Critical path drag
View on WikipediaCritical path drag is a project management metric[1] developed by Stephen Devaux as part of the Total Project Control (TPC) approach to schedule analysis and compression [2] in the critical path method of scheduling. Critical path drag is the amount of time that an activity or constraint on the critical path is adding to the project duration. Alternatively, it is the maximum amount of time that one can shorten the activity before it is no longer on the critical path or before its duration becomes zero.
In networks where all dependencies are finish-to-start (FS) relationships (i.e., where a predecessor must finish before a successor starts), the drag of a critical path activity is equal to whichever is less: its remaining duration or (if there is one or more parallel activity) the total float of the parallel activity that has the least total float.[3]

In this diagram, Activities A, B, C, D, and E comprise the critical path, while Activities F, G, and H are off the critical path with floats of 15 days, 5 days, and 20 days respectively. Whereas activities that are off the critical path have float and are therefore not delaying completion of the project, those on the critical path have critical path drag, i.e., they delay project completion.
- Activities A and E have nothing in parallel and therefore have drags of 10 days and 20 days respectively.
- Activities B and C are both parallel to F (float of 15) and H (float of 20). B has a duration of 20 and drag of 15 (equal to F's float), while C has a duration of only 5 days and thus drag of only 5.
- Activity D, with a duration of 10 days, is parallel to G (float of 5) and H (float of 20) and therefore its drag is equal to 5, the float of G.
In network schedules that include start-to-start (SS), finish-to-finish (FF) and start-to-finish (SF) relationships and lags, drag computation can be quite complex, often requiring either the decomposition of critical path activities into their components so as to create all relationships as finish-to-start, or the use of scheduling software that computes critical path drag with complex dependencies. [4]
A quick way to compute the drag of a critical path activity that has one or more start-to-start or start-to-start plus lag successors is that the drag of the critical path activity that has such successors will be equal to whichever is less: the duration of the predecessor activity OR the sum of the lag plus total float of whichever SS successor has the LEAST lag plus total float. This is shown in the diagram where Activity A has four SS+lag successors: B, C, E, and F. The drag-plus-lag of B is 3 + 12 = 15. For each of C, E, and F, it is 20, 12, and 10 respectively. The lowest is F with 10. Since Activity A's duration is 20 which is higher than F's drag-plus-lag of 10, A's drag is 10. In other words, A is adding 10 units of time to the project duration. (If there were another separate parallel path, not in this diagram, that had float of 9 or fewer units, then A's drag would be equal to that float amount as it would be less than 10.)

Note that in the SS + lag relationship, the drag is in the work scheduled in the predecessor activity, e.g., digging the first 100 metres of trench in order to start laying the pipe. If the volume of work in the first part of the activity can be performed faster, the lag to the trench-digging can shrink, decreasing the drag in the predecessor and compressing the critical path. Occasionally, however, the lag on an SS relationship may be strictly a "time lag" representing a waiting period rather than work in the predecessor. In that case, the drag should be associated with the lag as that constraint is the delaying factor that must be addressed to shorten the project. Time lags are far more common on finish-to-start and finish-to-finish relationships ("Wait for cement to dry") than on SS relationships.
Critical path drag is often combined with an estimate of the increased cost and/or reduced expected value of the project due to each unit of the critical path's duration. This allows such cost to be attributed to individual critical path activities through their respective drag amounts (i.e., the activity's drag cost). If the cost of each unit of time in the diagram above is $10,000, the drag cost of E would be $200,000, B would be $150,000, A would be $100,000, and C and D $50,000 each.
This in turn can allow a project manager to justify those additional resources that will reduce the drag and drag cost of specific critical path activities where the cost of such resources would be less than the value generated by reduction in drag. For example, if the addition of $50,000 worth of resources would reduce the duration of B to ten days, the project would take only 55 days, B's drag would be reduced to five days, and its drag cost would be reduced to $50,000.
