Integrated Cost And Scheduled Project Risk Analysis

Integrated Cost and Schedule Project Risk Analysis David T. Hulett, Ph.D.1 Hulett & Associates, LLC

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, 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.

Simple Exploration of Project Cost Risk Elements Cost Risk Model – One Activity Risk The components of cost for a specific activity include duration, labor hours and labor compensation. Other inputs of cost such as materials and subcomponents are included, of course, but their risk can be handled in the traditional fashion so they are excluded from this paper. A specific project activity may have the following parameters: Cost Estimate Estimate Task Duration Labor Hours Daily Rate Total Cost

40 5 800 160,000

Cost Risk Parameters Most Low High Likely 30 40 60 3 5 8 750 800 875

Duration, hours and rate are each subject to variation because of risk. For instance, the number of days may be under- or over-estimated because the difficulty of the task may have been poorly understood or the productivity of the workers inaccurately estimated. The number of workers may be different than planned because the tasks were not well thought out or different skills may be needed. Finally, the availability of specific workers may not have been assured, giving rise to a skill mix that is different than planned on the activity. The project manager can examine the risk of each in order to assess cost risk. The three-point estimates show the uncertainty in the estimate and will be used to construct a triangular distribution of the cost parameters.

Cost Risk Analysis – One Activity Risk The typical cost risk analysis might incompletely assess the uncertainty of time. Organizations may consider their cost estimating to be completed even though the schedule is slipping on a weekly basis. Alternatively, a risk analysis that considers only uncertainty in time may assume that the labor hours and daily rate are fixed as estimated – some 1

David T. Hulett, Ph.D. is president of Hulett & Associates, LLC, Project Management Consultants of Los Angeles, CA, USA. He can be reached at (310) 476-7699, [email protected] and www.projectrisk.com. David T. Hulett, Ph.D.,

Integrated Cost / Schedule Risk Analysis

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organizations may be surprised to see 7 people when they budgeted for 5, or that the people actually on the project are higher-paid workers than they originally bid.

Cost Risk Results – One Activity Risk The chart below illustrates the cost risk analysis of this activity under three assumptions: 1. Using the traditional cost elements (labor hours and compensation per day) holding time constant. 2. Assuming duration is uncertain but that the labor hours and compensation per day are estimated accurately. 3. Considering the risk in all uncertain elements simultaneously. Cost Uncertainty Varying only Cost Elements, Only Task Druation and Both Duration and Cost Elements 100% Cost Risk Only

Percentile

80%

Time Risk Only

60% 40%

Cost & Time Risk

20% 0% 80,000

130,000

180,000

230,000

Cost

280,000

330,000

From the chart it is clear that examining only duration or only cost uncertainty will provide an estimate of cost risk that is too optimistic. The right-hand (red) curve indicates that the combined or total cost uncertainty is greater, especially at the upper end, than either partial analysis. If an organization wishes to provide a contingency reserve for, say, the 80th percentile of cost risk, they should include both two types of risk that are represented by the “Cost & Time Risk” curve. The percentile table for these three curves indicates the magnitude of the effect on one activity. It highlights the 80th percentile showing that the estimate is $28,000 to $22,000 above those estimates that take account of only cost or time elements. Cost Risk (000) Varying Cost & Cost Time Percentile Time Elements Elements Elements 0% 98 122 82 10% 129 142 133 20% 143 151 148 30% 152 158 159 40% 161 164 171 50% 171 171 183 60% 179 178 194 70% 190 186 206 80% 202 196 224 90% 220 209 248 100% 262 238 350 A useful chart is a scatter plot of cost and time (or date) results of the joint simulation. The chart below uses the results from 1,000 Monte Carlo simulations of time and cost. A focus is on the point which represents the time target of 40 days and the cost target of $160,000. The scatter shows that there is a serious likelihood that this activity will overrun both targets. This is a result that takes advantage of the schedule risk interim result. (40 days is equivalent to 10/10.)

