Lee Merkhofer Consulting Priority Systems

Technical Terms Used in Project Portfolio Management (Continued)





























hedonic price method

A method for inferring the value of something not traded directly in the market place based on market prices. The premise is that the prices of goods traded in the market, such as houses, depend on internal factors (e.g., house size, age, appearance) and external factors (distance to schools, level of local air and water pollution). Price data for the marketed good is analyzed (typically, via regression analysis) to determine the contribution of each factor to price, thereby inferring a monetary value for changes in that factor. The approach is often used to estimate the monetary value of environmental outcomes for cost benefit analysis.

Helmsman complexity scale

A scale, developed by the Helmsman Institute of Australia, for measuring the relative complexity of projects. The scale ranges from 1 to 10 and is logarithmic, similar to the Richter scale for measuring earthquake magnitude. Definitions are provided for various levels of the scale. For example, the scale defines a moderate score between 4 and 5 as indicative of the complexity of projects typically performed in the business units of large organizations, such as product maintenance and competitive enhancements to ongoing business operations. A high score between 8 to 9 is defined as the level of complexity associated with rare and highly complex projects undertaken by countries that produce significant impacts on the national economy, for example, conducting the Olympics.

The scale is designed to be applied to assess project complexity in five areas: (1) context complexity (complexity of the project's leadership and the political environment), (2) people complexity (how large and deep the sociological change will be for recipients of the project), (3) ambiguity (in the approach and design of the project), (4) technical challenge (of core systems and integration requirements), and (5) project management challenge (such as contract complexity, risk sharing, schedule and project structure, supplier complexity and external project interdependencies). Since project complexity has been shown to relate to project risk, the scale has been used as a proxy for assessing the level of risk associated with complex projects. The approach may also be used to provide guidance on where to focus efforts for risk mitigation.


Within the field of psychology, a simple mental rule proposed to explain how people make decisions, come to judgments, or solve problems, particularly when faced with more complex problems or incomplete information. Although efficient, such rules may lead to systematic errors or biases. Presumably, heuristics are the result of evolutionary processes or learned behavior.

In computer science, a heuristic is a technique for solving a complex problem that is faster or otherwise more practical than an approach that results is a solution that is provably optimal.

hierarchical model

A model with a top-down, tee-like structure, such that each subsystem is linked to at most one "parent" subsystem. A hierarchical model is distinct from a network model, wherein each subsystem may have links to multiple parents.


To store (a website or other software) on a server or other computer so that it can be accessed over the Internet or other network.

human resource management

See resource management.

hurdle rate

A specified rate of return for a project or other investment intended to represent the minimum return that the organization will accept. The hurdle rate is also often referred to as the required rate of return.

Typically, the hurdle rate is the risk adjusted discount rate to be applied when computing the net present value (NPV) of the cash flows anticipated from a project. If the NPV of the cash flows using the hurdle rate is negative, the project is rejected. Alternatively, the hurdle rate may refer to the minimum acceptable internal rate of return (IRR) for projects—If a project's IRR is less than the hurdle rate, the project is rejected.

According to investment theory, the hurdle rate should be set equal to the rate of return that the organization could obtain by investing in alternative investment opportunities having similar risks. If the project generates a return greater than what the organization could earn elsewhere (i.e., greater than the opportunity cost of the required investment), the project will add value. In practice, hurdle rates for projects are often specified by adding a risk premium to the risk free interest rate or by adding or subtracting an incremental amount from organization's marginal cost of capital, so that a higher rate is specified for project considered more risky.

Hurdle rates are generally a poor way to account for risks when prioritizing projects. As explained in one of the papers, hurdle rates tend to produce a bias toward short-term, quick payoff projects relative to projects of similar risks whose benefits accrue over longer periods of time. Also, while hurdle rates can be used to decrease the value of projects whose benefits are more uncertain, they do not achieve the converse effect of increasing the value of projects that, if not conducted or if delayed, would tend to increase risk.


importance weight

A weight (scaling constant) assigned for multi-criteria analysis based on the decision-maker's perception of how important a criterion is relative to other criteria. For example, if there are two criteria, 60% of the weight might be assigned to the first and 40% to the second, based on a judgment that the first criterion is one and one-half times as important as the second. Importance weights should not be used as they result in flawed analysis and indefensible results. The proper type of weights for multi-criteria analysis are swing weights. Despite the problem with importance weights, it is not uncommon to find them used for project prioritization, though the documentation for such systems typically refer to the flawed scaling factors as "weights" rather than "importance weights."

