Hashemite University Department of Civil Engineering ... · Construction Project Management (CE...
Transcript of Hashemite University Department of Civil Engineering ... · Construction Project Management (CE...
Network CalculationsPart 4
Construction Project
Management
(CE 110401346)
Hashemite University
Department of Civil Engineering
➢Early Activity Start (ES): Earliest time an activity can start—as
determined by the latest of the early finish times of all immediately
preceding activities (IPAs)
➢Early Activity Finish (EF): Earliest time an activity can finish—
determined by adding the duration of the activity to the early start
time
➢Late Activity Start (LS): Latest time an activity can start without
delaying the project completion
➢Late Activity Finish (LF): Latest time an activity can be finished
without delaying project completion
Calculations On a Precedence Network
Early Event Occurrence Time: Earliest an event can occur—determined by the latest early finish
Late Event Occurrence Time: Latest an event can occur
Calculations On a Precedence Network
Step 1: Perform Forward Pass Calculations to determine:➢Early Start (ES) and Early Finish (EF) of each activity.
ES (initial activities) = S
ES (x) = Latest (EF (all predecessors of x))
EF (x) = ES(x) + D(x)
Where,
S= Project start time.
D(x) = Duration of activity x.
ES(x) = Earliest start time of activity x.
EF(x) = Earliest finish time of activity x.
Calculations On a Precedence Network
Early Times (Early Start [ES] and Early Finish [EF])
Calculations On a Precedence Network
1. Assign 1 as the early start date of the first activity
2. Calculate the early finish time for the activity
3. The early start of activities will be determined by the early
finish times of preceding activities
➢Other than the first activity or activities
4. Repeat steps 2 and 3 for each network activity until ES &
EF are determined for the last activity
Calculations On a Precedence Network
Step 5: Perform Backward Pass Calculations to determine:
➢Late Start (LS) and Late Finish (LF) of each activity.
LF (end activities) = T
LF (x) = Earliest (LS (all successors of x))
LS (x) = LF(x) - D(x)
Where,
T = Project completion time.
D(x) = Duration of activity x.
LS(x) = Latest start time of activity x.
LF(x) = Latest finish time of activity x.
Calculations On a Precedence Network
Calculations On a Precedence Network
Calculations On a Arrow Network
▪When an activity start date is fixed in this way, the activity is
said to have no float , Such activities are said to be “critical”
▪If the activity starts later than the assigned date, or takes
longer to complete than the assigned duration, the project
completion date will be extended by the same amount of time
Identify the Critical Path
▪Total Float (TF): maximum amt of time that the activity can be delayed without delaying the completion time of the project.
▪Float (FF): maximum amount of time that the activity can be delayed without delaying the early start of any of its successors, assuming its predecessors were completed early.
▪Free Float: Amount of time an activity can be delayed before it impacts the start of any succeeding activity
Activity Floats
▪Independent Float (IF): maximum amount of time that the activity can be delayed without delaying the early start of any of its successors, assuming its predecessors were completed late.
Activity Floats
Successors Started
Early Late
Predecessors
Completed
Early Free Float Total
Float
Late Independent
Float
Activity Floats
Float Type Calculation
Total FloatTF = LS – ESTF = LF – EF
Free Float FF = Min (ES of all successors – EF)
Independent
Float
IF =Min (ES of all successors
-LF of the same activity)
Activity Floats
▪Once the early and late start times, early and late finish times, free
float, and total float of all activities are determined, the
calculations are completed
Calculations On a Precedence Network
Activity TF FF IF
Mobilize 0 0 0
Remove old Cabinets 0 0 0
Buy materials 3 0 0
Install new flooring 0 0 0
Hang wallpaper 3 0 -3
Install new cabinets 0 0 0
Touch-up paint 3 3 0
Demobilize 0 0 0
Calculations On a Precedence Network
Critical Path
Critical Path – series of interconnected critical activities through the network diagram. The delay of any of the critical activities will delay the project completion date (A critical activity is an activity with a total float value equals to zero).
