SanDiegoPresentation

A New Paradigm for
Delay Analysis
The Hybrid Dynamic Simulation Engine
Anders Axelson
Director, Pezala Consulting
Melbourne, Australia
Marriott Marquis Marina
San Diego CA
16 January 2015
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Data Inputs Into a Delay Analysis
• Consider the Data Required to Perform a Delay
Analysis…
• There are three types of inputs into setting up a
network model for delay analysis -
• Planning (including estimating and modelling)
• Factual
• Legal
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Data Inputs Into a Delay Analysis
Recorded Progress
Measurements
Facts About
Causative Events
Estimated Durations
Other Constraints on the
Network Model:
Availability
Precedence
Resource Gang Sizes
Resource Pool Sizes
Unary
WBS
FACTUAL INPUTS
PLANNING/ MODELLING
INPUTS
LEGAL INPUTS
Excusability
Causal Chain Initiation
and Severance
Factual Deeming
Provisions
Resolution of Concurrency
Cases
“Float” Ownership
SCHEDULING
Forward Pass
Backward Pass
Resource Levelling
Heuristic
Standard of Proof
SIMULATING
RESULTS
START
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Legal Aspects of Delay Analysis
• Consider the usual way in which the law deals with matters of causation
• Identifying dominant/ proximate cause
• A matter of common sense (cf. juries, drunk driver)
• Problems arise when the court has difficulty discriminating between two or more causes that have equal
causative potency…
• “Concurrent” causes - a special rule is required (cf. wills)
• Concurrency problems recur in different areas of law.
• Legal system is completely deterministic…
• Uncertainty is dealt with by a cascading system of appeals, not hedging bets as to outcomes.
• The place for fuzzy logic/ stochastic/ probabilistic/ Monte Carlo analysis within the context of forensic
scheduling is limited. (cf. sentencing)
• It’s about making determinations, not about probability!
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• It is in this context that CPM-based methods can be considered…
• CPM deals with causation problems in the special context of project delay…
• CPM is best regarded as replacing or refining the dominant cause/ proximate cause paradigm
• In this regard, the critical path or critical delay may be deemed to be the dominant/ proximate
cause
• In the context of forensic scheduling, the whole point of CPM is to provide a more objective and
scientific method for identifying the dominant/ proximate cause of a particular delay event,
thereby replacing the impressionistic or “common sense” approaches that courts and tribunals
would otherwise have to rely on.
• In theory at least, this supposedly should reduce the ambiguity and the extent to which
“concurrency problems” arise.
• CPM also ties in well with the deterministic requirement (unlike Monte Carlo method, PERT,
GERT etc.)
Relationship with Law on Causation
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• Computational complexity theory
• Computer science differentiates between….
• Computationally “easy” problems that can be solved by the application of mathematical formulae, algebra or
algorithms that are guaranteed to converge straightforwardly on a solution. Methodologies are either correct or
incorrect. A methodology that produces an incorrect answer in a case can be dismissed as wrong.
• “Puzzle-like” problems that require searching for a solution…
• (a) Problems that can be solved by brute force or a process of elimination. For example, look at every possible
configuration and then eliminate each sub-optimal solution by brute force. (e.g. tic-tac-toe a.k.a. noughts and
crosses there are 39 = 19,683 possible configurations).
• (b) Puzzle-like problems for which the domain of the solution space is too large for a brute force search and so
require the application of a heuristic/ rule of thumb/ artificial intelligence in order to search for the best possible
solution for the computational capacity available (e.g. chess there are 1364 = 196,053,476,430 possible
configurations). Known as “non-polynomial deterministic complete” or “NP-complete” or “NP-hard”.
• Note that numbers are based on factorial number series so the number of items that put it beyond the threshold of
(a) are very modest, even with modern day computers.
• Solutions are either optimal (correct) or sub-optimal (incorrect) but a superior methodology for one case will not
necessarily be a superior methodology in other cases. A methodology that produces an inferior or sub-
optimal solution in a case cannot be dismissed as wrong because it may produce a superior or optimal
solution in another case.
• A schedule without resource levelling is computationally easy. Forward pass and backward pass. This is the same for
all software (save for quirks such as dealing with “ladders”).
• Resource levelling, however, is an NP-hard problem. Requires searching for an optimal solution. No guarantee that
the configuration your software finds for you will be the optimal one.
• More exotic types of constraint are available in some software (e.g. modelling of transition times).
Relationship with Computer Science

