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Analysing the AoA network

Analysing the AoA network. Project Management. Total Project Time. The minimum time in which the project can be completed. Calculation: forward pass Forward pass : calculating the earliest event times (EETs) and the earliest start times (ESTs) of all activities.

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Analysing the AoA network

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  1. Analysing the AoA network Project Management

  2. Total Project Time • The minimum time in which the project can be completed. • Calculation: forward pass Forward pass: calculating the earliest event times (EETs) and the earliest start times (ESTs) of all activities. Earliest Finishing Time = EST + Duration

  3. Critical path • Path: continuous series of project activities connected by logical relationships as designated in the project schedule network diagram. • Critical path: sequence of activities that has no float time, and that determines the duration of the project. It is the longest path. Activities on the critical path are the critical activities. • The critical path can be identified by a backward pass, calculating the Latest Event Times (LETs) and the Latest Finishing Times (LFTs). • Latest Starting Time = Latest Finishing Time - Duration

  4. Activity times & event times • EET = EST of all emerging activities • LET = LFT of all entering activities Deadline EET EET Duration 1 2 Activity identifier LET LET

  5. TPT EST0 EFT14 0 14 14 1 2 a 0 14 LST0 LFT14 TPT = 14

  6. Float • Float on activity ‘a’: 20 EST0 EFT14 0 14 14 1 2 a 6 20 LST6 LFT20 Float: 6

  7. Calculate the… • EET of event 6 • LETs of event 4 and 5 • ESTs and EFTs of activity ‘d’ and ‘e’ • LSTs and LFTs of activity ‘d’ and ‘e’ 22 8 4 d ? ? 6 34 24 10 5 e ?

  8. 22 8 4 d 26 • EST and EFT of ‘d’: 22 and 30 • EST and EFT of ‘e’: 24 and 34 • LST and LFT of ‘d’: 26 and 34 • LST and LFT of ‘e’: 24 and 34 34 6 34 24 10 5 e 24

  9. 10 a 10 ? ? ? 15 20 10 25 30 35 25 ? 12 b 8 c

  10. 10 a 10 18 22 20 15 20 10 25 30 35 25 17 12 b 8 c

  11. Calculate all event and activity times and the float-times, find the critical path

  12. Calculate all event and activity times and the float-times, find the critical path 16 16 24 24 30 31 8 29 20 35 38 0 20 35 38 50 51 36 0 0 20 20 35 39 39 51 51 21 35 30

  13. Activity times and float for the previous diagram

  14. Activity times and float for the previous diagram

  15. Four characteristics of the critical path • It starts at the first node • It is continuous • It ends at the last node • It has no float

  16. Floats in the AoA network

  17. Activity and event times • Activity times: • EST • LST • EFT • LFT • Event times: • EET • LET

  18. Float • Time available for an activity or path in addition to its duration. • It can be positive or negative • It is a property of activities (and available only at given activities) • In case of more succeeding activities, the minimum have to be taken. • Types of float: • Total float • Free float

  19. Total float ? 0 ? ? 3 4 1 2 • The total float possessed by an activity. • Calculation for activity j: Total floatj = LFTj – EFTj • Identify the activity possessing float below, and calculate the total float. ? 35 ? ? 10 12 c a 15 8 b d

  20. Total float • The total float possessed by an activity. • Calculation for activity j: Total floatj = LFTj – EFTj = LFTj – (ESTj + Dj) • Identify the activities possessing float below, and calculate the total float for each. Total float = = 11 – (0+5) = 6 Total float = 23 – (5+12) = 6 5 2 12 5 11 c a 0 23 1 4 15 8 0 23 b 15 d 3 15

  21. Calculating free float • The float possessed by an activity which, if used, will not change the float in later activities. • Free floatj = ESTj+1 – EFTj = EEThead – EETtail - D Free float = = 5 – 0 – 5 = 0 Free float = 23 – 5 – 12 = 6 5 2 12 5 11 c a 0 23 1 4 15 8 0 23 b 15 d 3 15

  22. Negative float 0 ? ? 1 2 3 • If the target time (deadline) for the project (or for a part of the project) is grater than TPT, than the float will appear on the critical path or even on some other paths. • Negative float = the time by which activities on the path or paths concerned must be reduced if the TPT is to be met. • Negative float is a type of the Total Float. ? ? ? 15 10 10 a c

  23. Negative float 0 10 20 1 2 3 • If the target time (deadline) for the project (or for a part of the project) is grater than TPT, than the float will appear on the critical path or even on some other paths. • Negative float = the time by which activities on the path or paths concerned must be reduced if the TPT is to be met. • Negative float is a type of the Total Float. 15 -5 5 15 10 10 a c Total float: -5 Total float: -5

  24. Slack • Refers to events and not to activities. • Slack = LET - EET Slack: 6 Total float = = 11 – (0+5) = 6 Total float = 23 – (5+12) = 6 5 2 12 5 11 c a 0 23 1 4 15 8 0 23 b 15 d 3 Slack: 0 Slack: 0 15 Slack: 0

  25. Readings • Lockyer – Gordon (2005) Chapter 13

  26. Analysing the AoN network Project Management (seminar)

  27. Data on the activity node Activity label & description Total Float EST EFT LST LFT Duration

  28. Total Project Time • The shortest time in which the project can be completed. Determined by the critical path. • Calculation: forward pass Forward pass: The earliest start times (EST) of all activities are calculated. Trom these the earliest finishing times (EFT) are also calculated

  29. Critical path • sequence of activities that has no float time, and that determines the duration of the project. It is the longest path. Activities on the critical path are the critical activities. • The critical path can be identified by a backward pass, calculating the Latest Finishing Times (LFT), and from these the Latest Starting Times (LST).