10 - 17
10 - 18
A
EF
LS
ES
LF
Example 2: Bridge Construction
Activity Duration
(O, M, P)
Mean
Duration
Predecessors
Pile and foundation W
Pile and foundation C
Pile and foundation E
Substructure W
Substructure C
Substructure E
Cast-in-place span
Precast span
Bridge deck
Finishes
(9,10,11)
(4,5,6)
(6,8,10)
(20,23,26)
(16,17,18)
(19,20,21)
(28,30,32)
(4,5,6)
(4,5,6)
(12,14,16)
10
5
8
23
17
20
30
5
5
14
--
--
--
Pile and foundation W
Pile and foundation C
Pile and foundation E
Substructures W and C
Substructures C and E
Cast-in-place and precast
spans
Bridge deck
Start
Pile foundation W
Pile foundation C
Pile foundation E
Substructure W
Substructure C
Substructure E
Cast-in-place span
Precast span
Bridge deck Finishes
0Start
10Pile foundation W
5Pile foundation C
8Pile foundation E
23Substructure W
17Substructure C
20Substructure E
30Cast-in-place span
5Precast span
5Bridge deck
14Finishes
ES D EFDescription
LS TF LF
Forward Pass
33 or 22?
63 or 33?
22 or 28?
0 0 0Start
0 10 10Pile foundation W
0 5 5Pile foundation C
0 8 8Pile foundation E
10 23 33Substructure W
5 17 22Substructure C
8 20 28Substructure E
33 30 63Cast-in-place span
28 5 33Precast span
63 5 68Bridge deck
68 14 82Finishes
ES D EFDescription
LS TF LF
58 or 33?
Backward Pass
ES Dur EFDescription
LS TF LF
0 0 0Start
0 0
0 10 10Pile foundation W
0 10
0 5 5Pile foundation C
11 16
0 8 8Pile foundation E
30 38
10 23 33Substructure W
10 33
5 17 22Substructure C
16 33
8 20 28Substructure E
38 58
33 30 63Cast-in-place span
33 63
28 5 33Precast span
58 63
63 5 68Bridge deck
63 68
68 14 82Finishes
68 82
Total Float
TF=LST-EST=LFT-EFT
ES D EFDescription
LS TF LF
0 0 0Start
0 0 0
0 10 10Pile foundation W
0 0 10
0 5 5Pile foundation C
11 11 16
0 8 8Pile foundation E
30 30 38
10 23 33Substructure W
10 0 33
5 17 22Substructure C
16 11 33
8 20 28Substructure E
38 30 58
33 30 63Cast-in-place span
33 0 63
28 5 33Precast span
58 30 63
63 5 68Bridge deck
63 0 68
68 14 82Finishes
68 0 82
Activity Floats
• In addition to total float, the following floats
can be estimated for each activity:
– Free Float (FF)
– Interfering Float (IF)
– Independent Float (Ind. F)
Free Float (FF)
• FF is the total time that an activity can be
delayed without causing any delay to the
early start of the following activities.
• FFA = min. (ES activities following A - EFA)ESB=13
A
C
B
EFA=10
ESC=16FFA = min (3,6) = 3
Interfering Float (IF)
• IF is the total time utilized in the current
activity that interferes with its following
activities:
– IFA = TFA - FFA
• Example: Assume TFA is 3 days and FFA is 0
days. IFA = 3 – 0 = 3. This implies that
although 3 days of delay can occur on activity
A without impacting the project duration, each
day of IF for A will interfere with the float
available for following activities.
Independent Float (Ind. F)
• Ind. F is the total time between an activity
late finish and the early start of the
following activities.
• Ind. FA = min. (ES activities following A - LFA)ESB=13
A
C
B
ESC=16Ind. FA = min. (1,4) = 1
LFA=12
THE CPM EXPLAINED THROUGH EXAMPLES
•Example 3: Draw the logic network and perform the CPM calculations for the schedule shown next.
Solution: The Forward Pass
• The project starts with activity A, which starts at the beginning of day 1 (end of day 0).
• It takes 5 days to finish activity A; it finishes on day 5 (end of the day).
• At this point, activities B and C can start. Activity B takes 8 days; it can start on day 5 (directly after activity A finishes), so it can finish as early as day 13.
• Similarly, activity C can finish on day 11 (5 + 6).
• Activity D follows activity B. It can start on day 13 (end of B) and end on day 22.
• Activity E must wait until both activities B and C are finished.
Solution: The Forward Pass
• Activity C finishes on day 11, but activity B does not finish until day 13. Thus, activity E cannot start until day 13. With 6 days’ duration, activity E can then finish on day 19.
• Activity F depends on activity C only. Thus, it can start on day 11 and finish on day 14.
• The last activity, G, cannot start until activities D, E, and F are finished.
• Through simple observation, we can see that activity G cannot start until day 22 (when the last activity of D, E, and F finishes).
• Activity G takes 1 day, so it can finish on day 23.