Relationship with Planning and Scheduling
• Consider the difference between planning and scheduling…
• Scheduling…
• A purely mathematical exercise in problem solving,
• Projects are modelled as a network (= network optimization).
• Lends itself to being solved by computational methods (algorithms/ heuristics).
• Minimizing project duration/ makespan (or cost) subject to a set of constraints…
• The work tasks that need to be carried out for the project to be complete (i.e. WBS)
1. The time it takes to complete each work item (i.e. activity durations).
2. The precedence relationships between work items.
3. The availability of resources to complete each work item (i.e. ‘calendars’)
4. Unary decision domain constraints (i.e. SNET, FNLT, SO, FO etc.)
5. Resource gang requirements associated with each activity and resource pool sizes associated with the
whole project.
• More exotic types of constraint are available in some software (e.g. modelling transition times).

• The complexity of scheduling…
• The work tasks that need to be carried out for the project to be complete (i.e.
WBS)
• The time it takes to complete each work item (i.e. activity durations).
• The precedence relationships between work items.
• The availability of resources to complete each work item (i.e. ‘calendars’)
• Unary decision domain constraints (i.e. SNET, FNLT, SO, FO etc.)
• Resource gang requirements associated with each activity and resource pool
sizes associated with the whole project. —-> NP-hard
• More exotic types of constraint are available in some software (e.g. modelling
transition times).

• Scheduling:
• Consider t = value of time clock (work front, “time now”, “data date” etc.)
• t versus m diagram
• Scheduling = minimizing m for a fixed value of t
• But delay occurs across multiple values of t
• Delay analysis:
• An extension of scheduling.
• t is changed from a constant to a variable.
• Delay is just the difference in time between two scenarios. So tallying delay between timeframes is computationally
simple.
• Mathematical methods are performed across multiple values of t in order to measure delay.
• Therefore, it is all math and it’s about getting the mathematical methods right (not case law, not art).
• It is only NP-hard to the extent that it incorporates a resource levelling process from the scheduling process.

Inputs Into Delay Analysis
• Legal Inputs
• The standard of proof (that is, the weight of factual evidence that is
required before a fact can be modelled)
• Which delays are excusable and which are inexcusable
• When causal chains leading to events initiate and when they are
severed
• How concurrency problems are resolved
• How ‘float ownership’ is resolved
• Deeming provisions that relate to how facts are interpreted by the law
(e.g. the postal rule)

• Factual Inputs:
• Progress records (e.g. activity, percent
complete, recording time)
• Records about the timing of causal events
leading to delay

• Planning Inputs
• Estimating = calculations of activity durations
• Modelling = professional (engineering )judgment
calls about how project is to be represented as
a network

• Planning:
• Estimating activity durations.
• Devising an appropriate network model.
• Quantifying the constraints that apply to the network model that determine
the project makespan.
• Making professional judgement calls about how the work should be
modelled as a network.
• Note that modelling is core competence of the engineering profession
and, as with all professions, entails an aspect of “art”
• The outputs of planning are the inputs of scheduling

Relationship with the Scientific Method
• What is “the scientific method”? (cf. Daubert etc.)
• Misleadingly named - a general set of principles that allow factual conclusions that are objectively grounded (and
therefore legitimate) to be distinguished from illegitimate conclusions that arise from arbitrary, subjectively-grounded art
or from pseudoscience. Basically ensures objectivity and transparency.
• Reproducibility - a result can be reproduced by another who follows the same technique.
• Falsifiability - a conclusion is either correct or incorrect. It is not a case of “there are no right or wrong answers”.
• Other principles that relate to transparency and facilitate reproduction such as full disclosure and peer review.
• cf. Art is subjective. Different for different people. No right or wrong.
• cf. Pseudoscience. Irreproducible or arbitrary methodologies dressed up to look like science. e.g. astrology, homeopathy,
reiki.
• So, for delay analysis to be considered at one with scientific method:
• The same set of inputs (network model, constraints, progress records, and legal inputs) should produce the same
conclusion about EOT.
• The conclusion should be correct irrespective of whether it was reached on behalf of the developer/owner or contractor

• Conclusion
• Project delay analysis (1) as it currently represented in professional literature (e.g. UK SCL
Protocol and the AACE 29RP-03) and (2) as it is practised by experts around the world fails to
meet basic standards to qualify it as a legitimate field of science which is wholly consistent with
the scientific method.
• Why??
• Multiple solutions (4 methods in the SCL Protocol, 13 in the AACE RP). Only one solution
should be correct for a computational problem that is not NP-hard.
• Lack of falsifiability… there is no right or wrong methodology prescribed… “Well, I applied the
time impact evaluation method. You applied the as-built collapsed method. Your results may be
correct for the method you used and the assumptions you made but mine are correct for the
method I used…”
• Lack of reproducibility. Hiding behind walls of assumptions. Hiding behind software.
• Scientific method implies that, for a given set of inputs (modelling, estimating, recording,
factual, legal) the conclusions that an expert reaches in relation to EOT entitlement should be
the same irrespective of which party the expert is hired by.
• cf. Failure of single joint experts to take off.
Relationship with the Scientific Method

