# Integrated cost and schedule project risk analysis

### Introduction

#### Why Integrate Cost and Schedule Risk

Cost estimates often become disconnected from the project reality as schedules slip. Cost estimators sometimes believe their estimates are still valid even as one of the major components of those estimates, activity duration, changes. Since each activity's cost depends on assumptions of duration Cost risk depends on risk in all components of the cost equation, including duration of the activities.

The thesis of this paper is that the estimate of cost risk can be made more accurate and better understood if the sources of risk are disaggregated into those that affect time and those that affect the burn rate per unit time.

This approach requires conducting a schedule risk analysis first, and then using those results as input to a cost risk analysis if the cost estimates are based outside the schedule, say, in a spreadsheet. If resources are loaded and priced in the schedule, there are at least two programs that will conduct the integrated cost and schedule risk analysis simultaneously, driving the cost uncertainty by schedule uncertainty. As a bonus, the risk to the schedule objective is computed and available for those who are concerned that the project may not achieve its time objective.

### Analysis where the Project Schedule and Cost are in Different Programs

Cost / schedule risk analysis is usually conducted for a project schedule that has many tasks. The schedule shown below (Exhibit 1) includes two components that begin at the start date and an integration and test phase that begins when the components are available.

Exhibit 1: Simple Input Schedule

The resources shown in the schedule are priced as Exhibit 2 below illustrates. When the number of resources, their hourly rate and the number of days duration are multiplied together, the total cost of this project is estimated to be \$1,629,040, before risk analysis.

Exhibit 2: Resources and Prices Applied

Several issues must be addressed in developing an integrated cost / schedule risk analysis on a real schedule:

1. The schedule is usually developed to a lower level of detail than the cost estimate. In our schedule, while the schedule includes tasks of Design 1, Build 1 and Test 1, the cost estimate may be developed and actual costs collected at the Component 1 summary level. In real project schedules, schedules tend to drift further and further away from the WBS structure as they are developed, while cost elements usually stay fairly true to the WBS.
2. We need uncertainty in duration of the summary tasks, whereas most schedule risk analysis focuses on uncertainty in dates. Dates and durations are not equivalent, e.g., in this schedule, we cannot tell when the integration and test phase begins because of the uncertainty in its predecessor activities.
3. Typically schedule risk and cost risk analysis are computed in two different environments. To represent that problem, the analysis of schedule is built in Microsoft Project®, the simulation is conducted by Risk+® by C/S Solutions and the analysis of cost is conducted in Microsoft Excel® and Crystal Ball® by Decisioneering. (If resources are completely specified, priced and loaded in the scheduling package, an integrated cost / schedule risk analysis may be performed. There are at least two packages that can conduct the integrated analysis, Pertmaster® Monte Carlo® from Primavera. These results are also shown in this paper.)
4. Cost uncertainty requires uncertainty in the average labor resources and average compensation per day, whereas project managers ramp up and ramp down their resources, at least at the summary level. Often the project manger or team leader do not think in terms of average labor force or compensation, so some context must be established to assist their thinking. The information on average labor and compensation come from the basis of estimate where these assumptions in the baseline estimate are recorded.

The analysis with schedule and cost in separate programs starts with the schedule shown above and proceeds as follows:

1. Conduct the risk interviews for the schedule uncertainty
2. Simulate the schedule using Risk+, collecting the results of each iteration at the appropriate level. For this schedule, that level is Component 1, Component 2 and Integration and Test summary tasks.
3. Import the duration results, not the date results, for each iteration of the schedule simulation into a spreadsheet.
4. Fit the probability distributions statistically to the duration outputs using Crystal Ball. The fit provides the closest distribution and can be used to represent time uncertainty in the cost risk simulation.
5. Simulate the cost risk model with inputs representing burn rate uncertainty and the distribution from the fitting technique that represents time uncertainty.

Conducting a schedule risk analysis requires three-point estimates and specification of the probability distribution at the level of the detailed tasks. The schedule risk analysis, an intermediate result, is shown below for the possible dates of completion of the total project as shown in Exhibit 3, below. It indicates that the CPM date, February 10, is very unlikely to occur, given the assessed risks. This is a dramatic but not unusual result.

