Lee Merkhofer Consulting Priority Systems

Technical Terms Used in Project Portfolio Management (Continued)






























Stands for Software as a Service (typically pronounced "sass"). Also called on-demand software, SaaS is means for making software applications available to customers, wherein the application is hosted by a vendor or service provider and made available to customers over a network, typically the internet. Instead of installing the software application on each end-user's computer or device, SaaS software uses native web technology to deliver HTML and objects directly to the user's browser. The software is not sold for local installation but is made available as a service on a subscription basis. Many project portfolio management (PPM) tools, especially those with less sophisticated analytics, are provided as SaaS. More information on SaaS is provided in the paper chapters on PPM tool differences and on PPM tool costs and risks.


A term used to describe a safe testing environment with controlled or limited access within which a user or application program can "play" without risking damage to the a larger system. Project portfolio management (PPM) tools are often advertised as providing a "sandbox" for users to enter and analyze project data without committing that data to the project database available to other users.

simple additive weighting

See weighted sum model (WSM).


A graduated range of numbers used as a means for measuring something. In the context of project prioritization, scales are used as a basis for assigning numbers to projects or to specified attributes of the projects. The numbers are combined using an aggregation equation, and the results of the computations used to select or prioritize the projects.

Because the goal for project selection is to choose projects that collectively create the most value, the scales and associated aggregation equation should produce estimates of project and portfolio value, although that is not always the case. For example, in the most common scoring model used by many project portfolio management (PPM) tools, the assigned numbers (scores) are simply weighted and added, without regard to whether the specified scales allow such operations (or whether the results have anything to do with project value). One requirement for producing estimates of project value is the use of the proper kinds of scales.

The most familiar type of scale for measuring project attributes is a natural scale. A natural scale is a commonly used scale for the attribute, expressed in original or natural units. For example, project cost is commonly measured in dollars (or other currency), and time to complete may be measured in months.

Although it might seem that it would always be best to use natural scales for quantifying project attributes, that is not the case. A natural scale for the attribute in question may not exist, or there may be so many considerations relevant to prioritization that defining a natural scale for each would make project assessment too complex. When natural scales do not exist or are inconvenient to use, context-specific constructed scales may be defined. For example, a four-level constructed scale for "impact on community jobs" might be defined as:

Instructions: Select a score, that on balance, best reflects your judgment of the impact on jobs.

Note: You may choose a score between the integer values (e.g., 2.5)

Constructed scale

A sample constructed scale.

In this example, the scores on the scale for impact on jobs are defined in terms of two attributes, the number of jobs created and salary, both expressed in natural units.

A critical consideration for defining scales is whether those scales will allow the computations needed to compute project priorities. In this regard, there are three major categories of scales: ordinal scales, interval scales, ratio scales and cardinal scales.

An ordinal scale is one that merely indicates how something is ranked. For example, 10 projects could be ranked in terms of preference. The project ranked 2 is preferred over the project ranked 3, but the scale doesn't indicate by how much. Ordinal scales tend to be easy for people to apply, but, because the differences between scale numbers are not specified, no mathematical operations can be meaningfully applied to the scores from such scales. Thus, for example, if a scoring model uses an ordinal scale to rank projects based on two criteria, say "impact on corporate image" and "financial attractiveness," adding or averaging those rankings would lead to meaningless results.

A scale is interval scaled if the numbers assigned are in units of equal magnitude. The Fahrenheit and Celsius scales for temperature are examples of interval scales—in each case the scale units (degrees) don't change at different locations of the scales. The difference between 100 degrees and 90 degrees is the same difference as between 90 degrees and 80 degrees. Because distances between numbers in an interval scale have meaning, the numbers assigned with such scales can be added or subtracted. Thus, for example, if you're using interval scales you can use aggregation equations that weight, add, or subtract the assigned numbers. Weighting and adding scores from scales that are not interval scaled produces meaningless results.

Although you can meaningfully weight and add interval scaled numbers, you cannot generally multiply them. This is because interval scales may have arbitrary zero points. The Celsius temperature scale arbitrarily defines zero as the temperature at which water freezes. This makes ratios expressed using scale numbers meaningless—a temperature of 50 degrees is not twice as hot as a temperature of 25 degrees, as demonstrated by the fact that the corresponding temperatures on the Celsius scale, 10 and -3.9 degrees are not in the ratio 2 to 1.

A scale is ratio scaled if, in addition to being interval scaled, it has a zero level that corresponds to "none of the attribute" (also referred to as an absolute scale). With ratio scales, attributes are assigned numbers such that (1) the differences between the numbers reflect differences in the amount of the attribute and (2) ratios between the numbers reflect ratios of the attribute. This ensures that the numbers assigned to various degrees or amounts of the attribute bear a direct relationship to the absolute amount of the attribute. With such a scale, we can say not only that one project has so many units more of a attribute than a second project, but also that the first project has so many times "as much" of the attribute than the second project. Time measured in months, for example, is a ratio scale. A project that requires 4 months takes twice as long as a project that requires 2 months. Costs and probabilities are defined on ratio scales. Also, the weights defined in the additive value function are defined along a ratio scale. All arithmetic operations are permitted on numbers that fall along a ratio scales. Also, you can multiply ratio scale values by interval scaled values.

