"How much will it cost?"  This is a question heard by all project engineers the world over.  We are asked this question from the very earliest phases of the project, when only the broadest scope is understood (where, what, and how big), all the way through the project until the facility is handed over to the client and a complete accounting is possible. 

Answering this question accurately is of vital importance regardless of what phase of the project-life-cycle you are in.  Answering it accurately in the earliest phases poses significant problems, however.  If the cost estimate is too high, then the client may cancel the project. If you commit yourself, your project team, and your client to an unrealistically low estimate, then you may not have enough budget to complete the project.

Parametric Estimating

Preliminary cost estimating is generally performed by using a process called parametric estimating whereby a unit cost is applied against a known parameter of the project.  For example, the cost estimate for a tunneling project needs to be performed at the earliest stages of the project when the only things known are the size and length.  The parametric estimate process for this project could be

$project = A x B 

Where:
                     A is the unit cost for tunneling ($/foot)
                     B is the number of feet to be tunneled. 

To understand the degree of confidence that can be placed in the estimate, we have to understand the confidence that can be placed in the parameters, A and B. 

• Parameter A (unit cost) is generally determined by the estimator based on historical data from similar projects that have been completed and have finalized costs.      
• Parameter B (tunnel length) is generally defined by the client in the scope of the project and is out of the control of the project engineer.

Parametric estimating lends itself nicely to the risk management process whereby the uncertainty of the cost can be quantified using statistics and, therefore, managed.  The project engineer can use the risk management process to answer the question about costs by asking:  "How confident do we want to be in our estimate?"

This means that the estimator can place limits on the accuracy of the preliminary estimate by selecting an estimated cost with the understanding that there will be a defined probability that the actual project cost will not exceed the estimated cost.  This is best demonstrated in a worked example.

An Example

A combined sewer overflow (CSO) tunneling project in the midwest U.S. requires an 11,000-foot, 10-foot diameter tunnel through rock to provide storage for storm water runoff.  The estimator consults a historical database of costs from previously constructed tunneling projects and develops a normalized unit cost parameter database for 10-foot diameter tunnels as shown in Table 1.

The first impulse is to use the mean (average) cost for the estimate giving a project cost of

$project  = 11,000 feet X $2294/feet = $25,234,000   or $25.2 million.

By definition, however, using the mean cost of $2294/foot indicates that there is a 50 percent chance that the actual cost will be greater than $25.2 million.

Probablistic Estimating

Is it an acceptable risk to put forward to a client a cost that has only a 50 percent chance of meeting the final budget?  This is something for the project manager and client to decide.  However, the appropriate application of statistics can provide the project engineer with a range of estimated costs and associated levels of confidence.  Figure 1 provides an indication of the confidence that can be placed in an estimated cost so that the final project cost will not exceed this estimated value. 

Continuing with the tunneling example, we can see that:      

• An estimated cost of $22 million has only a 23.6 percent chance of the project being on or under budget (76.4 percent chance of it being over budget).       
• A more conservative estimate of $30 million has an 85.5% chance of the project being on or under budget (14.5% chance of it being over budget). 
• A very conservative estimate of $33 million provides a confidence of 95.5 percent chance that the final project cost will be on or under budget. 

Advantages of Probablistic Estimating

The probablistic method of estimating does several things that a straight parametric estimate does not do in that it:      

• Provides a range of reasonable costs that can be brought forward to the client
• Enables the project manager and the client to understand the variable nature of estimating at early phases of a project
• Allows the project manager and/or client to select a cost according to how much risk they wish to assume for an over-budget project.

The natural tendency is to select a cost with a high degree of confidence, say 95 percent, but the corresponding estimate is $32.6 million.  By lowering the degree of confidence the estimated costs decrease proportionally-an estimate of $31.0 million has a 90 percent confidence; an estimate of $28.3 million has a confidence of 75 percent and so forth.

Probabilistic estimating provides a powerful tool for managing risks on a project at the earliest phases.  It provides a graphic representation of the inherent nature of the variability of estimating and allows the project manager and client to start the risk management process early. 

Tools are Available to Help You Make Optimal Choices

We have a number of similar risk management tools that can provide project managers with critical information and optimal choices.  Such tools can help:

• Quantify true project risks        
• Identify optimal cost/benefit decisions      
• Help make efficient life-cycle costing decisions
• Minimize repair/replace cost.

We invite inquiries about these and other risk management tools from any interested PB staff member.