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Date Cost Scatter And Analysis 400,000 54% Likely Overrun Both

350,000 300,000 250,000 200,000 150,000 100,000 17% Likely Underrun Both

50,000 0 9/26

10/1

10/6

10/11

10/16

10/21

10/26

10/31

Integrated Cost and Schedule Analysis Starting from a Project Schedule Cost / Schedule Risk Analysis Based on the Simple Schedule Cost / schedule risk analysis is usually conducted for a project schedule that has many tasks. The schedule shown below includes two components that begin at the start date and an integration and test phase that begins when the components are available. ID 0 1 2 3 4 5 6 7 8 9 10 11 12 13

Task Name

Duration

Start

Finish

Integrated Cost-Schedule Start Com ponent 1 Design 1 Build 1 Test 1 Com ponent 2 Design 2 Build 2 Test 2 Integration and Test Integrate System Test Finish

163 d 0d 98 d 28 d 45 d 25 d 95 d 32 d 38 d 25 d 65 d 40 d 25 d 0d

9/1 9/1 9/1 9/1 9/29 11/13 9/1 9/1 10/3 11/10 12/8 12/8 1/17 2/10

2/10 9/1 12/7 9/28 11/12 12/7 12/4 10/2 11/9 12/4 2/10 1/16 2/10 2/10

3rd Quarter

4th Quarter

1st Quarter

Designers[5] Build ers[10] Testers[8] Designers[7] Build ers[8] Testers[5] Integrators[12 Testers[9]

Cost Estimate using the Simple Schedule Notice that the schedule activities have resources loaded. Resource Name

Type

Max. Units

Standard Rate

Designers Builders Testers

Work Work Work

50 50 50

$90/hr $80/hr $105/hr

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Integrated Cost / Schedule Risk Analysis

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Integrators Work 50 $110/hr Total cost of this project is estimated to be $1,629,040, before risk analysis, as shown in the table below. Cost Estimate from the Schedule with Resources Integrated Cost-Schedule Component 1 Design 1 Build 1 Test 1 Component 2 Design 2 Build 2 Test 2 Integration and Test Integrate System Test

163 d 98 d 28 d 45 d 25 d 95 d 32 d 38 d 25 d 65 d 40 d 25 d

$1,629,040 $556,800 $100,800 $288,000 $168,000 $460,840 $161,280 $194,560 $105,000 $611,400 $422,400 $189,000

Issues in Integrated Cost / Schedule Risk Analysis Several issues must be addressed in developing an integrated cost / schedule risk analysis on a real schedule, of which this is a simple representation: 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. Uncertainty in duration must be analyzed for a concept that can be matched with the cost uncertainty model concept. In real project schedules, the time and cost concepts are not often as clearly related as they are in this hypothetical example. 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 concepts when the summary task does not start at a fixed point. In this schedule, we cannot tell when the integration and test phase begins because of the uncertainty in its predecessor activities, Components 1 and 2. 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® and the simulation is conducted by Risk+® by C/S Solutions. The analysis of cost is conducted in Microsoft Excel® and Crystal Ball® by Decisioneering. 4. If resources are completely specified, priced and loaded into 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. 5. 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.

Steps in Integrated Cost / Schedule Risk Analysis – Separate Programs 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

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2. 3. 4. 5.

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. Import the duration results, not the date results, for each iteration of the schedule simulation into a spreadsheet. 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. Simulate the cost risk model with inputs representing burn rate uncertainty and the distribution from the fitting technique that represents time uncertainty.

Schedule Risk Analysis Model based on Simple Schedule Conducting a schedule risk analysis requires three-point estimates and specification of the probability distribution at the level of the detailed tasks. The following table shows these values for Component 1 as an example: Schedule Risk Analysis Input Information -- 3-point Estimates and Curve Report Min. Rdur ML Rdur Max. Rdur Component 1 Summary Task 1 0d 0d 0d Design 1 0 20 d 28 d 40 d Build 1 0 35 d 45 d 55 d Test 1 0 15 d 25 d 40 d

Curve 0 2 2 2

The schedule risk analysis results, an intermediate result, are shown below for the total project dates. They indicate that the CPM date, February 10, is very unlikely to occur, given the assessed risks. This is a dramatic but not unusual result. Date: 9/1/2003 4:05:56 PM Samples: 1000 Unique ID: 18 Name: Integration and Test

Completion Std Deviation: 12.72 d 95% Confidence Interval: 0.79 d Each bar represents 4 d 1.0 0.9

Frequency

0.12

0.8

0.10

0.7 0.6

0.08

0.5 0.06

0.4

0.04

0.3 0.2

0.02

0.1 2/8

3/7

4/15

Completion Probability Table

Cumulative Probability

0.14

Prob 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Date 2/17 2/21 2/23 2/25 2/27 2/29 3/1 3/3 3/4 3/6

