a variable whose value is unknown an subject to
variations due to chance. Random variables can be discrete, which
means they can only take on a finite number of possible values, or
continuous, which are variables that can have any values within a
Random variables are typically denoted by a capital
letter (e.g., X). If a probability distribution can
be associated with a random variable, the distribution tells what the
possible values of X are and the probabilities assigned to each.
range sensitivity index (RSI)
An index defined to measure the degree to which subjects, when assigning weights, properly
account for the ranges specified for their assessment. Experiments show that for most subjects and most weight assessment methods, there is
insufficient adjustment based on range. The RSI is equal to 1.0 when the weights are adjusted fully based on range
and equal to 0 when no weight adjustment is made. The farther the RSI is from 1.0, the less sufiient the adjustment.
range sensitivity principle
A mathematical result demonstrating that the weights assessed for an additive value
function must be sensitive to the ranges used for their assessment. The normalized form of the additive value function:
= w1V1(x1) +
w2V2(x2) ... +
will be such that each single-attribute value function, Vi(xi),
will equal zero or one when its performance measure xi is at its worst or best performance level,
respectively. Each wi weight will equal the value assigned by the decision maker to
swinging the xi performance measure from its worst to its best level.
Suppose that the range encompassing the worst and best levels of performance for the i'th performance
measure is changed from R to R'. If the change in range produces new worst and/or best levels of performance,
a correction factor will need to be applied to the previously assessed wi weight. If the value function
is linear, for example, the correction is simpy the ratio R'/R. Doubling
the range will, in the linear case, cause the weight to double. The range sensitivity principle merely states that
weights are sensitive to the ranges used for their assessment. This fact can be used to strategically set ranges to produce weights
consistent with importance weights so as to minimize the impact of importance weight bias.
A graph derived from a ranked list of projects, where the ranking is based on the
ratio of some measure of project benefit to project cost. Specifically, the
curve is a plot of cumulative cost (as projects are added to the project
portfolio in rank order) vs. cumulative benefit (obtained by cumulating the
benefit measure). Most project portfolio
management tools provide a ranking curves as outputs. As explained in
the paper on efficient frontiers vs. ranking
curves, ranking curves appear similar to, but are different than, the
efficient frontier of
A result of the principle of economic efficiency. Suppose
there are multiple, independent projects that compete for funding from a fixed
budget. It those projects are ranked based on the ratio of project value to project cost and then selected from the
top down until the budget is exhausted, then the value of the resulting
project portfolio will either equal or come
very close to that of the value maximizing portfolio. The first project on this list yields the
biggest bang-for-the-buck and should be funded fi rst, followed by the second
on the list, etc., up to the point when the budget has been exhausted (or the benefit-to-cost ratio drops below 1,
whichever comes first).
Project costs and benefits
are the incremental costs and benefits that result from the decision to conduct the
project compared to what would occur if the project is not conducted. Project costs
must include all costs required to secure the project benefits. In comparing the
various projects, those projects with the highest B/C ratio would be ranked as the most efficient
The only potential for error (assuming the above assumptions includng that
projects are independent and that the capital budget is the active constraint
for selecting projects) occurs if the portfolio identified through ranking
fails to consume the entire budget. In that case, it is possible that there is
another portfolio that spends more of the available budget that would produce a
higher total value. In practice, especially if the budget is large enough
to fund many projects, the difference in the value obtained from strict
ranking and that of a truly optimal portfolio is typically small.
There are several real-world complications for applying
the ranking theorem. For one, project costs and benefits often occur over
time. To account for timing, discounted, present-value equivalents are typically used
to express project values and project costs. Another complication is projects conducted over
multiple budget periods (e.g., multi-year projects), Such projects often require funding
not just from the current budget period, but from one or more future budgetting
periods as well. In this case, multi-year projects are typically priotized along
with other projects in each budget period based on the ratio of total discounted
project value to total discounted remaining costs. Risk is another complication.
To account for risk, project value is expressed as a risk adjusted value.
Benefi t-to-cost ranking demands that there be only one dimension to cost. It is unable to accommodate multiple constraints.
