2. 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.

3. PERT reflects PROBABILISTIC nature of durations
assumes BETA distribution
same as CPM except THREE duration estimates
optimistic
most likely
pessimistic

4. PERT Calculation a = optimistic duration estimate
m = most likely duration estimate
b = pessimistic duration estimate
expected duration:
variance:

5. 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

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

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

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.

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)

10. 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.

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)

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)

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

14. Excel Model

15. 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

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

17. why should a manager care?
simulation provides greater accuracy than PERT
simulation the most flexible analytic tool

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