The Critical Path Method (CPM) schedules activities to start on early dates, which results in an unrealistic completion distribution in CPM risk analysis. CPM risk analysis tools, thus, cannot model what commonly occurs when a project unfolds and activities start on dates later than early dates due to floating or pacing decisions based on schedule progress. Graphical Path Method (GPM®) risk analysis allows activities in each realization to float as a function of random sampling and decision rules, accurately modeling the real world where activities are delayed to take advantage of total float. This paper and presentation demonstrates how the early bias in CPM risk analysis leads to optimistic completion distributions, and how GPM risk analysis corrects for the early bias by allowing floating and pacing scenarios. A novel approach is also introduced for developing a bounding completion distribution envelope for selecting realistic probabilistic completion dates and for monitoring safe-float use as the project progresses. Presented at AACE’s 2016 Annual Meeting.

1. (RISK‐2196) Removing the Early‐Dates Bias
in CPM Risk Analysis
Gui Ponce de Leon, PhD, PE, PMP
Vivek Puri, PhD, PMP

2. PLEASE USE MICROPHONE FOR ALL
QUESTIONS AND COMMENTS!
2

3. BIO of Dr. Gui Ponce de Leon
3
• Professional experience includes executive and senior roles
as program manager, project manager, project controls
engineer, planner/scheduler, and forensic scheduler
• A project management inventor, who holds 4 US patents on
his groundbreaking graphical path method aka GPM
• Awarded in 1972 the first PhD from the construction
management program at the University of Michigan
• In 1969, with Prof. Tom Schriber as co‐author, presented
Determination of Criticality Indices in the PERT Problem at
the Third Conference on the Application of Simulation
Founder/CEO of PMA Consultants, LLC,
a pure project management firm with a
45-year track record

4. BIO of Dr. Vivek Puri
• Experience in construction management research,
simulation and risk management, and construction planning
and execution
• PhD in Civil Engineering (2012) from Purdue University and
M. Tech in Construction Technology and Management (2005)
from Indian Institute of Technology Madras, India
• PhD thesis focused on combined continuous and discrete
event simulation of project operations and its use in project
planning
4
Senior Associate/Lead Developer
PMA Consultants, LLC

5. AGENDA
• Introduction
– Conventional Scheduling
– Scheduling Under Uncertainty
– Float Use Impact on Project Completion
• Graphical Path Method
• Case Study
• Bounding Completion Risk Envelope
• Safe float
• Conclusions
5

6. INTRODUCTION
6

7. Conventional Scheduling
• In critical path method (CPM) scheduling, activity durations
are assumed to be known with certainty
– Single‐point duration estimates
– Schedule uncertainty is dealt with through contingency, e.g.,
AACE RP 70, Principles of Schedule Contingency Management
• CPM algorithms functionality
– Using a forward pass, activities are scheduled to start on the
earliest possible dates largely based on network logic
– Using a backward pass, late dates and total floats are
determined by fixing the project completion date
• CPM is not used where activity durations are uncertain
7

8. Before CPM, Activities Had One Start Date
8

9. With CPM, Activities Have Early & Late Dates
9

10. CPM Early & Late Bounding Distribution Curves
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1,600,000
9/14/2011 11/3/2011 12/23/2011 2/11/2012 4/1/2012 5/21/2012 7/10/2012 8/29/2012 10/18/2012
Early Cumulative Cost
Late Cumulative Cost
10

11. Scheduling Under Uncertainty
• Common sources of uncertainty
– Production rates, weather, estimating tolerance
– Internal and external risks impacting durations
• PERT introduced in 1957 for estimation of uncertainty
– Activities have three‐point duration estimates
– Duration variability follows Beta‐PERT distribution
– Using a forward pass much as CPM does, PERT calculates the
PERT project duration mean and variance
– Appealing to the central limit theorem, project duration is
assumed to follow a normal distribution
11

12. The PERT Merge Bias
• The PERT solution is essentially a longest path algorithm that
uses activity mean durations (as approximated by PERT)
rather than single‐point durations as CPM does
• The PERT approach introduces a merge bias
– By calculating mean start dates based on the maximum of
the merging paths’ mean durations, PERT underestimates
mean start dates as the mean of the longest path is greater
than or equal to the maximum of the merging paths’ mean
durations
12

13. Schedule Simulation or Schedule Risk Analysis
• Van Slyke (1963) introduced a Monte Carlo simulation
approach to correct for the underestimation from merge
bias inherent in the PERT expected completion date
• Schedule simulation overcomes PERT limitations
– Uses any distribution to model activity duration uncertainty
– Rather than using mean durations to develop one early‐
schedule occurrence of the project schedule, simulation uses
sampled activity durations to develop multiple early‐
schedule occurrences of the project schedule
– Each early‐schedule occurrence is based on the sampled
longest path thereby removing the PERT merge bias
– Models risks & correlations
13