Despite the existence of critical path drag in all project schedules, the concept was included in the Project Management Institute's PMBOK Guide, Eighth Edition for the first time in November 2025. [5]
- ^ Devaux, Stephen A. Total Project Control: A Manager's Guide to Integrated Project Planning, Measuring, and Tracking. John Wiley & Sons, pp. 138 - 146, 1999. ISBN 0-471-32859-6.
- ^ William Duncan and Stephen Devaux "Scheduling Is a Drag" Archived 2012-09-03 at the Wayback Machine Projects@Work on-line magazine
- ^ Stephen A. Devaux "The Drag Efficient: The Missing Quantification of Time on the Critical Path" Archived 2013-03-13 at the Wayback Machine Defense AT&L magazine of the Defense Acquisition University.
- ^ Lyaschenko, Alex (2024-11-20). "Project delivery plan optimisation metrics: Critical Path Drag and Activity Spread". PMWorld Library. Retrieved 2024-12-02.
- ^ Project Management Institute (2025). A Guide to the Project Management Body of Knowledge – Eighth Edition (Eighth ed.). USA: Project Management Institute Inc. (published 2026). p. 160. ISBN 978-1628258295.
{{cite book}}: CS1 maint: date and year (link)
Sources
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Further reading
[edit]- Devaux, Stephen A. (2014). Managing Projects as Investments: Earned Value to Business Value. CRC Press. ISBN 978-1482212709.
- Devaux, Stephen A. (2015). Total Project Control (2nd Edition): A Practitioner's Guide to Managing Projects as Investments. CRC Press. ISBN 978-1498706773.
- Wideman, R. Max (2004). Total Project Control: A book review
- Borfitz, Deb (2009). [www.ecliniqua.com/2009/08/07/prochain.html "ProChain Solutions: Diagnosing the Drag in Clinical Development" eCliniqua Magazine]
- Mosaic Projects. Basic CPM Calculations
Critical path drag
View on GrokipediaFundamentals of Project Scheduling
Critical Path Method (CPM)
The Critical Path Method (CPM) is a deterministic algorithm for scheduling project activities by modeling them as a network of interdependent tasks to identify the longest sequence, known as the critical path, which determines the minimum project duration. Developed in 1957 by James E. Kelley of Remington Rand and Morgan R. Walker of DuPont, CPM was initially applied to chemical plant construction to optimize planning and reduce costs.[6][7] Key components of CPM include activities, which are the individual tasks with estimated durations; dependencies, such as finish-to-start relationships where one activity must complete before the next begins; and events, represented as nodes marking the start or end of activities. The method employs a forward pass to compute the earliest start and finish times for each activity, beginning from the project start at time zero and progressing through the network by adding durations along each path. A backward pass then calculates the latest allowable start and finish times, working from the project end date backward to determine allowable delays. The critical path consists of activities where early and late times are identical, leaving no slack.[6][8] To illustrate, consider a simplified house-building project with activities like clearing the site (2 days), digging the foundation (4 days), setting forms (3 days), framing walls (4 days), and roofing (5 days), connected by finish-to-start dependencies. The network diagram uses nodes as circles labeled with activity identifiers and durations (e.g., "a,2" for clearing), linked by directed arrows showing sequence: start → a → b (dig) → c (forms) → d (frame) → j (roof) → finish, among other paths. The forward pass reveals the longest path (a-b-c-d-j) totals 18 days, identifying it as critical since any delay here extends the project.[8] CPM plays a vital role in project management by accurately predicting the overall duration based on the critical path length and highlighting resource needs for bottleneck activities to avoid delays and control costs. In practice, it enables managers to focus efforts on critical tasks, as demonstrated in early applications where it shortened a major construction project by months without added expense.[6][8]Float and Slack Concepts