• Error is a scientific concept, not necessarily pejorative. It refers to
any discrepancy between anticipated and actual inputs or outputs…
• Estimating error <— inevitable, cannot be helped
• Modelling error <—-professional judgment, inevitable
• Recording error <—- inevitable, but can be minimized
• Methodological error <—- the thing to focus on minimizing !!
• Rounding error <— easy to eliminate
• Legal error <—- can model different scenarios
Error in Delay Analysis

Conclusions from the UK
• Conclusion
• Described as “dark art” (Barry, Lowsley and Linnett) - I partly agree and partly
disagree.
• See UK cases where delay experts have been criticised:
• Skanska v. Egger - expert criticized for presenting “computer programme logic
demonstrably collided with fact”
• London Borough of Lambeth - adjudicator criticized for performing his own delay
analysis rather than deferring to the parties.
• Great Easter Hotel - expert criticized for a lack of objectivity and producing an
analysis unreasonably favourable to his client
• The fact that there are aspects of error and professional art inevitably needed in
representing a project as a model and that other inputs (legal, factual) are inevitably
subject to error does not excuse a less-than-scientific approach to the computational
methodology.

AACE and SCL Approaches
• SCL: UK Society of Construction Law (2002) Protocol on Delay and
Disruption
• Four named methods: as-planned versus as-built, as-planned impacted,
as-built collapsed, time impact analysis
• AACE: Recommended Practice 29R-03
• Nine “Method Implementation Protocols” (MIPs):
• Designed to be used in conjunction with PPM software with a single
instance of t (or at least, simple static variance comparisons with no more
than a couple of baselines)
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•
SCL Method
(SCL Protocol, 2002)
AACE Method
(AACE Recommended Practice 29R-03, 2011)
As-Planned versus
As-Built
MIP 3.1 Observational/ Static/ Gross
MIP 3.2 Observational/ Static/ Periodic
MIP 3.3 Observational/ Dynamic/ Contemporaneous/ As-Is
MIP 3.4 Observational/ Dynamic/ Contemporaneous/ Split
MIP 3.5 Observational/ Dynamic/ Modified or Recreated
Impacted As-Planned MIP 3.6 Modeled/ Additive/ Single Base
Time Impact
Analysis
MIP 3.7 Modeled/ Additive/ Multiple Base
As-Built Collapsed MIP 3.8 Modeled/ Subtractive/ Single Simulation
MIP 3.9 Modeled/ Subtractive/ Multiple Base
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SCL Method
(SCL Protocol,
2002)
AACE Method
Time Intervals
Between Iterations
As-Planned versus
As-Built
MIP 3.1 Observational/ Static/ Gross Single iteration for
whole project.
MIP 3.2 Observational/ Static/ Periodic Typically months.
Impacted As-
Planned
MIP 3.6 Modeled/ Additive/ Single Base Typically weeks to
months.
Time Impact
Analysis
Best Practice
Hours.
• Typical time intervals between iterations?
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SCL Method
(SCL Protocol,
2002)
AACE Method
Are Iterations
Automated?
As-Planned versus
As-Built
MIP 3.1 Observational/ Static/ Gross No.
Impacted As-
Planned
MIP 3.6 Modeled/ Additive/ Single Base
Time Impact
Analysis
Best Practice
Yes.
• Are iterations automated?
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SCL Method
(SCL Protocol,
2002)
AACE Method
Does the Delay Analysis
Method Incorporate the
Critical Path Method?
As-Planned versus
As-Built
MIP 3.2 Observational/ Static/ Periodic Yes.
Impacted As-
Planned
MIP 3.6 Modeled/ Additive/ Single Base Partially (only forward pass is
used).
Time Impact
Analysis
As-Built Collapsed MIP 3.8 Modeled/ Subtractive/ Single Simulation Partially (only backward pass is
used).MIP 3.9 Modeled/ Subtractive/ Multiple Base
Best Practice
Yes.
• Does the method incorporate the critical path method?
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SCL Method
(SCL Protocol,
2002)
AACE Method
Does It Take Into Account
Instances When Delays Are
Causally Pre-Empted by
Discrete Events?
As-Planned versus
As-Built
Impacted As-
Planned
MIP 3.6 Modeled/ Additive/ Single Base Yes.
Time Impact
Analysis
As-Built Collapsed MIP 3.8 Modeled/ Subtractive/ Single Simulation No.
Best Practice
Yes.
• Does the method take into account instances when delays are
causally pre-empted by discrete events?
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SCL Method
(SCL Protocol,
2002)
AACE Method
Does It Accurately Account for the Effects of
Delays Occurring At the Same Time?
As-Planned versus
As-Built
MIP 3.2 Observational/ Static/ Periodic Yes - uses critical path to determine which of
continuous delays occurring within same time
window is deemed causative of delay for whole
window.
Impacted As-
Planned
MIP 3.6 Modeled/ Additive/ Single Base No. All delays are deemed to occur serially. If
delays occur in parallel an arbitrary order needs
to be chosen to model them as events occurring
one after the other if their respective effects are
to be accounted for separately.
Time Impact
Analysis
Best Practice
Yes.
• Does the method accurately account for the effects of delays
occurring at the same time?
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SCL Method
(SCL Protocol,
2002)
AACE Method
Does It Accurately Account for the
Effects of Delays Occurring One
After the Other?
As-Planned versus
As-Built
MIP 3.2 Observational/ Static/ Periodic No - if delays occur in same time
window.
Yes - if delays occur in different time
windows.
Impacted As-
Planned
MIP 3.6 Modeled/ Additive/ Single Base Yes.
Time Impact
Analysis
Best Practice
Yes.
• Does the method accurately account for the effects of delays
occurring one after the other?
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SCL Method
(SCL Protocol,
2002)
AACE Method
Does It Take As-
Planned Times
Into Account?
As-Planned versus
As-Built
MIP 3.1 Observational/ Static/ Gross Yes.
Impacted As-
Planned
Time Impact
Analysis
MIP 3.9 Modeled/ Subtractive/ Multiple Base Yes.
Best Practice
Yes.
• Does the method take as-planned times into account?
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SCL Method
(SCL Protocol,
2002)
AACE Method
Does It Take As-
Built Times Into
Account?
As-Planned versus
As-Built
MIP 3.1 Observational/ Static/ Gross Yes.
Impacted As-
Planned
MIP 3.6 Modeled/ Additive/ Single Base No.
Time Impact
Analysis
MIP 3.7 Modeled/ Additive/ Multiple Base Yes.
Best Practice
Yes.
• Does the method take as-built times into account?
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SCL Method
(SCL Protocol,
2002)
AACE Method
Does It Take Interim Progress
Measurements Into Account?
As-Planned versus
As-Built
MIP 3.2 Observational/ Static/ Periodic Yes - if time windows are chosen that
coincide with times when progress is
measured.
Impacted As-
Planned
Time Impact
Analysis
MIP 3.7 Modeled/ Additive/ Multiple Base Yes - if time windows are chosen that
measured.
MIP 3.9 Modeled/ Subtractive/ Multiple Base Yes - if time windows are chosen that
measured.
Best Practice
Yes - each part of an activity spanning
between successive progress measurements
is analysed separately.
• Does the method take interim progress measurements into account?
