Project Management Institute

GPM® and forensic total float


The critical path method (CPM) is widely used as a project management tool for planning and scheduling. Basic to CPM is drawing a project network, from which project completion, total floats, and the critical path are calculated. Once actual dates are introduced in a CPM network, we lose total floats left of the data date, and the critical path can no longer be calculated. The ability to determine total floats and the critical path for the as-built portion of a schedule (left of the data date) is solved by the graphical path method (GPM). This paper presents the concept of GPM forensic total float and its role in retrospective schedule analysis, whether in updating or forensic analysis. A compendium of CPM and GPM floats is provided for context.

The CPM Alternative

Evaluation of a project schedule is required for successful performance, both before the project starts and once it is under way. If performed before the project starts, the analysis is prospective. Once a project is under way, analyzing the project schedule at a point in time to verify completion is on track and to possibly revise the plan and schedule going forward, is a common process. Retrospectively evaluating actual performance of a completed project may be of interest for lessons learned or, if completed late, to reconcile prolongation to the impacted activities and the time-impacting events.

CPM was developed in the late 1950s as a prospective method for planning and scheduling complex projects. (Kelley & Walker, 1959) In CPM, planning states what activities must occur and in what order for the project to complete, and ends with a network of all activities in logical sequence without dates. With activities' elapsed times and the network, scheduling first calculates early start and finish times for all activities. Using the project completion as the late finish of the last activity, late finish and start times for all activities are then calculated. If the time from early start to late finish available to any activity exceeds its elapsed time, it has positive total float and is a floater; if not, the activity has a total float of zero and is critical.

With late times limited by project completion, a floater may be delayed within total float range without delaying completion. CPM's emphasis on late times is thus essential to timely completion; however, typical to CPM is to continue to focus on the earliest possible times, thereby relinquishing the ability to interpret float as measuring the available schedule gain, not just delay.

As a prospective method, the basic application of CPM was for an entire project, before any work was started. CPM did not originally consider updating and maintaining the network and schedule current with progress once the project started. In the early 1960s, varying updating methods for planning, scheduling, and controlling what remained of a partly completed project were introduced. (Moder & Phillips, 1964, p 265; O'Brien, 1965; Antill & Woodhead, 1965, p 183; Shaffer, Ritter & Meyer., 1965) The methods statused completed activities differently, but shared the common goal of applying the CPM calculations only to the portion of a network right of the data date. Updating did not extend to applying the CPM calculations left of the data date.

Retrospective Calculations – The CPM Workaround

Once actual dates are introduced into the scheduling process, CPM algorithms cease to function for the portion of the network left of the data date. CPM calculations go inactive to the past of the data date for two reasons: (1) total floats can no longer be calculated using the CPM equation of late finish date (or actual finish) less early finish date (also actual finish); and (2) for a completed activity, float measured from its actual dates is not as-built total float unless its actual dates, along with the actual dates of all its preceding activities, back to the project start event, are exactly on their respective earliest possible actual dates.

With CPM unable to calculate total floats in the past, the critical path cannot be calculated for the fully-statused portion of a schedule, or for the as-built schedule. Analysts work around this CPM forensic void by pushing the data date out of the way. To deploy CPM calculations, analysts using a baseline (AACE, 2009, p 17), hold the data date at the project start or at the start of the period being evaluated. Statusing is limited to making the durations of activities experiencing progress within the period match their actual or would-be remaining durations and to actualizing logic, and excludes introducing actual dates.

To deploy CPM calculations, analysts working with as-built schedules, perform prospective simulations of the as-built in its entirety, or for an as-built window. (Ponce de Leon, 1984; Keane & Caletka, 2008, p 141) For the as-built schedule, these simulations reset the data date back to the project start, remove actual dates, set activity durations as the time between actual start and finish dates and actualize logic, yielding a prospective model of the as-built, for which CPM calculates early dates and total floats for the actual durations; this reveals the as-built critical path. Prospective simulations woik around CPM's inability to calculate total floats left of the data date by moving the data date back to the project start, or to a prior data date.

Problems Stemming from the CPM Modus Operandi

A CPM schedule chock-full of earliest possible dates that do not make use of available floats is counterintuitive to those responsible for delivering the project. Left on their own to develop more realistic working schedules, personnel in the field use bar charts and other methods to schedule the work efficiently, regrettably, often disconnected from the CPM schedule. Furthermore, CPM limits options by treating float as only measuring leeway with respect to project completion. The fact that an activity scheduled between its early and late dates has float available in either direction is a novel idea to CPM schedulers.

