Specifications that control who can read and/or alter
computer files or directories. Project
portfolio management (PPM) tools, especially web-based tools, like other sensitive
software intended for multiple users, often utilize access permissions to
ensure that users are only able to view and alter information contained in
the software in ways that are appropriate given their specified roles.
Also called an additive function, a function f(x1, x2,...,xN) with
some number of arguments N, such that for any set of argument values x1, x2,... ,xN for which the function is defined,
f(x1, x2,...,xN) = f1(x1) + f2(x2) + ... + fN(xN)
In other words, an additive equation is an equation that can be expressed as a summation of functions each of which
has just a single argument.
Also called utility additive independence, the condition that ensures a utility function has the form of an additive utility function. If
additive independence applies, the utility function may be expressed
= w1U1(x1) +
w2U2(x2) ... +
Two attributes, 1
and 2, are called additive independent, if the preference between two
lotteries (defined by a joint probability
distribution on the two attributes) depends only on their marginal probability
distributions (the marginal probability distribution on attribute 1 and
the marginal probability distribution on attribute 2).
An example, though contrived, may help clarify the test for utility additive independence. Suppose you are interested in purchasing
a high-performance European sports car. For simplicity, assume you care only about 3 attributes: cost, horsepower, and looks. You've
identified several cars that interest you. Since utility functions are only appropriate if there is uncertainty over outcomes, assume that
the government is considering two new regulations. One is an environmental law that would require you to install on your selected car an
emissions-reducing device that would cut the car's horsepower by 10%. The other is a safety regulation that would require you to attach a
plastic bumper at the rear end of your car that, in your opinion, would make your selected car less attractive.
The lotteries below could be used by you to determine whether the horsepower and looks attributes are additive independent
(the cost of the auto is assumed to be same for each lottery).
Example lotteries for testing for utility additive independence.
If you are indifferent between these two lotteries, your utility function will be additive in horsepower and looks,
If there are more than two attributes in your utility function, as in the above example, then you must repeat the test for
all pairs of measures. If any test indicates that the additive form cannot be assumed, then you'll either need to use a more complex form for
the function, or you'll need to change the definitions of objectives and their performance measures until independence does apply.
Although a highly technical concept, additive
independence is important for constructing value models for projects whose outcomes are uncertain.
Unfortunately, it is common for organizations to use weight-and-add
aggregation equations for
prioritizing projects in
situations where additive independence does not apply. If this error is
made, the prioritization model will not correctly rank projects.
additive utility function
Analogous to an additive value function, but
applies to a utility function rather
than a value function. In other
words, an additive utility function is a utility function that is expressed
as an additive function of single attribute utility
functions. If a utility function is additive, its assessment is much easier.
In this situation, the assessment of the multi-attribute utility function does not
require considering preference tradeoffs among more than two attributes simultaneously, nor is it necessary to consider lotteries
with more than one level of an attribute being varied. In fact, the assessment can
be accomplished by assessing the single attribute utility functions and the weights.
additive value function
Also called additive value model, a value function expressed as a weighted
sum of single-attribute value
= w1V1(x1) +
w2V2(x2) ... +
The additive value function, like other value functions,
assigns a number indicating a decision maker's preference for an
alternative or outcome characterized by attributes, denoted in the equation as
x1,x2...xN. With the
additive function, the value so assigned
is a weighted sum of the decision maker's preferences over the individual
attributes, as specified by the single attribute value functions,
The additive form of a value function is often used in
models for prioritizing or
selecting projects because it is
relatively easy to create and it produces an intuitive model form wherein
different components of value are
weighted and added. As an example, a government transportation agency might
be considering projects addressing a segment of a highway. Suppose there
are only two objectives: to reduce the commute time for travelers and to
reduce the frequency of accidents. With an additive value model, single
attribute value functions would be constructed to indicate the value of
reducing commute time and the value of reducing the frequency of accidents.
A project's total value would then be computed by weighting and adding its
commute time value and its accident reduction value.
