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Information Systems Project Management—David Olson9-1

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Information Systems Project Management—David Olson9-2

Chapter 9: Probabilistic Scheduling Models

project evaluation and review technique (PERT)

Simulation

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PERT

• reflects PROBABILISTIC nature of durations• assumes BETA distribution• same as CPM except THREE duration estimates

optimisticmost likelypessimistic

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PERT Calculation

a = optimistic duration estimate

m = most likely duration estimate

b = pessimistic duration estimate

expected duration:

variance:

Tea + 4m + b

6

V =b - a

6

2

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Information Systems Project Management—David Olson9-5

PERT Example

activity durationpredecessor teA requirements analysis 2/3/6 weeks - 3.33B programming 3/6/10 weeks A 6.17C get hardware 1/1/2 week A 1.17D train users 3/3/3 weeks B, C 3.00

CRITICAL PATH: A-B-DEXPECTED DURATION: 3.33+6.17+3=12.5VARIANCE: {(6-2)/6}^2 +{(10-3)/6}^2+{(3-3)/6}^2=1.805

STD = 1.344

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Information Systems Project Management—David Olson9-6

PERT Path Variance

• IF YOU ASSUME INDEPENDENCEthe 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=1.354target=10 Z=(10-9.5)/1.354 = .369

probability = .644

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Information Systems Project Management—David Olson9-8

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 with “What won’t be exceeded 95% of the time” is blowing in the wind.

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Information Systems Project Management—David Olson9-9

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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Why Simulate?

uncertaintytool for study of expected performance

for uncertainty, complexity

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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

A B C D E

1 Activity Duration Predecessor Start Finish

2 A 3 - 0 =B2+D2

3 B 7 A =E2 =B3+C3

4 C 1 A =E2 =B4+C4

5 D 3 B,C =MAX(E3,E4) =B5+C5

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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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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