Information Systems Project Management—David Olson
9-1
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David Olson
9-2
Chapter 9: Probabilistic Scheduling
Models
project evaluation and review
technique (PERT)
Simulation
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David Olson
9-3
PERT
• reflects PROBABILISTIC nature of durations
• assumes BETA distribution
• same as CPM except THREE duration estimates
optimistic
most likely
pessimistic
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David Olson
9-4
PERT Calculation
a = optimistic duration estimate
m = most likely duration estimate
b = pessimistic duration estimate
a + 4m + b
T

expected duration: e
6
variance:
b - a

V=

 6 
© McGraw-Hill/Irwin 2004
2
Information Systems Project Management—David Olson
9-5
PERT Example
activity
duration
A requirements analysis 2/3/6 weeks
B programming
3/6/10 weeks
C get hardware
1/1/2 week
D train users
3/3/3 weeks
predecessor
A
A
B, C
te
3.33
6.17
1.17
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
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David 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
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David 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=10 Z=(10-9.5)/1.354 = .369
probability = .644
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David Olson
9-8
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.
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David 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)
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David Olson
9-10
Why Simulate?
uncertainty
tool for study of expected performance
for uncertainty, complexity
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David 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)
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David 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)
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David 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
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David Olson
9-14
Excel Model
A
1
B
C
D
Activity Duration Predecessor Start
E
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
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David 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
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David 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
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David Olson
why should a manager
care?
9-17
• simulation provides greater accuracy than PERT
• simulation the most flexible analytic tool
© McGraw-Hill/Irwin 2004
Information Systems Project Management—David 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
© McGraw-Hill/Irwin 2004