1. Project Planning, Scheduling and Control Planning: –defines objectives, tasks and preceeding relationships; estimates time and resources Scheduling: –identifies critical tasks which, if delayed, will delay the project’s completion time. Control: - monitoring and revising progress of a project Define activities Identifying precedence relationships (Sequencing activities) Determining activity times & costs Develop schedule Determining critical activities Estimating material & worker requirements Monitor and control project

2. Techniques –Gantt chart –CPM –PERT –Microsoft Project Graphically displays project activities Estimates how long the project will take Indicates most critical activities Show where delays will not affect project Consider precedence relationships Each uses a different activity times PERT and CPM

3. Critical Path Scheduling CPM (Critical Path Method) –Developed by DuPont for chemical plants (1956) to schedule preventative maintenance shutdowns. –Identifies longest time-consuming path required to complete a project (i.e. shortest time in which project can be completed). –Deterministic task times PERT (Program Evaluation and Review Technique) –Found by U.S. Navy for planning Polaris missile project. –Multiple task time estimates –Estimate probability that project will be completed by a given deadline

4. CP Definitions Earliest Start Time (ES) is earliest time a task can start Earliest Finish Time (EF) is earliest time a task can end. EF = (ES + duration of activity) Latest Finish Time (LF) is latest time a task can end, without delaying project. Latest Start Time (LS) is latest time a task can start, without delaying project. LS = (LF – duration of activity)

5. CPM : Forward Pass * Finds the ES and EF times * Goes through jobs in order * Start each job at the earliest time while satisfying the precedence constraints EF i = ES i + t i * ES for an activity leaving a node is equal to the largest of the EF for all activities entering that node

6. Backward Pass Fix the finishing time Look at tasks in reverse order Start the task at its LS time LS i = LF i - t i * LF time for an activity entering a particular node is equal to the smallest of the LS times for all activities leaving the node.

7. Critical Path Minimum length of project is the length of longest path Longest path is called the critical path Look for tasks whose earliest start time and latest start time are the same. ES=LS (equally, EF=LF) These tasks are critical, and are on a critical path. No flexibility in tasks on the critical path Total Slack is the difference between LS and ES, or LF and EF. An activity with a slack of zero is on the critical path

8. example for CPM ActivityPredecessorsDuration(days) A-6 B-9 CA, B8 D 7 ED10 FC, E12 AOA 1 65 42 3 A,6A,6 B,9B,9 Dummy C,8C,8 D,7D,7 E,10 F,12 Node 1 = starting node Node 6 = finish node

9. 9 Forward Pass (ES,EF) 16 26 9 16 26 38F,12 0 9 B,9B,9 9 17 0 6 Dummy A,6A,6 E,10 1 65 42 3 C,8C,8 D,7D,7

10. 9 Backward Pass (LS,LF) 16 26 9 16 26 38 F,12 0 9 B,9B,9 18 26 3 9 Dummy A,6A,6 E,10 1 65 42 3 C,8C,8 D,7D,7

11. ActivityES(i)LS(i) A03 B00 C918 D99 E16 F26 Total Slacks are computed as Activity A: 3 Activity B: 0 Activity C: 9 Activity D: 0 Activity E: 0 Activity F: 0 Critical path Activity with a slack of zero is a critical activity Path from node 1 to the finish node that consists entirely of critical activities is called a critical path. B-D-E-F is a critical path. The Makespan is equal to 38

12. Slacks (Floats) Free Float (FF) = Amount the termination of an activity can be delayed before delaying a successor. FFi = (ESi+1) min - ESi – Di Total Float (TF) = Amount of slack an activity has before it would cause the path on which it lies to become critical. TFi = LFi - EFi

14. CPM Network for Computer Design Project

16. 3.0 Sys. design 1.0 300 Pwr supply 3.0 43 1.0 Int & test 5.0 870 1.5 Finalize 6.0 9.580 1.5 Prototype 7.0 119.50 3.0 Packaging 4.0 631.0 4.0 Main board 2.0 730 11.0 Proj mgmt 8.0 1100 Start End Task no. Elapsed time End week Slack time Start week Network Diagram (Activity on Node)

17. How much time do you need to prepare and consume the meal? Menu consists of soup and baked chicken Soup must be boiled 35 minutes and will allow 15 minutes to serve and consume Chicken dish requires 30 minutes to boil rice, 15 minutes to brown chicken in frying pan, 15 minutes to bake rice and chicken in baking dish Sauce takes 5 minutes to prepare in frying pan and 15 minutes to boil peas Only have two pots and one frying pan Wine takes 5 minutes to uncork and 30 minutes to let breath before serving Allow 25 minutes to serve and consume entrée and wine

18. Meal Planning Exercise : WBS Boil Soup (Pot 1) Boil Rice (Pot 2) Brown Chicken (Fry Pan) Open WineWine Breathes Eat Entree Bake Entree Prepare Sauce (Fry Pan) Boil Peas (Pot 2) Eat Soup (Pot 1) Activity Name (Resource)

19. Meal Planning Exercise Critical Path Method - Forward Pass 015 Brown Chicken 15 05 Open Wine 5 030 Boil Rice 30 035 Boil Soup 35 50 Eat Soup 15 3045 Boil Peas 15 20 Prepare Sauce 5 535 Wine Breathes 30 45 Bake Entree 15 5075 Eat Entree 25 ESEF Activity Name duration