A cardinal scale is an umbrella term for interval and ratio scales. A ratio scale is a cardinal scale with a zero level.

The figure below summarizes differences in the information communicated depending on the type of scale used for a ranking. If an ordinal scale is used to communicate the results of a horse race, the only thing you'd know is the order in which the horses finished. If an interval scale is used, you'd know the order in which the horses finished and the differences in the times run by each horse. If a ratio scale is used, you'd know everything: the order in which the horses finished and their times. For example, you might be able to determine that the first place horse finished 3rd all time for races at that track.

Constructed scale

Different scales provide different levels of information.

To help avoid errors in project selection decision models, you should strive to define scales that are ratio scaled, or be careful not to apply computations that aren't permitted for the types of scales you've defined. The example scale for job creation shown above is neither interval scaled nor ratio scaled. However, it is anchored in natural units that give meaning to differences in scale values and has an absolute zero. In such cases it is often possible to use a scaling function to translate the such scales to alternative units such that the result is ratio scaled. For example, if total income from new jobs is viewed as a reasonable measure for the impact on jobs, a scaling function for making the measure ratio scaled would be the product of the number of jobs created and the average salary for those jobs.

scaling function

A functional relationship for translating scales. For example, if the units on a scale aren't of equal magnitude (e.g., as in a logarithmic scale), a scaling function might be applied to convert the scale into one with equal-sized units. This approach is often used to obtain interval scales that allow differences in scale values to reliably indicate differences in the amount of the measure.

A common use of scaling functions for project prioritization is to convert a measure of project performance relative to some objective into a measure indicating the value of that level of performance. In this instance, the scaling function may be referred to as a value curve or value scaling function, a scaling function is a functional relationship used in a decision model that translates a level of performance, as expressed by a performance measure, into a number that indicates the value or desirability of that level of performance. In the example below, which might apply to an electric utility concerned with quickly restoring service to customers without power, the x axis denotes the amount of time the customer is without power. The y-axis is a relative measure of value, defined such that 100 indicates maximum value and 0 represents the value associated with the worst level of performance that the utility expects could occur (in this case, an outage lasting 24 hours). In the example, the scaling function is non-linear to reflect that fact that residential customers will often suffer greater losses when the duration of an electric outage approaches 4 to 8 hours, because, for example, an outage of such duration may cause refrigerated food to spoil.

An example scaling function

A sample scaling function

A decision model may require a scaling function for each of its performance measures. However, if the incremental value of obtaining a unit of improvement as expressed by the performance measure does not depend on the current level of performance, the scaling function will be linear (a straight line). Performance measures are often defined in such a way that the linear assumption holds.

Mathematically, a scaling function has the form V = S(p), where "p" is the performance measure, "S" is the scaling function, and "V" is the measure of value. The differences in the values of V produced under various levels of performance p indicate by how much the higher levels of performance are preferred. As in the above example, by convention, a scaling function often expresses value on a zero-to-100 scale. In technical terms, a scaling function is a single-attribute utility function—a utility function with only a single independent variable for measuring performance.


An internally consistent description of a possible sequence of events, or situation, based on assumptions and factors chosen by the scenario creator. Scenarios are commonly used as a basis for estimating the implications of taking some action. For example, a project might be evaluated assuming one or more scenarios, or visions of what the future might bring.

Scenario building refers to the process of generating scenarios. Scenario analysis involves using multiple scenarios and considering the implications of those possible futures. Scenario analysis is a form of risk analysis in that it helps to create understanding of the implications of uncertainty.

Scenarios have been likened to "mental movies," and the term is the same as that used in the film and television industry to describe the script that ties a story's events together. Creating scenarios is a common technique for forecasting the possible consequences of situations or actions, especially in support of long-range planning.

scenario analysis

Similar to sensitivity analysis except that cominations of variables are simultaneously varied to mimic the combined impact of changes to related assumptions.


When used as a noun, a number assigned to a project to represent some characteristic of the project relevant to assessing its merit. Project scores are inputs to a model for the comparative evaluation of projects. Oftentimes, score refers to a number selected from a constructed scale. The type of model that relies on scores for input may be a scoring model, though the term may also be used to describe subjective estimates generated for input to other types of models as well. When used as a verb, the term refers to the task of generating a judgmental input for a model.


A table, usually displayed on a single page or screen, that summarizes the results of generating inputs for a scoring model. The purpose is to quickly convey information relevant to specifying judged performance (e.g., project performance) relative to various dimensions or objectives of interest.


