Using Parametric Cost Modeling

Certain industries have been around long enough that project managers who work in those industries have developed standardized mathematical formulas for estimating project costs. The use of mathematical formulas in cost estimating is called parametric modeling.

For most projects, the main parameters, or characteristics, that affect costs are time and materials. A good example of a parametric model is the cost of residential home construction. Builders often base cost estimates for a house on so many dollars per square foot of living space. Examples of simple and complex parametric models are provided below.

• Simple. The costs to build a road are based on a standard cost per mile. The cost to blast through bedrock is based on the volume of rock to be removed.
• Complex. A model for estimating software development may incorporate several adjustment factors for each function within an application.

Some parametric models are meant to give a rough estimate of costs, while others are designed to provide more accurate estimates. You can use parametric modeling when the following three criteria are in place.

1. Your project has quantifiable parameters.
Since a parametric model is a mathematical formula, the variables or parameters of a project that you use must be readily quantifiable. This means that the component or components upon which you base costs must have a unit of measurement, such as weight, length, number, or grade.

Most types of projects contain quantifiable variables. For example, a training company could estimate costs to be so many dollars per hour of instruction, or a food manufacturer could estimate so many dollars per pound of finished product.

2. The parametric model is scalable.
To be reliable, a parametric model must also be scalable, meaning that it must apply to a large project as well as it does to a small one. Most projects, even those of a similar nature, vary in terms of product scope, so you need a model that allows for a range in the number or size of products delivered.

Some models, though perfectly scalable, may have upper and lower limits that invalidate the model if project scope exceeds the limits. For example, economies of scale may come into effect for a large project, reducing costs proportionately. For other models or types of projects, larger scale means extra work, thereby increasing costs.

3. Accurate historical information has been used to develop an appropriate model.
The third main criteria for determining whether using a parametric model is appropriate for your project is whether there is an existing model, or the potential to build one, based on historical information. The accuracy of your estimates increases with the accuracy of the data used in the model.

Many companies develop their own parametric models specific to the types of projects they perform. All you need is enough data from previous projects to establish the mean costs of products or services provided in the past.

Many industries have used historical information to develop parametric models in the form of software applications. The time that the software saves you in estimating costs quickly, and the accuracy it provides, are worth the cost.

In summary, you can use parametric modeling when your project has quantifiable characteristics and there is sufficient accurate historical data to develop a scalable and dependable mathematical formula for estimating costs.

Deciding if a Project Needs Resource Leveling

Another tool used for schedule development is resource leveling heuristics. The mathematical analysis process often results in the creation of a project schedule that requires more resources than are available at a given time. This is where resource leveling heuristics come into effect.

Resource leveling heuristics is a prioritization process that allocates scarce resources to critical path activities first. In other words, it is a technique that resolves resource conflicts by delaying tasks within their slack allowances.

Projects seldom have an abundance of resources. In many situations, a project will require a critical resource that must be available at certain project points. To ensure availability, the critical resource will need to be scheduled in reverse from the project ending date, this is known as reverse resource allocation scheduling.

To use the reverse resource allocation scheduling method, you must be able to complete the activity with the limited number of resources that are available. For example, the resource requirements for a renovations project indicates that three electrical engineers are needed. However, the project manager discovers that the work, which was scheduled to be done by three people, must now be done by two. The result is that the activity may take three weeks with two engineers instead of two weeks with three engineers as originally planned.

Another method of resource leveling is the resource-based method. This involves looking at the workload for each resource in a given work period and assigning a more realistic workload.

Resource leveling is the activity in which project teams encounter problems when developing their project schedules. If a company has multiple projects running simultaneously that require the same resources, problems can arise. Problems may occur when not enough attention is paid to resource allocations and their conflicts.

When conducting resource leveling heuristics, there are a number of details that must be taken into consideration. Asking the following questions will help you to determine where leveling is required or possible.

Does the activity have slack time?
If activities have little or no slack time, they are usually critical path activities. They are provided with the necessary resource requirements, when possible. If for example, activity A has zero float, activity B has a three-day float and activity C has a two-day float. Activity A is allocated resources first.

Is this activity high priority?
If resources are limited, higher-priority activities are allocated resources before lower-priority activities. Activities that are higher priority are normally on the critical path. For example, if activity D is a critical path activity and activity B a non-critical activity, activity D is allocated resources before activity B.

Can this activity be split?
If resources for an activity are only available at particular times, splitting the activity may be required. For example, the resources for activity E are only available on Mondays, Wednesdays and Fridays. Therefore, the manager must split the activity into three non-consecutive days.

Is this a flagged activity?
If an activity is flagged, it means that a component of that activity has a significant detail attached. Flagged activities have a higher priority than others. For example, a computer design project may require a special part that is only available at a certain time. The activity requiring this part would be flagged.