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SCL Method
(SCL Protocol,
2002)
AACE Method
Does It Accurately Account for Activity Progress
Between Progress Measurements?
As-Planned versus
As-Built
MIP 3.2 Observational/ Static/ Periodic Yes - if time windows are chosen that coincide with
times when progress is measured.MIP 3.3 Observational/ Dynamic/ Contemporaneous/ As-Is
Impacted As-
Planned
Time Impact
Analysis
MIP 3.7 Modeled/ Additive/ Multiple Base No - adopts a forward stepwise interpolation from start
of window (which assumes that all progress within a
time window is equal to the progress measurement at
the start of the window).
MIP 3.9 Modeled/ Subtractive/ Multiple Base No - adopts a backward stepwise interpolation from
end of window (which assumes that all progress within
a time window is equal to the progress measurement at
the end of the window).
Best Practice
Yes - adopts a linear interpolation (takes both the
previous and the next progress measurements into
account and derives an intermediate value on a straight
line basis).
• Does the method accurately account for activity progress between
progress measurements?
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An Optimal Method of Delay Analysis?
• Key Features:
1. Hybrid (Continuous and Discrete) Timescale
2. Three Delay Types Treated Separately:
A. Discrete Event delays (occur in discrete time)
B. Arc delays (occur in continuous time)
C. Node delays (occur in continuous time)
3. Continuous Delays: Emphasis on Modelling the Path Growth Rate
4. Discrete delays: can be modelled with before versus after comparison using fragnets etc.
5. Incorporation of Interim progress measurements
6. Introduction of the Excusability Coefficient
7. Adapt network so that the path growth rate is a constant for each element
8. Dealing with Concurrent Delay and Float Ownreship in a Sound Manner
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The Continuous-Discrete Dichotomy
• Some delays occur gradually as a result of work proceeding on activities
at a slower rate than forecast. Such delays occur in ‘continuous time’.
• e.g. excavation - ground harder than expected, contractor waiting for
the release of design information
• Other delays arise from events in ‘discrete time’ - that is, independently
founded events that bring about (or are deemed by the application of
relevant legal doctrine to bring about) an instantaneous change to
downstream scheduled activities planned or forecast for the future.
• e.g. change order to work downstream of current work front.
• Hybrid timescale…
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The Hybrid Timescale
Hour 1
Time (t)
Hour 2 Hour 3 Hour 4 Hour 5 Hour 6 Hour 7
Continuous Time
Event 1
Event 2
Event 3
Discrete Time
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SCL Method
(SCL Protocol,
2002)
AACE Method
As-Planned versus
As-Built
MIP 3.1 Observational/ Static/ Gross
Impacted As-
Planned
Time Impact
Analysis
Best Practice
Discrete
Continuous
• MIPs 3.1 - 3.5 model delay as continuous only
• MIPs 3.6 - 3.9 model delay as discrete only
• Best practice: a hybrid timescale…
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The Three Types of Delay
• Three types of delay:
• e.g. excavation - ground harder than expected, contractor
waiting for the release of design information
• Other delays arise from events in ‘discrete time’ - that is,
independently founded events that bring about (or are deemed
by the application of relevant legal doctrine to bring about) an
instantaneous change to downstream scheduled activities
planned or forecast for the future.
• e.g. change order to work downstream
• Hybrid timescale
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Set Clocktime = 0
FINISH
Discrete Simulation
Process
yes
yes
no
Is Next Step
Discrete?
Continuous Simulation
Process
no
Has Simulation
Reached End?
Clocktime++
Simulation allows Continuous
and Discrete Steps to be
Interwoven with Each Other…
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Accounting for Arc and Node Delays
PROJECT
START
PROJECT
FINISH
Logic Link
Task
Milestone
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PROJECT
START
PROJECT
FINISH
Arc (experiences arc delay)
Arc (does not experience delay)
Node (experiences node delay)
Node (does not experience delay)
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PROJECT
START
PROJECT
FINISH
Path Growth Rate
of Node is 1 Path Growth Rate
of Arc is n2
Path Growth Rate
of Node is 1
Path Growth Rate
of Arc is n1
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PROJECT
START
PROJECT
FINISH
Making Task Start Nodes
Separate Elements of
Network So That Node Delay
to Task Start (a.k.a.
“Commencement Delay”)
is Tracked Separately
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• Discrete Event Delay (on the discrete timescale)
• Arc Delay (on the continuous timescale)
• Node Delay (on the continuous timescale)
•
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Arc Delay
• Network delay that arises spontaneously on the work front when a forecast task is carried out at a lower
(or different rate) of progress to that planned or forecast.
• Examples: excavation in tougher than expected geological conditions; a task with lower resource
• Arc delay is meaningfully represented as a path growth rate (q). This is the rate per unit time at which the
activity path that the arc falls on is lengthening. It equals unity minus the progress ratio (r).
• For example, if a task is planned to take 60 working hours and takes 80 working hours, then:
The progress ratio (r) is (60/80) = 0.75.
The rate of path growth (q) = 1 - r =0.25
dp/dt = 1 - dr / dt
The resultant arc delay is 80 - 60 = 20 hours.
• Arc delay from every task or sub-task on a network is derived from a comparison between the planned
or forecast duration, and the actual duration of the task or sub-task.
• Arc delay only occurs in relation to tasks or sub-tasks; never to logic links.
•
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Node Delay
• Network delay that arises when waiting for a milestone
to occur or a node to materialize.
• Progress Rate is always 0.
• Path Growth Rate is always 1.
• Examples: waiting for a task to start (“commencement
delay”), waiting for a client to release design information,
waiting for a client to issue free issue materials.
•
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Discrete Event Delay
• Network delay that arises spontaneously on the work front when a
forecast task is carried out at a lower (or different rate) of progress to
that planned or forecast
• Causes an instantaneous change to the network or the constraints that
apply to it and arises from a discrete event.
• Associated with causal chains, stemming from a root cause - unless
there is the intervention of a novus actus interveniens that severs the
chain of causation.
• Discrete event can be
• May be represented by fragnets - network fragments that model
instantaneous change.
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Forecast Actual PGR
Discrete Delay ∞
Node Delay 1
Arc Delay q ∈ [0,∞)