  30. Floats in AoN • Total float: the time by which an activity can be delayed or extended without affecting the TPT.It can be used to delay the start of an activity or to increase its duration. TF = LST - EST • Free float: the time by which an activity can be delayed or extended without affecting the start of any succeding activity. FF = ESTj+1 - EFTj

  31. Example: organising a conference • Objectives: to organise a 3 days long open scientific conference with 100-200 participants, 30-50 lectures, buffet reception,a conference book of the best studies and TV and radio interviews with some of the most known lecturers. • Create the WBS chart and create the task list with estimated durations and precedence relations (in a table form) • Plot both the AoA and AoNdiagram • Calculate the TPT, identify the critical path the total and the free float times.

  32. Example: WBS Project Book Event management Marketing Editing Publishing Infra-structure Organising participants Arranging event Invitation and marketing Organising interviews Collecting articles Peer reviewing Facilities Staff Materials

  33. Task list with precedence relations

  34. AoA 3 c 4 d 2 1 8 4 3 6 7 9 5 2a 12 10 15 20 10 21 2 9 6 0 4b 1h 10 3e 1j 19 12 19 20 15 19 2 0 6 21 6 5 TPT = 21 f i 3g CP: a-b-f-g-i-j

  35. AoN 1 b a h f i d j c g e 6 6 15 20 6 0 6 10 12 2 10 9 0 6 10 9 6 10 9 0 0 0 15 11 20 12 0 0 21 2 0 0 0 0 9 1 0 0 0 4 3 6 5 1 4 3 2 1 3 2 15 20 16 0 15 19 12 6 16 19 15 12 20 20 19 19 6 2 21 TPT: 21 CP: a-b-f-g-i-j

  36. Activity times for the previous diagram(finalize individually)

  37. Example 2 (for individual practice) a) Draw the AoA and AoN diagram with the data below: b) Determine the TPT and the critical path and activity floats. c) Compute the EETs, LETs and slack for every node in the AoA & ESTs, LSTs, EFTs, LFTs in the AoN diagram.

  38. 3 1 6 2 4 5 7 1 7 0 5 4 3 11 11 7 5 3 0 1 7 Solution: AoA Float: 0 2 b 2 e Float: 0 2 f Float: 0 Slack: 0 Slack: 0 5 c 1 a 4 g T. float: 1 F. float: 1 Float: 0 Float: 0 Slack: 0 Slack: 0 Slack: 0 Slack: 0 3 d 0 T. float: 3 F. float: 3 Slack: 3 TPT: 11 CP: a-b-e-f-g

  39. 0 g 7 0 11 4 7 11 Solution: AoN 0 0 0 b a e f d c 1 1 5 0 3 1 1 3 0 0 0 0 4 1 7 3 6 5 0 1 3 2 2 1 3 5 2 4 3 5 2 1 0 2 7 7 7 3 1 TPT: 11 CP: a-b-e-f-g

  40. Example 3 • Calculate the EETs and LETs. • Create a precedence table (with task, duration, immediate predecessor, total and free floats). 3 2 b 5 3 e 5 1 2 5 7 5 c 0 2 2 a 8 14 1 f 0 2 14 8 4 6 0 4 g 2 12 2 h 3 d 12 5

  41. Solution

  42. ‘Crashing’ – reducing task durations by increased costs

  43. 0 0 1 0 0 c b c d e a b a d e 0 0 4 6 6 8 0 1 0 1 0 6 11 4 10 8 4 2 5 5 2 2 2 2 4 2 4 9 6 0 0 7 11 6 4 9 11 0 f f 11 0 14 3 3 11 14 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:

  44. 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.

  45. 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. Benefit of reducing TPTby one day: 400€/day

  46. 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.

  47. Solution After crashing: • there are two critical paths • TPT is 10 days • total benefit of crashing is €890

  48. g b a c d e f 0 3 5 2 2 3 3 3 0 Example 2 (for individual work) • Identify the critical path and the TPT. 7

  49. 0 0 0 3 0 0 0 e f d g c b a 12 7 5 3 3 0 6 0 3 0 0 0 1 0 15 5 6 9 7 12 3 2 3 5 3 2 3 3 0 9 4 12 3 7 5 7 5 12 3 7 12 15 Example 2 (for individual work) Critcal: a-b-d-e-g TPT: 15 Using tbe table on the next slide, calculate the optimal TPT with crashing. 7

  50. Benefit of reducing TPTby one day: 1200€/day • What is the new TPT? • What is the total profit on crashing? 10 days €3000

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