An individual who provides estimates used by a project prioritization or project selection model to assess project performance. The individual may be labeled an "expert" to indicate that person was selected for his or her knowledge or expertise needed for providing the desired estimate. For example, if the scores are inputs needed for a project prioritization model, the scorer would normally be someone particularly knowledgeable about the projects being prioritized and the consequences that would likely result from conducting those projects. The process of generating scores is termed scoring because providing estimates of performance may involve selecting inputs to the model from one or more predefined scales.


An assessment of performance that involves assigning a score, usually a number based on one or more predefined scales.

scoring model

A type of decision model often used for project selection that involves scoring projects against multiple criteria. Various criteria (considerations) for choosing projects are identified. These typically include financial criteria (e.g., net present value), plus criteria related to customer service, safety, contribution to strategy, risk, etc. Each project is evaluated (scored) against each criterion, and the scores are combined in some way to obtain an overall measure intended to represent the attractiveness or to provide a figure of merit for each project. Scoring models differ mainly in how the criteria are defined and measured, and how the individual assessments are aggregated to obtain an overall project figure of merit. Such differences significantly affect the complexity, information requirements, reliability, and defensibility of the model.

Although there are a number of sophisticated, multi-criteria decision models that involve scoring, including AHP, ELECTRE, goal programming, and PROMETHEE, the term scoring model typically refers to the least complicated type of multi-criteria model wherein the project figure of merit is obtained by simply adding, or, more commonly, weighting and adding, the scores assigned to the individual criteria. This results in a method of evaluation that is very simple to implement and understand, but one that, typically, is not very reliable or defensible. Many, if not most, project portfolio management tools are limited to using this type of simple scoring model for evaluating or ranking projects.

There are three types of scoring models: checklist models, un-weighted scoring models, and weighted scoring models:

  • With a checklist model, the criteria are expressed as yes/no statements (e.g., "Payback period less than 5 years", "Project involves no safety risk") listed in a table. Individuals then evaluate each project by indicating (checking) those criteria from the list that the project satisfies. The checks are counted for each project, and the totals are used as the measure for ranking the projects. Since a check counts as a score of "1" when totaling scores, the checklist model is sometimes referred to an un-weighted, 0/1 factor model.
  • An un-weighted scoring model is similar to a checklist model, but allows for gradations in project scores. Instead of expressing the criteria as yes/no statements, a scale is used. Often, a 5-point scale is selected, where 5 means the project is very good with respect to the criterion, 4 means good, 3 means fair, 2 means poor, and 1 means very poor. The scores are summed, and the totals are used as the measure of project attractiveness.
  • A scoring model is a weighted scoring model if it allows weights to be assigned to the criteria. A weighted scoring model has the mathematical form:

  • Formula for weighted scoring

    where Sj is the total score for the jth project, N is the number of criteria, wi is the weight assigned to the ith criterion, and sij is the score of the jth project on the ith criterion. The weights are typically assumed to represent some concept of the relative importance of each criterion. Methods used for assigning weights include paired comparison, AHP and the swing weight method. Although it is not necessary and has no effect on relative rankings, weights are often scaled to sum to one, expressed mathematically as:

    Normalized weights

    This allows the weight on each criterion to be interpreted as the percent of the total weight assigned to that particular criterion.

The main advantage of scoring models is that they provide a way to capture the multiple considerations that are relevant when deciding whether or not to conduct a project. Scoring models are very easy to create and simple to understand. A scoring model can easily be implemented in Excel or one of the other standard computer spreadsheet tools. The model is flexible and can be easily altered or changed to accommodate changes in organizational preferences or managerial policy. Another advantage of a scoring model is that although the model is developed to support project selection, that same model can be used as a guide for project improvement. A project's scores on each criterion can be compared with the best possible score. The differences, when multiplied by the weights, indicate the types of improvements that would most improve the project's attractiveness as measured by the scoring model.

The main disadvantage of scoring models is that the model output is typically not a reasonable measure of the value of doing the project. Without a sound measure of project value, it is impossible to know whether the project is worth its costs or to identify the portfolio of projects that produces the most value given the resources available. Under the standard scoring model, the mathematical equation for computing total scores is linear, implicitly assuming that a unit improvement on any criterion always contributes the same amount to project attractiveness regardless of how well the project performs against that criterion or on any other criterion. Many relevant criteria, such as risk, can't be reasonably captured using linear equations.

Also, because it is so easy to define criteria, it is common for scoring models to contain many criteria. The criteria often overlap or represent similar or related objectives, and this overlap can produce significant biases. Such errors can be reduced by placing restrictions on how criteria are defined and measured, but this complication effectively means applying a different approach (see multi-attribute utility analysis). Such complications, though needed for accuracy, eliminate the simplicity of design that is the main attraction of scoring models.

sensitivity analysis

A method for determining how the variation in the outputs of a model depend on variations in the model's various inputs and other assumptions. In the simplest form of sensitivity analysis, each input variable is varied over a range representing its uncertainty, and the impact on model outputs is observed. Those variables that produce the biggest changes to model outputs are identified as the variables whose uncertainties are most critical to model predictions. Other forms of sensitivity analysis involve varying the structure of the model, or its underlying assumptions, and observing the affect on outputs.