Prob 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

Date 3/8 3/9 3/11 3/13 3/16 3/18 3/21 3/25 3/31 4/15

Completion Date Duration Analysis

Transferring Schedule Risk Duration Results into the Cost Risk Model 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 below:

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Interviewing for the Cost Risk Input Data 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. For instance, the table below represents the baseline data and the interview results for Component 1 cost risk. Input Data for Burn Rate Risk Baseline Low Avg. Workers / Day 8.1 6 Baseline Low Avg. Rate / hour 88 80

Workers Component 1 Daily Rate Component 1

Most Likely

High

8

12

Most Likely

High

88

91

Structure of the Integrated Cost / Schedule Risk Analysis Model – Input Data Included

Component 1 Avg. Workers per day Avg. Rate / Hour Duration from Schedule Component 1 Cost Component 2 Avg. Workers per day Avg. Rate / Hour Duration from Schedule Component 2 Cost Integration and Test Avg. Workers per day Avg. Rate / Hour Duration from Schedule Integration and Test Cost Total Project Cost

Cost Risk Model with Inputs Baseline Most Low High Estimate Likely 8.1 6 8 12 88.1 80 88 91 98.0 Est. Lognormal distribution 557 6.9 88.2 95.0 461

5 7 11 77 88 90 Est. Lognormal distribution

10.8 108.4 65.0 611 1,629

7 95

11 14 108 120 Est. Gamma distribution

The simulation results shown below 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.

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Time, Cost and Time/Cost Project Cost Risk 100% Time Risk Only

80% 60%

Cost Risk Only

40%

Time & Cost Risks

20% 0% 1,200

1,500

1,800 Cost (000)

2,100

2,400

The cost – date scatter diagram 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.

Cost / Schedule "Football" All Risks 2,600 Cost / Schedule

Cost (000)

2,200

Target

1,800 1,400 1,000 1/24

2/13

3/4

3/24

Date The results of this hypothetical risk analysis show a serious likelihood of overrunning, and a rather remote likelihood of meeting both cost and time objectives. This result is often found even though the cost estimate looks to be well constructed and the schedule seems to be viable. Results of Integrated Cost / Schedule Risk Analysis Objective(s) Tested Percentage Likelihood Overrun Cost Objective 81% Overrun Time Objective 93% Overrun Cost and Time Objectives 78% Underrun Cost and Time Objectives 3%

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Integrated Cost / Schedule 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 will read this MS Project schedule including its uncertain durations and its resources and resource costs. The cost is the same, by component as seen below in comparison with the table above:

Then, the duration and resource costs per day can be varied so there is a true integration of uncertain duration and uncertain burn rate. An example is the Design 1 activity.

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. Here is the example for total project costs:

David T. Hulett, Ph.D.,

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Integrated Cost-Schedule Entire Plan : Finish Date 100% 31/Mar/04 12/Mar/04

90%

08/Mar/04

85%

176

04/Mar/04 02/Mar/04

70%

29/Feb/04

65%

28/Feb/04

Hits

60% 132

88

26/Feb/04

55%

25/Feb/04

50%

24/Feb/04

45%

22/Feb/04

40%

21/Feb/04

35%

44

05/Mar/04

80% 75%

20/Feb/04

30%

19/Feb/04

25%

18/Feb/04

20%

16/Feb/04

15%

14/Feb/04

10%

12/Feb/04

5%

08/Feb/04

Cumulative Frequency

220

95%

0

12/Feb/04

27/Jan/04

31/Mar/04

15/Mar/04

28/Feb/04

Distribution (start of interval)

The joint distribution is charted in a scatter plot, which is easy to do in the program because it is computing both time and money in a scheduling package. This scatter plot is not

Integrated Cost-Schedule Scatter Plot

$2,163,709

Entire Plan Cost

$2,081,622 $1,999,536 $1,917,449 $1,835,363 $1,753,276 $1,671,190 $1,589,103 $1,507,017 $1,424,930 27/Jan/04

08/Feb/04

21/Feb/04

05/Mar/04

18/Mar/04

Entire Plan Finish

In Monte Carlo from Primavera, the set up uses the same parameters that Pertmaster uses:

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The cost-time envelope 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.

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

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risk analysis results are provided. Risk responses can be developed that address the time- and cost-type risks individually as appropriate.

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