Solution: The Forward Pass
Solution: The Forward Pass
• For this example, we have calculated two types of dates:
1. The expected completion date of the project: day 23
2. The earliest date when each activity can start and finish
• These dates are called the early start (ES) and the early finish (EF) dates for each activity. As you will soon learn, an activity cannot start earlier than its ES date and cannot finish earlier than its EF date, but it may start or finish later than these dates.
Solution: The Forward Pass
• In mathematical terms, the ES time for activity j (ESj) is as follows:
ESj = max(EFi) (4.1)
• where (EFi) represents the EF times for all immediately preceding activities.
• Likewise, the EF time for activity j (EFj) is as follows:
EFj = ESj + Durj (4.2)
• where Durj is the duration of activity j.
• The forward pass is defined as the process of navigating through a network from start to finish and calculating the early dates for each activity and the completion date of the project.
Solution: The Backward Pass
• Now let us start from the end of the project and work our way back to the start.
• We already know the end-of-project date: day 23.
• Activity G must finish by day 23.
• Its duration is only 1 day, so it must start no later than day 22 (23 − 1) so that it does not delay the project.
• Similarly, activities D, E, and F must finish no later than day 22 so that they will not delay activity G. Through simple computations, we can find their late start dates: activity F: 22 − 3 = 19; activity E: 22 − 6 = 16; and activity D: 22 − 9 = 13.
• Activity C must finish before activities E and F can start. Their late start dates are 16 and 19, respectively.
Solution: The Backward Pass
• Clearly, activity C must finish by the earlier of the two dates, day 16, so that it will not delay the start of activity E.
• Thus, its late start date is day 10 (16 − 6). Similarly, activity B must finish by the earlier of its successors’ late start dates: day 13 for D and day 16 for E. Therefore, the late finish date for activity B is day 13, and its late start date is day 5 (13 − 8).
• The last activity (from the start) is A: It must finish by the earlier of the late start dates for activities B and C, which are day 5 for B and day 10 for C. Consequently, the late finish date for activity A is day 5, and its late start date is day 0 (5 − 5).
Solution: The Backward Pass
• In mathematical terms, the late finish (LF) time for activity j (LFj) is as follows:
LFj = min(LSk) (4.3)
• where (LSk) represents the late start times for all succeeding activities.
• Likewise, the late start (LS) time for activity j (LSj) is as follows:
LSj = LFj − Durj (4.4)
• The backward pass is defined as the process of navigating through a network from finish to start and calculating the late dates for all activities.
• This pass, along with the forward-pass calculations, helps identify the critical path and the float for all activities.
Solution: The Backward Pass
Solution: The Backward Pass
• If you refer to the Figure on the previous slide, you can see that for some activities (light lines), the late dates (shown under the boxes) are later than their early dates (shown above the boxes). For other activities (thick lines), late and early dates are the same.
• For the second group, we can tell that these activities have strict start and finish dates. Any delay in them will result in a delay in the entire project. We call these activities critical activities.
• We call the continuous chain of critical activities from the start to the end of the project the critical path.
• Other activities have some leeway. For example, activity C can start on day 5, 6, 7, 8, 9, or 10 without delaying the entire project. As mentioned previously, we call this leeway float.
Solution: The Backward Pass
• There are several types of float. The simplest and most important type of float is total float (TF):
TF = LS − ES or TF = LF − EF or TF = LF − Dur − ES
Solution: The Backward Pass
• With the completion of the backward pass, we have calculated the late dates for all activities. With both passes completed, the critical path is now defined and the amount of float for each activity is calculated.
A
Example 4: Draw the Activity-on-Arrow network for the following
activities. Remove any redundant dependencies and label dummy activities as dummy1, dummy2, etc.
