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Accepted for publication at

PMI Global Congress 2010 – North America
Washington – DC – EUA – 2010

Russian Project Management Conference
(Русская конференция Управление проектами)
Moscow – Russia – 2010

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Abstract

The objective of this paper is to present, discuss and apply the principles and techniques of the Analytic Hierarchy Process (AHP) in the prioritization and selection of projects in a portfolio. AHP is one of the main mathematical models currently available to support the decision theory.

When looking into how organizations decide over which projects to execute, we can notice a constant desire to have clear, objective and mathematical criteria (HAAS & MEIXNER, 2005). However, decision making is, in its totality, a cognitive and mental process derived from the most possible adequate selection based on tangible and intangible criteria (SAATY, 2009), which are arbitrarily chosen by those who make the decisions.

This paper also discusses the importance and some possible criteria for prioritizing projects, and by using a fictitious project prioritization example, it demonstrates AHP in a step-by-step manner, where the resulting priorities are shown and the possible inconsistencies are determined.

The importance of project selection and prioritization

One of the main challenges that organizations face today resides in their ability to choose the most correct and consistent alternatives in such a way that strategic alignment is maintained. Given any specific situation, making the right decisions is probably one of the most difficult challenges for science and technology (TRIANTAPHYLLOU, 2002).

When we consider the ever changing dynamics of the current environment like we have never seen before, making the right choices based on adequate and aligned objectives constitutes a critical factor, even for organizational survival.

Basically the prioritization of projects in a portfolio is nothing more than an ordering scheme based on a benefit cost relationship of each project. Projects with higher benefits, when compared to their costs, will have a higher priority. It’s important to observe that a benefit cost relationship does not necessarily mean the use of exclusive financial criteria like the widely known benefit cost ratio, but instead a broader concept of the reaped benefits from executing the project and their related efforts.

Since organizations belong to a complex and varying context, often times even chaotic, the challenge of the aforementioned definition resides exactly in determining what are costs and benefits to any given organization.

Possible Definitions for Low Costs

Possible Definitions for High Benefits

Cheaper

More profitable

Less resource needs

Greater return of investment

Easier to be executed

Increase in the number of customers

Less complex

Increase in competitiveness

Less internal resistance

Improvements for the society

Less bureaucratic

Increase in Market Share

Less risks (threats)

Executives and shareholders happier

When analyzing the above table, one can observe that the different dimensions demonstrate how complex it is to come up with an exact translation for the meaning of low cost and high benefits. That is the reason why a unique criterion or translation is not viable enough to determine which project(s) should or should not be executed. Thus it is necessary to employ a multi-criteria analysis (TRIANTAPHYLLOU, 2002) which allows for decisions while taking into consideration the different dimensions and organizational needs altogether.

PMI’s Standard for Portfolio Management (PMI, 2008) says that the scope of a project portfolio must stem from the strategic objectives of the organization. These objectives must be aligned with the business scenario which in turn may be different for each organization. Consequently, there is no perfect model that covers the right criteria to be used for any type of organization when prioritizing and selecting its projects. The criteria to be used by the organization should be based on the values and preferences of its decision makers.

Current criteria used in the prioritization of projects

Although decisions are based on values and preferences of the decision makers, a set of criteria or specific objectives can be used while prioritizing projects and determining the real meaning of an optimal relationship between benefits and costs.

The main criteria groups are:

Financial – A group of criteria with the objective of capturing the financial benefits of projects. They are directly associated with costs, productivity and profit measures. A few examples are:

  • Return on Investment (ROI) – It is the percentage of the profit margin of the project. It allows comparing the financial return of projects with different investments and profits.
  • Profit (currency) – The value (in currency) of the financial profit gained by the project. A project may have a smaller ROI but its nominal profit can be bigger.
  • Net Present Value (NPV) – It is the difference between the project benefits and costs taking into consideration that all incomes and expenses are converted to be realized in the current date. In order to do so, it is necessary to bring all future values to the current date by using a given interest rate. That allows the assessment and comparison between projects which have future incomes and expenses from different time periods.
  • Payback – It is the number of time in periods necessary to recover all of the original project investments.
  • Financial Benefit / Cost Rate – It is the ratio between the present value of the benefits and the present value of the costs. The higher the ratio, the more viable is the project under the perspective of benefit/costs.

