Forecasting project duration as a function of scope changes and delay



Generally, project managers are under pressure to meet deadlines and satisfy customers under conditions of uncertainty, without sacrificing cost or quality. Nevertheless, projects are hardly ever completed within their original forecasted time frame. Let us begin by defining and clarifying some concepts used throughout the paper:

The scope of a project, according to A Guide to the Project Management Body of Knowledge (PMBOK® Guide), “should include all the work required, and only the work required, for successful completion” (Project Management Institute, 2000: p. 51). Scope refers to the range of action that should be performed in order to execute a specific project, and it is usually presented via a Work Breakdown Structure (WBS). The WBS divides the overall project into sub-elements, known as Work Packages (WPs), which are associated with the different tasks of the project. All the same, a project can be structured in various ways, depending upon factors as its duration, its work content, levels of uncertainty, organizational structure and more (Shtub, Bard, & Globerson, 1994).

Scope change, as defined by the PMBOK® Guide, is “…any modification to the agreed upon project scope, as defined by the approved WBS” (p. 63). Scope changes are inherent in the nature of projects; and appear due to reasons such as: (a) initial wrong diagnosis of the needs, (b) discovery of unforeseen problems, and (c) additional understanding of the circumstances gained (Ertel, 2000). Indeed, when the scope of a project is not properly defined, scope changes are more likely to be introduced. There is some evidence that scope changes have a significant impact on the cost of projects. Chick (1999) showed that the later a change occurs on a project, the more effect it will have on its cost. The cost of a scope change is correlated to its nature, e.g., adding a reactor costs 30% more than adding a pump, however, to change a pump, once installed, costs as much as double the price of changing a reactor. Though he mentioned a possible impact of scope changes on project's schedule, a thorough investigation of the relationship between scope changes and project duration has not yet been conducted.

Delays. Considerable evidence on project delivery extensions and delays due to scheduling problems exist in project management literature (Singh, 2001; Tenah, 2001; Thilmany, 2001; etc.). The studies suggest that delays might result from either lack of production capacity or impractical planning. Delays might also result from multitasking, which is defined as the performance of multiple project activities at the same time by the same resource. Leach (1999) claims that multitasking often makes good use of the time spent waiting for inputs or for someone to call back, before getting on with an activity. However, Goldratt (1997) claims that it is a major source of delays since completion of all tasks are delayed.

Duration estimation is a critical stage in project planning. It requires the ability to predict how long it will take to perform a certain task. However, a potential bias in time estimation prevails. In the psychology literature, it is known as the planning fallacy, i.e., the tendency to underestimate the amount of time needed to complete a given project, or overestimate the amount of work that can be completed within a given time frame (Pychyl, Morin & Salmon, 2000). Buehler, Griffin, and Ross (1994) claimed that planning fallacy occurs because individuals focus primarily on the future, i.e., how they will perform the task, what steps they will take and so on, and ignore past experiences, when making predictions about future outcomes. However, Burt and Kemp (1991) proposed predicting task durations from knowledge about the durations of categories of tasks, and claimed that memory plays a vital role in the process. All the same, as many duration estimation models are based on memory or categories, they are claimed to be inaccurate, inconsistent, unreliable, and usually lead to project failure (Chatzoglou & Macaulay, 1996).

An alternative approach for duration estimation is based upon mathematical models. In those models, the dependent variable is the task duration, or its cost, and the independent variables are technical parameters of the task and the experience of the individuals performing the task. A well-known example for duration and cost prediction model used in software projects is COCOMO (Boehm et al., 2000). The effort, expressed in labor-months, required for a software project is:



K, SFi = parameters depend on the mode of the software system to be developed

S = size of the software project (thousand of source lines of codes) EMi = effort multipliers, which represent the job to be performed.

The 17 effort multipliers reflect the characteristics of the software systems and the production environment, such as: (a) required software reliability; (b) analyst capability; (c) programmer capability; (d) time constraints, and more (for a complete list—see Boehm et al., 2000). All the same, experience on past scope changes and/or delays are not included in the model as parameters of future effort estimation.

