Modeling project behavior

dynamic tools for early estimates in construction project management

Alberto De Marco

In most industries, projects encounter chronic delays and cost overruns, despite the rigorous application of project management expertise and techniques. Some surveys suggest that overruns of 40-200% are common (Morris & Hough, 1987).

Changing external conditions—such as customer changes, procurement delays, and resource availability— affect or even obliterate the initial budgets and schedules, thus requiring costly rework and additional resource procurement.

To stay on time and within the budget, project managers most often respond with schedule pressure, overtime, hiring, and quality reduction.

Such decisions result in the project performance decreasing even more: they cause lower productivity and, as a consequence, more rework, longer delays, and increasing costs in a recurring, virtually exponential, causal reaction, which finally leads to divisive litigations between customers and contractors over responsibility for missing goals (Sterman, 1992).

It becomes obvious that the internal operative structure and the managerial approach to project control themselves are the key factors in understanding the way that the project will respond to external changes.

While the Project Management traditional approach faces misbehaviors thanks to useful and analytic techniques (such as PERT scheduling, risk assessment, and contract management), the new approaches, based on system dynamics, assume a holistic view of the project organization focusing on the behavior of projects and its relation to managerial strategies, and corrective actions related to project control outcomes (Rodrigues & Bowers, 1996).

Among different existing applications for project management—that is, network-based tools with integrated dynamic feedback relationships, system dynamics permits the defining and testing of a formal computer-based model that considers the main variables and management actions in a systemic perspective, thus enhancing decision-making at a strategic level.

In this sense, system dynamics modeling is useful at the starting stages (feasibility and planning phases, or once the initial budget and the scheduled date become available) to simulate the project trends and to, early on, estimate cost and duration final ranges. Moreover, it is of practical value to project managers during the project execution to control overruns and adopt appropriate managerial approaches towards human resources and customers.

In this paper, first the main characteristics of project dynamics are presented and a construction project management model is developed as a general tool; second, the model is retrospectively validated on the basis of real project data. Then, limitations are discussed together, with practical conclusions.

Traditional and systemic approaches to Project Performance

The traditional approaches of project management produce reasonable estimates of overall duration and costs, based on the premise that each element of the project is - more or less - known.

This is possible both at the planning step and during project control. On the one hand, Work Breakdown Structure (WBS)decomposition, Cost Breakdown Structure (CBS) and network-based planning permit the scheduling of original work, the defining of the budget, and the setting of the finish date for the sum total project; on the other hand, earned-value analysis assures on-the-go estimates to completion, based on cost and time progress measurement. Mainly, the estimates to completion at a given time can be calculated according to real progress of work scheduled (WS), work performed (WP), budget cost (BC), and actual cost (AC):

  1. estimated completion date = (budget-BCWP) / (budget-BCWS) / SPI * (scheduled completion date-Time now) + Time now ;
  2. estimated costs at completion= ACWP+(BAC budget at completion-BCWP)*CPI ;

SPI and CPI are defined, respectively, as the time schedule performance index and the cost performance index (Project Management Institute, 2004)

During the project execution, the estimate-to-completion process suggests, and sometimes compels, project managers to take corrective actions enabling ongoing cost and time adjustments; namely, to bring the budget in line and schedule monthly revisions of the latest forecasts. Consequently, a monthly revision process causes fluctuation and oscillation in resource usage, work rates, productivity, quality, and schedule pressure.

Briefly, project management is dynamic, updating variables as information becomes available, and adapting the plan rather than keeping rigidly to the original. Accordingly, projects are complex systems and are based on multiple causal feedback loops. The characteristic dimension of project complexity requires supporting system dynamics modeling to accompany and enhance traditional techniques (Williams, 2002).

In particular, construction projects consist of multiple interdependent elements that are not closely related in time and space; as a result, construction managerial linear decisions often cause multiple unattended and even unintended side effects, which cannot be completely understood using mental models and traditional analytic-based approaches only, such as risk management causal techniques and other deterministic decision-support systems.

The failure to consider these project dynamics may not only confirm time and cost overruns, but also ignore opportunities and positive effects. However, there are several successful histories of project dynamic modeling to support construction management in different industries, especially for plant, infrastructure, and building construction.