Strategic – A group of criteria directly associated with the strategic objectives of the organization. The strategic criteria/objectives are determined by methods used to cascade corporate strategy like the Balanced Scorecard. They differ from the financial criteria because strategic criteria are specific for any organization. Organizations with different strategies will certainly have different prioritization criteria. Some examples may be to increase the capacity to compete in international markets, to use eco-friendly practices, to optimize internal processes, to cut expenses in comparison with benchmarking competitors, to improve the reputation of products and services, etc.

Risks (Threats) – It determines the level of risk tolerance that an organization accepts to execute a project. The threat-based risk assessment criteria can also incorporate the assessment of opportunities (HILSON, 2003). However, often times the assessment of opportunities that a project can yield are already covered and taken care of by the strategic criteria. Another equally possible perspective for this criterion entangles the organizational risk of not undertaking the project.

Urgency – It determines the urgency level of the project. Projects considered to be urgent require immediate decision and action, and so they have a higher priority than projects that are not urgent.

Stakeholder commitment – A group of criteria that aims to assess the level of stakeholder commitment towards the project. The higher the commitment to the project, the higher priority the project receives. Commitment may be assessed in a broad manner where all stakeholders are considered as a unique group, or it can be decomposed into different stakeholder groups, like for example:

  • Customer commitment
  • Community commitment
  • Organizational commitment
  • Regulatory bodies
  • Project team commitment
  • Project manager commitment

Technical Knowledge – It assesses the technical knowledge necessary to execute the project. The more technical knowledge readily available, the easier will it be to execute any given project and, consequently, it will cause the project to use fewer resources. It is important to note that, if it is necessary to establish criteria or objectives related to the learning and growth process, these criteria need to be associated with the organization’s strategic criteria, and not with any technical knowledge.

Analytic Hierarchy Process

The multi-criteria programming made through the use of the Analytic Hierarchy Process is a technique for decision making in complex environments where many variables or criteria are considered in the prioritization and selection of alternatives or projects.

AHP was developed in the 70’s by Thomas L. Saaty and has been since then extensively studied, being currently used in decision making for complex scenarios, where people work together to make decisions when human perceptions, judgments and consequences have a long term repercussion (BHUSHAN & RAI, 2004).

The application of AHP begins with a problem being decomposed into a hierarchy of criteria so as to be more easily analyzed and compared in an independent manner (Figure 1). After this logical hierarchy is constructed, the decision makers can systematically assess the alternatives by making pair-wise comparisons for each of the chosen criteria. This comparison may use concrete data from the alternatives or human judgments as a way to input subjacent information (SAATY, 2008).

3104.pngFigure 1 – Example of a hierarchy of criteria/objectives

AHP transforms the comparisons, which are most of the times empirical, into numeric values that are further processed and compared. The weight of each factor allows the assessment of each one of the elements inside the defined hierarchy. This capability of converting empirical data into mathematical models is the main distinctive contribution of the AHP technique when contrasted to other comparing techniques.

After all comparisons have been made, and the relative weights between each one of the criteria to be evaluated have been established, the numerical probability of each alternative is calculated. This probability determines the likelihood that the alternative has to fulfill the expected goal. The higher the probability, the better chances the alternative has to satisfy the final goal of the portfolio.

The mathematical calculation involved in the AHP process may at first seem simple, but when dealing with more complex cases, the analyses and calculations become deeper and more exhaustive.

The comparison scale (Saaty scale)

The comparison between two elements using AHP can be done in different ways (TRIANTAPHYLLOU & MANN, 1995). However, the relative importance scale between two alternatives suggested by Saaty (SAATY, 2005) is the most widely used. Attributing values that vary from 1 to 9, the scale determines the relative importance of an alternative when compared to another alternative, as we can see in Table 1.

