Activity on Arrow

1. Activity on Arrow Project Management

2. Elements of an AoA (Activity-on-Arrow) diagram • Activity (arrow) • Work element or task • Can be real or not real • Name or identification of the tasks (label) must be added • Event (node) • The start and/or finish of one or more activities • Tail (preceding) and head (succeeding) nodes

3. Conventions • Time flows from left to right • Arrows’ direction • Labels’ order • Head nodes always have a number (or label) higher that of the tail node. This is the same with the arrow labels (alphabetic order). • Activity labels are placed below the arrow (despite the pictures in the textbook), duration of activity is based above the arrow • A network has only one starting and only one ending event. • These conventions are not universal. There are many other to choose from.

4. Graphical representation • Arrows, nodes, bending • Identification of activities • Representation of time • Representation of deadlines (external constraints)

5. b 1 a c Dependency rule b depends on a (b is a successor of a): 1 2 13 12 4 3 2 3 a b b and c are independent from each other: 13 12 8

6. Consequences of the dependency rule • An event cannot be realised until all activities leading to it are complete. • No activity can start until its tail event is realised.

7. Merge and burst nodes • Merge nodes: • Events into which a number of activities enter and one (or several) leave. • Burst nodes: • Events that have one (or more) entering activities generating a number of emerging activities.

8. 5 6 e f g 7 1start 2 4 5end d c a b 3 Two typical errors in logic • Looping: underlying logic must be at fault • Dangling: an activity is undertaken with no result

9. 11 13 aa ac ab 1222 13 ba 24 21 bc bb bd 24 Interfacing • When an event is common to two or more subnetworks it is said to be an ‘interface’ event between those subnetworks and is represented by a pair of concentric circles.

10. 1/1/2014 Milestones • Events which have been identified as being of particular importance in the progress of the project. • Identified by an inverted triangle over the event node (occasionally with an imposed time for the event) 3 1 2 a b

11. Multiple starts and finishes • Only used in computer programs • All starting activities can occur at the start and all finish activities will occur at the end of the project.

12. Hammock activities • Artificial activities created for the representation of the overhead cost with the aim of cost control. • Embrace activities belong to the same cost centre • Zero duration time (not taking part in the time analysis) • Overhead cost rate is assumed to be constant over the life of the hammock.

13. Hammock activity 1 2 3 4 1 2 12 a c b 0 h(hammock)

14. Dummy activities • Activities that do not require resources but may in some cases take time. • They are drawn as broken arrows. • They are always subject to the basic dependency rule. • Thre occassions to use dummies: • Identity dummies • Logic dummies • Transit time dummies

15. 1 3 a b 2 Identity dummies • When two or more parallel activities have the same tail and head nodes. 4 3

16. Logic dummies • When two chains of activities have a common node yet they are at least partly independent of each other. Hint: examine ANY crossroads. • Example: • Activitiy c depends on activity a • Activity d depends on activities a and b • Solution: • separate c from b with a dummy activity

17. 2 6 4 c e g a 1 8 b h 3 5 7 d f Logic dummy example:

18. Logic dummy example:

19. 2 4 2 1 c a 1 5 2 2 b d 3 Transit time dummies • If a delay must occur after the competition of an activity before the successor activity can start. 2

20. 1 2 3 3 7 a1 a2 5 15 b Overlapping activities • If the activities are not fully discrete • The second activity can start before the first is completed but not before it is at least partly completed. 1 2 3 10 15 a b

21. Earliest Event Time Activity Activity Event Label Latest Event Time Tail Head • Network Analysis (Computation) Occurrence times of Events = Early and late timings of event occurrence = Early and late event times Standard layout for recording data

22. Early Event Time (EET = E =TE) Early Event Time (Earliest occurrence time for event) is the earliest time at which an event can occur, considering the duration of precedent activities. Forward Pass for Computing EET Each activity starts as soon as possible, i.e., as soon as all of its predecessor activities are completed. Direction: Left to right, from the beginning to the end of the project Set: EET of the initial node = 0 Add:EETj = EETi + Dij Take the maximum The estimated project duration = EET of the last node. j Activity EETj EETi i Dij

23. 0 3 4 12 10 20 30 40 A B C 1 8 3 • Early Event Times (EET = E =TE)

24. K 4 L 80 9 12 40 M 5 • Early Event Times (TE) 4 15 24 70 50

25. 40 10 30 20 50 60 70 3 2 3 4 4 5 7 3 1 • Early Event Times (TE)

26. 40 10 0 3 30 20 50 60 70 3 2 3 4 4 5 7 3 1 • Early Event Times (TE) 2 8 4 16 9

27. Late Event Time (LET = L =TL) Late Event Time (Latest occurrence time of event) is the latest time at which an event can occur, if the project is to be completed on schedule. Backward Pass for Computing LET Direction: Right to left, from the end to the beginning of the project Set: LET of the last (terminal) node = EET for it Subtract:LETi = LETj - Dij Take the minimum j EETi Activity EETj i LETi LETj Dij

28. 8 13 16 16 • Late Event Times (TL) 50 3 9 9 60 7 40

29. 2 10 4 0 3 20 30 50 60 70 3 2 3 4 4 5 7 3 1 • Late Event Times (TL) 8 16 9 40

30. 2 10 4 40 0 3 20 30 50 60 70 3 2 3 4 4 5 7 3 1 • Late Event Times (TL) 8 10 13 16 16 4 0 9 9 8

31. Network Analysis (Computation) Activity Times (Schedule) Early Start (ES): The earliest time at which an activity can be started. ESij = EETi Early Finish (EF): The earliest time at which an activity can be completed. EFij = ESij + Dij Late Finish (LF): The latest time at which an activity can be completed without delaying project completion. LFij = LETj Late Start (LS): The latest time at which an activity can be started. LSij = LFij Dij

32. 2 10 4 40 0 3 20 30 50 60 70 3 2 3 4 4 5 7 3 1 • Example: Activity Times 8 10 13 16 16 4 0 9 9 ES20-50 = EET20 = 2 EF20-50 = ES + D = 2 + 3 = 5 LF20-50 = LET50 = 13 LS20-50 = LF – D = 13 – 3 = 10 8

33. Network Analysis (Computation) Activity Floats • Total Float (TF) • Total float or path float is the amount of time that an activity’s completion may be delayed without extending project completion time. • Total float or path float is the amount of time that an activity’s completion may be delayed without affecting the earliest start of any activity on the network critical path.

