Analysing the AoA network

1. Analysing the AoA network Project Management

2. Analysing the AoN network Project Management

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

4. 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

5. Critical path • sequence of activities that has no float time (or has the maximum negative float time in absolute value), 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).

6. 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 = LFT – EST – Duration • 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

7. 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 the AoNdiagram • Calculate the TPT, identify the critical path, the total, and the free float times.

8. 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

9. Task list with precedence relations

10. 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

11. 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

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

13. 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.

14. 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

15. 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

16. 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

17. Solution

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

19. 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 a unit of time. • Let’s see the following example:

20. 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.

21. 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

22. 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.

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

24. 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

25. 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

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

27. Reading • Lockyer – Gordon (2005) Chapter 8 pp. 61-63. & Chapter 14

28. Thanks for the attention!