2004 AACE International Transactions
CDR.09
Calculating Imaginary Numbers:
Time Quantification in Acceleration
John C. Livengood and Christopher R. Bryant
ow long would the project have taken if the work
had not been accelerated? This question confronts
most forensic scheduling experts when attempting
to justify the costs incurred in accelerating the
project to overcome delays. The time projection, since it never
actually happened, is an "imaginary number." It is a number that
never really occurs—the schedule consultant only imagines what
would have occurred, "but for" the acceleration efforts. Such a
calculation is often essential to support the cost incurred in performing acceleration. It renders a tangible number on the contractor's efforts.
This paper will explore one of the few reliable and detailed
methodologies available to a schedule expert to quantify the acceleration efforts undertaken to complete a project—the application
of Time Impact Analysis (TIA) methodology to a forward-looking
sequential analysis. This paper will examine both the similarities
with this common usage of TIAs as well as the nuances of using
the method to prove acceleration.
H
IDENTIFYING THE PROBLEM
Forensic schedule consultants have been asked to justify
acceleration costs more frequently in recent years. These costs are
generally related to increasing the number of labor workhours,
management and equipment needed to complete a task in a time
period less that originally estimated.
There are two types of acceleration—constructive and
directed. Constructive Acceleration requires denial of a
valid time extension request and you must actually
accelerate the work. Directed Acceleration is due to a
written demand by the owner/general contractor. All
acceleration affects productivity but the longer an accelerated effort continues, the more labor is lost due to the
impacts from acceleration [1].
quickened. Acceleration occurs when the contractor performs its work at a faster rate than required by the original contract [2].
Recently, the calculation of acceleration has often entailed
quantifying acceleration simultaneously with delay. The contractor often argues that changes or impacts to its work beyond its control have increased the scope and complexity of the work required
to be performed. Yet the time allowed for this increased scope is
not sufficient to perform the additional work. As a result, the actual achievement of activity completion is delayed, but the work
required accomplishing that work is increased or accelerated:
Constructive Acceleration occurs when a contractor has
a justified claim for an extension of time and the owner
or general contractor refuses to adjust the completion
date for performance, and instead, requires the contractor to finish the project by the original contract completion date [3].
The result is simultaneous delay and acceleration. The
methodology explained in this paper quantifies the delay to which
the contractor was entitled, thus establishing one element of "constructive acceleration." The resultant costs associated with acceleration are generally related to increased labor costs but the full
range of acceleration costs can include:
•
•
•
•
•
•
•
•
Overtime Costs
Additional Labor Costs (more crews or double shifting)
Stacking of trades costs
Loss of labor efficiency costs
Additional equipment costs
Additional supervision costs
Increased material delivery costs
Increased overhead costs.
Throughout this text, the authors have used an example to
Either type of acceleration involves working at a more aggres- explain the acceleration time quantification methodology. This
sive rate than conditions would otherwise support.
model assumes a major industrial complex, with a contract start
date of 01-Feb-99, and a completion date scheduled 626 calendar
Acceleration is the process by which the ordinary and
days later on 18-Oct-00. The project involved several major phasexpected progress of events in a construction contract is
es during which the owner initiated numerous changes. In the
CDR.09.1
2004 AACE International Transactions
Figure 1—Overall Delay and Acceleration Summary
example, completion was achieved on 24-Apr-01, 188-calendar
days late. However, considering the overall delay to the project
and the original planned rate of execution of the work, the contractor would not have achieved project completion until 08-Mar02, but for the accelerated efforts undertaken to mitigate the
delays and impacts.
In Figure 1, the calculated delay and acceleration are shown.
As the figure indicates, the overall delay exceeds the acceleration,
or recovered time, achieved by the contractor. The unrecovered
delay, which occurred between 18-Oct-00 and 24-Apr-01, 188
calendar days, represents the number of days of delay that the contractor's acceleration efforts were unable to overcome.
sequence of construction events. These natural breaks provide an
opportunity for the evaluator to measure progress. While the contractor may have maintained CPM updates on a monthly basis,
the breaks do not always occur exactly at a schedule update.