Simulation is a form of sensitivity analysis which can be used to explore how simultaneous variations in the values of input variables affect model outputs. Other forms of sensitivity analysis show how variations in the outputs of a model can be apportioned to different sources of variation in inputs.

Sensitivity analysis is useful for many purposes. For example, it can indicate where additional effort might be most useful for improving confidence in model predictions. Suppose a sensitivity analysis showed that a small change in the assumed growth rate for the market served by a new product results in a very large change in the computed value to be derived from that product. The result would suggest that it might be useful to use a probability distribution to describe uncertainty in market growth rate and to use a probabilistic analysis to characterize the resulting uncertainty in the value of the new product. Additionally, the result would suggest that it may be worthwhile to devote additional effort to estimating market growth rate before committing to produce the new product. Furthermore, it would suggest that, after introducing the new product, the growth in market size should be measured and tracked closely to support future decisions regarding the product.

Sensitivity analysis can be used to test a model and explore how closely it corresponds to the real world processes that it is meant to represent. Depending on the results of such tests, sensitivity analysis will identify errors that need to be corrected or build confidence in the model and its predictions. In this way, sensitivity analysis promotes model improvement via application of the Scientific Method.


A software program, or the computer on which it runs, that shares data and software resources in response to requests made by to other programs or computers referred to as clients. This architecture, known as the client-server model, may be established within a single computer, a local area network (LAN), or a wide area network (WAN) over the Internet. The client provides the user interface, for example, a GUI (graphical user interface) and performs some or all of the processing related to the requests it makes from the server. The server maintains the data and processes the requests.

Client-server architecture

Client-server architecture

Servers are named after the primary functions they perform: for example, file servers receive, store, and send files, web servers store webpages, mail servers receive, store, and forward emails, and application servers install, operate and host applications. Many project portfolio management applications are constructed using client-server architecture.

shadow price

Term used in optimization to indicate the amount by which the objective function under the optimal solution would increase if a constraint were relaxed by one unit. Thus, in a business application, a shadow price could indicate the maximum price that management should be willing to pay for an extra unit of a given limited resource. Suppose, for example, that a production line is set to operate for a normal, 40-hour week. The shadow price for operating hours would be the maximum price the manager should be willing to pay for operating the line an additional hour, based on the benefits to be obtained from the additional hour of operation. Computing shadow prices can help organizations identify constraints that ought to be relaxed.

Some project portfolio management tools allow computation of shadow prices for portfolio resource constraints. Suppose the tool uses an optimization engine to identify the project portfolio that produces the greatest portfolio value subject to meeting some constraint, such as a maximum allowable budget year cost. A natural question would be, "By how much would the value of the optimal portfolio increase if the constraint were relaxed?" The shadow price for the budget constraint is the amount by which portfolio value could be increased if the constraint were relaxed by one dollar.


A technique for predicting or analyzing the outcomes of a real world situation using an analytic model represented within a computer program. In the context of project portfolio management, simulation typically involves predicting the consequences of individual projects or portfolios of projects. The simulation model takes as input assumptions regarding the project and produces as output project consequences relevant to the achievement of the organization's objectives (these outcomes are project or portfolio performance measures). The simulation process involves generating scenarios consisting of assumptions for the project or project portfolio and using the model to determine (simulate) what the corresponding business consequences might be. Monte Carlo simulation is a form of simulation that involves using a built-in random process to select assumptions for the scenarios. The distribution of model outputs is then used to assign probability distributions representing uncertainty over project or portfolio consequences.

A dynamic simulation is one wherein the model represents the time sequence by which the various relevant changes and impacts occur. For example, a model for simulating a new product development project might first represent the attributes of the product likely to result from the project, then represent the sales likely to occur based on those product attributes, and, finally, translate those sales into a corresponding revenue stream for the organization.

In theory, any project outcomes that can be anticipated and represented as mathematical cause-effect or influencing relationships can be simulated. In practice, however, simulation is often difficult because there are so many factors that influence outcomes and those influences are complex and only partially understood. An efficient simulation captures only those factors and influences that are most important.

single attribute utility function

Analogous to a single attribute value function, but describes a single-variable utility function rather than to a value function. Unlike a value function, which applies in cases where there is no uncertainty over the performance outcomes for alternatives, a utility function applies to conditions of uncertainty and must capture decision maker attitudes to taking risks.

