1. In Chapter 5: Scheduling the Project From Action Plan and WBS to Gantt chart and project network.  Gantt Chart  Project Network  Activity-on-arrow  Activity-on-node  CPM and PERT  Risk analysis involves determining the likelihood that a project can be completed on time  Statistics  Simulation 6/4/2016Ardavan Asef-Vaziri5-1

2. In Chapter 5: Scheduling the Project 6/4/2016Ardavan Asef-Vaziri5-2

3. History Late 1950s  Critical Path Method (CPM)  Dupont De Nemours Inc. developed the method  Deterministic activity durations  Program Evaluation and Review Technique (PERT)  U.S. Navy, Booz-Allen Hamilton, and Lockeheed Aircraft  Probabilistic activity durations 6/4/2016Ardavan Asef-Vaziri5-3

4. The Language of PERT/CPM  Activity  Task or set of tasks  Takes time and needs resources  Precedence Relationships  The immediate predecessor activities  Event  Completion of one or more activities (to allow the next activity or activities to start)  Zero duration, zero resource  Milestones  Significant events – showing completion of a significant portion of the project 6/4/2016Ardavan Asef-Vaziri5-4

5. The Language of PERT/CPM  Network  Diagram of nodes connected by directed arcs  Shows technological relationships among activities  Path  A set of connected activities such that each activity on both sides is connected to one and only one other activity (with exception!).  Critical Path  A path where a delay in any of its activities will delay the project  The longest path on the network  The shortest time to complete the project  Critical Time  The total time to complete all activities on the critical path 6/4/2016Ardavan Asef-Vaziri5-5

6. Two Types of Network Diagrams  Activity-on-Arrow Network (Arrow Diagramming Method)  Easier to show events and milestones  More compatible with network theory techniques  Sometimes requires dummy (artificial) activities  Activity-on-Node Network (Precedence Diagramming Method)  Easier representation  No dummy activity 6/4/2016Ardavan Asef-Vaziri5-6

7. Activity on Arrow Network An Activity is an arc with two nodes at its beginning and its end 6/4/2016Ardavan Asef-Vaziri5-7 a b c d

8. AoA: Activity Predecessors A list of immediate predecessors is needed. 6/4/2016Ardavan Asef-Vaziri5-8 TaskPredecessor abcabc -- a b abc TaskPredecessor abcdabcd --- -- b a a b d c

9. AoA: Activity Predecessors 6/4/2016Ardavan Asef-Vaziri5-9 TaskPredecessor abcdabcd --- a a b d c TaskPredecessor abcdabcd --- -- a,b,c a b d c

10. AoA May Need Dummy Activity  Two activities have the same starting and ending nodes  A single activity connects to two or more nodes 6/4/2016Ardavan Asef-Vaziri5-10 TaskPredecessor abcdabcd --- a b,c a b d c  Try this: a,b  c and a,d  e

11. AoA: A Power Plant Construction Project 6/4/2016Ardavan Asef-Vaziri5-11 TaskDescriptionPredecessor abcdefghijabcdefghij Design & engineering Select site Select vendor Select personnel Prepare site Manufacture generator Prepare operation manual Install generator Train operators Obtain license --- a b c e,f d,g h,i

12. 6/4/2016Ardavan Asef-Vaziri5-12 a b cf d g e h i j AoA: A Power Plant Construction Project a:- b:a c:a d:a e: b f:c g:c h:e,f i: d,g j: h,i

13. 6/4/2016Ardavan Asef-Vaziri5-13 Draw AoN Network a:- b:a c:a d:a e: b f:c g:c h:e,f i: d,g j: h,i

14. Draw AOA 6/4/2016Ardavan Asef-Vaziri5-14

15. Transform into AON 6/4/2016Ardavan Asef-Vaziri5-15 1234567 a = 6 b = 2g = 9 h = 9 k = 6 d = 4 c = 5 e = 3 i = 4 f = 8 j = 7 a:- b:- c:- d:a e: a f:c g:b,e,f h:c i: b,e,f j: h k:d,i

16. Draw AoN Network 6/4/2016Ardavan Asef-Vaziri5-16 a:- b:- c:- d:a e: a f:c g:b,e,f h:c i: b,e,f j: h k:d,i

17. Critical Path and Critical time  The critical path is the shortest time in which a project can be completed  If a critical activity is delayed, the entire project will be delayed.  There may be more than one critical path.  Brute force approach to finding critical path: 1.identify all possible paths from start to finish 2.sum up duration of activities on each path 3.largest total indicates critical path 6/4/2016Ardavan Asef-Vaziri5-17

18. Critical Path Method: The Network A1 A3 A4 A6 A5 A2 4 3 6 4 2 3 E S Find the Critical Path.

19. Critical Path Method: Paths A1A3A4A6A5A2 4 3 6 4 2 3 ES 10 Critical Path is the longest path 118 How many path? It is the shortest time to complete the project

20. Forward Path; Earliest Starts A1 A3 A4 A6 A5 A2 4 3 6 4 2 3 E S 0 0 0 0 0 0 4 3 3 4 4 3 4 410 8 5 5 8 8 11

21. 10 30 20 Max = 30 5 35 Forward Path 35

22. Backward Path; Latest Starts A1 A3 A4 A6 A5 A2 4 3 6 4 2 3 E S 0 0 0 0 0 0 4 3 3 4 4 3 4 410 8 5 5 8 8 11 5 5 8 8 8 8 8 4 6 4 6 6 3 3 40 0

23. 30 Min = 35 5 35 45 30 Backward Path

24. Activity Slack  Slack, or float: The amount of time a noncritical task can be delayed without delaying the project  Slack—LFT – EFT or LST – EST  EST—Earliest Start Time  Largest EFT of all predecessors  EFT—Earliest Finish Time  EST + duration for this task  LFT—Latest Finish Time  Smallest LST of following tasks  LST—Latest Start Time  LFT – duration for this task 6/4/2016Ardavan Asef-Vaziri5-24

25. Computing Slack Times 6/4/2016Ardavan Asef-Vaziri5-25 Task = duration slack = xxxx ESTEFT LSTLFT

26. Critical Path, Slacks A1A3A4A6A5A2 4 3 6 4 2 3 ES 0 0 4 3 3 4 4 10 8 5 8 11 5 8 8 8 4 6 6 3 4 0

27. Slack Times Example Task Pred. Dur. a -- 4 g c,d 1 b -- 3 h e 4 c a 3 i f 5 d a 2 j e,g 6 e b 6 k h,i 1 f b 4 For each task, compute ES, EF, LF, LS, slack 6/4/2016Ardavan Asef-Vaziri5-27

28. Slack Times Example 6/4/2016Ardavan Asef-Vaziri5-28 Start Finish a=4 slack= b=3 slack= c=3 slack= d=2 slack= e=6 slack= f=4 slack= g=1 slack= h=4 slack= i=5 slack= j=6 slack= k=1 slack= Task=dur slack=xxx ESTEFT LFTLST