1. Project Management Dr. Ron Lembke Operations Management

2. What’s a Project? Changing something from the way it is to the desired state Never done one exactly like this Many related activities Focus on the outcome Regular teamwork focuses on the work process

3. Examples of Projects Building construction New product introduction Software implementation Training seminar Research project

4. Why are projects hard? Resources- –People, materials Planning –What needs to be done? –How long will it take? –What sequence? –Keeping track of who is supposedly doing what, and getting them to do it

5. IT Projects Half finish late and over budget Nearly a third are abandoned before completion –The Standish Group, in Infoworld Get & keep users involved & informed Watch for scope creep / feature creep

6. Project Scheduling Establishing objectives Determining available resources Sequencing activities Identifying precedence relationships Determining activity times & costs Estimating material & worker requirements Determining critical activities

7. Work Breakdown Structure –Fig 17.2 Hierarchy of what needs to be done, in what order For me, the hardest part –I’ve never done this before. How do I know what I’ll do when and how long it’ll take? –I think in phases –The farther ahead in time, the less detailed –Figure out the tricky issues, the rest is details –A lot will happen between now and then –It works not badly with no deadline

8. Mudroom

9. Mudroom Remodel Big-picture sequence easy: –Demolition –Framing –Plumbing –Electrical –Drywall, tape & texture –Slate flooring –Cabinets, lights, paint Hard: can a sink fit? D W DW Before: After:

10. Project Scheduling Techniques Gantt chart Critical Path Method (CPM) Program Evaluation & Review Technique (PERT)

11. Gantt Chart

14. PERT & CPM Network techniques Developed in 1950’s CPM by DuPont for chemical plants PERT by U.S. Navy for Polaris missile Consider precedence relationships & interdependencies Each uses a different estimate of activity times

15. Completion date? On schedule? Within budget? Probability of completing by...? Critical activities? Enough resources available? How can the project be finished early at the least cost? Questions Answered by PERT & CPM

16. PERT & CPM Steps Identify activities Determine sequence Create network Determine activity times Find critical path Earliest & latest start times Earliest & latest finish times Slack

17. Activity on Node (AoN) 2 4? Years Enroll Receive diploma Project: Obtain a college degree (B.S.) 1 month Attend class, study etc. 1 1 day 3

18. Activity on Arc (AoA) 4,5 ? Years Enroll Receive diploma Project: Obtain a college degree (B.S.) 1 month Attend class, study, etc. 1 1 day 234

19. AoA Nodes have meaning Graduating Senior Applicant Project: Obtain a college degree (B.S.) 1 Alum 234 Student

20. Network Example You’re a project manager for Bechtel. Construct the network. ActivityPredecessors A-- BA CA DB EB FC GD HE, F

21. Network Example - AON ACEFBDGHZ

22. Network Example - AOA 2 4 5136879 A C F E B D H G

23. AOA Diagrams 231 A C B D A precedes B and C, B and C precede D 241 A C B D 354 Add a phantom arc for clarity.

24. Critical Path Analysis Provides activity information Earliest (ES) & latest (LS) start Earliest (EF) & latest (LF) finish Slack (S): Allowable delay Identifies critical path Longest path in network Shortest time project can be completed Any delay on activities delays project Activities have 0 slack

25. Critical Path Analysis Example

26. Network Solution A A E E D D B B C C F F G G 1 6 2 3 1 43

27. Earliest Start & Finish Steps Begin at starting event & work forward ES = 0 for starting activities ES is earliest start EF = ES + Activity time EF is earliest finish ES = Maximum EF of all predecessors for non-starting activities

28. Activity A Earliest Start Solution For starting activities, ES = 0. A A E E D D B B C C F F G G 1 6 2 3 1 43

29. Earliest Start Solution A A E E D D B B C C F F G G 1 6 2 3 1 43

30. Latest Start & Finish Steps Begin at ending event & work backward LF = Maximum EF for ending activities LF is latest finish; EF is earliest finish LS = LF - Activity time LS is latest start LF = Minimum LS of all successors for non-ending activities