The single-attribute value functions,
Vi(xi), are, in effect, scaling functions that translate the
individual attribute measures, expressed in their natural units (e.g.,
annual numbers of accidents), into units of value. As in the above example,
attributes typically indicate levels of achievement relative to objectives.
By convention, value is typically expressed on a scale of 0-to-1 (or
0-to-100), where a value of 0 is assigned to the least desirable level that
the attribute could have (e.g., zero advancement of the objective).
Alternatively, the value zero is sometimes assigned to the least desirable
attribute level achieved by any of the alternatives under consideration.
Likewise, the value of 1 (or 100) is typically assigned to the
best-possible attribute performance (or the best performance achieved by
any of the alternatives). Typically, weights are scaled to sum to 100 (or
1), so that value, as expressed by the additive model, ranges from 0 to 100
(or zero to 1). Regardless, the resulting value number is directly
proportional to preference; for example, an alternative with a computed
value of 100 is twice as desirable as one with a computed value of 50. In
technical terms, it is a cardinal
Value functions, like utility functions, may be encoded from
decision makers by seeking answers to questions regarding preferences for
outcomes. The number of required questions and answers increases greatly
with the number of attributes used. However, if the value function is
additive, it may be constructed in two steps: (1) assessing the single
attribute value functions and (2) assessing swing weights. The weights may be assessed
using the swing weight method.
For the additive value function to apply, independence
assumptions must hold. The most common approach to proving additivity for a
value function is to demonstrate mutual preferential independence
and difference independence. Preferential independence
basically requires that the decision maker's preferences for achieving any
level of performance against any objective does not depend on the performance
achieved against any other objective.
Value functions specified over single attributes are sometimes referred to as
conditional value functions. Conditional value functions express preferences over one
attribute assuming other attributes are set to specific levels. However, with the additive value function, the
particular levels of other attribute are not important to the assessment of single-attribute value functions.
With additivity, these value functions will be the same for any levels of the other attributes. Mutual preferential
independence thus makes it possible to discuss single value functions over each of the attributes.
As used in agile software development, refers to
software development practices and methodologies wherein requirements and
solutions evolve through collaboration among cross-functional teams,
typically involving customers, designers, and developers. The goal is to
promote timely, responsive solutions based on frequent reassessment of
requirements and interim deliverables. The most common agile method, known
as Scrum, utilizes multiple small teams working in an intensive and
independent manner, with daily meetings, execution of tasks in brief,
high-intensity work sessions, and frequent reviews aimed at identifying
ideas for improvement. Similarly, agile, as used in agile project
management, refers to project
management methodologies that emphasize collaboration, quick delivery
time, and ability to respond to changing requirements. Six sigma and PRINCE2 are examples of a methodologies that
incorporate principles of agile project management.
As used on this website, an equation used to compute a
metric (number) for prioritizing (ranking) projects. Most
methods for prioritizing projects are multi-criteria methods, since it is typically
assumed that multiple criteria are relevant to determining project
priorities. Thus, an aggregation equation typically includes multiple variables, each of which represents a
different consideration for choosing projects. An aggregation equation also may include
weights meant to represent some concept of
the relative importance of the various criteria.
The exact formula used for the
aggregation equation differs greatly from method to method, since different
prioritization methods use different logics for ranking projects. Thus,
determining what metric a prioritization method uses and how that metric is
calculated is of central importance to understanding and judging the
quality of a prioritization method.
According to decision theory, independent projects
should be prioritized based on the ratio of project value to project cost. According to multi objective decision analysis (MODA),
the discipline concerned with implementing decision theory for situations where the decision
maker has multiple objectives, project value
may be computed using a function called a utility function (if the prioritization
method includes consideration of uncertainty and risk) or a
(if the prioritization method ignores risk and uncertainty). MODA provides a step-by-step
process for deriving utility and value functions and, thereby, provides a way to determine an
aggregation equation for prioritizing projects based on decision theory. Because the methods for valuing and prioritizing
projects advocated on this website are often based on MODA, by aggregation equation
I typically mean a utility function or value function derived using
the methods of MODA.