The problem with importance weights is that they cannot be meaningfully specified. To illustrate, suppose the context is transportation projects and two criteria are relevant, costs and safety. Suppose costs are measured in dollars, and the metric for safety is number of accidents avoided. If you were to be asked, "Which is more important, accidents or costs?", you might answer "accidents." Does that mean that you think avoiding one accident is more important that $1,000? Maybe so. Does it mean that you think avoiding one accident is more important than $1 billion? Maybe not. The point is you must specify and consider the amounts of the different metrics (their "swings," in order to logically judge and compare importance. Weights assigned based on judged relative importance are meaningless so any results produced through their use are not defensible.

independent projects

Projects that are independent of one another in the sense that the choice to conduct or not to conduct any project does not affect either the costs or benefits of conducting any other project. According to the ranking theorem, if independent projects are ranked based on the ratio of value to cost and then selected in rank order until the budget is exhausted, the result will be the either the project set that would generate the greatest value or a project set that comes very close to generating the greatest value. The only time that ranking may fail to identify the portfolio having the most value is if ranking fails to spend all available funds. Then, if there are less costly projects with nearly the same ratio values as the last projects funded, then substituting these may produce higher aggregate benefit. However, in practical settings, sorting on benefit-cost ratios is a reasonable heuristic solution with only a small deviation from the aggregate value achievable through constrained optimization. Constrainedoptimzation is a solution approach that may apply if projects cannot be made independent.

A form of project dependency that arises in many settings is mutual exclusivity of project choices. For instance, when considering alternative versions of the same project, choice is restricted to choosing at most one version of the project. Another common form of project dependency occurs when projects are contingent, meaning that one project can be chosen only when a second project is also selected. An example of project contingency is a computer software purchase that is only feasible if necessary computer hardware components are acquired simultaneously. Oftentimes it is convenient to treat contingent projects as a single project with combined costs and value. However, unless there is mutual contingency, this requires introducing mutual exclusivity, to allow for scenarios where one wishes to acquire one project but not the other. For instance, when considering constructing a new office building, one might consider a new parking garage as contingent on the construction of the offices, if the garage would have no useful purpose without the new offices. Alternatively, one could consider “office building” versus “office building plus garage” as mutually exclusive projects.

indifference curve

Also called risk-reward tradeoff curves, a curve identifying portfolios of investment assets with different combinations of risk and return for which a decision maker is indifferent. Indifference curves are plotted on a two-dimensional graph where the horizontal axis indicates risk, typically measured by the variance of the distribution over portfolio return, and the vertical axis indicates reward, measured by expected return. Any portfolio combination of assets will have a risk, represented by its variance, and an expected return. Typically, decision makers are assumed to be risk averse, which means that, to accept a portfolio with more risk, the decision maker would require greater expected return. If you were to plot all the possible combinations of portfolio risks and returns for which the decision maker is indifferent is an indifference curve.

indifference curves

Indifference curves

Since the decision maker is indifferent among the portfolios on the indifference curve, different indifference curves have different utilities. The higher the curve and the furthest to the left, the higher the utility.

influence diagram

An influence diagram is a type of decision model that has a graphical representation composed of nodes denoting model variables connected by arrows. A rectangular node represents a decision variable, a choice that a decision maker can make among various alternatives. An elliptical node represents an uncertain variable, something relevant that is not directly under the decision-maker's control. Sometimes another shape (e.g., a rectangle with rounded corners, as shown below) is used to represent a performance measure computed from other model variables indicating the degree to which a decision objective is achieved.

Influence diagrams can be constructed in an informal way, such that the arrows connecting nodes represent a generalized concept of influence, or in a mathematically rigorous way, where an arrow from an ellipse (an uncertainty) or a rectangle (a decision) pointing to an ellipse (an uncertainty) means that the probabilities describing the possible outcomes for the latter uncertainty depend on the choice made or the outcome of the former variable. An arrow pointing from an ellipse or a rectangle to a rectangle means that the latter decision can be made after the outcome to the uncertainty is known or the prior choice is made. Influence diagrams used in this rigorous fashion may be referred to as Bayesian networks. Software tools for drawing influence diagrams often provide algorithms for automating the conversion of an influence diagram to a decision tree, and then solving the tree to identify decision strategies that maximize expected utility and show probability distributions over decision value.

