1. Project Management: Tools & Techniques

2. Generally….
as project we may refer to a set of interdependent activities that have certain characteristics like :
Start – end dates
Well- defined goals
Production of certain results
They are no repetitive
They consume money, time and resources

3. From planning to scheduling
Define when each activity will be executed.
Produce a map for project’s Execution and Monitoring
Activities that can be executed at the same time period
Finish to Start relationships
Activities that need priority such that they don’t cause delay to the project duration
Are there activities that may delay without cause delay to the project duration?

4. Our input From WBS: Precedence relationships List of activities
Estimation for their duration
Precedence relationships
Finish-to-start: Activity B can’t start before the completion of activity A.
Start-to-start: Activity B can’t start before activity A starts.
Finish-to-finish: Activity B can’t be completed before the completion of activity A.
Start-to-finish: Activity B can’t be completed before activity A starts.

5. Representing activities and relationships-1
Use nodes and arcs
Depending the way we decide to represent the activities there are to types of networks:
Activity-on-the-Node (AoN)
Activity-on-the-Arc (AoA)
In each case the result is an oriented graph that consists of nodes and arcs.

6. Representing activities and relationships-2
Activity Activity 2
Activity (1,2) Activity (2,3)
Event Event Event 3
AON 1 2
AOA 1 2 3

7. Example
Activity
Predecessor A -  B C D E
B,C F
D,E

8. Time lag

9. Relationships

10. AoN (activities on nodes)
END
START D B
Assume a project consists of 4 activities: A, B, C and D.
Let A and B are starting activities.
Activity C can’t start before the completion of A and B,
Activity D can’t start before the completion of activity B.

11. AoA (activities on arks)3 C A 4 1 B 2 D

12. Critical Path Method - CPM
Assumption: Constant duration for all activities
Questions to be answered
Which is the minimum duration for the project completion?
Which activities may delay without effect to the minimum project duration?
What about the earliest start time of each activity?
What about the latest finish time of each activity?

13. Critical Path Method - CPM
What about the minimum project duration?
Let’s calculate the possible paths!!
START-A-B-END 7+3=10 days
START-C-END 11 days A 7 B 3
START
END C 11

14. Critical Path Method - CPM
Which of the activities may delay? A 7 B 3
START
END C 11

15. Critical Path Method - CPM
What about the earliest start time (ESj) of activity j?
ESA=0
ESB=7
ESSTART=0 A 7 B 3
ESEND=11
START
END C 11
ESC=0

16. Critical Path Method - CPM
What about the latest finish time (LFj) of activity j?
LFA=8
LFB=11
LFSTART=0 A 7 B 3
LFEND=11
START
END C 11
LFC=11

17. Critical Path Method - CPM
ESB=7
EFB=10
LSB=8
LFB=11
ESA=0
EFA=7
LSA=1
LFA=8
ESEND=11
EFEND=11
LSEND=11
LFEND=11
ESSTART=0
EFSTART=0
LSSTART=0
LFSTART=0 A 7 B 3
START
END
ESC=0
EFC=11
LSC=0
LFC=11 C 11

18. Critical Path Method - CPM
AN EXAMPLE A 14 D 12 F 9
END
START B 9 E 6 C 20

19. ACTIV
DURATION dj
PRED PJ
SUC SJ
ESJ
EFJ
LSJ
LFj
START -
A,B,C A 14 D B 9 C 20 E 12
A,B F 6
C,D
END
E,F

20. Critical Path Method - CPM
AN EXAMPLE A 14 D 12 F 9
END
START B 9 E 6 C 20

21. Expected duration (weeks)
Path
Tasks
Expected duration (weeks) 1
START-A-D-F-END
=35 2
START-A-D-E-END
=32 3
START-B-D-F-END
9+12+9=30 4
START-B-D-E-END
9+12+6=27 5
START-C-E-END
20+6=26

22. Critical Path Method - CPM
AN EXAMPLE A 14 D 12 F 9
END
START B 9 E 6 C 20

23. ΔΡΑΣΤ
ΔΙΑΡΚΕΙΑ dj
ΠΡΟΑΠ PJ
ESJ
EFJ
LSJ
LFj
START - A 14 B 9 5 C 20 29 D 12
A,B 26 E 6
C,D 32 35 F
END
E,F

24. CPM – EARLIEST AND LATEST TIME
Let Pi the set of immediate predecessors of activity i and Si the set of immediate successors.
ESi = max {ESj + dj for any activity j Є Pi}
ESi = 0 if i is a starting activity
EFi = ESi + di
LFi = min {LFj – dj for any activity j Є Si}

25. CPM – SLACK (FLOAT) Total Slack of activity i
TS(i)=LFi – ESi -di= LFi – (EFi +di)= LFi – EFi
Let’s define as ESimin = min{ESj, for any j Є Si}
Free Slack of activity I
FS(i)=(ESimin – ESi)-di=ESimin – (ESi+di)=ESimin-EFi

26. ACTIV
DURATION dj
ESJ
LFj
TS(i)
FS(i)
START A 14 B 9 5 C 20 29 6 D 12 26 E 35 3 F
END

27. The project TARGET: To change the carpet in the office
Available time: Saturday and Sunday 06:00 – 18:00 (1 hour lunch break)
Constraint : The market is closed on Sunday

28. Activities To empty office from furniture
To prepare a room for storing the furniture
New carpet selection
Moving old carpet
Counting office surface
Ordering new carpet
Waiting for the new carpet delivery
Preparing the floor
Laying the new carpet
Glue drying
Putting the furniture back