In project management, particularly within the Critical Path Method (CPM), float—also referred to as slack—represents the scheduling flexibility available for activities that are not on the critical path.[9] Total float is defined as the amount of time an activity can be delayed from its early start date without delaying the overall project completion date or violating any schedule constraints.[10][9] Free float, in contrast, is the amount of time an activity can be delayed without delaying the early start date of any immediately succeeding activity or breaching constraints.[11][9] These measures highlight the buffer inherent in non-critical paths, allowing project managers to allocate resources or handle uncertainties without impacting the project's end date. Several types of float extend these core concepts to address specific scheduling dynamics. Project float arises when the calculated project duration using CPM is shorter than the required completion date, providing overall leeway for the entire schedule; it is computed as the difference between the CPM end date and the required end date.[11] Independent float quantifies the flexibility an activity has without affecting the timing of either its predecessors or successors, representing the excess time available solely within the activity's own constraints.[9] Interfering float, equivalent to end event slack, measures the portion of total float that, if consumed, would delay subsequent activities; it is derived as the difference between total float and free float.[9] Basic calculations for float rely on forward and backward passes through the project network to determine early and late dates for each activity. Total float is calculated as the late finish time minus the early finish time (TF = LF - EF) or equivalently as the late start time minus the early start time (TF = LS - ES).[12][9] Free float is determined by subtracting the activity's early finish time from the earliest early start time of its successors (FF = ESsuccessor - EF).[9] Independent float uses the formula IF = ESsuccessor - LFpredecessor - duration, ensuring no impact on adjacent activities.[9] Interfering float follows directly as IF = TF - FF.[9] Activities on the critical path exhibit zero total float, underscoring their lack of flexibility compared to those with positive values. To illustrate, consider a simple activity-on-node (AON) network for a construction project with four activities: A (design, duration 1 day), B (foundation, 3 days, successor to A), C (permitting, 2 days, successor to A and predecessor to D), and D (build, 1 day, successors B and C). The early start (ES) for A is day 0, yielding an early finish (EF) of 1. B and C both start at day 1 (ES=1), with EF=4 for B and EF=3 for C. D's ES is the maximum of B's and C's EF, so ES=4 and EF=5, setting the project duration at 5 days. In the backward pass, assuming a project finish constraint at day 5, D's late finish (LF)=5 and late start (LS)=4. B's LF=4 (tied to D's LS) and LS=1, giving total float TF=0 (LS - ES =1-1=0). C's LF=4 (as its successor D's LS=4 under finish-to-start logic) and LS=2, resulting in TF=1 (LS - ES=2-1=1) and free float FF=1 (ESD - EFC=4-3=1). Here, activity C demonstrates positive float, allowing a one-day delay without affecting D's start or the project end, while B on the critical path (A-B-D) has zero float, illustrating the contrast between flexible and inflexible activities.[9]Definition and Core Metrics
Overview of Critical Path Drag
Critical path drag is a key metric in project management that quantifies the amount of time an activity on the critical path adds to the total project duration, representing the potential reduction in project timeline achievable by shortening or removing that activity.[13] Developed as part of advanced scheduling techniques, it enables project managers to prioritize efforts on activities that directly influence completion time, beyond the standard identification of the critical path itself.[3] Unlike float, which measures the slack or flexibility allowing non-critical activities to be delayed without affecting the project end date, drag specifically assesses the "time liability" contributed by critical path activities.[1] Drag is always non-negative for activities on the critical path and equals zero for non-critical ones, highlighting the binding constraints rather than scheduling leeway.[14] For activities without parallel paths, the drag equals the activity's duration. However, when parallel activities exist, it is the minimum of the activity's duration or the total float of the parallel path with the least float.[1][2] For instance, in a simple linear project with three sequential tasks—A lasting 5 days, B lasting 3 days, and C lasting 4 days—the drag of B is 3 days, since removing or shortening B by that amount would reduce the overall project duration from 12 days to 9 days.[3]Devaux's Removed Activity Gauge (DRAG)
