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Project Scheduling

Project Scheduling. Professor Stephen Lawrence Graduate School of Business Administration University of Colorado Boulder, CO 80309-0419. Project Management. When to use:. Management complex projects Many parallel tasks Deadlines and milestones must be met

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Project Scheduling

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  1. Project Scheduling Professor Stephen Lawrence Graduate School of Business Administration University of Colorado Boulder, CO 80309-0419

  2. Project Management When to use: • Management complex projects • Many parallel tasks • Deadlines and milestones must be met • Difficult to know “what to do first” • Difficult to know when project is in trouble • Often have competition for limited resources

  3. Examples • Building a new airport • Designing a new computer product • Launching an advertising campaign • Construction projects of all types • Maintenance projects • Curriculum reviews

  4. Project Mgmt Techniques • Critical Path Method (CPM) • Developed by DuPont (1950’s) • Plan and control maintenance of chemical plants • Credited with reducing length of maintenance shutdown by 40% • Project Evaluation and Review Technique (PERT) • Developed by Navy (early 1960’s) • Plan and control the Polaris missile project • Credited with speeding up project by 2 years

  5. Critical Path Method(CPM)

  6. Critical Path Method (CPM) • Graphical method of portraying relationship of project activities • An activity is any discrete part or task of a project which takes resources and time to complete • Activities exhibit precedence relations (some must be completed before others can start) • Activities with their precedence relations form a project network • Critical Path Method finds the longest path through the resulting project network

  7. A (Start) B A C A D B, C Precedence Relations Activity Immediate Predecessor Duration (days)

  8. Simple Project Network B D A C

  9. Activity Name Early Start Time Early Finish Time ES EF LS LF Late Finish Time Late Start Time Activity Duration Activity Start/Finish Times

  10. A Finding the Critical Path B 3 D 4 2 C 5

  11. CPM Terminology • Critical Path: the chain of activities along which the delay of any activity will delay the project • Early Start Time (ES): the earliest that an activity could possibly start, given precedence relations • Late Start Time (LS): the latest that an activity could possibly start without delaying the project • Early Finish Time (EF):the earliest that an activity could possibly finish • Late Finish Time (LF):the latest that an activity could possibly finish without delaying the project • Activity Slack: the amount of “play” in the timing of the activity; slack = LST-EST = LFT-EFT

  12. Example Suppose you are an advertising manager responsible for the launch of a new media advertising campaign. The campaign (project) has the following activities: Activity Predecessors Time A. Media bids none 2 wks B. Ad concept none 6 C. Pilot layouts B 3 D. Select media A 8 E. Client check-off A,C 6 F. Pre-production B 8 G. Final production E,F 5 H. Launch campaign D,G 0

  13. Example Project Network D 8 A 2 H 0 Start E 6 C 3 B 6 G 5 F 8

  14. Program Evaluation and Review Technique (PERT)

  15. PERT • Similar to Critical Path Method (CPM) • Accounts for uncertainty in activity duration estimates • Provides estimates of project duration probabilities • Best used for highly uncertain projects • new product development • unique or first-time projects • research and development

  16. Simple Project Network B D A C

  17. A Simple Example a m b Activity Most Optimistic Most Likely Most Pessimistic A 2 3 10 B 1 7 2.5 C 4 6 5 D 0.5 5.5 1.5

  18. Distribution Assumption Assume a “Beta” distribution density activity duration a m b

  19. a + 4m + b 6 (b - a)2 36 Expected Duration & Variance For the Beta Distribution: Expected Time = Variance =

  20. Distribution Assumption expected duration density activity duration a m b

  21. a + 4m + b 6 2+4(3)+10 6 = = 4.0 (b - a)2 36 (10-2)2 36 1.778 = = Expected Duration & Variance Activity A ET = Var =

  22. Critical Path of the Example B 3 A D 4 2 C 5 Critical Path Duration =

  23. Time and Variance Example Activity Expected Time Variance Critical Path? A 4 1.778 B 3 1.0 C 5 0.111 D 2 0.694

  24. Sum of the Variances on the Critical Path z Probability of Completion What is the probability that a project will be completed by a specified due date? Due Date - Expected Completion Date z= Expected Completion NormalDistribution Due Date

  25. 12 - 11 1.778 + 0.111 + 0.694 Completion Probability Example What is the probability of completing the project within 12 days? = z = From a Z-table for standard Normal distributions: Probability of completion =

  26. Larger Example Suppose the duration of the activities of the ad campaign are, in fact, uncertain: (a) (m) (b) ActivityPredsOptimisticLikelyPessimistic A. none 1 2 3 wks B. none 4 6 8 C. B 3 3 3 D. A 2 8 10 E. A,C 3 6 9 F. B 1 8 15 G. E,F 4 5 6 H. D,G 0 0 0

  27. Activity D Suppose the duration of the activities of the ad campaign are, in fact, uncertain: (a) (m) (b) ActivityPredsOptimisticLikelyPessimistic A. none 1 2 3 wks B. none 4 6 8 C. B 3 3 3 D. A 2 8 10 E. A,C 3 6 9 F. B 1 8 15 G. E,F 4 5 6 H. D,G 0 0 0

  28. a + 4m + b 6 2+4(8)+10 6 = (b - a)2 36 (10-2)2 36 = Activity D Expected Activity Duration for “D”: ET = Variance of Activity Duration for “D”: Var =

  29. D A 2 H 0 Start E 6 C 3 B 6 G 5 F 8 Example Project Network 7.33 Critical Path Duration = 20 days

  30. Project Duration Statistics ActivityCritical? MeanVar C.P. Var A. 2 0.11 B. 6 0.44 C. 3 0.00 E. 6 1.00 F. 8 5.44 G. 5 0.11 H. 0 0.00 D. 7.33 1.78

  31. x -   18 - 20 sqrt(1.55) Z = = Using Project Statistics What is the probability that the ad campaign can be completed in 18 weeks? 20? 24? 18 weeks: Corresponding probability from standard normal Z-Table is 0.9463: Prob(x<18) = 1 - 0.9463 =

  32. 18 weeks: Z = -1.61 Prob(x<18) = 20 weeks: Z = 0.00 Prob(x<20) = 24 weeks: Z = 3.21 Prob(x<24) = Using Project Statistics What is the probability that the ad campaign can be completed in 18 weeks? 20? 24?

  33. Other Project Mgmt Techniques • Project crashing • where to devote extra resources to reduce activity/project durations while minimizing costs • Resource leveling • how to schedule resources (equipment, people) to minimizes peaks and valleys • Multiple resource scheduling • how to schedule resources when activities can require more than one resource type • Cash flow and budgeting • combine cash and budget information with project scheduling to track expenditures, project cash flows

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