Modelling Discrete Delay
• Relatively straightforward comparison - before versus after on a
ceteris parabis basis, such as with a time impact analysis/ MIP 3.7.
• Note role of causal chain theory…
• Unlike node delays and arc delays, discrete event delay is
ascertainable without reference to the critical path.
• Discrete event delay does not show up in an as-planned versus as-
built comparison.
• It is simply the change in terminal-to-terminal length of the longest
path that the event being modelled brings about.
• Discrete change may be modelled by fragnets - fragments of the
network.
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Modelling Discrete Delay
• Fragnets can be incorporated into the network from project
commencement and then turned on or “activated” when the discrete
event occurs A fragnet means a ‘network fragment’ that is added or
subtracted to a network in order to model the effects of
instantaneous change.
• It is a joined set of network elements - arcs and nodes for a
topological network, or activities and links for a CPM network.
• This way, all data structures needed for the simulation can be
inducted in advance of the simulation All network elements are
incorporated within the topology of a single master network. Change
is then modelled by activating and deactivating elements. A
deactivated element plays no part in critical path calculations..
• Virtually all discrete change can be modelled by fragnets…
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PROJECT
START
PROJECT
FINISH
Accounting for Discrete Events
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PROJECT
START
PROJECT
FINISH
Accounting for Discrete Events
Addition of Fragnet…
Arcs and Nodes Are
Incorporated Into The
Network But Are Inactive
Until the Clock Time
Reaches the
Discrete Event Milestone -
Then Are Activated…
Discrete Event
Milestone
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No Type of Discrete Change Input Data Specified by User How Change is Modelled with Fragnets
1 Add new activity Definition of entire new activity Defined activity is part of fragnet that is initially inactive, but then
activated at the start time of the associated discrete causative event.
2 Subtract activity Activity Specified activity is part of fragnet that is initially active,but then
deactivated at the start time of the associated discrete causative event.
3 Increment task duration (only if no
interim progress measurements)
Task; Amount to add (subtract) to
existing task duration in working
hours
Specified task is duplicated. Duplicate with altered duration is part of
fragnet that is initially inactive, but then activated at the start time of
associated discrete causative event. Original is part of fragnet that is
deactivated at the same time.
4 Change task duration (only if no
interim progress measurements)
Task; Duration that replaces
existing duration in hours.
Specified task is duplicated. Duplicate with altered duration is part of
5 Increment logic link lag Logic Link; Amount to add
(subtract) to logic link lag in
working hours.
Specified logic link is duplicated. Duplicate with altered lag is part of
6 Change logic link lag Logic Link; Duration that replaces
existing duration in working hours.
Specified logic link is duplicated. Duplicate with altered lag is part of
7 Change calendar of activity Activity; Define entire new
calendar that replaces specified
Calendar of activity.
Replacement calendar is defined as a separate calendar within the
calendar data set. Duplicate activity with altered calendar is part of
associated discrete causative event. Original activity is part of fragnet
that is deactivated at the same time.
8 Change calendar of logic link Logic Link; Define entire new
calendar that replaces specified
Calendar of activity.
Replacement calendar is defined as a separate calendar within the
calendar data set. Duplicate logic link with altered calendar is part of
associated discrete causative event. Original logic link is part of fragnet
that is deactivated at the same time.
9 Increment task resource
requirement profile
Resource; Amount to increase
gang size of resource
Duplicate task with altered task resource requirement profile is part of
associated discrete causative event. Original task is part of fragnet that
is deactivated at the same time.
10 Change task resource requirement
profile
Resource; New gang size of
resource.
Duplicate task with altered task resource requirement profile is part of
associated discrete causative event. Original task is part of fragnet that
is deactivated at the same time.
11 Change resource capacity profile Resource; New array of vectors
that defines the resource capacity
function of the resource over the
project range.
Resource is duplicated with altered resource capacity profile in
resource data set. Duplicate task with duplicated version of original
resource capacity profile is part of fragnet that is initially inactive, but
then activated at the start time of the associated discrete causative
event. Original task is part of fragnet that is deactivated at the same
time.
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Causal Chain Theory
• The modelling of discrete events is governed by theory that mixes legal doctrine with rational scientific logic, known as
causal chain theory. What consequences or ‘knock-on effects’ of a discrete causal event should be attributed to the effects
of the event itself? How far should a chain of causation be inferred, given that ultimately, if one goes back far enough,
everything is just a consequence or knock-on effect of the Big Bang?
• causa proxima est non remota spectatur - spawned ‘reasonable foreseeability’.
• All of the consequential or ‘knock-on’ effects of a discrete event are deemed to vest at the very instant the event occurs,
unless they are supervened by a novus actus interveniens.
• A nail is an intervening or ‘fresh’ event or action that packs enough of a punch to ‘sever’ the discrete event’s ‘chain of
causation’.
• e.g. deliberateness or carelessness (especially negligent or criminal behaviour) - C deliberately deciding to proceed slowly
on additional work..
• The extent of a causal chain is usually resolvable by common sense but sometimes may be disputable.
• e.g. instruction to install a waterproof membrane in a bathroom wall will not be considered a fresh event if the membrane
is already part of the design that a contractor has agreed to build, or if it is to remedy a shortcoming that arises from
shoddy workmanship by the contractor. In such cases the instruction is simply a link in a causal chain that was initiated
earlier. It will, on the other hand constitute a fresh event and found a new causal chain if it arose from, say, a design
change materialising from revised client requirements.
• Causal chains are modelled by adding or subtracting fragnets to and from the network (or possibly, in some instances,
changing the resource capacity profile that pertains to a particular resource).
pezalaconsulting