Single-attribute utility functions are typically encountered in two circumstances. First, if objectives and performance measures have been defined such that additive independence is satisfied, then the multi-attribute utility function can be expressed as a sum of single-attribute functions. Single-attribute utility functions are much easier to assess. The second circumstance where single-attribute utility functions are encountered is where a value function has been defined to collapse the multiple performance measures relevant to the decision problem down to an equivalent monetary value. In this case, the purpose of the single-attribute function is to account for the decision maker's attitude toward risk.

The minimum number of points that need to be established in order to approximate a single-attribute utility function is probably five. If the function is normalized by assigning a utility of zero to the worse level of performance and a utility of one to the best level of performance, then the certain equivalents method can then be used to obtain the performance levels associated with three additional utilities equal to 0.25, 0.5, and 0.75.

Alternatively, a single-attribute utility function can be obtained by selecting a mathematical form for the function and and then fitting that function to a few assessed points. Commonly used mathematical forms include:

    Exponential utility function
  • Exponential. The exponential function is convenient for representing the risk attitude of the decision maker. The constant a is the risk tolerance, which for a = 0 indicate risk neutrality, a < 0 indicates risk preferring, and a > 0 indicates risk aversion. The exponential function is said to have constant absolute risk aversion, since a is a constant. The exponential utility function is often simply written as U(x) = -e-ax, since the constant 1 has no effect on the performance levels xthat maximize the function. Logarithmic utility function
  • Logarithmic The natural logarithm exhibits declining marginal utility with the level of x, in fact, marginal risk tolerance is 1/x. Note that the function is defined only for x > 0. It attributes great undesirability for performance levels that approach zero. In fact, if x is uncertain and there is any probability of x = 0 the expected utility with be -∞. If an individual has a utility function with this shape, then it can be shown that he/she will be willing to pay, in some circumstances, for insurance.
  • Power utility function
  • Power Some empirical studies suggest that individuals exhibit constant relative risk aversion but diminishing absolute risk aversion, meaning that they are willing to take on more risk as they gain wealth. The power utility function has this characteristic. It is also known as the isoelastic function for utility. The value η is a measure of risk aversion, with η = 0. This is the only utility function with constant relative risk aversion. Power utility is appealing because it implies stationary risk premiums and interest rates even in the presence of long-run economic growth. Also, it is tractable in the presence of multiplicative lognormally distributed risks. A negative η represents a subsistence level.
  • Power utility function
  • Quadratic. The quadratic utility function is increasing only for x < 1. This function has increasing absolute risk aversion and a "bliss point" where the parabola achieves its maximum. Thus when working with a quadratic utility function we want to have the bliss point at a level of consumption far above anything that the consumer might actually realize. Increasing absolute risk aversion and the existence of a bliss point are important disadvantages, although quadratic utility is tractable in models with additive risk. In financial economics, the utility function most frequently used to describe investor behaviour is the quadratic utility function. Its popularity stems from the fact that, under the assumption of quadratic utility, mean-variance analysis is optimal.

A risk attitude that is sometimes appropriate (especially for personal investment decisions) is one where the decision maker's willingness to accept risks increases as total wealth increases. A mathematical form with this characteristic is U(x) = h + k (-e-ax - be-cx), where a, b, c & k ≥ 0

single attribute value function

Also called, preference function, marginal value function, partial value function, and a scaling function, a value function that contains only one attribute, expressed, for example, as V(x). The function defines a relationship between value, V, and the level specified for the attribute, x. A single attribute value function is also referred to as a scaling function, is a particular application of a scaling function because it transforms and scales (if needed) the measure used to express performance (the attribute) into a a number indicated the decision maker's preference for that preference.

In the context of valuing projects, for example, a relevant attribute might be the amount of learning provided by the project. A single attribute value function would indicate the assumption that the value of the learning provided by the project is a function only of the attribute indicating the amount of learning provided. If the value function for learning is single attribute, then no other attributes defined for characterizing projects, for example the type of project, matter when estimating the value of the learning.

Six Sigma

A popular business and project management methodology, developed originally by Motorola in the 1970s, for improving the quality of business process outputs. Some project portfolio management tools incorporate templates and aids to support Six Sigma as applied to projects.

The Six Sigma methodology aims to identify and remove the causes of defects (errors or variations in process outputs) that lead to customer dissatisfaction. There are five steps in the methodology (abbreviated DMAIC): (1) define the customer and business goals for the process, (2) measure defects in the performance of the current process, (3) analyze the data to identify root causes of defects, (4) improve the process to reduce defects, and (5) control the variables that cause defects. Six Sigma defines metrics for measuring process quality, employs statistical analysis, and establishes an infrastructure of people within the organization to advance the methodology ("Green Belts," "Black Belts," etc.). The term "six sigma" refers to a concept in statistics for measuring how far a given process deviates from perfection, and suggests that errors be reduced to at most a few per million.


In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a random variable about its mean. The skewness can be positive or negative depending on which direction the "tail" of the distribution extends.