However, the analysis is predicated on having monthly updates, so
identifying changes near in time to those updates is very helpful.
Not all monthly updates should be used in the analysis. To do so
would create a huge amount of unnecessary, and falsely detailed,
analysis. Therefore, the schedule analyst should identify natural
breaks in the construction where major events occurred. Some of
the possible considerations in identifying these breaks should be:
•
•
METHODOLOGY
•
The analysis is performed by taking an original schedule
(often a baseline schedule), modified if needed, and impacting it
to reflect what would have happened "but for" the contractor's
acceleration. Then, by comparing that modified schedule with
the actual events as reflected in the as-built schedule, a calculation can be made that identifies the acceleration (or delay)
achieved during the course of actual performance.
The "Time Impact Analysis" (TIA) methodology is used to
calculate the impact of the events occurring during each of three
separate time periods [4]. The facts associated with each impact
event are then examined and a "fragnet," a portion of a Critical
Path Method (CPM) schedule network, was developed for each
event allowing its specific impact on the project to be integrated
into the baseline schedule. The use of this methodology ensures
that the individual impact of each change is properly considered
with respect to its influence upon the schedule. When all of the
impacts for a particular time period have been developed and
inserted into the schedule, the schedule is recalculated.
Near to a data date of an update
Development of a new or substantially revised baseline
schedule
Issuance of an acceleration order (directed or constructive)
• Major construction event
• completion of a milestone
• start of a new phase
• arrival of a major element of equipment
• an accident
Using too few time periods is often misleading and not helpful to the contractor. In such cases, the measurement covers too
long a period and often includes non-acceleration periods as well
as acceleration. This results in weakening the "cause and effect"
relationship between events and accelerations. Conversely, using
too many time measurement periods unnecessarily complicates
the analysis, increases consultant costs, and subdivides continuous
acceleration efforts. In Figure 2, the authors have modeled an
acceleration analysis using three time periods.
Figure 2 depicts the three time periods used in performing
this example. The first period runs from start of the project
through initial engineering and general site civil construction.
The second period runs from the start of steel construction
through a major change order. The third period runs to the start
Step One—Identifying Time Periods
of the mechanical equipment installation through mechanical
The first step is to identify the major time periods associated equipment start-up and commissioning.
with the project. Generally, there are natural breaks in the
CDR.09.2
2004 AACE International Transactions
Figure 2—Time Periods
Step Two—Modifying the Baseline Schedule
The starting point for any schedule analysis that is intended
to identify delay or acceleration is to determine the appropriate
baseline schedule. The baseline schedule is the schedule that
most closely represents how the contractor originally planned to
perform or execute the work. Ideally, such a schedule is prepared
by the contractor shortly after commencement of the work and
complies with all aspects of the contractor's contract, depicting in
reasonable detail the sequencing, durations and relationships
among the design, procurement and construction activities of the
project. Sometimes the baseline schedule must be modified.
Typically such modifications might include:
Step Three—Impact Fragnets
Identifying Events—As with any complicated delay analysis, a
major task is identifying the impact events. Typically this work
involves detailed discussions with the appropriate staff, a careful
review of the correspondence, daily reports, monthly meetings
and proposed/approved change orders. Once a list of the major
events has been identified, a detailed understanding of the
sequence of those events is necessary to enable the schedule consultants to create a detailed description of the event, as a series of
schedule events, a fragnet. Unlike a more traditional TIA analysis,
there is no need to insert activities for which the contractor is
responsible. The reason is that the success (or failure) of the con• Removal of progress that was included in the baseline sched- tractor to recover from its own errors will be evident in the actual
ule
dates. So if the contractor is responsible for a significant delay, it
• Correction to logic connections that fail to reflect the actual will manifest itself by offsetting the calculated acceleration.