Modelling Continuous Delay
• Path Growth Rate (PGR) is key concept.
• Objective:
• divide the timescales into small intervals,
• identify the delay across the interval
• identify the critical element(s) that are deemed to be causative of delay across the interval (= dominant/
proximate cause)
• apportion blame for the delay to the critical elements
• excusability then considered to determine EOT associated with element
• Just as there is a growth rate for each path, there is also a growth rate for the project makespan as a whole
• If there is only one critical path, m’s growth rate for a small interval dt immediately following an instant on the
time clock t will be the growth rate of the fastest growing critical path.
• The fastest growing critical path can be deduced to have been on the cusp of overtaking the slower-growing
critical paths. The tie occurs only for an instant.
• cf. Daily Delay Measure
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• For snapshots (with no discrete events), note that there are two criteria for criticality:
• activity must be in progress
• activity must be on the longest path
• But across intervals, however, there are three criteria for determining criticality:
• activity must be in progress
• activity must be on longest path
• activity must be on fastest growing longest path.
• Just as there is a growth rate for each path, there is also a growth rate for the project makespan
as a whole.
• If there is only one critical path, m’s growth rate for a small interval dt immediately following an
instant on the time clock t will be the growth rate of the fastest growing critical path.
• The fastest growing critical path can be deduced to have been on the cusp of overtaking the
slower-growing critical paths. The tie occurs only for an instant
pezalaconsulting