Sample influence diagram

A sample influence diagram (new drug project decision model)

The basic concepts underlying influence diagrams were developed at SRI International in 1973, by Allen Miller, to analyze US intelligence gathering strategies for the Persian Gulf. The diagrams allow complicated decision situations involving many variables to be represented by a compact graph. Because they are intuitive and can be constructed using a top-down model building approach (What variable do you want to know? What variables would you need to know in order to estimate what you want to know?) influence diagrams support an efficient model building process that can be conducted as a facilitated, team exercise. Also, software tools are available that allow influence diagrams to be linked to other models (e.g., to a spreadsheet model for computing business outcomes) and analyzed to calculate optimal decision strategies, risk, and the value of information. Along with decision trees, influence diagrams are the most commonly used model forms for decision analysis.

information technology (IT)

Technology for managing information, especially computer hardware and software systems for acquiring, storing, organizing, analyzing, and communicating information. An IT project is a projectt related to information technology, such as a project to acquire, create, maintain, repair, or replace IT assets.

integer programming

Procedures for minimizing or maximizing an objective function when it is required that one or more of the more of the decision variables be integers (whole numbers such as -1, 0, 1, 2, etc.). If at the optimal solution some decision variables must be integers and some need not be, the solution procedure is often referred to as mixed integer programming. The use of integer variables greatly expands the scope of useful optimization problems that can be solved, since many real world problems require a choice among a finite number of alternatives (e.g., you can choose to do or not do option A, but you can't choose to do 1/6 of option A). Unfortunately, finding the solution to an integer programming problem is in general difficult. The most widely used algorithms for solving integer programming problems are branch and bound, the cutting plan method, and Bender's algorithm.


As in interdependent projects, a situation where two or more projects are related to each other in such a way that the costs and/or benefits of doing one project depend on whether or not the other project is conducted.

Project interdependencies arise in a number of ways, for example:

  • The same, scarce resource (e.g., an individual with unique skills) is needed by several projects. If all of the projects requiring the resource are initiated, resource conflicts can occur, increasing cost and schedule.
  • A project cannot be started until another project is completed. For example a project provides some knowledge or capability necessary to conduct the other project.
  • In the case of new product projects, market dependencies occur if a new product enters a market served by an already existing product. The success of the existing project may be harmed by the new product.

Interdependencies among projects complicates project selection, a key task of project portfolio management. Unless projects are independent of one another, the value-maximizing project portfolio cannot be found by the simple technique of ranking projects by the ratio of project value to project cost. Portfolio optimization methods are available for identifying the value-maximizing project portfolio, but the methods require the user to mathematically describe the dependencies, which is often difficult. Thus, the standard advice is to group interdependent projects into larger projects (or programs) in such a way that the combined projects are independent of each other.

internal rate of return (IRR)

The discount rate that equates the present value of the income stream generated by a project to the cost of that project. In other words, the IRR is the value that satisfies the equation:

Formula for computing IRR

Equivalently, the IRR is the discount rate that causes the project to have a zero net present value (NPV).

The IRR is sometimes misunderstood to be the annual profitability of a project investment. However, for this to be true, the cash inflows derived from the project would have to be reinvested in opportunities that produced a return equal to the project's IRR, which is rarely the case.

Like NPV, the IRR is a commonly used criterion for project-by-project selection decisions—all projects that have IRR's greater than the cost of capital are recommended for funding.

When used as a ranking metric, IRR has an advantage over NPV; it does not depend on the size or scale of the project (therefore, its use is more consistent with the concept of ranking based on "bang-for-the buck"). However, at best, the IRR is only a heuristic or approximate logic for prioritizing projects. It creates predictable and significant biases in project rankings and cannot be used to identify project portfolios that create maximum value.

IRR analysis is popular because it compares projects based on the familiar concept of rate of return (a metric analogous to interest rates charged on capital markets). For this reason, it is for many one of the easiest project evaluation methods to understand. Given two investment alternatives of comparable costs, the investment with the higher IRR should be selected. When used as a selection rule for project-by-project decision making, IRR and NPV recommend the same projects (provided that a unique IRR exists, see below). The IRR has a perceived advantage over NPV and other methods that quantify project value in dollars in that it downplays reliance on what might appear to be overly-precise dollar values.