predecessor-successor relationship
• Changing the duration to more realistically reflect the work. Creating the Fragnet—Each fragnet includes a description of the
additional or changed work, the sequence of new activities that
It is best not to adjust the baseline schedule [5]. However, it describe the work, durations for each of these activities, and the
often occurs. The most difficult baseline schedule to adjust, and existing schedule activities to which it is logically tied. The impact
one where such adjustment is most needed, is one where the activity is inserted given either non-accelerated durations or durasequence and timing of the activities is predicated on non-con- tions drawn from "actual" performance if appropriate. In other
tractual milestones rather than logic ties between activities. In words, the fragnet represents a CPM activity sequence that would
other words, the creator of the original schedule imposed "start no have been included in the original schedule if the contractor had
earlier than" or "finish no later than" constraints. This is known as known the work was going to be required at the time it created the
implied logic. If these problems remain unadjusted, the result is a baseline schedule.
schedule that when impacted with a fragnet and recalculated will
Impact events are then inserted into the "adjusted baseline
not demonstrate that a delay has occurred to the project. The solu- schedule." By linking these extra work requirements and impact
tion to this problem is to add logic ties in place of constraint dates. events to their proper existing schedule activities, each of the
However, these ties must not change the sequence or timing of the impacts is integrated into the appropriate adjusted baseline
activities. The "adjusted baseline schedule" must, like the original schedule to create an impact duration schedule. Each impact
baseline schedule, comply with the contract requirements.
event is described in detail as a "fragnet," a portion of a CPM
schedule. A fragnet is a sequence of new activities and/or activity
revisions that are added to the requisite baseline schedule in order
CDR.09.3
2004 AACE International Transactions
Table 1
Activity ID
CA31360010
CA31360020
CA31360030
CA31360040
CA31360050
CA31360105
CA31360115
CA31360205
Activity Description
Original
CHANGE NOTICE ISSUED
NOTICE TO PROCEED ISSUED
DESIGN & ISSUE FDN DRAWINGS
DESIGN & ISSUE STEEL DRAWINGS
FAB & DELIVER STR STEEL
INST ADDITIONAL BLDG PILING
F/R/P BLDG ADDITIONAL FDNS
ERECT & ALIGN ADDITIONAL STEEL
to assess the influence of an event upon the schedule's activity
sequencing and overall duration. It is part of a method for analyzing delays and impacts on a schedule. The following steps
describe the sequence of analysis generally followed in assessing a
delay by use of fragnets: 1) Select the time period related to the
date of the occurrence of the impact event; 2) Define the scope of
the impact event; 3) Review the appropriate period baseline
schedule and determine which activities are associated with the
impact and how they are impacted; 4) Prepare a fragnet illustrating the sequence of the impact event and define its relationship to
the current schedule and/or existing activity durations for added
work; and, 5) Repeat Tasks 1 through 4 for each selected event or
condition.
Special Issues Regarding Activities within the Fragnet—Two
special issues are involved in the development of fragnets. The
first is how to determine durations for activities that did occur, but
occurred under circumstances very different than what would
have been planned. For example, if additional engineering is
involved, how is that duration calculated. Two obvious methods
present themselves: First, the contractor's original planned productivity for engineering could be utilized. If the contractor
planned to produce one engineering drawing for every three workdays, then a change that required five drawings would be fifteen
workdays. But what if the contractor had doubled her engineering
workforce (or increased the hours worked per week)?
Alternatively, the actual time spent producing the additional drawings must be considered. This assumes the contractor's records
support such detail. But it is likely that the actual drawing production did not occur smoothly. The authors have concluded that
using the original planned production rate for the engineering
reflects the unaccelerated duration and is therefore appropriate.
