESH = 7EFH = 13
Titik I:
Dari G EFI = EFG + FFGI = 9 + 5 = 14ESI = EFI - DI = 14 – 4 = 10
Dari H ESI = ESH + SSHI = 7 + 2 = 9EFI = ESI + DI = 8 + 4 = 12
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Hitungan ke belakang
Titik H:LSH = LSI – SSHI = 10 – 2 = 8
LFH = LSH + DH = 8 + 6 = 14
Titik G:LFG = LFI – FFGI = 14 – 5 = 9LSG = LFG – DG = 9 – 3 = 6
Titik F:LSF = LFH – SFHF = 14 -4 = 9LSF = LSF + DF = 10 + 6 = 16
Titik E:LSE = LSH – SSHE = 8 -1 = 7LFE = LSE + DE = 7 + 9 = 16
Titik D:LSE = LSH – SSHE = 9 - 4 = 5LFE = LSE + DE = 5 + 4 = 9
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Titik C:
LFC = LFF – FFFB = 16 - 2 = 14
LSC = LFC – DC = 14 – 4 =10
Titik B:
Dari titik F LFB = LSF - FSFB = 10 – 0 = 10
LSB = LSB – DB = 10 – 6 = 4
Dari titik E LSB = LSB + DB = 10 – 6 = 4
LFB = LSB + DB = 4 + 6 = 10
Dari titik D LSB = LSD – SSDB = 5 – 2 = 3
LFB = LSB + DB = 3 + 6 = 9
Hitungan ke belakang (lanjutan)
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Hitungan ke belakang (lanjutan)
Yang diambil adalah dari D LSB = 3LSB = 9
Titik A:Dari titik C LFA = LSc + FSCA = 10 - 2 = 8
LSA = LFA - DA = 8 – 5 = 3
Dari titik B ESI = ESH + SSHI = 9 – 4 = 5LSA = LFA – DA = 5 – 5 = 0
Yang diambil adalah dari B LFA = 5LSA = 0
Jalur Kritis :A – B – D – G – ILama Proyek = 14 minggu