For several reasons, the IRR cannot be used to reliably prioritize projects. First, like other purely financial metrics, the IRR ignores the non-financial components of project value. Furthermore, IRR cannot be used to correctly prioritize based on financial return alone. Ranking projects based on IRR undervalues cash flows that occur late in a project's life (assuming that the IRR is greater than the cost of capital). It therefore creates a bias for projects with early positive returns relative to projects whose returns tend to occur later. The significance of this bias is greater the longer the duration of project cash flows and the more severely constrained the capital budget (if the budget is highly constrained then the IRR's of the projects being compared will tend to be significantly higher than the cost of capital, meaning that future cash flows will be very heavily discounted).

There are several additional disadvantages with IRR. There is no specific formula that can be used to calculate the IRR; it must be found by iteration and interpolation. Thus, computing the IRR takes more computation than does the NPV (most spreadsheets do, however, provide an IRR function). The IRR of the portfolio of projects cannot be calculated from the IRR's of the individual projects, so there is no easy way to quantify the performance of the portfolio based on the analysis of the individual projects that make up the portfolio. IRR analysis cannot be extended to account for consideration of project risks or project interdependencies. Finally, there are situations of multiple solutions (no unique IRR) when project cash flow changes direction more than once.


A solution process that involves approximating the value of a function at points between which it has been evaluated.

investment review board (IRB)

Term sometimes used to designate a decision-making group composed of senior managers responsible for evaluating and prioritizing projects or other investments. Organizations conducting information technology (IT) projects often establish IRB's. Initiatives and supporting data are presented to the board for review and discussion. Board members reach conclusions based on comparisons and trade-offs among the competing projects, relying substantially on their perceptions and judgments.


A solution process that requires repeating the execution of a set of instructions, typically many times, with the goal of gradually approaching a more accurate answer.


Joint probability distribution

A probability distribution that quantifies the simultaneous uncertain behavior of two or more random variables. Specifically, a joint probability distribution expresses the likelihood of obtaining specified outcomes for some number of random variables. If there are two random variables, the joint distribution is called a bivariate distribution. If there are more than two variables it is called a multivariate distribution. A probability distribution over a single random variable is called a univariate distribution.

Like single variable probability distributions, the variables in a joint distribution can be discrete or continuous. If there are two discrete random events A and B, the joint probability for A and B is the likelihood that both events occur. The joint distribution for discrete random variables may be called a joint probability mass function If there are two continuous random variables X and Y, the joint probability distribution gives the probability that X and Y each fall into a specified range of values. In this case the joint probability distribution may be called a joint density function. Like the case of a single-variable probability distribution, a joint probability distribution can be specified as a joint cumulative distribution, which gives the probability that the value of each random variable is less than or equal to any specified value.

Joint probability distributions are useful for quantifying the dependencies among uncertainties. Two events A and B are independent if the probability of both A and B occurring equals the probability that A occurs times the probability that B occurs. Likewise, if X and Y are two continuous random variables, and the distribution of X is not influenced by the value taken by Y, and vice versa, then the two random variables are independent.

When dealing with multiple random variables there are additional ways of expressing uncertainty that are useful for exploring interdependencies. Once we know the joint probability distribution for random variables, we can calculate their individual distributions. The conditional probability assumes that one event has taken place or will take place, and then asks for the probability of the other (e.g., the likelihood of A occurring, given that B has already occurred). Conditional probability distributions arise from joint probability distributions where by we need to know that probability of one event given that the other event has happened and the random variables behind these events are joint. The marginal probability is the likelihood of an event occurring (e.g., event A), irrespective of whether or not B occurs. It may be thought of as an unconditional probability. The marginal distribution of one of the variables is the probability distribution of that variable considered by itself. Note that if the events are independent, the conditional probability that A occurs given that B has occur will exactly equal the marginal probability of A occurring, since whether or not B occurs has no bearing on event A.

To provide an example, the bivariate normal distribution is an often used joint probability distribution for two random variables, X and Y, each of which is normally distributed. The distribution is specified by 5 parameters, the means of the distribution xy) the standard deviations of the distributions xy), and the correlation coefficient ρ between X and Y. In the example, the conditional density function for Y is more narrow than the marginal density function because the variables are positively correlated. Thus, if the value of the random variable X is known, that reduces the uncertainty over Y.

Bivariate normal distribution

Joint, marginal, and conditional distributions for a bivariate normal probability distribution