Can the activity requirements be altered without affecting the overall project?
If an activity can be altered to reflect the availability of resources, then that activity is finished when the resources are available. For example, an activity requires two engineers 100 percent of the time: one is only available 75 percent of the time. The activity will be finished when the other resource is available.

DataWare Software Development (DSD) is currently working on a project to develop education software. The project manager has been informed of both a reverse resource allocation scheduling conflict and a resource-based conflict. He has already determined that each of these activities has slack time and neither is on the critical path.
The resource requirements call for two graphic artists. Unfortunately, only one is available. The project manager will have to perform resource leveling by lengthening the schedule so that the work to be done by two people can be done by one.

The schedule calls for the audio to be recorded for three different projects at the same time. When the project manager applies resource leveling heuristics, these three projects will take three days for audio instead of the one day originally scheduled.

Resource leveling requires a degree of common sense. If an adjustment does not seem realistic, don't make it as it may do more harm than good.

An Introduction to CPM, PERT and GERT

How do project teams determine a project's duration? Is it an exact science? The answer is no, it is not an exact science. It is more a process of estimating activity durations, which can be made easier by utilizing mathematical analysis.

Mathematical analysis is used in project schedule development to determine early and late start dates, as well as early and late finish dates for all project activities. The outcome indicates the time period in which the activity should be scheduled. Note that this analysis phase does not take into account any resource pool limitations or constraints.

The most widely known mathematical techniques used by project management teams are the: Critical Path Method (CPM), Program Evaluation and Review Technique (PERT), and Graphical Evaluation and Review Technique (GERT).

Critical Path Method (CPM)
The most common mathematical technique is the Critical Path Method (CPM). The CPM is used to predict project duration by analyzing which sequence of activities, or path, has the least amount of scheduling flexibility.

Once you have determined the early and late start and finish dates, you can determine float. Float is equal to the difference between the late finish and early finish dates, or the difference between the late start and early start dates.

The next step in the CPM is to determine the critical path (CP), which is the longest path for the project that has little or no float. To determine the critical path, you begin with the first activity in the network. Look at its successors, compare the successors' float values, and select the one with zero float. This is the second activity on the critical path.

Next, you would continue from the second activity on the critical path and compare float for its successors, selecting the activity that has zero float and including it in the critical path.

You continue this process to the final activity for a complete critical path. The project can finish no sooner than the time it takes to complete the activities on the critical path.

To calculate an activity's duration, you subtract the early start from the early finish or the late start from the late finish. In example that follows, the numbers indicate days.

• activity A - 1 day
• activity B - 2 days
• activity C - 3 days
• activity D - 2 days

Adding the total of the activity durations will give you the duration of the critical path. In this example, the duration of the critical path would be 8 days.
Critical Path activities are, indeed, critical to a project's success. They need management's careful attention. The order and duration of these activities are important because any delays will result in the project going over the anticipated completion date. In addition, project improvements are most effective when made along the critical path.

Program Evaluation and Review Technique (PERT)
Have you ever performed activity duration estimates, then questioned your findings? There is a technique available for checking your findings.

Program Evaluation and Review Technique (PERT) is used when there is a high level of uncertainty about how long it will take to perform a given task.

PERT uses network logic—the collection of activity dependencies that make up a project network diagram—to determine duration. In PERT, network logic is used by applying the critical path method to a weighted average duration estimate.

Although very similar, there is one significant difference between PERT and CPM. CPM uses the most likely estimate instead of the expected value of the estimate that PERT uses.

PERT time estimating requires the following three estimates for each activity.

• TM = most likely time
• TO = optimistic time
• TP = pessimistic time

To determine the expected activity time you must insert the previous estimates into the PERT weighted average formula, which is optimistic (TO) + 4 x most likely (TM) + pessimistic (TP) all divided by 6.
Once you have calculated the estimated times for your project you can plot those values on an s-curve. The s-curve allows you to easily see all three times—optimistic, most likely, and pessimistic.

Graphical Evaluation and Review Technique (GERT)
There is one additional mathematical analysis method that is rarely used today because it has been proven to be less accurate than PERT and CPM. This method is the graphical evaluation and review technique (GERT). GERT allows for probabilistic treatment of both network logic and activity duration estimates. GERT is mainly used on project activities that are only performed in part, as well as those activities that may be performed more than once (loop). The above graphic illustrates a GERT diagram with a simple loop.

For example, on a high-rise development project, the electrical outlets for each floor may be installed as each floor is completed instead of waiting for the completion of the entire building. Since this activity will be performed more than once, using GERT will enable you to calculate the entire duration of this activity.

Regardless of the type of mathematical analysis you apply to your projects, the ultimate objective is to produce a schedule with realistic start and finish dates.