34. Network Analysis (Computation) Activity Floats • Total Float (TF) • Total path float time for activity (i-j) is the total float associated with a path. • For arbitrary activity (ij), the total float can be written as: • Path Float =Total Float (TFij) • = LSij ESij • = LFij  EFij • = LETj – EETi  Dij

35. 40 2 10 4 0 3 20 30 50 60 70 3 3 2 4 4 5 7 3 1 • Example: Total Float Times 8 10 13 16 16 4 0 9 TF20-50 = LS20-50 - ES20-50 TF20-50 = 10 – 2 = 8 TF20-50 = LF20-50 - EF20-50 TF20-50 = 13 – 5 = 8 TF20-50 = LET50 – EET20 - D20-50 TF20-50 = 13 – 2 - 3 = 8 9 8

36. Network Analysis (Computation) Activity Floats • Free Float (FF) • Free float or activity float is the amount of time that an activity’s completion time may be delayed without affecting the earliest start of succeeding activity. • Activity float is “owned” by an individual activity, whereas path or total float is shared by all activities along a slack path. • Total float equals or exceeds free float (TF ≥ FF). • For arbitrary activity (ij), the free float can be written as: • Activity Float = Free Float (FFij) • = ESjk EFij • =EETj – EETi  Dij

37. 2 10 4 40 0 3 20 30 50 60 70 3 3 2 4 4 5 7 3 1 • Example: Free Float Times 8 10 13 16 16 4 0 9 9 FF20-50 = ES50-70 - EF20-50 FF20-50 = 8 – 5 = 3 FF20-50 = EET50 – EET20 - D20-50 FF20-50 = 8 – 2 - 3 = 3 8

38. Network Analysis (Computation) Activity Floats • Interfering Float (ITF) • Interfering float is the difference between TF and FF. • If ITF of an activity is used, the start of some succeeding activities will be delayed beyond its ES. • In other words, if the activity uses its ITF, it “interferes” by this amount with the early times for the down path activity. • For arbitrary activity (ij), the Interfering float can be written as: • Interfering Float (ITFij) • = TFijFFij • = LETj EETj

39. 2 10 4 40 0 3 20 30 50 60 70 3 3 2 4 4 5 7 3 1 • Example: Interfering Float Times 8 10 13 16 16 4 0 9 9 ITF20-50 = TF20-50 - FF20-50 IFF20-50 = 8 – 3 = 5 ITF20-50 = LET50 – EET50 ITF20-50 = 13 – 8 = 5 8

40. Network Analysis (Computation) Activity Floats • Independent Float (IDF) • It is the amount of float which an activity will always possess no matter how early or late it or its predecessors and successors are. • The activity has this float “independent” of any slippage of predecessors and any allowable start time of successors. Assuming all predecessors end as late as possible and successors start as early as possible. • IDF is “owned” by one activity. • In all cases, independent float is always less than or equal to free float (IDF ≤ FF).

41. Network Analysis (Computation) Activity Floats • Independent Float (IDF) • For arbitrary activity (ij), the Independent Float can be written as: • Independent Float (IDFij) • = Max (0, EETj LETi – Dij) • = Max (0, Min (ESjk) - Max (LFli)  Dij)

42. 40 2 10 4 0 3 20 30 50 60 70 3 3 2 4 4 5 7 3 1 • Example: Independent Float Times 8 10 13 16 16 4 0 9 9 8 IDF20-50 = Max. (0, [EET50 – LET20 - D20-50]) IDF20-50 = Max. (0, [8 – 10 – 3]) = 0

43. Network Analysis (Computation) Critical Path • Critical path is the path with the least total float = The longest path through the network. Subcritical Paths • Subcritical paths have varying degree of path float and hence depart from criticality by varying amounts. • Subcritical paths can be found in the following way: • Sort the activities in the network by their path float, placing those activities with a common path float in the same group. • Order the activities within a group by early start time. • Order the groups according to the magnitude of their path float, small values first.

44. Example Draw an arrow diagram to represent the following project. Calculate occurrence times of events, activity times, and activity floats. Also determine the critical path and the degree of criticality of other float paths.

45. Example Activity on arrow network and occurrence times of events 30 12 70 28 15 30 E B [6] H [7] [4] 20 50 60 80 0 A 5 C 21 G 24 I 30 10 0 5 [4] 21 24 30 [5] [3] 6 D F [8] [8] 40 13 13

46. Example Activity times and activity floats

47. Example Critical path and subcritical paths

48. Case Study Installation of a new machine and training the operator

49. 30 1 30 1 • Case Study: Installation of a New Machine and Training the Operator 33 50 33 Hire the operator Train the operator 3 25 Install the m. Inspect the m. Hire labor to install the new machine 31 33 36 0 10 30 40 60 0 20 31 33 36 2 Inspect the machine after delivery Order & deliver the machine 20 30

50. Case Study: Installation of a New Machine and Training the Operator • Activity times and activity floats • Critical path: 10-20, 20-30, 30-40, 50-60. • Near critical path: 40-60 • Third most critical path: 10-50 • Path having most float: 10-30