The ranking theorem is useful because it provides an simple and
intuitive way to prioritize projects and identify high-value project portolios without
the need to use portfolio optimization tools designed to solve the knapsack
problem. The ranking theorem is often the basis for the project prioritization
capabilities provided by project portfolio management tools, though a few
include portfolio optimization capability.
Full-blown optimization, unlike simple ranking, recommends portfolios that yield the biggest bang-not just "for the buck"
(i.e., along a single cost dimension, but-for the multiple resource
constraints faced by an organization. MCDM often includes sophisticated optimization methods for choosing the values of decision
Optimization methods, such as
linear programming, integer programming, and dynamic programming, provide project
prioritization consistent with benefit cost and incremental benefit cost analyses, also taking
account of the impact of budget constraints in creating an optimized project set.
Arises when adding or deleting an alternative (e.g., a
candidate project) to the list of
options under consideration causes the ranking of other (independent)
alternatives to reverse.
Rank reversal example
This result occurs with some multi-criteria analysis scoring models, most notably for the
analytic hierarchy process (AHP), where
the inclusion or exclusion of even a poorly ranked project (an irrelevant
alternative) can cause project scores (which are derived from pairwise
comparisons across all alternatives) to change in such a way that project
rankings change. Although there is debate over the matter, rank reversals
based on irrelevant alternatives are generally regarded to be inconsistent
with rational decision making. (Why should my preference for one option
over another change if an option I don't want is removed from
consideration?). Project portfolio
management tools based on AHP may include a mode of operation that
prevents rank reversals from occurring, however this "fix" does not address
the fundamental logical questions involved.
real options analysis
A method for valuing projects, assets, and businesses using
concepts originally developed to value financial options. Real options
analysis is most useful for large capital budget decisions in situations
involving significant uncertainties (especially market uncertainties) and
where management has flexibility to adapt decisions to unexpected
developments. For example, real options analysis is often used for mergers
and acquisitions, facility expansion decisions, oil exploration, contract
valuation, and prioritizing R&D
Real options analysis is based on the recognition that
there is an important similarity between financial investments and business
projects. In finance, a stock option (specifically, a "call-option
contract") allows (but does not force) the owner to buy a fixed number of
shares of the stock at a specified date for a specified price. The owner
will want to exercise the option and buy the stock if its price goes up,
but not if the stock price goes down. Similarly, projects involve options.
For example, a project to construct a new factory provides options to
postpone construction if the economy slows. Building a new factory also
includes options to temporarily shut down or abandon the plant to cut
losses, as well as to expand its size to meet an unexpected demand for more
production. The options inherent in physical assets are termed "real" to
distinguish them from classic financial options.
In the 1997, Robert Merton, Myron Scholes, and Fischer
Black won a Nobel price for deriving a model for computing the price of
call- and other types of options. This work provided the foundation for
developing an analogous method for valuing the options (flexibility)
inherent in projects. As with financial options, the value of the options
implicit in a project increases the value of that project. For example, a
factory with operating options is more valuable than an identical factory
that does not include options, and the extra value is the value of the
options that are available.
Traditional financial valuation methods, including
net present value (NPV), typically
under-value projects because they fail to adequately account for the value
of management flexibility to exercise the project's inherent options.
Expected net present value (ENPV) can
include the value of flexibility (if "downstream decisions" are represented
in the decision tree), and most
authors include ENPV as subset of the methods available for real options
analysis. Similarly, multi-attribute utility
analysis (MUA) can account for the value of management flexibility by
evaluation criteria related to the option value of the project.
However, real options analysis also includes solution methods that derive
option values from the market prices of underlying assets. Thus, for
example, a real options analysis of an oil drilling project could derive
the project's value in part based on market prices for barrels of oil,
similar to the way the value of a call option on a stock can be derived
from the behavior of the market price of that stock.
A major benefit of real options analysis is the insights
that it provides for managing projects so as to leverage flexibility and
limit downside risks. Although in most cases it may not be practical or
even possible to apply the most sophisticated real option solution
techniques to value many projects, real options theory has shown how
simpler methods, including ENPV and MUA can be used to more accurately
account for option value by recognizing multiple decision pathways and
better accounting for the cost of risk.
