Real efficient frontiers tend to be more complex than the simple examples shown in the previous section. To illustrate, the business units within an organization proposed a total of 30 projects. Budget-year costs ranged from $40,000 to over $8 million. Some of the larger projects were multiyear in duration, and about a third of the projects were proposed in multiple versions (e.g., low cost, base, and enhanced versions). If all projects were funded (with multi-version projects funded at their highest funding levels), a total budget of roughly $33 million would be required. The organization's target budget was $17 million. Obviously, prioritization was necessary.
Figure 44 shows the efficient frontier, and Figure 45 shows how the projects included in the portfolios on the frontier depend on the total budget. Although the efficient frontier bends over in the typical fashion, there are the bumps in the curve. The labels in Figure 45 are unreadable, but what is important is the pattern.
Figure 44: A real efficient frontier.
Figure 45: Optimal project funding decisions for budgets between $1 million and $35 million in $1 million increments.
As in the previous simplified example, the rows in the table of Figure 45 correspond to projects and the columns (left to right) represent increasing funding levels. The colors in the cells indicate funding recommendations, with darker cells indicating recommendations to fund more expensive project versions. Although an increase in the budget is generally associated with an increase in funding for some project, sometimes increasing the budget causes the funding recommendation for a project to be reduced. This is typical behavior for real efficient frontiers.
The bumps in the efficient frontier are caused when the optimization engine identifies opportunities for moving projects into and out of the portfolio in ways that significantly increase total value. To take a dramatic example, notice the "jump" in the curve that occurs for a budget just above $5 million. The cause of the jump is a high-cost project with a minimum spending level of $5.05 million (it is the project in the 5th row in the table in Figure 45). At this spending level, the project provides a relatively high benefit-to-cost ratio of 8.78.
Figure 46 shows the detailed portion of the funding table corresponding to budgets near $5 million (the funding increments in this table are $25,000 per column, compared to $1 million in the previous table). If the total budget is less than $5.05 million, then, obviously, the $5.05 million project cannot be accommodated. However, when the budget hits 5.05 million, all of the smaller projects that were funded earlier are eliminated from the portfolio, which frees the entire budget to fund this one high-value project and results in the jump in the curve (an increase in portfolio value of $8.62 million!).
Figure 46: Optimal project funding decisions for budgets between $5 million and $5.01 million in $25,000 increments.
Although large jumps in the efficient frontier often occur at highly constrained budgets, such jumps are not of practical significance unless they occur near the organization's actual budget constraint (which typically happens when there are high-cost projects with high benefit-to-cost ratios that are in danger of not being funded). In such situations, the efficient frontier can identify opportunities for small increases in the total budget that can produce relatively large increases in total value.