Positive and negative skewness

Probability distributions with positive and negative skew


The steepness of a curve at some designated point. The slope of a curve or line indicates how much change in the dependent y-variable occurs when the independent x-variable changes one unit. A horizontal line has a slope of zero. A line that makes a 45 degree angle with the x-axis has a slope of one.



A multi-criteria analysis method originally developed in the 1970s by behavioral psychologist and decision analyst Ward Edwards. SMART is an acronym describing desired characteristics when specifying decision objectives—the objectives should be Specific, Measurable, Achievable, Realistic, and Time-based. SMART has been incorporated into many decision aiding tools and several project portfolio management tools rank projects using the technique. Compared to multi-attribute utility analysis, SMART makes simplifying assumptions for the purpose of enabling quick assessment techniques.

SMART recommends a multi-step ranking method that begins with identifying the criteria, or value dimensions to be used for evaluating alternatives. The value dimensions are then ranked based on judged importance, and the least important dimension is assigned a value weight of 10. The next-to-least-important dimension is assigned an importance weight representing the ratio of its relative importance to that of the least-important dimension. For example, if this dimension was viewed as twice as important as the least important dimension, it would be assigned a weight of 20. Weights are assigned to the other dimensions in the same way, preserving importance ratios. The weights are then normalized to sum to one by dividing each weight by the sum of all of the weights. Each alternative is then rated on each dimension using a zero-to-100 scale. The ratings are weighted and summed, and the results used to rank the alternatives.

The simplifications inherent in SMART can lead to errors. In particular, if the value dimensions are not preferentially independent (e.g., if the importance of a dimension depends on the performance of the alternatives with respect to some other dimension) or if value is not directly proportional to rating (e.g., if a rating of 50 is not half as valuable as a rating of 100, in which case a scaling function is needed), then there may be significant errors in the rankings produced by SMART. Edwards and colleagues also developed "improved" versions of SMART, called SMARTS and SMARTER. SMARTS is simply SMART using the more defensible swing weight method for eliciting weights. SMART’s common applications are in environmental, construction, transportation, military, manufacturing and assembly problems. Its ease of use helps in situations where a fair amount of information is available and access to decision-makers is easy to obtain. Its simplicity is what keeps this method fairly popular. Several tools for project portfolio management use SMART to prioritize projects.

software suite

A collection of software applications with related functionality typically sharing a more-or-less common interface and ability to exchange data with each other.

source code

The lines of code and algorithms as originally written by a computer programmer that determine how the software works. Source code is typically written in human-readable form. In the case of most tools for project portfolio management that incorporate decision models, access to the source code is required to modify in any significant way the model or logic by which projects are evaluated and prioritized.


Stands for standard query language, a standardized computer language used to create, modify, retrieve and manipulate data from a relational database. SQL uses regular English words for many of its commands, which makes it easy to learn and understand. The original version, called SEQUEL (structured English query language) was designed by an IBM research center in 1974 for use on mainframe computes. SQL was first introduced as a commercial database system in 1979 by Oracle Corporation.

standard deviation

A measure of the spread or variability within a set of data. The standard deviation is usually calculated as the square root of the sum of the squares of the distance of each data point from the mean divided by the number of data points minus 1:

Formula for computing standard deviation

In the equation, the xi are the various data values, n is the number of values, and xAvg is the average value of the xi. The standard deviation is the square root of the variance, another measure of data variability. However, the standard deviation is often preferred because it has the same units as the quantity being measured.

standard gamble invariance

An independence condition relevant to multi-attribute utility analysis. If the condition applies in the presence of a zero condition attribute, the utility function must have a multiplicative form. An attribute Xi satisfies standard gamble invariance if the certain equivalent of two-outcome gambles over Xi does not vary depending on the levels of the other attributes, provided that none of the zero condition attributes are at their zero levels.

Medical decision making is a field where recognizing standard gamble invariance can be useful. For example, suppose as a result of an injury a woman is experiencing severe, chronic back pain and is, therefore, considering a risky operation that may eliminate or reduce her pain but may also impact her remaining life expectance. Suppose two attributes characterize the outcome of the decision: XP the level of back pain following the operation and XT, the number of remaining years she will. The attribute XT is a zero condition attribute because, if XT = 0 (the patient dies during the operation), she will obviously be indifferent regarding the outcome of XP, the level of pain she would have had if she survived.

To check for standard gamble invariance, the patient imagines a specific outcome for XP, for example, "mild back pain," and then estimates the certain equivalent for a gamble over the number of years she will continue to live. For example, suppose she is indifferent between the certain outcome of living 15 years with mild back pain and a 50/50 gamble of 35 years with mild back pain versus 1 year of mild back pain. If, when she assumes a different outcome for XP, say, no back pain, the certain equivalent remains the same—15 years of no back is the certain equivalent of a 50/50 gamble of 35 years of no back pain versus 1 year of no back pain—then standard gamble invariance applies. The utility function in that case will have a multiplicative form. If UP(XP) is the patient's utility function for different levels of back pain and UT(XT) is the patients utility function over number of years of remaining life (with UT(0) = 0), then the multi-attribute utility function for level of pain and years of remaining life will have the form U(XP,XT) = UP(XP) × UT(XT).