The second special issue is how to treat construction durations. Even more so than the engineering activities, there is no
clear way to estimate the duration of a construction activity in an
unimpacted, unaccelerated environment. For this reason, contemporaneous change order estimates are sometimes suspect as
they usually incorporate some impact factor. Another alternative
is to use actual durations for these added activities. Since this work
is performed under impacted conditions, the fragnet would contain a potentially major activity that reflects the delay and acceleration efforts. This clearly does not reflect unimpacted durations,
but is the most "conservative" estimate available. The authors
believe that the best method, like that for engineering, is to use
originally planned productivities in estimating the duration of the
impact work.
Duration in CDs
1
20
20
20
60
2
3
15
Fragnet Example: Addition of Building Extension—This fragnet/change was the result of modifications to the buildings as
ordered by the owner. It required that the "low bays" be extended
on the east and west sides of one building. The contractor's estimate for this work was 315 engineering workhours, most of which
dealt with foundation and steel design and 1,300 construction
workhours, most of which is for steel erection. The impact fragnet,
that included eight different activities, was developed from the
information contained in the contractor's files. See Table 1.
The fragnet in Figure 3 charts the added activities in a timebased format. The fragnet starts on 10-May-99 when the contractor issued a change notice to advise that extra work was required
to increase the size of the building. On 08-Jun-99, the owner
issued a Notice to Proceed with the change. The duration of the
activities was determined based on the engineering and construction workhours estimated by the contractor. These activities were
then linked to the appropriate schedule activity. Figure 3 illustrates the time scaled fragnet.
The fragnet was inserted into the impact duration schedule.
The schedule was then calculated to determine if this change had
any critical impact on the overall project completion. The result
indicated that this fragnet would, in fact, have extended the anticipated completion date of the Project. The bar chart depicts the
additional activities associated with this impact fragnet and their
relationship to some of their predecessor and successor schedule
activities.
Step Four—Recalculate The Impact Schedule
The impact duration schedule is recalculated, and the new
projected completion date is identified. Not all fragnets result in
an increase to the overall projected performance period since only
impact fragnets falling on the critical path of the new schedule
result in a change to the projected completion date. However, the
authors believe that all reasonable possible impacts should be
considered and inserted, even though many will have no impact
on the overall delay. This is for two reason: First, complete inclusion ensures that no impact or possible delay is inadvertently overlooked. Second, if needed, certain impacts could be deleted from
the analysis to ascertain near critical paths—an important feature
if the owner asserts concurrency.
Step Five—Insert Actual Progress
The actual schedule update at the end of the period is used
with progress based upon contemporaneous records of actual
CDR.09.4
2004 AACE International Transactions
Figure 3—Activity Fragnet
Figure 4—Period One Delay and Acceleration Summary
progress reported on individual activities. Added to this schedule Oct-00. This represents an acceleration benefit of 69 calendar
are the fragnets that were not completed during the period. This days, 13-Dec-00 vs. 05-Oct-00. Through schedule re-sequencing,
impact schedule, with actual status, is given a new name.
additional engineering workhours and field acceleration, the contractor accelerated the progress of its performance and recovered
69 calendar days of the projected 72 calendar day delay. This
Step Six—Compare to Contemporaneous Update
acceleration was not, however, wholly sufficient to overcome all of
The final step is to compare the projected completion date the delays that occurred in Period One. The remaining three calcalculated in Step 4 with the projected completion date calculat- endar days would have to be recovered, if possible, in subsequent
ed in Step 5. Step 4 is comprised of the baseline activities and work efforts.
impacts, while Step 5 is comprised of the baseline activities,
Figure 5 shows the impact critical path for the first period
impacts, and progress. This comparison shows what the impacted along with the accelerated path showing a recovery of 69 calendar
projected completion date would have been if there had been no days. As shown, this recovery was accomplished by performing out
acceleration and what it should have been with actual progress of sequence work along with reducing durations of follow-on
incorporated. See Figure 4.
activities.