aggregated indices randomization method (AIRM)
A multi-criteria analysis
(MCA) method applicable to decisions with uncertainty. AIRM evaluates
"objects" using multiple, single-index criteria interpreted as being
characteristics of the object associated with a single or specific point of
view. The single points of view are synthesized into one, general point of
view via an aggregation
equation. The aggregated index value is determined by the single
indices values and varies depending on weights, which are interpreted as measures of
the relative significance of the corresponding single criteria indices. Only
ordinal information about weights is assumed, so that weights can be considered
random and restricted
to intervals based on a system of equations defined by equalities and inequalities.
distinguishing feature of AIRM is its ability to compute the single
indices, weights, and aggregation equation using non-numeric (ordinal),
non-exact (interval) and incomplete information. AIRM was developed in the
early 20th century by a Russian naval applied mathematician.
A procedure composed of a sequence of instructions or
steps for solving a problem (typically a problem expressed
A course of action actively being considered in the context of a decision making process.
Projects are the alternatives for the organization's
project portfolio. Alternatives are actions available to a
decision maker to achieve objectives.
A systematic approach to building understanding based on
identifying and investigating the component parts of a whole and their
relationships. The word can be traced to ancient Greek terms meaning
"breaking up" and "a loosening". The technique has been applied in the
study of mathematics and logic for thousands of years, though analysis as a
formal concept is a more recent development.
Today, the most powerful methods of analysis involve
applying theories and techniques developed within specific fields of
expertise, such as those from the natural science, social science, and
decision science. Project
prioritization and portfolio
optimization, for instance, rely heavily
on analytic methods from the field of decision analysis.
A person who conducts analysis, short for systems analyst or
decision analyst. See decision maker for
analytic hierarchy process (AHP)
A popular, theory-based, decision-aiding approach,
developed by Thomas Saaty in the early 1970s. Like multi-attribute utility analysis (MUA)
and outranking methods,
AHP is a form of multi-criteria analysis.
The approach involves decomposing a decision problem into a hierarchy of sub-problems.
As illustrated below, the hierarchy contains the decision goal,
the objectives or criteria to be achieved, and the alternatives to be evaluated
using the criteria.
Once the hierarchy is built, the various elements of the hierarchy are evaluated, typically
using paired comparison.
As described below, AHP provides methods for quantifying the
elements of the hierarchy and for evaluating the alternatives. Some project
portfolio management (PPM) tools use AHP for project prioritization. There are many variations of AHP and how it is applied,
making it difficult to provide general statements about AHP's effectiveness for prioritizing projects.
AHP decomposes a decision problem into a hierarchy of subproblems.
As originally defined by Saaty, AHP involves asking
decision makers to express their preferences over pairs of elements
in the hierarchy with respect to the hierarchy element above them. For example, starting at the level of alternatives
in the hierarchy, the subject might be asked, "With regard to improving financial performance,
do you prefer alternative A or alternative B, and by how much?" A nine-point ratio scale
for specifying strength of preference (each score on the scale is defined qualitatively, for instance, 1 = "equal preference"
3 = "slight preference," 5 = "strong preference," etc., see this example). Reportably, Saaty established 9 levels for his scale because his experiments
showed that individuals cannot compare more than seven, plus or minus two, objects at a time,
Understanding the mathematical procedure by which a ranking of
alternatives is obtained requires an understanding of matrix algebra. The key
things to know are that a square, (n × n) matrix can be multiplied by another matrix
of the same size to produce a product (n × n) matrix. Likewise, a (1 × n) vector can
be multiplied by an (n × n) matrix to produce another (1 × n) vector. An
eigenvector of a matrix is a vector that when multiplied by that matrix
simply scales the entries in the vector; in other words, the vector doesn't change direction,
it merely changes size. The eigenvalue associated with the eigenvector is the amount
by which the vector entries are scaled.