B
C
D F H
I
G
J K L
E
Dummy1 Dummy2
Dummy3
Activity A B C D E F G H I J K L
Predecessor - - A, B B C C, D F F F G H, I, J E, K
▪LAG: The amount of time that exists between the early finish of an activity and the early start of a specified succeeding activity
Calculations On a Precedence Network
Example 5: Network Calculations
Activity Description Predecessors Duration
A Preliminary design - 6
B Evaluation of design A 1
C Contract negotiation - 8
D Preparation of fabrication plant C 5
E Final design B, C 9
F Fabrication of Product D, E 12
G Shipment of Product to owner F 3
Activity Duration ES EF LS LF
A 6
B 1
C 8
D 5
E 9
F 12
G 3
Activity Duration ES EF LS LF
A 6 1 7 2 8
B 1 7 8 8 9
C 8 1 9 1 9
D 5 9 14 13 18
E 9 9 18 9 18
F 12 18 30 18 30
G 3 30 33 30 33
Activity Duration ES EF LS LF TF FF IF
A 6 1 7 2 8
B 1 7 8 8 9
C 8 1 9 1 9
D 5 9 14 13 18
E 9 9 18 9 18
F 12 18 30 18 30
G 3 30 33 30 33
Activity Duration ES EF LS LF TF FF IF
A 6 1 7 2 8 1 0 0
B 1 7 8 8 9 1 1 0
C 8 1 9 1 9 0 0 0
D 5 9 14 13 18 4 4 4
E 9 9 18 9 18 0 0 0
F 12 18 30 18 30 0 0 0
G 3 30 33 30 33 0 0 0
Activity Description Predecessors Duration
A Site clearing - 4
B Removal of trees - 3
C General excavation A 8
D Grading general area A 7
E Excavation for utility trenches B, C 9
F Placing formwork and
reinforcement for concrete
B, C 12
G Installing sewer lines D,E 2
H Installing other utilities D,E 5
I Pouring concrete F,G 6
Example 6: Network Calculations
Example 6: Network Calculations
Activity Duration
Early
Start
Early
Finish
Late
Start
Late
Finish
A 4
B 3
C 8
D 7
E 9
F 12
G 2
H 5
I 6
Example 6: Network Calculations
Activity Duration
Early
Start
Early
Finish
Late
Start
Late
Finish
A 4 1 5 1 5
B 3 1 4 10 13
C 8 5 13 5 13
D 7 5 12 16 23
E 9 13 22 14 23
F 12 13 25 13 25
G 2 22 24 23 25
H 5 22 27 26 31
I 6 25 31 25 31
Example 6: Network Calculations
Activit
y
Duration ES EF LS LF TF FF IF
A 4 1 5 1 5
B 3 1 4 10 13
C 8 5 13 5 13
D 7 5 12 16 23
E 9 13 22 14 23
F 12 13 25 13 25
G 2 22 24 23 25
H 5 22 27 26 31
I 6 25 31 25 31
Example 6: Network Calculations
Activit
y
Duration ES EF LS LF TF FF IF
A 4 1 5 1 5 0 0 0
B 3 1 4 10 13 9 9 9
C 8 5 13 5 13 0 0 0
D 7 5 12 16 23 11 10 10
E 9 13 22 14 23 1 0 0
F 12 13 25 13 25 0 0 0
G 2 22 24 23 25 1 1 0
H 5 22 27 26 31 4 4 3
I 6 25 31 25 31 0 0 0
Example 6: Network Calculations
▪Types of Logical Precedence Relationships in PDM
➢ Finish to Start (with or without lag):
Each activity depends on the completion of its preceding activity
Precedence Diagram Relationships
Typical Sequence of Finish-to-Start Relationships
Finish-to-Start Relationship with a 28-Day Delay (lag)
Precedence Diagram Relationships
Types of Logical Precedence Relationships in PDM
➢ Start to Start (with or without lag).
Precedence Diagram Relationships
Activities with Start-to-Start RelationshipsPrecedence Diagram Relationships
Activities with Start-to-Startwith a Delay Relationships
Precedence Diagram Relationships
Activities with Start-to-Startwith a Delay Relationships
Precedence Diagram Relationships
Types of Logical Precedence Relationships in PDM
➢ Finish to Finish (with or without lag).
Precedence Diagram Relationships
Finish-to-Finish (FF)
Precedence Diagram Relationships
Finish-to-Start Relationshipfor Window Installation
Finish-to-Finish (FF) — with Delay
Precedence Diagram Relationships
Activities with Finish-to-Finishwith a Delay (lag) Relationships
Precedence Diagram Relationships
Types of Logical Precedence Relationships in PDM
➢ Start to Finish (with or without lag).
Precedence Diagram Relationships
Start-to-Finish with a Delay — RelationshipsPrecedence Diagram Relationships
Start-to-Finish with a Delay — RelationshipsPrecedence Diagram Relationships
Start-to-Finish with a Delay — RelationshipsPrecedence Diagram Relationships
▪Advantages of PDM Over CPM:
➢ Easier to construct & modify network.
➢ No need for dummies.
➢ Less activities in presentation.
➢ Precedence relationships with lag times are more effective in modeling project activities.
Precedence Diagram Method