Knowing that completed activities and the start of in-progress activities are left out of CPM calculations, few practitioners feel compelled to actualize logic ties and lags—the forgotten step in updating. (O’Brien & Plotnick, 2009, p 535) It does not help that schedulers’ propensity for ignoring logic/lag status left of the data date is encouraged by software out-of-sequence rules. (Glavinich, 2004, p 173; Keane & Caletka, 2008, p. 65) In addition, without figuring in float calculations, the rigor applied to recording actual dates is inconsistent amongst schedulers. (Wickwire, Driscoll, Hurlbut, & Hillman , 2003; O'Brien & Plotnick, 2009, p 536)

Although actual start/finish dates do not affect CPM calculations, they document the as-built schedule; to qualify as an as-built, the cause of delays need not be shown as long as the delay effect is shown. (AACE, 2009, p 21) However, without total floats, there is no algorithmic way to calculate the critical path. “The as-built critical path cannot be directly computed using CPM logic since networked computations that generate float values can be generated only to the future (right) of the data date.” (AACE, 2009, p 99) This guidance is only partly correct because total floats are needed for criticality, not just floats.

Some analysts overcome CPM's retrospective void by using observational methods on contemporaneous updates. “The closest the analyst can determine the as-built critical path is to cumulatively collect from successive schedule updates the activities that reside on the critical path between the data date and the data date of the subsequent update.” (AACE, 2009, p 99) One such method gleans floats from updates and groups and filters driving activities to determine the as-built critical path. The authors warn that float values can be manipulated by a planner in many ways and should therefore never be used as the sole indicator of determining the location of the driving path or as-built critical path. (Keane & Caletka, 2008, p 240)

The Graphical Path Method Alternative

Like CPM, the graphical path method (GPM) is a rule-based planning/scheduling method that uses a network of activities in logical sequence to calculate the project completion, total floats, and the critical path. However, owing to different scheduling principles, alternate algorithms, and computer graphics relying on object-base principles and using gestural technology, there exist differences and enhancements that underscore how GPM retools schedule analysis. (Ponce de Leon, May 2008 & July 2008)

Unlike CPM, the GPM scheme of thought is that of an interactive process enabling real-time analysis—when planning the schedule, when updating the schedule, and when performing schedule analysis. GPM is rooted in algorithms that focus on planned dates, without ignoring early dates, and GPM calculates total floats to the left of the data date. With the GPM algorithms active on either side of the data date line, retrospective schedule analysis is not stymied by the CPM forensic void.

Unique to GPM planning is configuring the project into a network of logically related and dated objects (activities, fixed and floater milestone events, etc.). (Ponce de Leon, May 2009) Using logical ties and object dates, GPM continuously calculates link gaps and total floats for all dated objects. Link gaps are calculated from the dates of the two related activities; total floats are algorithmically calculated from the link gaps. An activity that may be delayed from planned dates without causing an overrun of the project completion, or any other deadline, has float and is a floater. An activity that may gain schedule and/or extend to earlier dates, without causing an earlier project start, or release date, has preceding float, or drift, and is a drifter. An activity with neither float nor drift is critical. In GPM, float plus drift is a constant, which equals CPM total float.

Once actual dates and re-planning (right of the data date) are introduced in the network, forensic gaps left of the data date are calculated from actual dates, and gaps right of the data date are calculated from planned dates. For remaining activities, calculation of floats, drifts, and total floats is prospective (i.e., based on planned dates). For in-progress activities, calculation of total float relates to remaining durations and is prospective; actualized link offsets (similar to PDM lags) are left out of the calculations, and forensic drifts are calculated from forensic gaps. For completed activities, calculation of forensic floats, forensic drifts, and forensic total floats is retrospective, but is a function of both forensic gaps and gaps right of the data date.

Out-of-sequence progress causes negative forensic gaps and reduces forensic total floats. Corrected logic and omitted logic rules solve the ambiguity through equivalent zero-gap links or finish-to-start links (in the latter case by subdividing the predecessor and/or successor). (Lu & Lam, 2009) Exhibit 1 provides examples (notice total float increases for predecessors).

Corrected Logic Rule Options (Data Date of 09/30/09)

Exhibit 1 – Corrected Logic Rule Options (Data Date of 09/30/09)

Forensic drifts and floats are a function of forensic gaps, which are commonly fixed, and gaps, which refresh to current planned dates. From update to update, as activities are statused left of the data date, and re-planned right of the data date, forensic floats and drifts continuously refresh algorithmically, just as their counterparts right of the data date. This transient property of forensic total float introduces three premises. Except for delays occurring in the later stages of the project, delay analysis relying on an as-built schedule without collapsing probably mixes delays occurring in one period with forensic floats materializing in later periods. Retrospective analysis relying on windows must use windows of adequate duration to sufficiently consider the transient nature of forensic total float. As a transient attribute, like the critical path itself, forensic total floats convert to as-built total floats in the final update (data date coincides with the project completion date).

due to the forensic gap of 10 days and the float of its successor. Also, note how the forensic float of 1 day for Footings & Subgrade Conc increases to 5 days.