20. Meal Planning Exercise ( Backward Pass) Critical Path 015 30 Brown Chicken 15 05 20 Open Wine 5 15 030 35 Boil Rice 30 15 035 Boil Soup 35 0 50 Eat Soup 15 35 3045 50 Boil Peas 15 35 1520 35 Prepare Sauce 5 30 535 50 Wine Breathes 30 20 3045 50 Bake Entree 15 35 5075 Eat Entree 25 50 ESEF LF Activity Name duration LS FF = 50 - 30 - 15 = 5

21. Complete Network AON

22. Complete Network AON

23. Activity-on-Node Network

24. Activity-on-Node Network Forward Pass

25. Activity-on-Node Network Backward Pass

26. Activity-on-Arrow Network

27. Activity-on-Arrow Network Forward Pass

28. Activity-on-Arrow Network Backward Pass

29. AOA Network Backward Pass, Forward Pass, and Slack

30. Project Network For A House 124 6 7 3 5 3 2 0 1 3 1 1 1 Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house All Possible Paths A: 1-2-3-4-6-7 => 3 + 2 + 0 + 3 + 1 = 9 months; critical path B: 1-2-3-4-5-6-7 => 3 + 2 + 0 + 1 + 1 + 1 = 8 months C: 1-2-4-6-7 => 3 + 1 + 3 + 1 = 8 months D: 1-2-4-5-6-7 => 3 + 1 + 1 + 1 + 1 = 7 months

31. Early Times (Housebuilding example) ES 12 = 0 EF 12 = ES 12 + t 12 = 0 + 3 = 3 months ES 23 = max (EF 2 ) = 3 months ES 46 = max (EF 4 ) = max (5,4) = 5 months EF 46 = ES 46 + t 46 = 5 + 3 = 8 months EF 67 =9 months, the project duration

32. Computing Late Times LF 67 = 9 months LS 67 = LF 67 - t 67 = 9 - 1 = 8 months LF 56 = minimum (LS 6 ) = 8 months LS 56 = LF 56 - t 56 = 8 - 1 = 7 months LF 24 = minimum (LS 4 ) = min(5, 6) = 5 months LS 24 = LF 24 - t 24 = 5 - 1 = 4 months 124 6 7 3 5 3 2 0 1 3 1 1 1 ES=0, EF=3 LS=0, LF=3 ES=3, EF=5 LS=3, LF=5 ES=5, EF=5 LS=5, LF=5 ES=5, EF=8 LS=5, LF=8 ES=6, EF=7 LS=7, LF=8 ES=8, EF=9 LS=8, LF=9 ES=3, EF=4 LS=4, LF=5 ES=5, EF=6 LS=6, LF=7

33. Activity Slack Activities on critical path have ES = LS & EF = LF Activities not on critical path have slack S ij = LS ij - ES ij S ij = LF ij – EF ij S 24 = LS 24 - ES 24 = 4 - 3 = 1 month ActivityLSESLFEFSlack (S) 1-2*00330 2-333550 2-443541 3-4*55550 4-565761 4-6*55880 5-676871 6-7*88990* Critical path

34. AON Network for House Building Project 1 3 2 2 4 3 3 1 5 1 6 1 7 1Start Design house and obtain financing Order and receive materials Select paint Select carpet Lay foundations Build house Finish work

35. 1 3 2 2 4 3 3 1 5 1 6 1 7 1Start Critical Path A:1-2-4-7 => 3 + 2 + 3 + 1 = 9 months B:1-2-5-6-7 => 3 + 2 + 1 + 1 + 1 = 8 months C:1-3-4-7 => 3 + 1 + 3 + 1 = 8 months D:1-3-5-6-7 => 3 + 1 + 1 + 1 + 1 = 7 months

36. Activity Start Times 1 3 2 2 4 3 3 1 5 1 6 1 7 1 Start Start at 3 months Start at 6 months Start at 5 months Finish at 9 months Finish

37. Mode Configuration 103 303 Activity number Activity duration Earliest start Latest start Earliest finish Latest finish

38. Earliest Activity Start and Finish Times 103 1 235 2 334 1 556 1 458 3 667 1 789 1 Start Design house and obtain financing Select pain Lay foundations Select carpet Build house Finish work Order and receive materials

39. Latest Activity Start and Finish Times 103 103 235 235 334 145 556 167 458 358 667 178 789 189 Start Design house and obtain financing Select pain Lay foundations Select carpet Build house Finish work Order and receive materials

40. * Critical Path 0099998888*7*7 117788667766 116677556655 0088885555*4*4 114455334433 0055553333*2*2 0033330000*1*1 Slack S EF LF ES LS Activity Activity Slack

41. Project Control Gantt Chart Graphical technique (bar chart) that shows the amount of time required for each activity. Developed by Henry Gantt in 1914 Provides visual display of project schedule Graph with bar for representing time for each task Also shows slack for activities

42. Gantt Chart for building a house |||||||||| Activity Design house and obtain financing Lay foundation Order and receive materials Build house Select paint Select carpet Finish work 0246810 Month Month 13579135791357913579 slack

43. Pour foundation & frame Buy shrubs etc. 14 2 3 3 wk. 4 wk. 2 wk. 6 wk. Do interior work Landscape Roof Critical path is longest path: 12 weeks. Critical Path in Network

44. 1-2 Fdn & frame 1-3 Buy shrubs 2-3 Roof 2-4 Interior work 3-4 Landscape 4 4 5 5 6 6 7 7 8 8 9 9 1 1 0 0 1 1 1 1 1 1 2 2 3 3 2 2 1 1 Activity Build House Project Gantt Chart :Earliest Start and Finish

45. 1-2 Fdn & frame 1-3 Buy shrubs 2-3 Roof 2-4 Interior work 3-4 Landscape 456789 1 0 1 1 1 2 3 2 21 Activity Build House Project Gantt Chart : Latest Start and Finish