Scale

Numerical Rating

Reciprocal

Extremely Preferred

9

1/9

Very strong to extremely

8

1/8

Very strongly preferred

7

1/7

Strongly to very strongly

6

1/6

Strongly preferred

5

1/5

Moderately to strongly

4

¼

Moderately preferred

3

1/3

Equally to moderately

2

½

Equally preferred

1

1

It is common to always use odd numbers from the table to make sure there is a reasonable distinction among the measurement points. The use of even numbers should only be adopted if there is a need for negotiation between the evaluators. When a natural consensus cannot be reached, it raises the need to determine a middle point as the negotiated solution (compromise) (SAATY, 1980).

The comparison matrix is constructed from the Saaty scale (Table 2).

Criteria 1

Criteria 2

Criteria 1

1

Numerical Rating

Criteria 2

1/Numerical Rating (Reciprocal)

1

An example of the application of AHP in a portfolio

In order to serve as an example of the AHP calculations for a prioritization of projects, the development of a fictitious decision model for the ACME Organization has been chosen. As the example is further developed, the concepts, terms and approaches to AHP will be discussed and analyzed.

The first step to build the AHP model lies in the determination of the criteria that will be used. As already mentioned, each organization develops and structures its own set of criteria, which in turn must be aligned to the strategic objectives of the organization.

For our fictitious ACME organization, we will assume that a study has been made together with the Finance, Strategy Planning and Project Management areas on the criteria to be used. The following set of 12 (twelve) criteria has been accepted and grouped into 4 (four) categories, as shown on the hierarchy depicted in Figure 2.

image002.pngFigure 2 – Hierarchy of Criteria for the fictitious ACME organization

Determining the comparison matrix, the priority vector (Eigen) and the inconsistency

After the hierarchy has been established, the criteria must be evaluated in pairs so as to determine the relative importance between them and their relative weight to the global goal.

The evaluation begins by determining the relative weight of the initial criteria groups (Figure 3). Table 3 shows the relative weight data between the criteria that have been determined by ACME’s decision makers.

image003.png

Figure 3 – ACME’s initial group of criteria/objectives

Stakeholders C

Financial

Strategic

Other Criteria

Stakeholders C

1

1/5

1/9

1

Financial

5

1

1

5

Strategic

9

1

1

5

Other Criteria

1

1/5

1/5

1

In order to interpret and give relative weights to each criterion, it is necessary to normalize the previous comparison matrix. The normalization is made by dividing each table value by the total the total column value (Table 4).

Stakeholders C

Financial

Strategic

Other Criteria

Stakeholders C

1

1/5

1/9

1

Financial

5

1

1

5

Strategic

9

1

1

5

Other Criteria

1

1/5

1/5

1

Total (Sum)

16.00

2.40

2.31

12.00

Results

Stakeholders C

1/16 = 0.063

0.083

0.048

0.083

Financial

5/16 = 0,313

0.417

0.433

0.417

Strategic

9/16 = 0.563

0.417

0.433

0.417

Other Criteria

1/16 = 0.063

0.083

0.087

0.083

The contribution of each criterion to the organizational goal is determined by calculations made using the priority vector (or Eigenvector). The Eigenvector shows the relative weights between each criterion it is obtained in an approximate manner by calculating the arithmetic average of all criteria, as depicted on Exhibit 10. We can observe that the sum of all values from the vector is always equal to one (1).

The exact calculation of the Eigenvector is determined only on specific cases. This approximation is applied most of the times in order to simplify the calculation process, since the difference between the exact value and the approximate value is less than 10% (KOSTLAN, 1991).

Eigenvector (Calculation)

Eigenvector

Stakeholders C

[0.063+0.083+0.048+0.083]/4 =0.0693

0.0693 (6,93%)

Financial

[0.313+0.417+0.433+0.417]/4 =0.3946

0.3946 (39,46%)

Strategic

[0.563+0.417+0.433+0.417]/4 =0.4571

0.4571 (45,71%)

Other Criteria

[0.063+0.083+0.087+0.083]/4 = 0.0789

0.0789 (7,89%)

For comparison purposes, a mathematical software application has been used to calculate the exact value for the Eigenvector through the use of potential matrices. The results are shown on Table 6.