Model Description

As previously discussed, there are many reasons for the discrepancy between estimated and actual project completion times. However, present estimation techniques are a-priory and static, and thus do not make use of: (1) the extent of scope changes introduced into a project's original baseline plan, and (2) delays in executing the plan. Moreover, the nature of the discrepancy between the initial duration estimation and the actual duration has not been investigated in the project management literature. Thus, we propose a contingency model for dynamic estimation of work package (WP) duration, based upon scope changes and initiation delay that are concerned with the package. The model is described herein:

Scope Change

The scope change factor of a change event introduced into a work package is defined as the estimated effort required for performing the additional scope, divided by the original WP effort estimation. Thus, the scope change factor of the j-th change event introduced into WPi (SFi,j) is calculated as the ratio:



Si,j = estimated effort for the additional required work in WPi resulting from change j (working hours)

Hi = original estimated effort for WPi (working hours).

Timing of Change

The timing factor of a change event is defined as the number of days between the arrival of a WP at its executor's station, and the introduction of the change into it—divided by the original estimated duration of that package. Thus, the timing factor of change event j introduced into WPi (TFi,j) is:



Ti,j = time elapsed between the WPi's input arrival, and the introduction of the j-th change into it (days)

Di = original duration estimated for WPi (days).

Change Intensity of a WP

Similar to the COCOMO approach (1), we derive the effect of a single change event on a WP by multiplying its scope and timing factors. Since the timing factor of a change might be zero, we introduce it into the model as an increment to a standardized unit of “1.” Thus, the intensity of the changes undergone by a WPi (CIi) is the summation of the effects of each of the n change events that were engendered in that package:


Initiation Delay

The second factor previously mentioned, which may cause a project duration extension, is the initiation delay of a work package, i.e., the extent to which initiation of the package was delayed. Thus, the delay intensity of WPi (DIi) is defined as the WP's initiation delay, divided by the estimated duration of the package:



Wi = initiation delay of WPi (days).

Duration Deviation of a WP

The deviation between actual and estimated duration of a WP is expected to be a function of both change and delay. To standardize the analysis, let us refer to the relative deviation. Similar to equation (1), we formulate a model for forecasting the relative duration of WPi (RDi) by multiplying both effects. Since the effects are independent, we need to make sure that if one of them equals zero it will not eliminate the impact of the other. In a multiplication model, this can be achieved by adding “1” to each factor. In addition, since it is not clear what the power function that represents this relationship is, we raise each factor to the power of a fixed coefficient. According to the same logic, we introduce a scale coefficient, γ,, into the model, as well:



Ai, = actual duration of WPi

α, β, γ = regression parameters.

Field Research

Investigation and calibration of the model was performed on 24 electrical design WPs of several construction projects. These design WPs included the preparation of a complete set of the electrical system layout, accompanied by a detailed list of the required electrical equipment. The data available on each WP consist of (a) its estimated duration, (b) its actual duration, and (c) the intensity and timing of every scope change that was introduced into that package.


Altogether, 44 changes were introduced into the 24 WPs of the research, varying from zero to three change events for a package.

Exhibit 1. Results of the Nonlinear Regression Analysis

Results of the Nonlinear Regression Analysis

Exhibit 2. WP's Relative Duration as a Function of Scope Change and Delay

WP's Relative Duration as a Function of Scope Change and Delay

The scope of two work packages was not changed at all, whereas the scope of five WPs was almost entirely changed. Statistical analyses of the data, using nonlinear regression analysis, resulted in the following parameter values of equation (6): α=0.777; β=1.019; and γ=0.555—See Exhibit 1 for complete results. Thus, the expression of the relative duration of a WP (RDi) has the form:


From Exhibit 1, it is evident that both regression parameters, α, β, and γ, are highly significant. Additionally, the mean corrected R2 of the model is as high as 0.938. Such a high value for R2 is an indicator of the model's ability to explain the impact of scope changes and delays on the deviation between actual and initially estimated duration of a WP.

