2. Chapter 9: Probabilistic Scheduling Models project evaluation and review technique (PERT) Simulation

3. reflects PROBABILISTIC nature of durations assumes BETA distribution same as CPM except THREE duration estimates optimistic most likely pessimistic PERT

4. a = optimistic duration estimate m = most likely duration estimate b = pessimistic duration estimate expected duration: variance: PERT Calculation

5. activity duration predecessor te A requirements analysis 2/3/6 weeks - 3.33 B programming 3/6/10 weeks A 6.17 C get hardware 1/1/2 week A 1.17 D train users 3/3/3 weeks B, C 3.00 CRITICAL PATH: A-B-D EXPECTED DURATION: 3.33+6.17+3=12.5 VARIANCE: {(6-2)/6}^2 +{(10-3)/6}^2+{(3-3)/6}^2=1.805 STD = 1.344 PERT Example

6. IF YOU ASSUME INDEPENDENCE the variance of any path = sum of activity variances for all activities on that path NORMALLY DISTRIBUTED variance of the PROJECT = variance of the CRITICAL PATH if more than one critical path, PROJECT VARIANCE=largest of CRITICAL PERT Path Variance

7. since NORMALLY DISTRIBUTED can estimate probability of completing project on time can estimate probability of completing project by any target date if critical path expected = 9.5, STD=1.354 target=10 Z=(10-9.5)/1.354 = .369 probability = .644 PERT Variance

8. so what do you mean by optimistic, pessimistic? value you expect to be exceeded at a probability level and not exceeded at 1-a probability PROBLEM: estimating the MOST LIKELY duration of most things is hard asking estimators to come up with “What won’t be exceeded 95% of the time” is blowing in the wind. PERT Estimates

9. a number of methods exist Gantt chart provides good visual network shows precedence well CPM identifies critical activities PERT reflects probability SIMULATION more accurate (still need data) Network Scheduling Methods

10. Why Simulate? uncertainty tool for study of expected performance for uncertainty, complexity

11. develop an abstract model of a system CPM is a precedence model whenever uncertain events are encountered, use random numbers to determine specific outcomes keep score (describe the DISTRIBUTION of possible outcomes) what is simulation?

12. CPM - sort out complexity (assumes certainty) PERT - considers uncertainty but assumes an unrealistic distribution SIMULATION set up model run it over and over keep score of the outcomes (any one of which are possible) project management tools

13. start all activities as soon as you can need to know when all predecessors done = start time duration is probabilistic (described by a distribution) use random number to determine specific duration from all possible outcomes finish time = start time + duration CPM model

14. Excel Model

15. Beta - assumed by PERT; mathematically convenient Normal requires symmetry, infinite limits Triangular - more flexible than normal, close approximation exponential - not likely lognormal - might fit, but inflexible distributions

16. Can generate as many samples as desired Can calculate probability by count do NOT have to assume any distribution count is easier, more accurate than normal formulas Simulation is often the means used to generate distribution tables Output Analysis

17. simulation provides greater accuracy than PERT simulation the most flexible analytic tool why should a manager care?

18. Project durations have high degrees of uncertainty PERT a probabilistic form of CPM Sound idea – reflects uncertain durations Not much more accurate – too rigid Simulation a much more flexible and appropriate tool for modeling uncertainty Summary