Graphical Path Method, Papers

In this paper, presented at the 2010 PMI Global Congress Conference, PMA Consultants’s Dr. Gui Ponce de Leon weighs the advantages and disadvantages between CPM and GPM’s use as an analytical tool in Forensic Schedule Analysis to demonstrate how GPM solves the CPM forensic void.


The critical path method (CPM) is widely used as a project management tool. Basic to CPM is for the planner to draw a project network first, and then to use CPM software to calculate activity dates and total floats, establish the project completion date and locate the critical path. Alas, all is not well in CPM utopia! The moment the planner takes control of activity dates by using constraint dates or resource leveling, total float is reduced (some would say sequestered); and once actual dates are introduced in a CPM network, the analyst loses total floats and the critical path can no longer be calculated left of the data date. The ability to schedule an activity later than its early dates without sacrificing total float, and 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 describes the float aspects of GPM, while emphasizing the concept of GPM forensic total float and its role in retrospective schedule analysis, whether in updating or forensic scheduling. A compendium of CPM and GPM float concepts is provided for historical context.

The CPM Alternative

CPM was developed in the late 1950s as a prospective method for planning and scheduling complex projects [Kelley & Walker, 1959]. In CPM, planning states which activities must occur and in which logical order for the project to complete, and ends with a network diagram of all activities in logical sequence without dates. With activities’ elapsed times and the network logic, CPM scheduling first calculates early start and finish times for all activities. In conventional CPM, 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 total float of zero and is deemed critical.

When late time calculations are limited by the project completion date, a floater may be delayed within its total float range without delaying completion of the project. CPM’s emphasis on late times is thus essential to timely project completion; however, it is typical of CPM to continue to focus on the earliest possible activity starting times, thereby relinquishing the ability to interpret float as also measuring available schedule gain, not just delay.

The CPM Workaround

Once actual dates are introduced in the scheduling process, the 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 (actual finish) less early finish date (also actual finish); and 2) even if total float, in the conventional CPM sense, could be inferred by observation, corrections would have to be made as, for any completed activity, actual dates may not have occurred on the earliest possible dates, a necessary condition for CPM to correctly calculate activity as-built total floats.

With CPM unable to calculate total floats in the past, the critical path cannot be located for the 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 match actual or would-be remaining durations and to actualizing logic, and excludes introducing actual dates.

Authored By:

Dr. Gui Ponce de Leon, PE, PMP, LEED AP

Originally Published as Part of the PMICOS 2010 Conference

Related News