The system dynamics method allows the representation of feedback interrelationships among a number of variables as an influence diagram (Coyle, 1996).

Figure 1, for example, illustrates the schedule slippage recurring cycle (Richardson & Pugh, 1981). The arrows represent influences between the different factors; the plus or minus sign indicates whether a positive change in the preceding variable has a positive or negative effect on the next. Thus a higher estimated schedule slippage results in a longer adjustment to schedule, which in turn causes a delayed schedule date. Eventually, a longer revised schedule date causes a shorter estimated schedule slippage.

The schedule revision cycle

Figure 1 – The schedule revision cycle

In a description of the complete causal feedback map for a project, the relations between the variables are elicited, either from data describing past projects or in discussion to mental models. A computer-based simulation may then be built, (Ventana Systems Inc., 2005) in which graphic outputs allow observation of the project behavior over time.

In both academic and professional literature, system dynamic models examine the project behavior from different points of view, according to the problem that the model tries to solve. One model may place emphasis on the effect of deadline and milestone control, while another may focus on design versus construction overlapping (Osgood, 2003). There are models considering change management (Park & Peña-Mora, 2003), project control, rework (Love, Holt, Shen, Li, & Irani, 2002), and human resources management toward overwork, morale, and fatigue.

Some references have deeply inspired this work: the research & development project model (Richardson & Pugh, 1981), its derived construction project management model (Chang, Ogunlana, & Saeed, 1991), the model investigating the effect of initial scope on the final performance (Chritamara, Ogunlana, & Bach, 2001), and the project dynamic management model by Lyneis (1999).

The construction project management model

Model aims

Traditional project management techniques are developed and applied to manage attended dynamics.

To help project managers understand and manage unintended and unattended dynamics on project performance, a causal loop model, based on the concepts of system dynamics, has been developed.

Its main purpose is to provide a simple and practical tool, which permits project managers to forecast cost and time performances on the basis of a very low number of information entries; namely, the original conditions for scope, schedule, and budget; the time required to procure new resources (both human and material); and the external scope change quantity that the project may have.

Running the model, at convenience either at the initial definition or during the project execution, can help project management teams to better understand their own decisions and to simulate, under different conditions, the options they may encounter.

Model description

Figure 2 represents, in causal loop terms, the complete structure of the model. For further detail, model equations describing the causal relations between variables are included in the Appendix.

The complete model causal map

Figure 2 – The complete model causal map

Primarily, the process execution is represented as a stock of ‘Work remaining’ flowing into a stock of ‘Work performed (WP)’ through the ‘work rate,’ defined as a combination of ‘scheduled work rate’ and ‘resource usage rate,’ which is in turn affected by work quality and productivity.

The work remaining is determined by scope, which equals 100% in original conditions plus any scope changes which may occur at a given time during construction. When WP attains the scope level, the project is finished.

In this model, rework is included in quality definition: in other words, if quality goes down, rework increases.

The model contains 19 feedback loops affecting the variable ‘estimated completion date.’ The main feedback loops are illustrated in Figure 3, which define the estimate-to-completion management process.

Loop 1 establishes the schedule revision process: a longer estimated completion date suggests to project managers a longer revised schedule, which in turn smoothes the work schedule, the schedule value, and the schedule performance index (SPI). Eventually, at the next time step, a newly estimated finish date is earlier.

Meanwhile, according to the reinforcing Loop 2, a longer estimated completion date makes a greater estimated delay and an increasing managerial pressure, which in turn decreases the work quality and the work rate. The final effect is an even worse SPI and a longer estimated duration.

Also, pressure affects productivity and requires more resources to keep the WP in line to the schedule, thus permitting a better SPI and a reduced estimated completion date.

Main loops affecting the project performance

Figure 3 – Main loops affecting the project performance

One of the main assumptions of this model is the scheduled work S-curve considered as a general logistic equation, attaining the 100% progress when time equals the scheduled duration:

WS = scope/(0.9953+100*EXP(-(10/scheduled completion date)*Time)

Figure 4 represents the curve of scheduled work for the project duration of 24 months.

Input curve of scheduled work

Figure 4 – Input curve of scheduled work

Figure 5 shows the estimated completion date and pressure behaviours.