Path Length
Path Growth Rate (PGR)
Activity C
Activity A
Activity D
Activity B
only activity that is
critical for the whole interval
only critical at very
start of interval
Four Activities in Progress:
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• Another way of thinking about the three criteria for interval criticality:
• ‘Triple zero slack’
• Distance between activity and work front = 0 (i.e. activity is in
progress).
• Distance between longest path in network and length of the path
activity is on (i.e. total float, Φ) = 0;
• Distance between path growth rate of activity and path growth rate of
fastest growing critical activity = 0 (i.e. dΦ / dt = 0). This is the first
order derivative of float over time.
• Each of these measurements can be thought of as a kind of ‘slack’.
The concept of ‘critical’ insofar as it pertains to an interval can be
thought of as ‘triple zero slack’ criterion!
pezalaconsulting

Accounting for Progress Records
PROJECT
START
PROJECT
FINISH
Path Growth Rate
of Second Segment is n2
Path Growth Rate
of First Segment is n1
Path Growth Rate
of First Segment is m1
Path Growth Rate
of Second Segment is m2
Progress
Record
Progress
Record
pezalaconsulting

PROJECT
START
PROJECT
FINISH
Path Growth Rate
of First Segment is m1
Path Growth Rate
of Second Segment is m2
Progress
Record
pezalaconsulting