Starting with the level in the hierarchy represented by alternatives, the results of the pairwise
comparisons are entered into matrices, one matrix for each criterion. For example, if there are 6 alternatives, the
matrix for comparing alternatives with respect to a criterion will have 36 cells within which the results of comparisons
are placed. The comparison s are expressed using a nine-level ratio scale as described above. If, for instance,
alternative A is judged to be "extremely more desirable" than alternative B, then, according to the scale, a "9" would be
placed in the cell (above and to the right of the diagonal) corresponding to A's row and B's column. The scores
summarizing the results of the other alternative comparisons are likewise placed in their appropriate cells (above and to the right
of the diagonal). Down the diagonal of the matrix, "1's" are placed, indicating that every alternative is "equally preferred"
to itself. Below the diagonal, the reciprocal results are placed; if A was judged "extremely more desirable than B,"
then B must be "extremely less desirable than A," in which case "1/9" would be placed in the corresponding cell. The matrix
of alternative comparisons (called a comparison matrix) for each criterion represents a linear system of equations (a matrix
equation) describing the relative desirability relationships among the alternatives.
Pairwise comparisons are likewise made at the next higher level of the hierarchy to obtain a system
of equations for the importance of the criteria. For example, criterion 1 may be judged two times as important as
criterion 2, criterion 2 judged three times as important as criterion 3, and criterion 1 judged four times as important
as criterion 3 (Note the inconsistency, since the first two judgments suggest that criterion 1 ought to be six times as
important as criterion 3). An important characteristic of AHP is that it allows for inconsistencies in input judgments.
To determine the relative weights of the criteria, an eigenvector for the comparison matrix is found.
One easy way to obtain an eigenvector of a matrix using a computer algorithm involves repeatedly raising
the matrix to successive powers using matrix multiplication and then computing the eigenvector of the
matrix. In other words, the pairwise matrix obtained by comparing the criteria is multiplied by itself to obtain a
product matrix. An eigenvector is found for the product matrix by summing the entries in the rows of
the product matrix, totaling the row sums, and then normalizing the row totals by dividing the row sums by the
row totals. This process is repeated by squaring the product matrix and then normalizing the row totals
from the new product matrix in the same way to obtain the eigenvector. The process is continued until the
resulting eigenvector solution does not change much from that obtained in the previous iteration. At this
point, the computed eigenvector provides the relative weights of the criteria.
In the same way as described above, an eigenvector is found for of the alternative pairwise comparison
matrices. The eigenvector in each case provides the relative ranking of alternatives under each criterion. Finally, multiplying
the matrix showing the ranking of each alternative under each criterion by the vector of criteria weights gives the overall
alternative desirabilities and rankings.
AHP is similar in many ways to MUA. Both are widely used
and both reflect a philosophy that alternatives should be selected based on
how much they are preferred by decision makers.
The approaches, however, reflect somewhat different philosophies. MUA is
regarded as a purely "prescriptive" approach in that it is aimed at
identifying the "correct" decision that a "rational" decision maker would
take. AHP, in contrast, is at least somewhat "descriptive" in that it expects errors and
inconsistencies in the inputs that people provide and seeks a solution that
best accommodates those errors. It can be shown mathematically that the eigenvector approach described above provides
this solution. The differences in philosophy and methods
for eliciting preferences have spurned a lively debate among academics and
practitioners over the pros and cons of the two approaches.
AHP's chief advantage is ease of application. The paired
comparison questioning process can be presented pictorially, and decision makers
typically find it easy to make the necessary judgments. AHP produces a
decision model that is simpler
than that typically produced with MUA in that AHP does not require the
intermediate step of estimating the consequences of projects. AHP is
particularly well suited to group decision making since the group members
do not need to be in agreement. Among AHP's outputs are measures of the
consistency in the input judgments, which can help participants reduce the
inconsistencies expressed in their comparisons. Also, it is relatively easy
for a group to structure a complex decision into the hierarchical structure
required by AHP, and the process helps participants to understand the
problem as well as each others' thoughts and opinions.