Random or randomly determined. Typically applied to describe a model or method of analysis whose outputs account for uncertainties and their probabilities. Probabilistic is another term used in this context with essentially the same meaning, except that the term stochastic is more often used in contexts where probabilities are derived through the statistical analysis of data. Compare with deterministic.

stochastic multi-criteria acceptability analysis (SMAA)

A family of multi-criteria analysis (MCA) methods and associated software intended to support groups deciding among discrete alternatives. With SMAA, the decision makers need not express their preferences explicitly. Instead the method is based on exploring the space of possible weights in order to describe the weights and valuations that would make each alternative the preferred one. SMAA, in effect, solves a problem that is the inverse of that addressed by most MCA methods. Rather than identify alternatives that are best given a decision maker's preferences, SMAA looks for the preferences that are best aligned with the choice of specific alternatives.

SMAA calculations are based on the assumptions that decision-making preferences may be described by an additive value model with specified criteria. Weights are assumed to be uncertain. The values that would be assigned to each alternatives performance relative to each criterion are likewise assumed to be uncertain. SMAA allows for defining constraints over the nature of these uncertainties.

In general, if there are N criteria for selecting alternatives, there will be an N-dimensional space of possible weights. Weights are assumed to be normalized so that they sum to one. Thus, if there are three criteria there will be three weights and the space of possible weights would be as illustrated in the figure below.

Weight space

The decision maker's weights are assumed to be represented by a joint probability distribution defined in the feasible weight space. Uncertainties over the value assignments are likewise assumed to be represented by probability distributions.

However, instead of eliciting probability distributions over weights and values from decision makers, SMAA allows for specifying constraints for defining weights. For example, assuming complete uncertainty, the probability distribution over weights is assumed to be described by a uniform distribution over the restricted weight space. For example, in the 3-criteria case, a constraint might be that W1>W2, and W2>W3. With these constraints, the restricted weight space is as shown below.

Weight space

The types of constraints allowed by the software include intervals for weights, intervals for weight ratios (trade-offs), linear or non-linear inequality constraints for weights, and a partial or complete ranking of the weights.

The probability distributions assigned to weights and the uncertain criteria values are used to compute confidence factors describing the reliability of the analysis. The original version of SMAA allowed computing three such measures: the acceptability index, the central weight vector, and the confidence factor.

The rank acceptability index describes the share of different weights and criteria measurements ranking an alternative at a specified rank. For example, if the top ranking is selected, the acceptability index describes the share of different weight valuations making an alternative the most preferred one. Acceptability indices can be used for classifying the alternatives into stochastically efficient A zero acceptability index means that an alternative is never considered the best with the assumed preference model. The acceptability index of the original SMAA method was not designed for ranking of the alternatives, but instead for classifying them as more and less acceptable ones, from which the earlier ones should be taken into future consideration.

The central weight vectors represent the typical preference favoring each alternative, and the confidence factors measures whether the criteria measurements are sufficiently accurate for making an informed choice. The CW's are used for inverse approach: instead of asking preferences and giving results, answers the question, "Which preferences support an alternative to be the most preferred one?" The central weight vector describes the preferences of a typical decision maker supporting this alternative with the assumed preference model. By presenting the central weight vectors to the decision makers, an inverse approach for decision support can be applied: instead of eliciting preferences and building a solution to the problem, the decision makers can learn what kind of preferences lead into which actions without providing any preference information.

The confidence factor is the probability for an alternative to be the preferred one with the preferences expressed by its central weight vector. CF measures whether the criteria measurements are accurate enough to discern the efficient alternatives. The central weight vector & confidence factor describes the preferences of a typical decision maker supporting this alternative with the assumed preference Model. The confidence factor is defined as the probability for an alternative to be the preferred one with the preferences expressed by its central weight vector. The confidence factors measure whether the criteria measurements are accurate enough to discern the efficient alternatives.

The various versions of SMAA have added output metrics. For example,SMAA-2 provides probabilities for alternatives to obtain certain ranks. SMAA-2 extends SMAA by taking into account all ranks and provides five new descriptive measures: the These new measures provide decision makers with more insight with the decision making problem. One of the advantages of SMAA over most other MCDA methodologies is that it can be used without any preference information if such is not available. Flexibility and maturity of the SMAA methodology allows \out of box" thinking and application of MCDA in new disciplines {most of real-life decision problems are multi-criteria by nature SMAA methods have been successfully applied in various real-life MCDA problems with imprecise criteria measurements and partial/missing preference information Cross-platform, open source implementation of SMAA methods is available from www.smaa.fi.