A statistical technique applied to data to determine the
degree of correlation among one or
more variables; that is, to quantify the extent to which the variables tend
to move together. Typically, regression analysis seeks an equation, called
a regression equation or regression function, that relates a dependent
variable to one or more independent variables. In this way, regression
analysis may be used to suggest potential cause-effect relationships,
although it cannot by itself be used to prove such relationships.
A collection of data elements organized into separate
tables (sometimes referred to as "relations") of predefined categories in a
way that makes it easier to access and combine data elements. The structure
allows data from different tables to be accessed and reassembled in
different ways without having to reorganize the tables.
The concept of a relational database was developed in
1970 by Edgar Codd, of IBM, whose objective was to accommodate in an
efficient way a user's ad hoc request for selected data. The standard
application program used to interface to a relational database is the
structured query language (SQL). Most
business database management systems use relational databases and project portfolio management tools are often
advertised as storing data in a relational database.
The coordination and bundling of projects and project tasks for the purpose of
optimally synchronizing the release of new products and services. Release
management can be important when business value depends on interdependent
projects, or when launch date serves as a rally point for the completion of
the projects. The term originated in the field of software engineering,
where it involves managing the IT project lifecycle, including development,
testing, deployment and support of software releases.
For projects focused on new products, release management
and project portfolio management are
closely related, since shifting projects dates for the purpose of resource balancing can have a
significant impact on the value of the portfolio.
The risks that remain
after management has taken action to mitigate the risks identified during
project planning. Residual
risks are those that must be considered when deciding whether to conduct
One of the basic and essential means available to an
organization for conducting projects and other operations, such as money,
plant, labor, assets, and raw materials.
A component of resource management focused on
balancing the supply and demand for the resources needed for conducting projects. Key
inputs for efficient resource balancing are forecasts of the demands for
various resources and the supply of those resources. The general goal is to
achieve near 100% resource utilization without over-allocating resources
across projects. Also, called resource leveling, the process mainly
involves leveling or smoothing the demand for resources by adjusting the
start and end dates for projects or
the tasks that make up those projects so as to reduce peaks and valleys in
Various software tools are available to support resource
balancing. However, as explained in the section of the paper on tools for resource balancing,
such tools rarely if ever attempt to optimize the selection of projects
based on the people and other resources that are available. Instead, the
typical approach is to select projects subject only to a constraint on
total project costs (including labor costs), and then to phase the selected
projects by shifting start and end dates for tasks. Since it is typically
undesirable to delay project completion dates, resource balancing mainly
looks for ways to shift work that is not on the critical path, and network analysis
techniques, including PERT charts, are
often used to aid the process.
The field concerned with effectively managing an
organization's resources, including
people, money, materials, equipment, and services. A key focus is resource
allocation, the efficient deployment and use of the organization's
resources. Human resource management refers to the special case of
managing people resources, and the topic is typically defined to include
the management of payroll and benefits, education and professional
development, and other human resource functions. Resource balancing is a key technique
used for resource management.
return on investment (ROI)
The ratio of project income to project cost. Typically,
project income is specified as the average annual net income from a
project, and project cost is the total
For example, a project that costs $100,000 and is
expected to return $20,000 annually would have an ROI of 20%.
As indicated by its definition, ROI is a measure of the
financial benefits obtained from a project over a specified time period in
return for the required investment, with the result expressed as a
percentage. ROI is widely used (especially in the private sector) both to
justify a proposed project and to evaluate, after the completion of the
project, the extent to which the desired return was achieved.
ROI is similar to internal
rate of return (IRR) in that it provides a measure of
"bang-for-the-buck." However, it is even simpler in that in that it does
not distinguish, nor is it sensitive to, the time at which project cash
Like IRR, ROI is most often used as a go/no-go screen for
selecting projects. A minimum required ROI is specified, referred to as the
hurdle rate. The hurdle rate is
often based on the company's weighted average
cost of capital (WACC), the average return on a portfolio of all the
firm's securities (equity and debt). Alternatively, the hurdle rate may be
set higher or lower depending on the company's appetite for risk and
shareholders' expectations for company performance. Projects with ROI's
less than the hurdle rate are rejected.
