1. Project Scheduling: Multiple dependencies, lags, Gantt charts, crashing, AoA

2. Lags in Precedence Relationships
The logical relationship between the start and finish of one activity and the start and finish of another activity.
Four logical relationships between tasks
Finish to Start
Finish to Finish
Start to Start
Start to Finish
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3. This lag is not the same as activity slack
Finish to Start Lag
Most common type of sequencing
Shown on the line joining the modes
Added during forward pass
Subtracted during backward pass A
Spec Design 6 B
Design Check 5 C
Blueprinting 7
Lag 4
This lag is not the same as activity slack

4. Finish to Finish Lag Two activities share a similar completion point
The mechanical inspection cannot happen until wiring, plumbing, and HVAC installation are complete A
Wiring 6
Lag 3
HVAC = Heating, Ventilation, Air Conditioning B
Plumbing 6 C
HVAC 5 D
Inspection 1
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5. Logic must be maintained by both forward and backward pass
Start to Start Lag
Logic must be maintained by both forward and backward pass A
Wiring 6
Lag 3 C
HVAC 5 D
Inspection 1 B
Plumbing 1
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6. Start to Finish Lag Least common type of lag relationship
Successor’s finish dependent on predecessor’s start A
Wiring 6
Lag 3 B
Plumbing 6 C
HVAC 5 D
Inspection 1
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7. Dependencies can be used in combination
Start-to-start & finish-to-finish: 5 ? ? a 3 ? b 5 9 ? 7 2 6
Example: a: marketing action b: measuring the effect of the action lags: the effect needs time to appear, and to fade out

8. Floats on multiple dependency networks
Total float = LFT – EST – Duration
Early total float = LFT – EFT
Late total float = LST – EST
In case of multiple dependence free float cannot be calculated

9. Solution 5 a 3 b 5 9 2 7 6

10. Calculations with finish-to-start lagsb 3 3 f 3 1 a 3 c 3 e 3 h 3 2 4 5 g 3 d 3 1 2

11. Calculations with finish-to-start lags6 a 3 b 6 9 12 15 c 7 10 f 20 23 d 4 13 e 18 g 21 24 h 27 5 1 2 3 6

12. Various dependencies Dangler activities! b f a c e h g d 3 5 1 2 4 5 21 c 3 e 4 h 3 2 4 5 g 5 2 2 d 4 1

13. Various dependencies b f a c e h g d 3 5 1 2 4 5 2 2 1 2 1 3 4 3 5 4 46 13 14 19 2 3 f 9 19 10 20 1 5 1 a 1 c 5 8 3 e 13 17 4 h 20 24 1 21 3 2 4 5 g 17 22 5 2 2 d 2 5 16 18 22 4 1

14. Practicing b 3 d 2 1 4 a 4 2 e 4 5 c 7 3

15. Practicing b 4 7 9 13 16 3 d 8 10 9 17 19 2 1 4 a 4 2 e 19 23 4 5 c 9 16 7 3

16. Gantt Charts Establish a time-phased network
Can be used as a tracking tool
Benefits of Gantt charts
Easy to create and comprehend
Identify the schedule baseline network
Allow for updating and control
Identify resource needs
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17. Create a Gantt chart based on the activities listed in the table.
Task
Time
Pred A 8 -- B 5 C D 4
B,C E
Task ES EF LS LF Z Y X W V U T S R
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18. Principal methods for crashing
The process of accelerating a project
Principal methods for crashing
Improving existing resources’ productivity
Changing work methods
Increasing the quantity of resources
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19. Managerial Considerations
Determine activity fixed and variable costs
The crash point is the fully expedited activity
Optimize time-cost tradeoffs
Shorten activities on the critical path
Cease crashing when
the target completion time is reached
the crashing cost exceeds the penalty cost
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20. Definition of crashing
Obtaining reduction in time at an increased cost (increasing the employed resources).
Cost-slope: the cost of reducing duration time by unit time.
Let’s see the following example: a 4 b 2 c e d 5 f 3 c 6 8 1 7 9 2 e 8 10 1 9 11 2 a 4 b 4 6 2 f 11 14 3 d 6 11 5

21. Procedure for crashing
Crash one time unit at a time
Only the crashing of critical activities has any effect on TPT
Crash that activity first that is the cheapest to reduce in time
Be aware of multiple critical paths
Stop crashing when:
the crash-time is reached at every ‘crashable’ activity,
benefits of possible crashing are lower than crashing costs.

