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**Chapter 9: Probabilistic Scheduling Models**

project evaluation and review technique (PERT) Simulation Chapter 6: Quantitative Project Scheduling Methods This chapter focuses on the critical path method, the fundamental project scheduling technique assuming certainty and unlimited resources. Project crashing is discussed as a means of analyzing alternative cost/time tradeoffs. Resource leveling and resource smoothing are discussed as ways to consider limited resources. Buffers are discussed as a way to cope with risk. Criticisms of the critical path method are reviewed.

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**PERT reflects PROBABILISTIC nature of durations**

assumes BETA distribution same as CPM except THREE duration estimates optimistic most likely pessimistic

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**PERT Calculation a = optimistic duration estimate**

m = most likely duration estimate b = pessimistic duration estimate expected duration: variance:

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**PERT Example CRITICAL PATH: A-B-D EXPECTED DURATION: 3.33+6.17+3=12.5**

activity duration predecessor te A requirements analysis 2/3/6 weeks 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: =12.5 VARIANCE: {(6-2)/6}^2 +{(10-3)/6}^2+{(3-3)/6}^2=1.805 STD = 1.344

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**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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**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=10 Z=(10-9.5)/1.354 = .369 probability = .644

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PERT Estimates 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.

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**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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**Why Simulate? uncertainty tool for study of expected performance**

for uncertainty, complexity Chapter 7 Probabilistic Scheduling Models This PPT provides a very brief overview of the benefits of simulation over PERT relative to evaluating the risk associated with information system project management. The generic EXCEL CPM model is the basis of simulation. Chapter 7 material requires working with EXCEL, following text material. Simulation is not typically covered in IS or IT courses, but provides a valuable means of analysis.

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**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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**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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**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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Excel Model

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**distributions Beta - assumed by PERT; Normal**

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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**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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**why should a manager care?**

simulation provides greater accuracy than PERT simulation the most flexible analytic tool

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**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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