When used to rank projects, ROI has significant
limitations. If project income varies from year to year, ROI will depend
significantly on the period chosen for computing average income. ROI also
has most of the limitations of IRR. It ignores non-financial project
benefits, can't properly account for
project risks and interdependencies, and does not provide a basis for
quantifying the value of alternative project portfolios. Since future cash
flows are not discounted, ROI ignores the preference that should be given
to projects whose cash inflows occur sooner in time. Thus, ROI is
particularly unsuitable for ranking projects that produce incremental
revenues or cost savings that persist over multiple years.
return on net assets (RONA)
A measure of the financial performance for a
Net income is after tax profit and working capital is
current assets minus current liabilities. Asset intensive businesses often
use RONA to indicate how effectively the firm's asset base is being used to
A characteristic of a situation or action wherein a
number of outcomes are possible, the particular one that will occur is
uncertain, and at least one of the possibilities is undesirable.
risk adjusted discount
A discount rate
intended for application to a risky (uncertain) future cash flow. A risk
adjusted discount rate is higher than a risk free discount rate. If an investment
involves risk, then it will have to provide a higher rate of return to
compensate for that risk.
The risk-free discount rate is often selected to be the
return available from market investments that involve little or no risks,
such as the rate of return available from short term US treasury
securities. The risk adjusted discount rate can be regarded as the
risk-free rate plus a risk premium
appropriate given the level of risk.
Risk adjusted discount rates represent one of two popular
methods for accounting for risk when valuing projects that produce
uncertain future returns. With risk-adjusted discount rates, the expected value generated by the project is
estimated in each future time period. The time stream of expected values is
then discounted at the risk adjusted rate to obtain the project net present value (NPV). A competing approach is
to compute the certain equivalent of each
uncertain value, and then to discount the certain equivalents at the risk
free discount rate. Both approaches involve questionable assumptions
related to the way they attempt to disentangle risk and time preference.
However, estimating a risk adjusted discount rate is particularly
problematic in that, for example, it can be shown that it is not
appropriate to use the same rate for cash flows that occur in different
risk adjusted value
A measure of value that accounts for risk or uncertainty.
Due to risk aversion, people and organizations typically assign a lower
value to assets or investment opportunities that have more risk than to
otherwise similar investments that are less risky. The most common way of
adjusting for risk is to compute a reduced value for the investment that is
said to be "risk adjusted." Various methods are available for computing a
risk adjusted value, including real
options analysis, certain equivalents,
discount rates, or applying subjective "haircuts" to forecasted
A systematic process of evaluating the likelihood and magnitude of the risks involved in a
projected activity or undertaking.
The preference that humans commonly have that causes them
to prefer certain or sure consequences over comparable uncertain ones. A
decision maker is said to display risk aversion if, when faced with the
choice between the expected value of the
uncertain consequences to a risky project and the uncertain consequences
themselves, he or she would choose the expected, certain value. The degree
of risk aversion can be quantified by measuring decision maker risk tolerance.
risk free rate
The rate of return available from riskless investments,
usually taken to be short-term US government securities.
Risk management refers to the practice of identifying
risks in advance of commitment, analyzing
them and taking precautionary steps to reduce/curb the risks.
A graphic display for visualizing and comparing risks. Initially adopted by the US military, the
tool is currently used by many organizations as a simple means for
analyzing risks. The idea behind the risk matrix is to distinguish various
levels for the two main dimensions of risk, (1) likelihood of occurrence
and (2) magnitude of impact. For example:
A basic risk matrix
Each cell in the risk matrix represents a possible
combination of likelihood and impact. Since the seriousness of a risk is
roughly related to the product of likelihood and impact, colors (e.g.,
green, yellow, and red) are often used to emphasize this result. The number
of rows and columns and the particular way in which they are defined (e.g.,
quantitatively or qualitatively) can be varied depending on the
To use the risk matrix, a list of relevant risks is
generated. For example, if a company is considering introducing a new
consumer product, a possible risk might be that a customer could be injured
by that product. For each identified risk, the likelihood of the risk event
(e.g., not very likely versus very likely) and the seriousness of the
consequences (e.g., minor cut versus serious permanent disability) are
estimated. The results are then used to place each risk within the
appropriate cell of the risk matrix. Risks can then be prioritized from
top-right down to bottom left.