Estimated completion date and schedule pressure behaviours

Figure 5 – Estimated completion date and schedule pressure behaviours

The following figure gives graphic results as two compared situations: the base case considers a 24-month-long project with unchanging conditions and one month required to procure additional resources; the test case is a 24-month project with three months required for procurement and a 20% of scope changes taking place after one year.

The base project ends in 26.6 months with a 10.9% delay, while the test case in 42 months or 74% delay with respect to the initial schedule. The final over costs compared to original budget are 12% in the base case and 11.55% in the test case.

Work performance in the base and test cases

Figure 6 – Work performance in the base and test cases

Also, the model takes into account initial delays. This aspect has been considered to respond to usual project histories.

System behavior and policy implication

Several experiments in model running have been performed to observe policy implications on the system behavior. The results are summarized below.

Monthly schedule revision is convenient only in changing conditions: if there are not any changes, a monthly revision may increase project delays.

Schedule pressure helps to reduce the project completion date for little variation from its standard value (1); if schedule pressure increases or decreases by large amounts, it worsens the system behavior and increases the project duration.

The project can respond to scope changes if they do not occur after the work performed has progressed by 70-80%.

Appendix 2 presents a model simulation.

Model boundaries and limitations

The presented project model des not consider the feedback loop affecting the relations between cost overruns and scope definition. It means that usually when there is a cost raise, project managers try to reduce scope and take corrective actions. These approaches will be considered in future research as balancing factors to the extreme outputs that the present model is able to provide.

Also, to apply to real cases, the model must input the real curve of work scheduled as the result of the network-based planning.

Model application to power plant construction projects

Eight large projects have been considered to really test the model.

The projects comprise the construction of power stations, such as thermal, hydro, gas-turbine-and-gas-heat-combined power plants, as well as associated transmission and transforming facilities to improve electric energy production and capacity within East and Far East Asian countries— namely, China, India, Indonesia, Jordan, Laos, and Thailand. The projects were part of a loan program carried by the Japan Bank for International Cooperation in the power sector (Japan Bank for International Cooperation, 2004) from 1993 to 2003.

The following exhibit shows the retrospective model results compared to real outcomes.

In the case studies, construction was the result of turnkey contracts, and the figures are related to a client cost perspective.

The following results show that the model can give project management teams a better comprehension of project performance because of its approximated forecasting approach.

Results of model application to the case studies

Figure 7 – Results of model application to the case studies


The construction project modeling approach is of practical value to customers and contractors because it assures both management teams the tools to better define the initial contract and scope, and because it makes them aware of the risks that they will pay for during the project execution, thus creating a tight mutual involvement.

First, it is a contract management tool because it assures the tools to better define the initial contract and scope, and because it makes them aware of the risks that they will pay for during the project execution, thus creating a tight mutual involvement.

Second, it is a change management tool: it sets a common discussion and communication platform to enable decision-making together with comprehension and participation on the part of the contract counterpart.

Chang, C. L., Ogunlana, S., & Saeed, K. (1991). Construction project management: A system dynamic approach. 10th International System Dynamic Conference, Bangkok, Thailand.

Chritamara, S., Ogunlana, S. O., & Bach, N. L. (2001). Investigating the effect of initial scope establishment on the performance of a project through system dynamics modelling. Engineering, Construction and Architectural Management, 8(5/6), 381-392.

Coyle, R. G. (1996). System dynamics modelling: A practical approach. London: Chapman & Hall.

Japan Bank for International Cooperation (JBIC). (2004). Evaluation of ODA Loan Projects from the JBIC. Retrieved September 21, 2005, from

Love, P. E. D., Holt, G. D., Shen, L. Y., Li, H., & Irani Z. (2002). Using systems dynamics to better understand change and rework in construction project management systems. International Journal of Project Management, 20, 425– 436.

Lyneis, J. (1999). Dynamics of project performance [course material], Department of Civil and Environmental Engineering, MIT, Cambridge, MA

Morris, P. W. G., & Hough, G. H. (1987). The anatomy of major projects: A study of the reality of project management. NewYork: John Wiley and Sons.

Osgood, N. (2003). Problem diagnosis & introduction to project dynamics [course material], Center for Construction and Research Education, MIT, Cambridge, MA.