The usual approach to apply SMAA in real applications is to use it repetitively with more and more accurate information until the information is sufficient for making a decision. Between the analyses, information can be added by making more accurate criteria measurements, or assessing the decision maker's preferences more accurately in terms of the various preference parameters. SMAA methods have proven most useful for aiding group decision making. It is well suited to any situation where when decision makers do not want to reveal their true preferences.

stochastic programming

A general category of mathematical solution techniques for problems involving uncertainty. In stochastic programming, probability distributions are typically used to quantify uncertainties. Stochastic programming is employed in some project portfolio management tools where the goal is to identify project decisions that maximize either the expected value or certain equivalent of the project portfolio subject to budget constraints.

strategic alignment

Also called strategic fit, a measure of the extent to which an organization's operational decisions are consistent with and implement its strategy. The logic is as follows. Organizations define their missions or visions based on their fundamental goals. They then define strategies for achieving their organizations' fundamental goals. For a strategy to be successful two things must occur. First, the strategy must provide the organization with a plan that will achieve its goals given the realities of the organization's resources, strengths and weaknesses, and the business environment within which it operates. Second, the day-to-day decisions that are made within the organization must successfully implement the strategy. Strategic alignment deals with the second issue. If the organization is not choosing projects that are consistent with its strategy, the likelihood that its strategy will allow it to achieve its goals is reduced considerably.

Strategic alignment seems intuitively to be a good thing, and this, no doubt, is one of the reasons that it is so often talked about in the context of project portfolio management (PPM). However, as often happens with fuzzy concepts, the logic fails when we try to apply it in the real world. How do we measure how well projects align with strategy? Even more importantly, why would having a portfolio of projects most highly aligned with strategy necessarily create the most value for the organization? Projects should contribute to the implementation of effective strategy. However, just because a set of projects is highly consistent with strategy does not mean that those specific projects will create the greatest value for the organization.

The approach most often used to quantify strategic alignment involves creating a scorecard composed of metrics linked to elements of the organization's stated strategy. For example, if policy makers have declared that one component of the strategy is to "become the low-cost provider," projects would be scored on, among other things, the degree to which they would permit price reductions. If another element of the firm's strategy is to "be acquired by a larger firm," projects would be scored based on whether they would make the firm appear more or less attractive to potential acquirers. The scores indicate the scorer's sense of the degree to which proposed projects are consistent with the various elements of strategy.

By itself, the balanced scorecard doesn't provide an overall measure of strategic alignment, only numbers that reflect judged alignment with different elements of strategy. Therefore, weights are assigned to the strategy elements to allow the scores to be aggregated. The weights typically reflect some judgment of the relative importance of the various strategy elements, for example, how critical each element is to achieving the organization's stated vision. (See the description of the typical strategic alignment process.)

Although the above application of the balanced scorecard approach for strategic alignment might provide useful insights on projects and strategy, it would be of no use for project prioritization. The main goal of PPM is to identify the portfolio of projects that creates maximum value. The value created per dollar spent ("bang for the buck," see Mathematical Theory) is often a reasonable metric for ranking projects. Alignment scores have nothing to do with bang for the buck. Just because a project achieves a high aggregate score because it reflects numerous elements of the corporate strategy does not mean it will create more value. Strategic alignment is not a surrogate for value, so prioritizing projects based on strategic alignment does not make sense.

strategic business unit (SBU)

A company division, product line, single product, or company brand that has a mission separate from other company businesses and that can be planned independently from the other businesses. The concept is that strategic business units can be managed autonomously. Organizing the enterprise into smaller business unit enhances flexibility, enabling a large firm to react more quickly to changing market and economic conditions.


A component or part of a larger model. A sub-model typically analyzes some portion of the problem addressed by the model or provides a portion of the outputs available from the larger model.

swing weight

A weight (scaling constant) indicating a decision maker's judgment about how valuable it is to obtain a specified improvement in performance ("swing") against one criterion relative to specified performance improvements against other criteria. Swing weights are typically assessed using the swing weight method.

swing weight method

One of the available methods for eliciting weights for the various criteria defined for multi-criteria analysis. The swing weight method requires specifying hypothetical changes (swings) in the level of performance against different objectives and then obtaining judgments of the relative preferences for obtaining those swings, typically using a 0-to-100 scale. For example, if the most desirable swing is given a swing weight of 100 points, how many points would be assigned to obtaining the next most desirable swing? Although the swing weight method is not necessarily the most accurate method for eliciting weights, it provides much more reliable results than assigning weights based on abstract "importance" of each criterion. A strength of the swing weight method is that most people find it relatively quick and easy. Some project portfolio management tools include routines and aids for applying the swing weight method.

SWOT analysis

A decision aid wherein the strengths, weaknesses, opportunities, and threats associated with a proposed project or other business decision are systematically identified and examined.