Lee Merkhofer Consulting Priority Systems

Technical Terms Used in Project Portfolio Management (Continued)





























theory of constraints (TOC)

A popular management approach originally developed in the 1980s in a series of books and articles by Eliyahu M. Goldratt . TOC promotes a "thinking process" and various "solutions" based on the idea of identifying and relaxing the constraints that limit an organization's ability to achieve its goals. TOC advocates have argued that the approach is applicable to project portfolio management. Although TOC does not dictate a specific model or logic for selecting projects, its perspective and techniques are useful for project portfolio management in some situations.

According TOC, every organization has at least one factor that inhibits its ability to meet its objectives. The constraining factors can be broadly classified as internal resource constraints, market constraints, and policy constraints. To better achieve its goals (e.g., profit maximization), the organization must increase throughput at the process that is a bottleneck due to the constraining factor.

According to Goldratt and others, the steps are: (1) identify the active constraint, (2) decide how to exploit the active constraint (how to increase its throughput utilization), (3) subordinate all other processes (manage all other processes to exploit the active constraint), (4) elevate the system's constraint (increase capacity, find alternatives to the constraint, etc.) and (5) repeat for the next constraint that becomes active.

In addition to being useful for project planning, TOC's various "problem-solving tools" are relevant to project selection. The TOC thinking process is aimed at answering three questions central to designing and choosing projects: What to change?, What to change to?, and How to cause the change? Project communication and management tools are provided to promote agreement. The loosely affiliated consulting organizations dedicated to applying TOC market numerous application-specific "solutions" for areas such as production, supply chain management, technology development, and sales and marketing.

time preference

A measure of the preference a decision maker has for obtaining desired outcomes (e.g., cash inflow) sooner rather than later. Time preference is captured mathematically using a discount function, such as net present value, characterized by a discount rate that reflects the degree to which near-term enjoyment is preferred.


Stands for Technique for Order of Preference by Similarity to Ideal Solution, a multi- criteria analysis (MCA) method based on the concept that best alternative is the one that is the shortest "distance" from the positive ideal solution and the greatest distance from the negative ideal solution. The positive ideal solution is a hypothetical alternative that achieves the most desirable levels with respect to each criterion across the options under consideration. The ideal negative solution is defined in an analogous way, it achieves the least desirable levels for any alternative with respect to each criterion. TOPSIS ranks the alternatives based on a mathematical concept of distance, the geometric distance in euclidian space from the positive and negative ideal solutions.

TOPSIS assumes that all criteria are either monotonically increasing or monotonically decreasing. In addition, TOPSIS assumes the criteria are additive independent. TOPSIS also assumes that the performance of each alternative with respect to each criterion has been established.

The steps for applying TOPSIS are as follows.

Step 1 is to construct the decision matrix. If there are M alternatives and N criteria, each cell in the M by N matrix is the estimated performance, xij, of the i'th alternative with respect to the j'th criterion.

TOPSIS decision matrix

Step 2 is to create a normalized matrix rij using a variation of the usual normalization approach.

TOPSIS normalization factor

Rather than convert the performance with respect to each criterion to the fraction of the difference between the maximum and minimum performances obtained for that criterion, TOPSIS normalizes each alternative performance with respect to each criterion using the square root of the sum of the squares of the performances achieved by any alternative relative to that criterion. The normalization allows performances with respect to the different criteria to be compared.

Step 3 is to construct the weighted normalized decision matrix. Assume we have a set of weights for each criteria wj for j = 1,…N. Multiply each column of the normalized decision matrix by its associated weight. An element of the new matrix is: vij = wj × rij

TOPSIS weighted normalization matrix

Step 4 is to determine the positive ideal and negative ideal solutions. The positive ideal solution is denoted

TOPSIS positive ideal alternative

where v1+ is the maximum normalized score achieved by any alternative for the first criterion (the maximum value in the first column of the normalized decision matrix), v2+ is the maximum value achieved by any alternative for the second criterion, and so forth. The negative ideal solution,

TOPSIS negative ideal alternative

where v1- is the minimum normalized score achieved by any alternative for the first criterion, v2- is the minimum value achieved by any alternative for the second criterion, and so forth.

Step 5 is to calculate the separation distances of each alternative from the positive ideal and negative ideal alternatives. The distances for the i'th alternative are computed using a distance concept referred to as Euclidian:

TOPSIS seperation

Step 6 is to measure the relative closeness of each location to the positive and negative ideal alternatives, which is computed as:

TOPSIS closeness

As shown, the measure of relative closeness is a normalized score defined on the interval between the distance to the positive ideal alternative and the distance to the negative ideal alternative.

Step 7 is to rank the alternatives using the relative closeness score, the higher the value of the relative closeness, the higher the ranking.

The attractiveness of TOPSIS comes from its simplicity and its ability to maintain the same steps regardless of problem size. However, its use of just two reference points can create problems, especially for problems for which the performance measures are non-linear problems.

tornado diagram

A type of chart used to display the results of a sensitivity analysis. It is bar chart showing the sensitivity of a model output to each of several model inputs or parameters. A tornado diagram, also called a tornado chart, supports understanding by displaying the "drivers" of a quantity of interest.

The figure below provides an example. In this case, the quantity of interest is the value of a proposed project. To construct the diagram, each of several inputs to the project decision model is individually varied over some range (e.g., its range of uncertainty). The corresponding range over which the output then varies is displayed as a horizontal bar. The bars are sorted by the length of the bar and stacked vertically, with the result that the shape of the diagram resembles that of a tornado.

Sample tornado diagram chart

A sample tornado diagram

By identifying variables that result in the widest swings, a tornado diagram helps identify specific areas where effort should be spent to reduce uncertainty or to improve performance. Many decision analysis tools, including some tools for project and project portfolio management, provide capability to generate tornado diagrams.

total cost of ownership (TCO)

All of the costs associated with a project, including those associated with deploying, managing, and ultimately disposing of any assets produced by that project. For example, the total cost of ownership of a car is not just the purchase price, but also expenses incurred through its lifetime of use, such as repairs, insurance, and fuel. Sometimes, TCO is expressed as an average annual cost figure.

TCO is a useful management tool for uncovering what might otherwise be overlooked costs. It's major disadvantage from the perspective of project prioritization is that it fails to address project benefits.

total shareholder return (TSR)

A measure of the growth in value that an organization creates for its shareholders. TSR combines the price appreciation of company stock with the dividends paid. Maximizing TSR is a primary objective for many companies, and project portfolio management (PPM) is often argued to be an important means for increasing TSR. The perspective calls for ppm tools and processes that quantify the contribution of project portfolios to shareholder value through consideration of the impacts of projects on market expectations of the company's ability to generate, sustain, and grow future cash flows.


The process of giving up or exchanging one benefit in order to obtain another. Tradeoffs (also called value tradeoffs) are required in decision situations whenever there are multiple objectives and not all can be achieved together. A decision maker's preferences regarding tradeoffs are a key input to project prioritization, as projects are typically proposed to achieve different objectives or achieve different objectives to different degrees. Tradeoff preferences are typically expressed in a decision model via weights. The swing-weight method is one technique for assessing willingness to make tradeoffs.