31. Earliest Start Solution A A E E D D B B C C F F G G 1 6 2 3 1 4 3

32. Latest Finish Solution A A E E D D B B C C F F G G 1 6 2 3 1 43

33. Compute Slack

34. Critical Path A A E E D D B B C C F F G G 1 6 2 3 1 43

35. New notation Compute ES, EF for each activity, Left to Right Compute, LF, LS, Right to Left C 7 LSLF ESEF

36. Example #2 A 21 E 5 D 2 B 4 C 7 F 7 G 2 21282835 3537 2833 25272125 021

37. Example #2 A 21 E 5 D 2 B 4 C 7 F 7 G 2 21282835 3537 2833 25272125 021 F cannot start until C and D are done. G cannot start until both E and F are done.

38. Example #2 A 21 E 5 D 2 B 4 C 7 F 7 G 2 2226 021 26283035 3537 21282835 21282835 3537 2833 25272125 021 E just has to be done in time for G to start at 35, so it has slack. D has to be done in time for F to go at 28, so it has no slack.

39. Example #2 A 21 E 5 D 2 B 4 C 7 F 7 G 2 2226 021 26283035 3537 21282835 21282835 3537 2833 25272125 021 E just has to be done in time for G to start at 35, so it has slack. D has to be done in time for F to go at 28, so it has no slack.

40. Gantt Chart - ES 051015 20 25 30 35 40 A B C D E F G

41. Solved Problem 1 A 1 B 4 C 3 D 7 E 6 F 2 H 9 I 4 G 7

42. Solved Problem 1 A 1 0101 0101 B 4 1515 1515 C 3 6969 1414 D 7 2929 1818 E 6 511 F 2 911 810 H 9 918 817 I 4 1822 G 7 1118

43. Can We Go Faster?

44. Time-Cost Models 1. Identify the critical path 2. Find cost per day to expedite each node on critical path. 3. For cheapest node to expedite, reduce it as much as possible, or until critical path changes. 4. Repeat 1-3 until no feasible savings exist.

45. Time-Cost Example ABC is critical path=30 Crash costCrash per weekwks avail A5002 B8003 C5,0002 D1,1002 C 10 B 10 A 10 D 8 Cheapest way to gain 1 Week is to cut A

46. Time-Cost Example ABC is critical path=29 Crash costCrash per weekwks avail A5001 B8003 C5,0002 D1,1002 C 10 B 10 A 9 D 8 Cheapest way to gain 1 wk Still is to cut A Wks IncrementalTotal GainedCrash $Crash $ 1500500

47. Time-Cost Example ABC is critical path=28 Crash costCrash per weekwks avail A5000 B8003 C5,0002 D1,1002 C 10 B 10 A 8 D 8 Cheapest way to gain 1 wk is to cut B Wks IncrementalTotal GainedCrash $Crash $ 1500500 25001,000

48. Time-Cost Example ABC is critical path=27 Crash costCrash per weekwks avail A5000 B8002 C5,0002 D1,1002 C 10 B 9 A 8 D 8 Cheapest way to gain 1 wk Still is to cut B Wks IncrementalTotal GainedCrash $Crash $ 1500500 25001,000 38001,800

49. Time-Cost Example Critical paths=26 ADC & ABC Crash costCrash per weekwks avail A5000 B8001 C5,0002 D1,1002 C 10 B 8 A 8 D 8 To gain 1 wk, cut B and D, Or cut C Cut B&D = $1,900 Cut C = $5,000 So cut B&D Wks IncrementalTotal GainedCrash $Crash $ 1500500 25001,000 38001,800 48002,600

50. Time-Cost Example Critical paths=25 ADC & ABC Crash costCrash per weekwks avail A5000 B8000 C5,0002 D1,1001 C 10 B 7 A 8 D 7 Can’t cut B any more. Only way is to cut C Wks IncrementalTotal GainedCrash $Crash $ 1500500 25001,000 38001,800 48002,600 51,9004,500