Saaty has provided an axiomatic theory to support the
basic approach to applying AHP. However, the theory has been criticized
based on the observation that AHP can produce "rank reversals," a result wherein the
addition of a new alternative can change the ranking of existing
alternatives, even though the new alternative does not influence the costs
or benefits of the existing alternatives. For example, it is possible with
a project prioritization system based on AHP to have the proposal of a new
project that might be ranked 8th cause a project ranked
4th to move up to 3rd. While such behavior is
undesirable and raises questions regarding the logical defensibility of
AHP, supporters have pointed out that rank reversals rarely occur in
AHP's cons include the very large number of comparisons
that must be made if there are a large number of alternatives and/or
objectives to be considered (that number can grow exponentially with the
size of the decision problem). For this reason, applications of AHP to
project prioritization often use a variation of AHP in which the preference
comparisons are expressed for objectives, not for the projects. For
example, "Compare the relative importance of the objectives 'improve time
to market' and 'improve financial performance.'" The answers are used to
derive a set of weights interpreted to represent the relative importance of
the objectives. Projects are then scored to indicate their contributions to
each objective (e.g., no contribution = 0, slight contribution = 0.1,...,
excellent contribution = 1). The scores are weighted and added to obtain an
overall measure for ranking projects.
Unfortunately, this common approach to applying AHP may
not accurately prioritize projects (it also violates the axioms of Saaty's
theory). It is not possible to obtain meaningful preference comparisons
between objectives unless the amounts of improvement are specified (e.g.,
How can I say how much I prefer the objective "improve financial
performance" without knowing by how much financial performance would be
improved?). Also, it is not correct to weight and add performance scores
unless the value of achieving a given level of performance on one measure
does not depend on the level of performance achieved on any other measure,
a condition known as preferential
An alternative approach to applying AHP overcomes the
above problems by using the so-called swing weight method to define specific
amounts of improvements for expressing preferences and by applying tests to
ensure that preferential independence holds. In effect, the resulting
approach to developing the model for valuing projects is then consistent
with MUA, however, Saaty's AHP's pairwise comparison technique is used to
determine the weights.
A final limitation important for applications to project
prioritization is AHP's inability to directly address risk. AHP does not
allow probabilities to be assigned to reflect uncertainty over project
performance. Decision makers can implicitly factor uncertainty into their
pair-wise comparisons, however, this is difficult to do. Although fuzzy logic has been proposed as a means for
addressing ambiguity within AHP, nearly all applications of AHP to project
evaluation are conducted assuming most likely scenarios for project performance.
analytic network process
A generalized form of the analytic hierarchy process (AHP) used in multi-criteria analysis. Whereas AHP structures a
decision problem into a hierarchy of components consisting of a goal,
decision criteria, and alternatives, ANP structures the problem as a more
general network, a form that allows for feedbacks and other forms of
interdependencies among the components.
Term used to describe the methods of analysis used to apply data and mathematical
logic to help make decisions. The term usually refers to the application of
more sophisticated forms of analysis.
Project portfolio optimization is an application of analytics.
application lifecycle management (ALM)
The process of managing the phases of the life of a
software application, including planning, coding, development, testing,
release, and support.
Various tools are available to
support ALM, addressing such issues as requirements management,
architecture, coding, testing, tracking and release management. Project portfolio management tools aimed at IT
project portfolios typically include or may be supplied with modules for
supporting elements of ALM.
application portfolio management (APM)
The management of an organization's various computer
software applications as a portfolio. APM may be viewed as a special case
of project portfolio management (PPM)
wherein the "projects" are investments intended to obtain optimal
performance from the firm's portfolio of computer software applications.
PPM tools aimed at IT project portfolios may include specialized techniques
for managing software applications.
Any self-contained software program that performs a
specific function directly for the user. This is in contrast to system
software such as computer operating systems that provide services to
support application programs.
application programming interface (API)
An interface provided by a project portfolio management tool or other
application program that
defines how that program can access the computer's operating system or
other programs to request data or services.