14. Early‐Dates Bias in CPM Schedule Risk Analysis
• By scheduling activities on early starts in every iteration,
CPM risk analysis does not account for the impact of delayed
or late starts (impact of float use) on project completion:
– The early‐dates limitation is a deviation from the actual
system modeled; on actual projects, activities off the critical
are often floated and start later, making use of total float
• By not modeling floating risk in any iteration, CPM risk
analysis merely develops the early completion risk function
because decisions to use float have a likelihood of causing
critical path delay and affect the project completion date
14

15. Project Completion Distribution Curve
0 %
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
100 %
8/26/2012 9/2/2012 9/9/2012 9/16/2012 9/23/2012 9/30/2012 10/7/2012 10/14/2012 10/21/2012
Iterations
Date
15

16. Float Use Impact on Project Completion
• On actual projects, it is common practice to delay non‐
critical work by using available total float
– Level resources
– Pace progress
– Other strategic reasons
• Where activities have uncertain durations, floating activities
in a simulation itera on─even within available float─alters
the merge risk, which in turn risks a delay in completion
– High‐total‐float paths do not affect early‐dates merge bias
– When a high‐total‐float activity is floated by a sufficient
amount of available float, the delay in start puts the activity
closer to the merge event, and coupled with duration
uncertainty has a likelihood of impacting completion
16

17. GRAPHICAL PATH METHOD
17

18. Graphical Path Method (GPM)
• Planning/scheduling method that allows planners to place
activities on GPM planned dates between early and late
dates while retaining the algorithmic early and late dates
• GPM planned dates generate drift
– Drift is unique to GPM as drift in CPM is always zero
• GPM planned dates also generate float
– Float as a subdivision of total float is unique to GPM, as float
in CPM is always equal to total float
18

19. Graphical Path Method
• In GPM, regardless of planned start date established for an
activity, drift + float always equals total float
– In GPM, planned dates generate drift without suppressing
total float thereby preserving total float continuity
• In CPM, date constraints that override logic do not generate
drift, suppress total float, and cause total float discontinuity
19

20. Graphical Path Method (cont’d)
• Planned dates obviate the need for SNE date constraints,
which makes GPM invaluable for assessing schedule risk as
date constraints can adversely impact simulation results
• AACEI Recommended Practice No. 57R‐09 recommends:
– The schedule should not rely on constraints to force activities
to start or finish by certain dates
– It should use logic for this purpose and not artificially reduce
or restrict total float
20

21. Core Tenets of GPM‐Based Schedule Simulation
• Tenet #1─Each itera on begins with the base‐case scenario
and unfolds activity by activity according to network logic, as
a simulated update of the base‐case scenario
– Each iteration is a simulated progression of time rather than
a batch replacement of activity duration
• Tenet #2─In each itera on, ac vi es may be scheduled on
GPM planned dates, either because
– GPM planned dates are present in the base case, or
– Positive‐float activities, through sampling, are allowed to
float by using a portion or all of then‐available float
• Tenet #3─In each itera on, the longest path has the least
total float; late finish date of the last activity on the longest
path equals its early finish date or the project finish date
21

22. CASE STUDY
22

23. Case Study
• Design‐build contract to rebuild food processing facility
• Project Completion
– Required by 10/06/2012
– Early planned completion by 08/26/2012
– Total Duration: 328 calendar days
– Early completion total float: 41 days (12.5%)
• Modeled and simulated using NetPoint®/NetRisk™
• For simplicity,
– 3‐point duration estimates follow triangular distribution
– All uncertainty in duration ranges, no other risks
23

24. Project Schedule─Base‐Case Scenario
24

25. Early‐Schedule Scenario–Completion Distribution
25

26. Early‐Schedule Scenario–Criticality Indices
26
Criticality
threshold = .250 x 98%
= .245

27. BOUNDING COMPLETION RISK ENVELOPE
27

28. Float Use by Modeling Floating and Pacing
• Floating
– Delayed start of activity to consume available float
– Independent of actual progress
– Random decision
• Pacing
– Delayed start of activity to consume available float
– Delay in another path increases available float
– Decision based on threshold of current float to
deterministic float
28

29. Optimism Bias in CPM‐Based Simulation
• CPM‐based simulation is unable to model floating/pacing
– Activities are scheduled on early dates in each iteration
– Impact of delayed start of any activity not considered
– No decision‐based rules to model floating/pacing
• CPM‐based simulation yields an optimistic completion
distribution because it is predicated on the early‐schedule
– For instance, a P80 date without considering floating may be
the P60 date under a postulated floating scenario
29

30. Modeling Bounding Completion Risk Envelope
• CPM‐based simulation provides the envelope upper bound
– Activities always scheduled to start on early dates
– The upper bound is the early‐schedule completion risk curve
• Although the maximum delay in project completion due to
floating is theoretically unbounded, an envelope lower
bound can be determined by assuming floating is limited by
then‐available float
– Modeled by floating activities off the critical path with 100%
probability and using 100% of then‐available float (meaning,
float available at that point in an iteration)
– Represents the late completion risk curve (different than
starting activities on late dates)
30