Exhibit 3: Schedule Risk Analysis

The schedule risk simulation saves a file of the results for each iteration (we ran 1,000 iterations) that includes durations denominated in minutes. The durations are converted into days, dividing by 480 for an 8-hour day schedule, in a spreadsheet file. For the cost risk analysis we need to estimate a Crystal Ball probability distribution for the three summary tasks, Component 1, Component 2 and Integration and Test. These distribution types and parameters for uncertain summary task durations serve as inputs to the cost risk model. Two typical results of these fitted functions are shown in Exhibit 4, below:

Exhibit 4: Statistical Fits of the Duration Simulation Results, Prepare for Cost Risk

The cost risk model is similar, at the summary task level, to the single-activity analysis that introduced this paper. The input assumptions include labor hours and compensation averages over the summary path time frame. If the interviewees, usually team leaders or project managers, do not think in these concepts, the baseline estimate can be used to identify baseline assumptions. Interviewees should use those estimates to orient themselves, although they should be careful not to give those data unrealistic credence. The input to the cost risk analysis model is shown in Exhibit 5 below for Component 1. Notice the estimated lognormal distribution of duration is the duration uncertainty.

Exhibit 5: Cost Risk Model with Burn Rate and Duration Input Assumptions

The simulation results, shown below in Exhibit 6, indicate the importance of considering both duration and burn rate uncertainty. Duration uncertainty is most accurately incorporated in the cost risk analysis as the result of a schedule risk analysis.

Exhibit 6: Cost Risk Model Results Cumulative Distributions

The cost – date scatter diagram that is shown in Exhibit 7 can be created in this way only if the schedule can be remade in the Excel program. This is only possible if the schedule is simple. In this case the schedule is reproduced in the spreadsheet although that is impractical for real schedules.

Exhibit 7: Cost and Schedule Risk Model Results Scatter Plot

The results of this hypothetical risk analysis for the four quadrants are summarized in Exhibit 8. They show a serious likelihood of overrunning, and a rather remote likelihood of meeting both cost and time objectives.

Exhibit 8: Results of the Four Quadrants on the Scatter Diagram

### Analysis when the Resources are Loaded and Priced in the Schedule

Most schedules are not fully resource-loaded with resource costs included. If this information is included in the schedule, there are two scheduling packages that can compute integrated cost / schedule risk analysis in which both time and burn rate can be varied simultaneously and the time uncertainty helps drive the cost uncertainty. Those two packages are Pertmaster and Monte Carlo (from Primavera). They will both be illustrated based on the schedule presented in this paper.

The project schedule shown above has been loaded with resources (designers, builders, testers, integrators) and their hourly rate has been entered as well. This is how the cost of \$1,620,040 was computed. Pertmaster reads this MS Project schedule including its uncertain durations and its resources and resource costs.

Then, the duration and resource costs per day can be varied in Pertmaster so there is a true integration of uncertain duration and uncertain burn rate. As an example, the time and burn rate uncertainties for Design 1are shown in Exhibit 9:

Exhibit 9: Inputs of Duration and Burn Rate Ranges in Pertmaster

The simulation chooses values of duration and daily hours for each detailed task for each iteration. It computes the implied date and total project cost for each iteration. The cost uncertainty that is computed includes both uncertain durations and uncertain burn rates. Exhibit 10 provides a schedule risk result example for total project:

Exhibit 10: Schedule Risk Analysis, One Result from Pertmaster

The joint distribution is charted in a scatter plot, shown in Exhibit 11, which is computed during the simulation of both time and resources are included in Pertmaster.

Exhibit 11: Cost / Date Scatter Plot from Pertmaster

To use Monte Carlo from Primavera, the risk parameters are set up in the Primavera P3 schedule (see Exhibit 12):

Exhibit 12: Schedule with Duration and Burn Rate Ranges in Monte Carlo

Monte Carlo, like Pertmaster, provides probability result distributions of schedule risk and cost risk. In addition, the cost-time envelope, such as that shown in Exhibit 13, gives the same information as Pertmaster. Monte Carlo adds a band around the “football” (American-style) that attempts to enclose some 90% of the cost-date pairs from the iterations.

Exhibit 13: Cost / Date Scatter Plot from Monte Carlo

### Summary

Usually the cost estimates are developed on spreadsheet platforms so the result of the schedule risk analysis, the uncertainty in durations of detailed tasks or of summary project components, have to be incorporated in a simulation of the spreadsheet. This paper has shown a way to use the schedule risk results from Risk+ to the cost model simulated by Crystal Ball.

If the resources are defined, priced and assigned to activities in the schedule software, there are at least two programs, Pertmaster and Monte Carlo, which will provide integrated cost / schedule risk analysis. These programs simulate cost and date uncertainties with the cost estimates allowing both the duration and burn rates to vary simultaneously.

Cost risk analysis that explicitly incorporates schedule risk analysis results, merging them with burn rate risk information in the estimates of cost risk that are more accurate than the typical approach. In addition, the schedule risk analysis results are provided. Risk responses can be developed that address the time- and cost-type risks individually as appropriate.

© 2004, David T. Hulett, Ph.D.
Originally published as a part of 2004 PMI Global Congress Proceedings – Prague

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