Lee Merkhofer Consulting Priority Systems
Implementing project portfolio management

Efficient Frontiers versus Ranking Curves

As indicated in the previous section, generating the efficient frontier requires a software tool with an optimization engine; that is, the ability to solve mathematical optimization problems with constraints. Many project portfolio management tools lack optimization engines and therefore lack the ability to generate efficient frontiers. As an alternative, such tools often create a graph that looks similar to an efficient frontier—they rank projects based on the ratio of project value (or some measure related to project value) to project cost and then plot cumulative value versus cumulative cost while adding projects to the portfolio in rank order. Although many authors erroneously refer to the result as the efficient frontier, it is more accurately referred to as a ranking (or productivity ranking) curve.

The reason that the efficient frontier and a ranking curve are often confused is due to the fact that there is an important special case for which the two curves will be very nearly the same. In particular, if projects are independent and risks are either independent or do not matter, the costs and value of the project portfolio are basically just sums of the costs and values of the individual projects that make up the portfolio. In this case, the value-maximizing portfolios can be obtained by ranking projects based on the ratio of project value to project cost, and the efficient frontier can be plotted by adding projects to the portfolio in the order of benefit-to-cost ratios. Figure 41 illustrates.

A project ranking curve

Figure 41:   A project ranking curve.



Although ranking produces portfolios on the efficient frontier for the special case where the choice is among independent projects, in general the curve produced by ranking projects will not be the efficient frontier. As explained below, there are several reasons for this difference.

The Ranking Curve Misses Opportunities to Use Unspent Budget

At best, a ranking curve will only match the efficient frontier at precisely the cumulative budget levels that result when projects are added to the portfolio in rank order. Ranking fails to identify the portfolios on the efficient frontier that lie between these points (e.g., the portfolio colored red in Figure 42).

Optimal portfolio not on ranking curve

Figure 42:   The efficient frontier identifies higher-value portfolios not on the ranking curve.



The yellow points in Figure 42 represent portfolios constructed by ranking. If the budget is A, the remaining funds are insufficient to include Project e, so Project d is the last project added to the portfolio. An optimization engine is needed to identify a better project combination (e.g., the portfolio designated by the red point) that comes closer to using the total budget. Such portfolios create more value, typically by replacing one or more higher ranked projects by a combination of lower ranked projects so as to use a greater fraction of the available budget. The error inherent in using the ranking curve rather than the efficient frontier tends to be more significant the more available projects differ in cost.

The Ranking Curve Misses Opportunities to Adjust Project Funding Based on Available Budget

As shown previously, providing multiple versions of proposed projects (i.e., different levels of project effectiveness based on different project scopes, approaches, etc.) can significantly shift the efficient frontier. Two versions of the same project are not independent project options. For example, if you choose a low-cost version of a project, that decision would obviously reduce the attractiveness of simultaneously funding a higher-cost version of the same project. This violates the basic requirement for ranking, meaning that a simple ranking approach cannot be used to approximate the efficient frontier when there are multiple project options available. Optimization is needed to select project versions that together best utilize the available budget.

Because adjusting project funding is often a better option than the all-or-nothing choice implied by project ranking, the efficient frontier generally lies above the ranking curve if there are multiple versions available for projects. Figure 39 provides an illustrative example. In this case, 3 versions are assumed to be available for each project, a low cost, mid cost, and high cost version. Project benefits are assumed to increase with project costs, and the project costs and the incremental costs of moving to more expensive project versions are assumed to be the same for all projects. These assumptions are sufficient to ensure that the efficient frontier will have the sort of smooth curve that is shown in the figure. Notice that higher budgets result in more expensive project versions being selected.


The efficient frontier varies project funding

Figure 43:   The efficient frontier varies project funding to increase portfolio value (illustrative data).



The Ranking Curve Fails to Account for Multiple Resource Constraints

A major limitation of the ranking curve compared to the efficient frontier is that the ranking curve cannot account for constraints other than the funding constraint. Only a single cost constraint can be addressed through the ranking approach. If, for example, some projects require funding over multiple budget cycles the constraints that may exist on funding for the various years cannot be addressed. Furthermore, in such cases, it is not entirely clear, when ranking projects based on the ratio of benefits to costs, what cost should be used in the denominator and what benefits should be used in the numerator. For example, should projects be ranked based on the ratio of total benefit (the benefit generated if the project continues to be funded until completion) to total cost (including the remaining, out-year costs required to secure those benefits)? Or, should projects be ranked based the ratio of total benefits less remaining costs to budget year costs? Or, should projects be ranked based on budget year benefits (the portion of benefits that are attributed to budget-year spending) to budget-year costs? Each approach will yield a different ranking.

With the efficient frontier, additional constraints can be established for the optimization. Thus, for example, the optimization engine can be used to generate efficient frontiers that show the value maximizing project portfolios under alternative budget-year costs subject to various specified constraints on out-year funding as well as subject to constraints on people and other resources needed for projects. Establishing additional constraints to be achieved by the resource allocation will change project recommendations (to ensure that the constraints are met), which will tend to lower the efficient frontier. A simple ranking curve cannot under these circumstances identify the optimal project portfolios.

The Ranking Curve Produces the Wrong Results if there are Interdependencies Among Projects

A main disadvatage of the ranking curve, which applies to any prioritization approach is that it provides the wrong ranking if there are project interdependencies. For example, looking at Figure 43, if project Project K (above the budget line) is dependent on Project E (below the budget line), both projects cannot be conducted without impacting any of the other projects that are above the budget line. This type of project dependency (one project requires doing another project)can be handled quite easily with binary integer logic, as described in the Mathematics paper.