Forensic Gaps, Drifts, and Floats Left of Data Date of 8 May 2009 and Left of the Data Date of 10 July 2009

Exhibit 2 – Forensic Gaps, Drifts, and Floats Left of Data Date of 8 May 2009 and Left of the Data Date of 10 July 2009

The as-built critical path is directly discernible with forensic total floats. Any completed activity with both forensic float and forensic drift of zero has a forensic total float of zero. Breaks in the as-built critical path stand out and are fixed by recognizing concealed delay otherwise posing as a positive-gap link. Consider the following figures: In Exhibit 3a., seemingly, there is no as-built path with both zero forensic drift and float. Exhibit 3.b. reveals the as-built critical paths with the addition of Mob Delay and Rebar Hold, two concealed delays that prevented the start of successor critical activities as originally envisioned.

Concealed Delays Cause Critical Path Breaks

Exhibit 3a. – Concealed Delays Cause Critical Path Breaks

As-Built Critical Paths Revealed

Exhibit 3b. – As-Built Critical Paths Revealed

Compendium of CPM and GPM Floats

The arrow diagramming method (ADM)—The Kelley & Walker network (1959) uses arrows between activity tail (i) and head (j) nodes to represent activity i,j. An activity that may start upon the finish of another is connected to the predecessor through a common node or dummy, which limits ADM to finish-to-start (FS) logic (FS logic rule). Using ADM notation (TE/TL is early/late time), total float is interpreted as from late finish (TLj) minus early start (TEi), subtract the duration for the activity. Free float is interpreted as from earliest early start of all successors (TEj) minus activity early start (TEi), subtract the duration. Interfering float is total float less free float or TLj minus TEj. Independent float is interpreted as from TEj (earliest early start of all successors) less TLi (latest late finish of all predecessors), subtract the duration, but it must be at least zero.

CPM with a backward pass premise—CPM assumes a project start date, from which the completion date is to be calculated (forward pass premise); this leads to floats rooted in early dates and head nodes. If the assumption is the project completion date, from which an optimal project starting date is to be calculated, the emphasis switches from early dates to late dates, with floats rooted in late dates and tail nodes. With a backward pass premise, free float, actually backward free float, becomes: from activity late finish (TLj) minus latest late finish of all predecessors (TLi), subtract the activity duration. (Zimmerman, 1967) Interfering float and independent float also have to be re-stated, but total float calculation remains unchanged.

Activity-on-node Network (AON)—Fondahl (1962) led an independent, parallel effort to develop an approach for manually applying CPM. The method substitutes a circle and line for the arrow notation, but holds onto the FS logic rule. The method calculates activities' early start and finish dates and late start and finish dates. Due to the FS logic rule, float calculations for activities are essentially the same, except they are driven by activity dates rather than event times. Fondahl originated the concept of driving links, and calculated link lags for non-driving links, albeit within the confines of the FS logic rule. For any link, the link lag value is interpreted as the early start of the successor minus the early finish of the predecessor.

Precedence diagramming method (PDM)—As originally developed, PDM extended the AON model to allow three types of relationships. (IBM, 1968; O'Brien, 1969, pp 99–115) The start-to-finish (SF) relationship type was added by Ponce de Leon. (1970, pp 42–47; Lu & Lam, 2009) In PDM, an activity may start or finish some time after a predecessor has started or finished. The minimum waiting time between the predecessor and successor connected, relevant dates, is the lead/lag factor. The relevant dates for each PDM dependency stem from the logic type. The calculation of free float changes for the four PDM relationship types, as free float can no longer be stated only in terms of start of successor and finish of predecessor. Instead, free float measures days the predecessor may be delayed from its early dates without delaying any of its successors from their respective early dates. Equations for total float and interfering float remain unchanged. PDM was eventually extended to calculate Fondahl's link lag concepts for SS, FF, and SF relationship types. (Ponce de Leon, 1972, pp 120-138)

Resource-constrained scheduling—In CPM, schedules conditioned on resource limits, resource-constrained float measures days an activity may be delayed from its recalculated dates while breaching neither resource limits nor completion. (Kim & de la Garza, 2003) The float sequestered by the resource-constrained float calculation, in their view, is phantom float.