PROJECT
START
PROJECT
FINISH
pezalaconsulting

Excusability
• ‘Excusability’ means the property of whether or not any terminal delays arising
from an element of the network will be ‘excusable’ (i.e. give rise to a concomitant
EOT).
• A mathematical distillation of a contractual concept.
• Based on the contractual EOT provisions.
• Independent from compensability or cost compensation.
• A rational number between 0 and 1. Normally 0 (not excusable) or 1 (excusable).
Intermediate values, however, may arise from a measured mile analysis or
similar.
• The excusability of node delays will often be obvious from the schedule
milestones (e.g. engineer releases design information, owner provides free issue
materials: milestones with exc. = 1).
• (Gross) EOT for Element = (Gross) Terminal Delay * Excusability
pezalaconsulting

Concurrent Delay
• Concurrency pertains to an indeterminacy in the context of
determining causation - a failure of the primary system to
isolate a single cause as dominant/ proximate(= identify a
single delay as critical). A special rule is thus required to
resolve this indeterminacy.
• It arises when multiple delays occur at the same time (but not
all delays occurring at the same time are “concurrent” in this
sense).
• Only delays on the continuous time scale can be concurrent.
This is because discrete events are always modelled one after
the other, never together at the same time.
pezalaconsulting

• For a single snapshot of time:
• Two criteria for determining the dominant/proximate
cause: (1) in progress and (2) on longest path
• For a small interval of time following a snapshot:
• Three criteria for determining the dominant/ proximate
cause: (1) in progress; (2) on longest path; (3) highest
growth rate of elements satisfying (1) and (2)
• What do we do if these ‘filters’ fail to isolate a single
element of the network?… Need a tiebreak rule…
Concurrent Delay
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• Potential tiebreak rules…
1. Where multiple elements are concurrently causative of the delay, ‘blame’ for the overall project
delay gets apportioned evenly between the members of the concurrent set.
• Excusability of concurrent set = the mean excusability of the set
delay gets apportioned to the member(s) of the concurrent set with the highest excusability.
• Excusability of concurrent set = the maximum excusability of the set
delay gets apportioned to the member(s) of the concurrent set with the lowest excusability.
• Excusability of concurrent set = the minimum excusability of the set
• In my opinion (1) is the best, simplest, and most logical approach. Some contracts, however,
expressly or impliedly specify (2) or (3).
Concurrent Delay
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• Why in my opinion is the ‘mean’ approach best?
• No two processes are ever truly in tandem and lockstep
• There will always be at least some stochastic variation in which of two
processes is in the lead or on the longest path, even if the average rate
of progress (e.g. concrete curing) of the two processes is tied.
• In this sense, concurrent delay doesn’t really exist. It’s only something
that arises from modelling assumptions.
• It is thus reasonable to assume, absent further progress records, that
for n processes occurring in tandem, each will be on the longest path
1/n of the time and thus causative of 1/n of the terminal delay.
Concurrent Delay
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Float Ownership
• ‘Float’ in this context really refers to two things:
• Accrued terminal gain
• Contractual milestone contingency
• Computation needs to distinguish between terminal
delay on a net and gross basis, if contractor ‘owns’
float.
pezalaconsulting

Time
Discrete
Terminal
Delay
Inexcusable Terminal Discrete Delay
Excusable Terminal Discrete Delay
Discrete
Terminal
Gain
(Discrete Delays)
Overall Discrete Delay: the Sum of
All the Lines (As Applicable)
hours
Presentation of Results
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Time
Path
Growth
Rate
Excusable Terminal Continuous Delay
(Continuous Delays)
Overall Continuous Delay: the Sum of
the Areas (As Applicable)
0
1
Delay
Gain
Partially Excusable Delay
(Excusability = 0.5)
Concurrent
Delay
pezalaconsulting

Time
Path
Growth
Rate
(Combined Timescale)
0
1
Delay
Gain
Time
Discrete
Terminal
Delay
hours
Excusable Terminal Discrete Delay
pezalaconsulting

Time
Path
Growth
Rate
(Continuous Delays)
0
1
Delay
Gain
Concurrent
Delay
Concurrency Treatment:
Even Apportionment
Approach
pezalaconsulting

Time
Path
Growth
Rate
(Continuous Delays)
0
1
Delay
Gain
Concurrent
Delay
Activity with
Minimum Excusability
Deemed to be Dominant/
Proximate Cause of
Terminal Delay
pezalaconsulting

Time
Path
Growth
Rate
(Continuous Delays)
0
1
Delay
Gain
Concurrent
Delay
Activity with
Maximum Excusability
Deemed to be Dominant/
Proximate Cause of
Terminal Delay
pezalaconsulting

anders@pezala.com
pezalaconsulting
Temporary US Phone No:
1917-891-4965

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