© McGraw-Hill/Irwin 2004 Information Systems Project Management—David Olson 9-1
Mar 26, 2015
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David Olson9-1
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David Olson9-2
Chapter 9: Probabilistic Scheduling Models
project evaluation and review technique (PERT)
Simulation
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Information Systems Project Management—David Olson9-3
PERT
• reflects PROBABILISTIC nature of durations• assumes BETA distribution• same as CPM except THREE duration estimates
optimisticmost likelypessimistic
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Information Systems Project Management—David Olson9-4
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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Information Systems Project Management—David Olson9-7
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=1.354target=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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Information Systems Project Management—David Olson9-10
Why Simulate?
uncertaintytool for study of expected performance
for uncertainty, complexity
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Information Systems Project Management—David Olson9-11
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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Information Systems Project Management—David Olson9-12
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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Information Systems Project Management—David Olson9-13
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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Information Systems Project Management—David Olson9-14
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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Information Systems Project Management—David Olson9-15
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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Information Systems Project Management—David Olson9-16
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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Information Systems Project Management—David Olson9-17
why should a manager care?
• simulation provides greater accuracy than PERT• simulation the most flexible analytic tool
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Information Systems Project Management—David Olson9-18
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