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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-1

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-2 Chapter 9: Probabilistic Scheduling Models project evaluation and review technique (PERT) Simulation

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-3 PERT reflects PROBABILISTIC nature of durations assumes BETA distribution same as CPM except THREE duration estimates optimistic most likely pessimistic

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-4 PERT Calculation a = optimistic duration estimate m = most likely duration estimate b = pessimistic duration estimate expected duration: variance:

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-5 PERT Example activitydurationpredecessorte A requirements analysis2/3/6 weeks-3.33 B programming3/6/10 weeksA6.17 C get hardware1/1/2 weekA1.17 D train users3/3/3 weeksB, C3.00 CRITICAL PATH: A-B-D EXPECTED DURATION: =12.5 VARIANCE: {(6-2)/6}^2 +{(10-3)/6}^2+{(3-3)/6}^2=1.805 STD = 1.344

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-6 PERT Path Variance 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

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-7 PERT Variance 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=10Z=(10-9.5)/1.354 =.369 probability =.644

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-8 PERT Estimates so what do you mean by optimistic, pessimistic? value you expect to be exceeded at probability level and not exceeded at 1- probability PROBLEM: estimating the MOST LIKELY duration of most things is hard asking estimators to come up withWhat wont be exceeded 95% of the time is blowing in the wind.

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-9 Network Scheduling Methods 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)

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-10 Why Simulate? uncertainty tool for study of expected performance for uncertainty, complexity

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-11 what is simulation? 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)

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-12 project management tools 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)

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-13 CPM model 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

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-14 Excel Model

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-15 distributions 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

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-16 Output Analysis 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

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-17 why should a manager care? simulation provides greater accuracy than PERT simulation the most flexible analytic tool

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© McGraw-Hill/Irwin 2004 Information Systems Project ManagementDavid Olson 9-18 Summary 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

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