Also called appserver, a type of server designed to install, operate and host
applications and associated services for end users. Many project portfolio management tools rely on
application servers. The user interface is often web based and accessed through a browser, but
it may be through other means as well.
A branch of computer science concerned with making
computers behave like humans. Artificial intelligence is concerned with the
theory and development of computer systems able to perform tasks that
normally require human intelligence, such as visual perception, speech
recognition, and translation between languages. Prioritizing projects, for
example, could be considered an application involving elements of artificial
The deliberate, long-term management of an organization's assets, usually physical assets,
with the goal of maximizing their contribution to the
achievement of the organization's objectives. Asset management is of critical importance
to organizationsthat that acquire and utilize expensive assets. Examples of organizations that view asset management as
an important function include companies in the energy, mining, and oil and gas
management typically involves making decisions about when to create and
acquire assets, how to use them, their repair or replacement, and their
ultimate disposal. Project portfolio
management applied to asset intensive organizations often focuses on
asset management and may be referred to as such.
A characteristic of an alternative or the
outcome to a choice of an alternative viewed as important to decision makers.
An attribute is a potentially useful
means for quantifying and evaluating
achievable levels of an objective. In the context of project
prioritization, attributes are
measurable characteristics relevant
to the evaluation of candidate projects; they are metrics, which may be specified objectively
(i.e., observed and measured) or subjectively (i.e., estimated based on
judgment). An attribute, when assigned a number expressed in some appropriate unit of measurement or in accordance with some
scale, quantifies some
consideration relevant to prioritizing or otherwise evaluating
that project, for example, its cost, how long it would take to implement,
or what outcomes it might produce. The number assigned to an attribute may
be a point estimate; that is, a
single number intended to represent a best estimate. Alternatively, if
there is uncertainty, a range or probability distribution might
be assigned to the attribute. In addition to being measurable, attributes
should be unambiguous, meaning that there is no ambiguity in interpreting
the meaning of the attribute or the numbers that are assigned to it. In the
context of multi-attribute utility analysis
(MUA) attributes are typically defined to quantify the degree to which
an alternative achieves various decision-maker objectives.
Attributes may involve natural scales,
constructed scales, or proxy measures. An attribute with a
natural scale quantifies the attribute based on commonly used, widely
accepted units. For example, cost, expressed in dollars (or euros,
rubles, yen, etc.) is a natural measure for project cost. Number
of fatalities is a natural measure if loss of life is an attribute of
concern. Most natural measures are expressed in some unit of measurement
(e.g., dollars, fatalities) and can be counted or physically measured.
A constructed scale is a scale that defines
different levels for the attribute in terms of descriptions or definitions
for each level of the scale. For example, while it might be difficult to
come up with a natural measure for "corporate brand image," it might be
possible to construct a 1-to-5 scale consisting of 5 different verbal
statements describing various negative-to-positive customer perceptions of
the corporation. A defined impact scale is a constructed scale
wherein the scale numbers are associated with narrative descriptions of
discrete levels of impact. In other words, the scale levels describe the
"delta" or amount of change that might result from the selection of an
A proxy measure
is an indirect measure selected because there is a presumed relationship
that exists between it and the relevant project characteristic. For
example, if the company concerned about its image participates in a market
analysis survey comparing customer perceptions, its ranking relative to its
competitors might serve as a proxy for its brand image. Like natural
measures, a proxy measure usually involves a scale that is in general use
and that can be counted or physically measured.
The specification of attributes and their associated
measures is a critical step in the construction of a decision model, as the choices made
strongly affect the accuracy, defensibility, practicality, and usefulness
of the model. A variety of techniques are available for identifying an
appropriate set of measurable attributes, including influence diagrams (graphical
representations of the different factors and relationships important to
understanding the concern) or simple brainstorming (e.g., asking, "What
information would you like to have to evaluate this concern?").
In the context of project
portfolio management (non-accounting sense), evidence in the form of
records, references, data or documents that enable a user to trace the path
of assumptions made, data changes, decisions, or other past actions that
are critical to understanding the results obtained.