Let us investigate the ideal case, where no change is introduced into a WP, and work on that package is not delayed at all. Substituting CI=DI=0 into equation (7), we obtain that the relative duration deviation is 0.777. That is, if there are no scope changes and no initiation delays, the actual duration of a WP is expected to be just 77.7% of the estimated one. In other words, the estimated value is 1/0.777 = 1.287 times the actual duration. This implies that a-priory duration estimates are approximately 30% greater than actual durations, under no-change and no-delay conditions. This is directly related to the human tendency to overestimate project duration, based on experience of project overruns. The results are in accordance with previous quotations, although not based on field research (Goldratt, 1997; Herroelen & Leus, 2001), where managers were claimed to overestimate duration by 50% or less.

Exhibit 2 shows that the change component of equation (6), (1+CI)α, has a high correlation with the WP relative duration, and a higher impact, as opposed to the delay component, (1+DI)β. This may suggest the scope change component alone can be a good explanatory variable to the actual duration of a work package. However, it is evident that reducing the delay to a minimum can decrease the effect of scope changes on extending WP duration—See the appendix for an illustrative example.

Implications and Applications

There are three possible applications for the research and the resulting model:

1. Dynamic forecasting. The model allows for a dynamic forecasting of the completion time of future WPs. It is based on the quantification of the impact of both the introduced scope changes, and initiation delays, and using them to correct the initial duration forecast. This can be done by calculating the adjusted scope and delay components of equation (6), and deriving an amended duration estimate for the reminder of the WP and of the whole project. Similarly, cost can be reassessed and the additional funds for the completion of the project could be allocated.

2. A-priory forecasting. The model presented here may serve as a practical tool in making a-priory estimates of future WP and project durations, based on historical data. Estimates would be based on the average effects of delays and scope changes, introduced in the past into similar packages and/or projects. See the appendix for an illustrative example.

3. Marginal impact of delays. The marginal cost of the delay or waiting in line, can be estimated. It is believed that the effect of initiation delay was caused mainly by working in a late-start mode, and thus can be controlled by the project manager, who may reduce it Once initiation delays are well understood, managers should look for logical approaches, e.g., those discussed by Levy (1998), to reduce the delay phenomenon to a minimum.


The two parameters: scope changes and initiation delays were found to have an impact on the duration of a WP Although one may expect that delay will have a stronger impact on the WP duration, the opposite is true. It is probably due to the nonlinear impact that scope changes has on WP duration, as compared to the linear impact that delay has on the duration.

Knowledge of the expected changes and delay's intensities in a certain environment may be used for improving the project manager's ability to forecast WP duration, and therefore the whole project duration. However, one should keep in mind that the parameters will probably get different values in different organizational cultures and environments. This requires the project manger to either measure or use previous data on scope change and delays of similar projects that had been the carried out by the organization.

Appendix—Illustrative Example

The research data suggests that the average change component in equation (6): (1+CI)α, has the value of: 1.829, and a standard deviation (SD) of 0.878. Similarly, the average delay component in equation (6): (1+DI)α, is: 1.394, with a SD of 0.208. Under the assumption that change component values are normally distributed, one can choose a safety degree for forecasting WP duration. A safety degree greater than 50%, means that the change component has to be added by the number of standard deviations, z, corresponds to that degree, times the change component's SD. Here it is assumed that the original duration estimations are based on technical parameters of scope and environment, as in the COCOMO model (1), with no extras added. For simplicity, let us not use statistical consideration regarding the delay component, and take its mean value.