Park, M., & Peña-Mora, F. (2003). Dynamic change management for construction: Introducing the change cycle into model-based project management. System Dynamic Review, 19, 213–242.

Project Management Institute. (2004). A guide to the project management body of knowledge (PMBOK® guide). Newtown Square, PA: Author.

Richardson, G. P., & Pugh III, A. L. (1981). Introduction to system dynamic modelling with Dynamo. Cambridge, MA: The MIT Press.

Rodrigues, A., & Bowers, J. (1996). The role of system dynamics in project management. International Journal of Project Management, 14(4), 213-220.

Sterman, J. D. (1992). System dynamic modelling for project management. MIT Sloan School of Management, Cambridge, MA.

Ventana Systems Inc. (2005). Vensim modeling guide version 5.1. Harvard, MA: Ventana Systems Inc..

Williams, T. (2002). Modelling complex projects. New York: John Wiley & Sons.

Stocks, flows and variables:

3. AC=Resources/10

4. ACWP= AC*WP/100

5. BAC budget at completion=ORIGINAL BUDGET*(1+scope changes/100)

6. BCWP= (BAC budget at completion/100)*WP

7. BCWS= BAC budget at completion*WS/100


9. estimated completion date=(BAC budget at completion-BCWP)/(BAC budget at completion-BCWS)/spi*(scheduled completion date-Time)+Time

10. estimated costs at completion= ACTIVE INITIAL (ACWP+(BAC budget at completion-BCWP)*cpi, ORIGINAL BUDGET)

11. estimated delay=estimated completion date-scheduled completion date

12. final overcost=IF THEN ELSE(project finished=0, (ACWP-ORIGINAL BUDGET)/ORIGINAL BUDGET, 0 )

13. normal productivity=NORMAL RESOURCE USAGE RATE/scope

14. pressure=IF THEN ELSE(estimated delay<= 0 ,1,ZIDZ( scheduled work rate , required work rate ))

15. productivity=normal productivity*pressure

16. project finished=IF THEN ELSE(WP<scope,0,1)

17. quality=pressure/NORMAL RESOURCE USAGE RATE

18. required resources= INTEG (rquired resources rate,0)

19. required resources rate=ZIDZ(scheduled work rate*NORMAL RESOURCE USAGE RATE , productivity)

20. required work rate=ZIDZ( Work remaining , scheduled time remaining )

21. resource usage rate=ZIDZ( required resources-Resources , time to hire )

22. Resources= INTEG (resource usage rate,0)

23. rev schedule compl date=IF THEN ELSE(monthly revision=0, scheduled completion date , revised compl date)

24. revised compl date=DELAY FIXED(estimated completion date, monthly revision , scheduled completion date)

25. scheduled completion date=ORIGINAL SCHEDULE+INITIAL DELAY

26. scheduled time remaining= ACTIVE INITIAL (IF THEN ELSE(project finished, 0 , scheduled completion date-Time ),scheduled completion date)

27. scheduled work rate=XIDZ( WS , Time , 0 )

28. scope=ORIGINAL SCOPE+scope changes

29. scope changes=STEP( changes , time when changes occur )

30. spi=IF THEN ELSE(BCWP=0, 1 , XIDZ(BCWP , BCWS , 1 ) )

31. total delay= ACTIVE INITIAL (IF THEN ELSE(project finished=0, (Time-ORIGINAL SCHEDULE)/ORIGINAL SCHEDULE*100 , 0 ),0)

32. work rate=IF THEN ELSE(project finished, 0 , IF THEN ELSE( estimated delay>0 , resource usage rate*quality , scheduled work rate) )

33. Work remaining= INTEG (-work rate,scope)

34. WP= INTEG (work rate,0)

35. WS=STEP( IF THEN ELSE(Time=0 , scope/(0.9953+100*EXP(-(10/scheduled completion date)*Time)) , scope/(0.9953+100*EXP(-(10/(rev schedule compl date-INITIAL DELAY))*(Time-INITIAL DELAY))) ) , INITIAL DELAY )


36. changes


38. time to hire

39. time when changes occur

40. monthly revision [=0 OR 1]





Appendix 2 – Model simulation

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©2006 Project Management Institute



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