GPM, forward pass premise—GPM provides five prospective float attributes. (1) Float measures days an activity may slip from and/or extend beyond planned dates without overrunning the project completion date or an interim completion date. As float results from planner-devised logic, it is not scheduled float (Antill & Woodhead, 1965, p 65) or remaining float. (Kim & de la Garza, 2003); (2) Drift measures days an activity may backslide from planned dates and/or extend to earlier planned dates without forcing an earlier project start or release date; (3) Float plus drift equals total float; (4) Buffer equals the minimum of all link gaps to the activity's successors; and (5) Drift-buffer equals the minimum of all link gaps from the activity's predecessors. In addition, forensic float, forensic drift and forensic total float counterparts (left of the data date) are provided. As forensic float is measured from actual dates forward, forensic drift is also required to properly calculate forensic total float.

Link gaps are keys in GPM calculations, as all floats and drifts originate at the gap level. Gap measures days the predecessor may slip and/or extend without delaying its successor. Drift-gap measures days the successor may gain and/or extend to earlier dates without forcing the predecessor back. PDM relationship leeway (essentially GPM gap), originally calculated by Ponce de Leon (1972, pp 120-138), has been recently posited as interactivity float/relationship slack. (Winter, 2004)

Relationship diagramming method (RDM)—RDM is a variant of ADM, with PDM features, that focuses on the rationale for each relationship (Plotnick, 2006). RDM introduces just-in-time float (JTF) to measure float of support activities leading to an i-node or merge point that is selected to be driven by another chain of activities. RDM calculates a multi-calendar float (MF) that homogenizes to a uniform calendar activity floats on a chain having dissimilar calendars. As with PDM logic, total floats for the start and finish nodes may differ. (Ponce de Leon, 1972, pp 139-177) Thus, RDM calculates start float and finish float, with total float as the lesser of the two. RDM adopts ADM or PDM calculations for free and independent floats.

Activity float interpretations—Activity float measures activity slippage from early dates without altering the early schedule tree, after allowing activities on the same chain a proportionate share of the chain's float based on activity-to-chain duration. (Ponce de Leon, 1983) Discrete activity float assigns to each activity on a path a proportionate share of the path's combined total float and free float, using activity-to-path duration as the basis for proportioning. (Woolf, 2007) If PDM calculations allow start float and finish float for an activity to differ, float embedded, if any, within the activity start and finish dates is internal activity float. (Pickavance, 2005, p 579) The difference between the duration assigned to an activity and the time necessary for the scope of work denoted by the activity is considered activity float. (Keane & Caletka, 2008, p 265)

Other float interpretations—Contract float measures days between contractual and projected completion available to offset critical path delay, pursuant to applicable contract clauses (Ponce de Leon, 1985). It is also called terminal or end float (Keane & Caletka, 2008, p 191) and external float. (Pickavance, 2005, p 594) Sequestered float is that concealed by a preferential link or other technique for the primary intent of reducing float. (Ponce de leon, 1985; Keane & Caletka, 2008, p 193) A float map lists activities in the baseline and contemporaneous updates along with their respective total float values, from update to update to highlight activities that are consistently critical in contemporaneous updates. (Keane & Caletka, 2008, p 238) A float trend sorts baseline activities and remaining activities in the updates by ascending total float; and plots, from update to update (x-axis), the total float (y-axis) for the 0%, 10%, 50%, 90%, and 100% percentiles. (Kilpatrick, 1972)

Summary and Conclusions

Once actual dates are introduced in a schedule, CPM loses the ability to calculate total floats in the past (left of the data date). This hinders the retrospective analysis of actual performance, as the critical path can no longer be

CPM-calculated for the as-built portion of the schedule. This retrospective void in CPM is well documented in the forensic scheduling literature.

The GPM updating mantra is for the planner to apply equal rigor to logic definition both right and left of the data date. In furtherance, for out-of-sequence progress, GPM posits that corrected logic rules (including omitted logic options) better portray as-built conditions than what results from rules currently in use by practitioners. A payback from more accurate as-built logic is true forensic total floats and more accurate delay analysis results. Calculation of forensic total floats has been the missing link in retrospective schedule analysis. That void has now been dealt with by the GPM scheme of thought.

In the last 50 years, researchers have proposed many measures of float beyond those interpreted by the CPM developers. Including the original 4 measures of float, over 35 float variations (5 are actually relationship-related), are reviewed. Based on three years of actual GPM application on real-world projects ranging from $15 million to $2 billion, it is posited that gap and drift-gap (based on planned versus early dates), float, drift, total float, and contract float yield sufficient float information for project management and control.

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© 2010 Dr. Gui Ponce de Leon, PE, PMP, LEED AP
Published as a part of 2010 PMI Global Proceedings – Washington, DC



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