22. Benefit of reducing TPT by one day:
Crashing table
If the costs to reduce times are known, then a table can be set up showing the relative costs for the reduction in time of each activity by a constant amount.
Crash-time is the minimum duration of an activity. It is given by technical factors.
Activity
(label)
Duration
(day)
Float (day)
Crash time
Cost-slope (€/day) a 4 2
100 b
150 c 1
110 d 5 3
200 e
160 f
500
Benefit of reducing TPT by one day:
400 €/day

23. Solution method step: identify the critical activities
step: find the critical activity with cheapest crash cost, and if its cost slope is lower than the daily benefit from crashing, reduce its duration with one day. If there is no activity to crash, or it is too costly, stop crashing and go to step 4.
step: reidentify the critical path, and go back to step two.
step: identify the final critical path(s), TPT and the total net benefit of crashing.

24. Path / activity crashed Path / activity crached
Solution
Path durations
Path / activity crashed
normal
step 1
step 2
step 3
step 4
step 5 – a d
d, c
none
a-b-c-e-f 13 12 11 10
a-b-d-f 14
Cost:
100
200
310
Cumulated net benefit:
300
600
800
890
Path durations
Path / activity crached
normal
step 1
step 2
step 3
step 4
step 5
Cost:
Cumulated net benefit:
After crashing:
there are two critical paths
TPT is 10 days
total benefit of crashing is €890

25. Example 2 (for individual work)b 2 d 2 e 5 a 3 g 3 7 c 3 f 3
Identify the critical path and the TPT.

26. Example 2 (for individual work)b 3 5 2 d 5 7 2 e 7 12 5 a 3 g 12 15 3 7 c 3 6 1 4 7 f 6 9 3 12
Critcal: a-b-d-e-g TPT: 15
Using tbe table on the next slide, calculate the optimal TPT with crashing.

27. Benefit of reducing TPT by one day:
Activity
(label)
Normal duration (day)
Float (day)
Crash time
Cost-slope (€/day) a 3 1
500 b 2
550 c
150 d 5
900 e 4
400 f
100 g
200
Activity
(label)
Normal duration (day)
Float (day)
Crash time
Cost-slope (€/day) a 3 1
500 b 2
550 c
150 d 5
900 e 4
400 f
100 g
200
Benefit of reducing TPT by one day:
1200 €/day
What is the new TPT?
What is the total profit on crashing?
10 days
€3000

28. Activity Pred Normal Time Min Time Normal Cost Crash Cost A -- 14 9
What is the lowest cost to complete this project in 52 weeks? Times are in weeks and costs in dollars. Plot the AON & AOA networks and the GANTT chart.
Activity
Pred
Normal Time
Min Time
Normal Cost
Crash Cost A -- 14 9
500
1500 B 5 2
1000
1600 C 10 8
2000
2900 D
B, C
2500 E 6 F
3000 G
E, F 7 4
600
1800 H 15 11
3600
Initial early and late start and finish times
Task ES EF LS LF Slack A B C D E F G H
Project 63
Reduce A by 5 days at $200/week = $1000 Project length is now 58 weeks
Reduce G by 3 days at $400/week = $1200 Project length is now 55 weeks
Reduce C by 2 days at $450/week = $900 Project length is now 53 weeks
Total cost to finish project in 53 weeks is $3100
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29. Activity on Arrow Networks
Activities represented by arrows
Widely used in construction
Event nodes easy to flag
Forward and backward pass logic similar to AON
Two activities may not begin and end at common nodes
Dummy activities may be required
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30. Calculate early and late event times for all activities. Activity Time
Use AOA to sketch the network that represents the project as described in the table.
Calculate early and late event times for all activities.
Activity
Time
Pred A 4 -- F 15 E B 2 G C 10 H 7
D,F,G D 3 I 11
B,C
Task ES EF LS LF A B C D E F G H K
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31. Activity on Arrow NetworkD I A B H E F C G
Task ES EF LS LF A B C D E F G H K
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32. Controversies in the Use of Networks
Networks can be too complex
Poor network construction creates problems
Networks may be used inappropriately
When employing subcontractors
The master network must be available to them
All sub-networks must use common methods
Positive bias exists in PERT networks
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