Devaux's Removed Activity Gauge (DRAG) is a project management metric developed by Stephen A. Devaux and first introduced in his 1999 book Total Project Control: A Manager's Guide to Integrated Project Planning, Measuring, and Tracking. The metric quantifies the amount of time an activity on the critical path adds to the overall project duration, representing the potential schedule compression gained by removing or shortening that activity. Unlike traditional float, which measures delay tolerance for non-critical activities, DRAG focuses exclusively on critical path elements to highlight their contribution to project delays.[15][1] The DRAG of an activity on the critical path with no parallel paths equals its duration. In networks with parallel paths, DRAG is the minimum of the activity's duration and the total float of the parallel path(s) with the least total float. This ensures the metric accurately reflects the unique time contribution of the activity without overestimating in branched schedules. Computation typically requires evaluating the network to identify parallel constraints, often using project management software for complex cases.[13][3][1] To illustrate in a network with parallel paths, consider a project where activity A (10 days) precedes B (20 days), which then branches: one path to C (15 days) to end, and a parallel path from B to D (25 days) to end. The critical path is A-B-C (total 45 days), while A-B-D is 55 days, giving the parallel B-D path a total float of 10 days (45 - (20 + 25) + 20 from B, but adjusted: full path float 10 days). For B, DRAG = min(20, 10) = 10 days, as shortening B by more than 10 days would make the parallel path critical. For A (no parallels), DRAG = 10 days. For C, DRAG = 15 days. Shortening B by 10 days reduces the project to 35 days, after which further shortening affects the parallel path. This demonstrates how DRAG accounts for parallel constraints to guide accurate compression.[1][3] The primary purpose of DRAG is to assign a time-based "cost" to each critical activity, enabling value-driven scheduling decisions. By revealing which activities most delay project completion, managers can prioritize optimizations—such as resource allocation or crashing—based on their potential to increase overall project value, often extended to "drag cost" by multiplying DRAG by the daily cost of project delay. This shifts focus from mere duration reduction to maximizing return on investment in schedule compression efforts.[15][1]Calculation and Implementation
Step-by-Step Computation of Drag
To compute drag values in a project network, a prerequisite is a complete Critical Path Method (CPM) schedule, which includes all activity durations, predecessor-successor relationships, forward and backward passes to determine early start/finish and late start/finish dates, total float calculations for every activity, and clear identification of the critical path (activities with zero total float).[1][2] The algorithm for drag computation focuses exclusively on critical path activities, as non-critical activities contribute zero drag by definition. Proceed systematically through the network, evaluating each critical activity individually: if the activity has no parallel paths (no concurrent activities or paths unbound by the same predecessors and successors), its drag equals its duration, since fully removing or shortening it would reduce the total project duration by that amount. If parallel paths exist, the drag is the minimum of the activity's duration and the total float of the parallel activity (or path) possessing the smallest total float; this value represents the maximum shortening possible before that parallel path becomes critical and limits further gains.[13][1][2] For networks with multiple paths merging at successors, aggregate drag by selecting the minimum total float among all relevant parallel alternatives for the given critical activity; this handles path convergence by prioritizing the tightest constraint that would dictate when another path assumes criticality upon further compression. The process is typically performed once on the baseline schedule but may require recalculation iteratively if optimizations alter the critical path.[1][13] A worked example illustrates this for a 5-activity critical path network (activities A through E in sequence, with select parallels). Assume the critical path durations are A (10 days), B (20 days), C (5 days), D (10 days), and E (20 days), yielding a total project duration of 65 days. Parallel activity F runs alongside B with 15 days total float; parallel activity G runs alongside D with 5 days total float. Activities A, C, and E have no limiting parallels. The computation iterates as follows:- For A: No parallel paths, so drag = duration = 10 days.
- For B: Parallel F has 15 days total float, so drag = min(20, 15) = 15 days.
- For C: No limiting parallel paths, so drag = duration = 5 days.
- For D: Parallel G has 5 days total float, so drag = min(10, 5) = 5 days.
- For E: No parallel paths, so drag = duration = 20 days.
| Activity | Duration (days) | Limiting Parallel Float (days) | Drag (days) |
|---|---|---|---|
| A | 10 | None (N/A) | 10 |
| B | 20 | 15 (activity F) | 15 |
| C | 5 | None (N/A) | 5 |
| D | 10 | 5 (activity G) | 5 |
| E | 20 | None (N/A) | 20 |