31. Bounding Completion Risk Envelope
CPM Base/All Early Scenario
Selective Floating Scenario
Selective Floating & Pacing Scenario
All Late/100% Floating Scenario
31

32. SAFE FLOAT
32

33. Safe Float
• Safe float: within modeled uncertainty, extent an activity
may be delayed from its base‐case early start date without
delaying the targeted (P value) project completion date
• Activity Elec Equipment Installation (early‐dates simulation)
– Stochastic earliest Start: 05/10/2012
– Stochastic latest Start: 07/15/2012
33
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0
20
40
60
80
100
120
5/10/2012 5/17/2012 5/24/2012 5/31/2012 6/7/2012 6/14/2012 6/21/2012 6/28/2012 7/5/2012 7/12/2012
Cumulative Probability
Iterations
Start Date
Num. of Iterations
Cumulative Probability

34. 0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
6/20/2012
6/21/2012
6/22/2012
6/23/2012
6/24/2012
6/25/2012
6/26/2012
6/27/2012
6/28/2012
6/29/2012
6/30/2012
7/1/2012
7/2/2012
7/3/2012
7/4/2012
7/5/2012
7/6/2012
7/7/2012
7/8/2012
7/9/2012
7/10/2012
7/11/2012
7/12/2012
7/13/2012
7/14/2012
7/15/2012
Cumulative Probability for Delay
Probability
Start Date for Electrical Equipment Installation
No Delay
Delay
Cumulative Percent
Safe‐Float Use–Stochastic Approach
34
Each iteration is analyzed to determine where both the
activity is critical and the schedule completion date
extends beyond the targeted (P80) completion date
Latest start date where activity is on
the longest path and completion does
not extend beyond 10/01/2012, so
safe float = 06/26 – 05/19 = 38 days

35. Safe‐Float Use–Analyzing Results
• 3000 iterations
• Targeted (P80 date) project completion by 10/01/2012
– Latest start without delay 06/26/2012
– 98 days to targeted project completion
• Remaining path length > 98 days
– Assuming the path to be always driving
– Probability ≤ 0.012, practically insignificant
• Safe float = safe float start date ‐ base‐case early start date
35

36. Unsafe‐Float Activities: No Safe Float Start Dates
36

37. Categorizing Activities Using Safe Float Range
• Unsafe‐float activities: under high duration variability, there
may be two types of activities without safe float whatsoever
– Type 1: no possible start date later than the stochastic
optimistic early start without delaying targeted completion
– Type 2: no possible start date later than the base‐case early
start date without delaying targeted (P value)completion
• Low safe‐float activities: have safe float below a threshold,
for example, safe float < 20 days
• Mid safe‐float activities: Have safe float above a threshold,
for example safe float ≥ 20 days
• High safe‐float activities: have unbounded safe float within
modeled uncertainty
37

38. Type 2 Unsafe‐Float Activities
38

39. Low Safe‐Float Activities
39

40. Mid Safe‐Float Activities
40

41. High Safe‐Float Activities
41

42. Safe‐Float Values (Low & Mid)
Activity Description Criticality
Base‐Case
Start Date
Safe‐Float
Start Date
Total
Float
Safe‐
float
Elec Equipment Fab/Delivery 0.249 2/14/2012 2/16/2012 56 2
Steel, Joists, Decking 0.537 2/20/2012 3/9/2012 36 18
SOG, Pour & Seal Decks 0.537 3/19/2012 4/7/2012 36 19
Power/Lighting/Low Voltage 0.441 4/23/2012 5/14/2012 36 21
Piping/HVAC/FS Rough‐In 0.131 4/23/2012 5/16/2012 43 23
MEP Process Equip 0.768 7/2/2012 7/27/2012 36 25
Install/Connect Process Equipment 1.000 7/16/2012 8/13/2012 36 28
Elec Equipment Installation 0.249 5/19/2012 6/26/2012 56 38
42

43. Safe‐float & Criticality Overlay
43

44. CONCLUSIONS
44

45. Conclusions
1. While correcting for the PERT merge bias, CPM risk analysis
determines only the early‐schedule completion risk curve
2. When merge bias from randomly selected delayed starts is
considered, multiple completion risk curves are revealed
3. The 100%‐float‐use scenario yields the stochastic
equivalent of the late schedule impact on completion risk
4. With GPM, risk analysis catches up with the notion of
bounding early/late distributions; targeted completion
dates have a reliable P value that considers floating risk
5. A method is introduced to determine safe float, regardless
of scenario, without impacting target completion (P date)
6. The method allows determination of unsafe‐float activities
7. Activities are categorized as low and mid safe float based
on selected safe‐float thresholds and high safe float where
safe float is unbounded by modeled uncertainty
45

46. QUESTIONS/COMMENTS?
(PLEASE USE MICROPHONE)
46