51. Time-Cost Example Critical paths=24 ADC & ABC Crash costCrash per weekwks avail A5000 B8000 C5,0001 D1,1001 C 9 B 7 A 8 D 7 Only way is to cut C Wks IncrementalTotal GainedCrash $Crash $ 1500500 25001,000 38001,800 48002,600 51,9004,500 65,0009,500

52. Time-Cost Example Critical paths=23 ADC & ABC Crash costCrash per weekwks avail A5000 B8000 C5,0000 D1,1001 C 8 B 7 A 8 D 7 No remaining possibilities to reduce project length Wks IncrementalTotal GainedCrash $Crash $ 1500500 25001,000 38001,800 48002,600 51,9004,500 65,0009,500 75,00014,500

53. Time-Cost Example C 8 B 7 A 8 D 7 No remaining possibilities to reduce project length Wks IncrementalTotal GainedCrash $Crash $ 1500500 25001,000 38001,800 48002,600 51,9004,500 65,0009,500 75,00014,500 Now we know how much it costs us to save any number of weeks Customer says he will pay $2,000 per week saved. Only reduce 5 weeks. We get $10,000 from customer, but pay $4,500 in expediting costs Increased profits = $5,500

54. Ex. AOA

55. AON Paths: ABF: 18 CDEF: 20 C5 B 10 A 6 D 4 E 9 F2 Activity AvailCost A0---- B2500 C1300 D3700 E2600 F 1800

56. Gantt charts to keep track Original A 6 B 10 C 5 D 4 E 9 2 F 2 Activity AvailCost A0---- B2500 C1300 D3700 E2600 F 1800 Consider CDEF C is cheapest, crash 1 day A 6B 10 C 4 D 4 E 9 1 F 2 C5 B10 A 6 D 4 E 9 F2 C4 B10 A 6 D 4 E 9 F2 Revised Pictures: Activity AvailCost A0---- B2500 C0 D3700 E2600 F 1800 Consider DEF E cheapest Crash E 1 day

57. Keep Track with Gantt Charts A 6B 10 C 4 D 4 E 9 F 2 C4 B10 A 6 D 4 E8 F2 New Pictures: Activity AvailCost A0---- B2500 C0 D3700 E1600 F1800 All Activities Critical ABF: 18 CDEF: 18 Options: Crash: F $800 B, AND D or E E is cheaper than D $500+$600 = $1,100 > 1,000 Cost > Benefit No more crashing to be done economically.

58. What about Uncertainty?

59. PERT Activity Times 3 time estimates Optimistic times (a) Most-likely time (m) Pessimistic time (b) Follow beta distribution Expected time: t = (a + 4m + b)/6 Variance of times: v = (b - a) 2 /36  

60. Example Activity a = 2, m = 4, b = 6 E[T] = (2 + 4*4 + 6)/6 = 24/6 = 4.0 σ 2 = (6 – 2) 2 / 36 = 16/36 = 0.444

61. Example ActivityambE[T]variance A2484.331 B36.111.56.482 C48107.671 Project18.54 Complete in 18.5 days, with a variance of 4. C C B B A A 4.33 6.48 7.67

62. Sum of 3 Normal Random Numbers 102030405060 Average value of the sum is equal to the sum of the averages Variance of the sum is equal to the sum of the variances Notice curve of sum is more spread out because it has large variance

63. Back to the Example: Probability of <= 21 wks 18.5 21 Average time = 18.5, st. dev = 2 21 is how many standard deviations above the mean? 21-18.5 = 2.5. St. Dev = 2, so 21 is 2.5/2 = 1.25 standard deviations above the mean Book Table says area between Z=1.25 and –infinity is 0.8944 Probability <= 21 wks = 0.8944 = 89.44%

64. Benefits of PERT/CPM Useful at many stages of project management Mathematically simple Use graphical displays Give critical path & slack time Provide project documentation Useful in monitoring costs

65. Limitations of PERT/CPM Clearly defined, independent, & stable activities Specified precedence relationships Activity times (PERT) follow beta distribution Subjective time estimates Over emphasis on critical path

66. Conclusion Explained what a project is Summarized the 3 main project management activities Drew project networks Compared PERT & CPM Determined slack & critical path Found profit-maximizing crash decision Computed project probabilities