The main benefit of the risk matrix is that it provides a
visual display that differentiates high-probability/low-impact and
high-impact/low-probability risks. Because multiple risks can be displayed
simultaneously, the approach benefits from the comparative ease that people
have in making pairwise comparisons as opposed to the greater difficulty
associated with drawing absolute judgments. Within a risk management
process, the matrix provides documentation demonstrating that risks have
been identified and deliberately evaluated. Also, the matrix can be used to
show how the likelihood and impact of risks change and therefore move
within the matrix, for example, over time at different stages in a
project's investment life cycle or as a result of candidate risk mitigation strategies.
Another attractive characteristic is that the matrix
works well in a group decision-making environment. For example, the risk
matrix can be drawn on a white board or pages taped together from a flip
chart. Post-It Notes can then be used to place risks within the matrix. The
exercise promotes brainstorming
and a team approach helps avoid the extremes of too pessimistic or too
optimistic views that might be expressed by individuals.
The main limitations of the risk matrix relate to the
simplistic, subjective way by which risk is measured. Poor resolution often
results because rows and columns are often defined qualitatively, so that
the same cells can be assigned to risks of very different magnitude. Also,
due to errors in either the assessment of risks or the cells in which they
are placed, the risk matrix can mistakenly assign higher qualitative
ratings to quantitatively smaller risks. The risk ratings assigned to cells
are typically just a function of the product of likelihood and impact, so
the approach ignores the fact that very high consequence/low probability
risks are generally of greater concern to organizations than the product
would suggest, and the error is greater for organizations with lower
risk tolerance. Effective
allocation of resources to risk-reducing countermeasures cannot be based
solely on the category ratings assigned by risk matrices—the
effectiveness of the risk-reducing measures must be considered as well.
These and other limitations imply that risk matrices should be used with
caution, and only with careful explanations of underlying judgments.
Actions taken to reduce risks based on lowering the
probability and/or impact of a risk to below some acceptable level or
threshold. In the context of project
management, risk mitigation typically involves revising the project's
scope, budget, schedule or objectives.
When used in the context of decision analysis, the difference
between the expected
value of a lottery and its certain equivalent.
The risk premium associated with a gamble can be interpretted as the amount of expected value the decision maker is willing to give up
in order to avoid the risk of the gamble. The
more risk averse the decision maker, the larger the
risk premium will be.
When used in the context of investing, the risk premium has an analogous definition, It is
the incremental return that compensates an investor for
accepting an investment considered to be risky. The risk premium is the
difference between the expected return from the risky investment and the
return available from a risk free
Also called a risk log. a table or spreadsheet
created by ah organization's risk managers that summarizes identified
risks, provides an assessment of their severity and indicates the action or
steps to be taken to manage those risks. Its key function is to provide
management and key stakeholders wit information on the main risks faced by
the organization and what is being done about them.
A measure of an individual's or organization's
willingness to accept risk when making
choices. Risk tolerance may be assessed and quantified as a parameter in a
utility function. See the section of the paper on risk for how this may be
root cause analysis
A method of problem solving focused on identifying the
root causes of problems, including problems for the successful completion
of projects. A factor is considered a
root cause if its removal from the event sequence doesn't merely make the
undesired problem consequence less likely, it prevents it from occurring in
the first place. The root causes of problems may be physical, human error,
or organizational. Root cause analysis is based on the philosophy that
effective management requires more than merely "putting out fires," but
finding a way to prevent them.
Root cause analysis can be conducted in two ways: you
can: (1) look for things that can go wrong and then identify the potential
impacts on the project of each such event or 2) identify all the essential
functions that the project must perform or goals that it must reach to be
considered successful and then identify all the possible modes by which
these functions might not be achieved