In this example, the contractor accelerated its work during
The authors have also encountered situations where the con2000 in an attempt to maintain the contract completion dates. As tractor's contemporaneous updates are not appropriate for coma result, Period One, adjusted for delay impacts, shows a project- parison. This may be because of incorrect monthly statusing, or
ed completion date of 13-Dec-00. The current update at the end the failure to status at all. In these situations, the authors have
of Period One with the addition of the lingering effects of the used a less desirable comparison, comparing the adjusted impactuncompleted Period One impacts shows a completion date of 05CDR.09.5
2004 AACE International Transactions
Figure 5—Period One Delay and Acceleration Detail
ed schedule with progress against the original adjusted baseline
schedule with progress through the same date.
SUMMARY OF THE STEPS TO PERFORM ANALYSIS
Because each of the three time periods involves a separate
calculation, the agreed baseline schedule was updated before the
new impacts were entered and the delays and accelerations calculated. Figure 6 illustrates this iterative analysis sequence, beginning with Impact Schedule IZ01 for Period #1, IZ06 for Period #2
and IZ15 for Period #3.
The steps described above are then repeated for each separate
time period. It is expected that each time period is different—the
delays identified and the resultant acceleration are different for
each.
In Figure 6, the TIA acceleration process is summarized. For
example, baseline schedule IP01, which predicted delivery on 18Oct-99, the bottom left-most box, is modified to better permit statusing. The modifications did not alter the intended logic: rather,
they permitted the schedule to better reflect ongoing progress.
These logic corrections create schedule AP01, which has the
same dates as IP01. Then AP01 was impacted with 18 events to
create IZ01, showing completion 17-Jan-01. Reported progress
reduced this to 31-Oct-00. This process was repeated for the second and third periods.
ACCELERATION ANALYSIS SUMMARY
Based upon the example, it can be concluded that, while
overall delivery of this example project was delayed to 24-Apr-01,
the contractor accelerated its performance so as to mitigate a total
of 318 calendar days of that delay (71 + 115 + 132). But for the
additional efforts by the contractor, including engineering, procurement and administration services and the extra efforts of the
subcontractors including additional craft labor and construction
equipment, additional shifts and overtime, completion would not
have been achieved until 08-Mar-02.
In Figure 7, the calculated delays (91+167+248 = 506) and
accelerations (71 + 115 + 132 = 318) are shown. The delays
incurred in a period do not match the accelerations for the same
period, and the overall delay incurred does not match the acceleration recovery of contractor. The unrecovered delay of 188 calendar days (506-318) between 18-Oct-00 and 24-Apr-01 is the
number of days of delay that the contractors' acceleration efforts
were unable to overcome.
The contractor and subcontractors' efforts to accelerate their
performance to deliver the project as timely as possible resulted in
the completion on 24-Apr-01. This effort represents a net acceleration of 318 calendar days, approximately one year, over and
above the time impacts caused by factors not attributable to the
contractor. See Table 2.
CDR.09.6
2004 AACE International Transactions
Figure 6—Schedule Development Diagram
Table 2
Planned Duration
Actual Duration
All Periods Impact
Projected Duration
Total Acceleration
Start Date
1-Feb-99
1-Feb-99
Overall Delay Summary Table
Delivery
Calendar Days
18-Oct-00
626
24-Apr-01
814
1-Feb-99
24-Apr-01
08-Mar-02
08-Mar-02
he use of a progressive analysis of impacts, with comparison to contemporaneous updates, provides a powerful tool for assisting a trier of fact in determining the
degree of acceleration. The analysis discussed here
must however be coupled with a detailed factual cause and effect
analysis. The result will be to confirm the calculation of imaginary numbers.
T
John C. Livengood
Vice President
Warner Consultants
2275 Research Boulevard, Suite 100
Rockville, MD 20850-3268
E-mail: [email protected]
CDR.09.7
1131
318
Calendar Days Early Completion Schedule
0
188
530
Christopher R. Bryant
Senior Consultant
Warner Consultants
2275 Research Boulevard, Suite 100
Rockville, MD 20850-3268
E-mail: [email protected]
2004 AACE International Transactions
Figure 7—Delay and Acceleration Summary by Period
CDR.09.8