Consider the case where a WP is highly critical. The project manager wants to estimate its duration in a 90% safety degree, i.e., the degree where the probability of having actual duration longer than estimated is 10%. From the normal distribution table, a 90% safety degree level corresponds to z=1.28. Suppose that the original duration estimate of the package is 20 days, we derive the amended estimate using equation (7):


Suppose now that this WP is an ordinary one, i.e., a 50% safety degree is employed. In this case, the amended duration estimate of that package, using equation (7), is:


This implies for a significant difference of 24 days between the estimates of “highly critical” and “ordinary” WP durations—a difference of more than 50%!

Suppose now, that the project manger reduced the initiation delay to zero. That might result in as much as a 40% decrease in the WP duration, relative to the normal duration estimate, where the average value of the delay intensity is taken into account. Using equation (7), we get for the highly critical WP of equation (8) an amended duration estimate of:


This result is quite similar to the duration estimate of the “ordinary” WP (9), where no special attention is given to the initiation delay's effect.


Boehm, B.W., Horowitz, E., Madachy, R., Reifer, D., Clark, B.K., Steece, B., Brown, A.W., Chulani, S., & Abts, C. 2000. Software Cost Estimation with COCOMO II. New Jersey: Prentice Hall.

Burt, C.D.B., & Kemp, S. 1991. Retrospective duration estimation of public events. Memory & Cognition, 19, pp. 252–262.

Buehler, R., Griffin, D., & Ross, M. 1994. Exploring the “Planning Fallacy”: Why People Underestimate Their Task Completion Times. Journal of Personality and Social Psychology, 67, pp. 366–381.

Chatzoglou, P.D., & Macaulay, L.A. 1996. A Review of Existing Models for Project Planning and Estimation, and the Need for a New Approach. International Journal of Project Management, 14, pp. 173–183.

Chick, D. 1999. The Time Value of Project Change. Cost Engineering, 41, pp. 27–31.

Ertel, D. 2000. Scope Change Negotiations: Are Write-Offs Inevitable? Consulting to Management, 11, pp. 3–8.

Goldratt, E.M. 1997. Critical Chain. New York: North River Press.

Herroelen, W. & Leus, R. 2001. On the merits and pitfalls of critical chain scheduling. Journal of Operations Management, 19, pp. 559–577.

Leach, L.P. 1999. Critical Chain Project Management Improves Project Performance. Project Management Journal, 30, pp. 39–51.

Levy, N. 1998. Managing High Technology and Innovation. New Jersey: Prentice Hall.

Nicholas, J.M. 2001. Project Management for Business and Technology. New Jersey: Prentice Hall.

Nobelius, D. 2001. Empowering Project Scope Decisions: Introducing R&D Content Graphs. R&D Management, 31, pp. 265–274.

Project Management Institute Standards Committee. 2000. A Guide to the Project Management Body of Knowledge (PMBOK® Guide). Upper Darby, PA: Project Management Institute.

Pychyl, T.A., Morin, R.W., & Salmon, B.R. 2000. Procrastination and the Planning Fallacy: An Examination of the Study Habits of University Students. Journal of Social Behavior and Personality, 15, pp. 135–150.

Singh, A. 2001. Claim Evaluation for Combined Effect of Multiple Claim Factors. Cost Engineering, 43, pp. 19–31.

Shepperd, M., & Schofield, C. 1997. Estimating Software Project Effort Using Analogies. IEEE Transactions on Software Engineering, 23, pp. 736–743.

Shtub, A., Bard, J., & Globerson, S. 1994. Project Management—Engineering, Technology, and Implementation. New Jersey: Prentice Hall.

Storey, C. 2001. Measuring the Performance of New Service Development Activities. The Service Industries Journal, 21, pp. 71–90.

Tenah, K.A. 2001. Project Delivery Systems for Construction: An Overview. Cost Engineering, 43, pp. 30–36.

Thilmany, J. 2001. FEA in a Snap. Mechanical Engineering. New York, 123, pp. 60–62.

Proceedings of the Project Management Institute Annual Seminars & Symposium
October 3–10, 2002 • San Antonio, Texas, USA



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