29. Time estimates A To empty office from furniture (3h)
B To prepare a room for storing the furniture (4h)
C New carpet selection (2h)
D Moving old carpet (2h)
E Counting office surface (0,5h)
F Ordering new carpet (0,5h)
G Waiting for the new carpet delivery (5h)
H Preparing the floor (2h)
I Laying the new carpet (3h)
J Glue drying (6h)
K Put the furniture back (3h)

30. Relationships Initial activities B, C, E B before A, A before D,
D before H,
C κand E before F,
F before G,
G and H before I,
I before J,
J before K

31. AON ES
DURATION EF
Activity ID LS
TOTAL FLOAT LF

32. AON 1 (FW) B A D H C I J K E F G ID 4 3 2 2 2 3 6 3 0,5 0,5 5 ES D EFLS TF LF

33. AON 2 (FW) B A D H C I J K E F G ID 4 3 2 2 2 3 6 3 0,5 0,5 5 ES D EF4 B 3 A 2 D 2 H 2 C 3 I 6 J 3 K
0,5 E
0,5 F 5 G ES D EF ID LS TF LF

34. AON 3 (FW) B A D H C I J K E F G ID 4 3 2 2 2 3 6 3 0,5 0,5 5 ES D EF4 B 3 A 2 D 2 H 2 C 3 I 6 J 3 K
0,5 E
0,5 F 5 G ES D EF ID LS TF LF

35. AON 4 (FW) B A D H C I J K E F G ID 4 4 3 2 2 2 3 6 3 0,5 2 0,5 5 ES D4 B 4 3 A 2 D 2 H 2 C 3 I 6 J 3 K
0,5 E 2
0,5 F 5 G ES D EF ID LS TF LF

36. AON 5 (FW) B A D H C I J K E F G ID 4 4 3 7 2 2 2 3 6 3 0,5 2 0,5 2,54 B 4 3 7 A 2 D 2 H 2 C 3 I 6 J 3 K
0,5 E 2
0,5
2,5 F 5 G ES D EF ID LS TF LF

37. AON 6 (FW) B A D H C I J K E F G ID 4 4 3 7 7 2 2 2 3 6 3 0,5 2 0,54 B 4 3 7 A 7 2 D 2 H 2 C 3 I 6 J 3 K
0,5 E 2
0,5
2,5 F
2,5 5 G ES D EF ID LS TF LF

38. AON 7 (FW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 2 2 3 6 3 0,5 2 0,54 B 4 3 7 A 7 2 9 D 2 H 2 C 3 I 6 J 3 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

39. AON 8 (FW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 2 3 6 3 0,5 24 B 4 3 7 A 7 2 9 D 9 2 H 2 C 3 I 6 J 3 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

40. AON 9 (FW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 3 6 3 0,5 24 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 3 I 6 J 3 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

41. AON 10 (FW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 6 34 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 I 6 J 3 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

42. AON 11 (FW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 64 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 6 J 3 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

43. AON 12 (FW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 J 3 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

44. AON 13 (FW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 3 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

45. AON 14 (FW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

46. AON 15 (FW – minimum project duration)4 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

47. AON 16 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

48. AON 17 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

49. AON 18 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

50. AON 19 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

51. AON 20 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

52. AON 21 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G ES D EF ID LS TF LF

53. AON 22 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G 11 ES D EF ID LS TF LF

54. AON 23 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F
2,5 5
7,5 G 6 11 ES D EF ID LS TF LF

55. AON 24 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F 6
2,5 5
7,5 G 6 11 ES D EF ID LS TF LF

56. AON 25 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 11 3 14 144 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 2
0,5
2,5 F
5,5 6
2,5 5
7,5 G 6 11 ES D EF ID LS TF LF

57. AON 26 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 5,5 11 34 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C
5,5 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E
5,5 2
0,5
2,5 F
5,5 6
2,5 5
7,5 G 6 11 ES D EF ID LS TF LF

58. AON 27 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 3,5 5,5 114 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C
3,5
5,5 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 5
5,5 2
0,5
2,5 F
5,5 6
2,5 5
7,5 G 6 11 ES D EF ID LS TF LF

59. AON 28 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 3,5 5,5 114 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C
3,5
5,5 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 5
5,5 2
0,5
2,5 F
5,5 6
2,5 5
7,5 G 6 11 ES D EF ID LS TF LF

60. AON 29 (BW) B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 3,5 5,5 114 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C
3,5
5,5 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 5
5,5 2
0,5
2,5 F
5,5 6
2,5 5
7,5 G 6 11 ES D EF ID LS TF LF

61. SCHEDULE B A D H C I J K E F G ID 4 4 3 7 7 2 9 9 2 11 2 3,5 5,5 11 34 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C
3,5
5,5 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 5
5,5 2
0,5
2,5 F
5,5
3,5 6
2,5 5
7,5 G 6
3,5 11 ES D EF ID LS TF LF

62. CPM 1 B-A-D-H-I-J-K C-F-G-I-J-K E-F-G-I-J-K B A D H C I J K E F G ID 44 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C
3,5
5,5 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 5
5,5 2
0,5
2,5 F
5,5
3,5 6
2,5 5
7,5 G 6
3,5 11 ES D EF ID LS TF LF

63. CPM 2 B-A-D-H-I-J-K 4+3+2+2+3+6+3=23 C-F-G-I-J-K 2+0,5+5+3+6+3=19,5
E-F-G-I-J-K 0,5+0, =18 4 B 4 3 7 A 7 2 9 D 9 2 11 H 2 C
3,5
5,5 11 3 14 I 14 6 20 J 20 3 23 K
0,5 E 5
5,5 2
0,5
2,5 F
5,5
3,5 6
2,5 5
7,5 G 6
3,5 11 ES D EF ID LS TF LF