Approximate Eigen Vector

Exact Eigen Vector

Difference (%)

Stakeholders C

0.0693 (6,93%)

0.0684 (6,84%)

0,0009 (1,32%)

Financial

0.3946 (39,46%)

0.3927 (39,27%)

0,0019 (0,48%)

Strategic

0.4571 (45,71%)

0.4604 (46,04%)

0,0033 (0,72%)

Other Criteria

0.0789 (7,89%)

0.0785 (7,85%)

0,0004 (0,51%)

It can be observed that the approximate and exact values are very close to each other, so the calculation of the exact vector requires a mathematical effort that can be exempted (KOSTLAN, 1991).

The values found in the Eigenvector have a direct physical meaning in AHP. They determine the participation or weight of that criterion relative to the total result of the goal. For example, in our ACME organization, the strategic criteria have a weight of 46.04% (exact calculation of the Eigenvector) relative to the total goal. A positive evaluation on this factor contributes approximately 7 (seven) times more than a positive evaluation on the Stakeholder Commitment criterion (weight 6.84%).

The next step is to look for any data inconsistencies. The objective is to capture enough information to determine whether the decision makers have been consistent in their choices (TEKNOMO, 2006). For example, if the decision makers affirm that the strategic criteria are more important than the financial criteria and that the financial criteria are more important than the stakeholder commitment criteria, it would be inconsistent to affirm that the stakeholder commitment criteria are more important than the strategic criteria (if A>B and B>C it would be inconsistent to say that A<C).

The inconsistency index is based on Maximum Eigenvalue, which is calculated by summing the product of each element in the Eigenvector (Table 5) by the respective column total of the original comparison matrix (Table 4). Table 7 demonstrates the calculation of Maximum Eigenvalue (λMax)1

1 The Eigenvector values used from this moment on will be based on the exact values, and not on the approximate values, because the exact values have been calculated and are thus available.

.

Eigenvector

0.0684

0.3927

0.4604

0.0785

Total (Sum)

16.00

2.40

2.31

12.00

Maximum
Eigenvalue (
λMax)

[(0.0684 x 16.00)+(0.3927 x 2.40)+(0.4604 x 2.31) + (0.0785 x 12.00)] = 4.04

5104.png

Where CI is the Consistency Index and n is the number of evaluated criteria.

For our ACME organization, the Consistency Index (CI) is5079.png

In order to verify whether the Consistency Index (CI) is adequate, Saaty (SAATY, 2005) suggests what has been called Consistency Rate (CR), which is
determined by the ratio between the Consistency Index and the Random Consistency Index (RI). The matrix will be considered consistent if the resulting ratio is less than 10%.

The calculation of the Consistency Index (SAATY, 2005) is given by the following formula

5086.png

The RI value is fixed and is based on the number of evaluated criteria, as shown on Table 8.

N

1

2

3

4

5

6

7

8

9

10

RI

0

0

0.58

0.9

1.12

1.24

1.32

1.41

1.45

1.49

For our ACME organization, the Consistency Rate for the initial criteria group is

5091.png

Since its value is less than 10%, the matrix can be considered to be consistent. The priority criteria results for the first level can be seen in Figure 4.

image010.pngFigure 4 – Results of the Comparison Matrix for ACME’s Criteria Group, demonstrating the contribution of each criterion to the goal defined for the organization

By looking at Figure 4 and the Eigenvector values, it is evident that the Strategic Criteria have a contribution of 46.04% to the goal, whereas the Stakeholder Commitment criteria contributes with 6.84% to the goal.

Other calculations involving the chosen criteria

Just like it was done with the initial criteria group for the ACME organization, it is necessary to evaluate the criteria’s relative weights for the second level of the hierarchy (Figure 5). This process is executed just like the step to evaluate the first level of the hierarchy (Criteria Group) as it was shown above.

image012.pngFigure 5 – Hierarchy of criteria for the fictitious ACME organization highlighting the second hierarchy level

The following tables (16 to 19) show the comparison matrices for the criteria with the pair-wise comparisons already taken by the decision makers.

Stakeholders Commitment Criteria

Team Commitment

Organizational Commitment

Project Manager Commitment

Team Commitment

1

3

1/5

Organizational Commitment

1/3

1

1/9

Project Manager Commitment

5

9

1

Financial Criteria

Return of Investment

Profit (US$)

Net Present Value

Return of Investment

1

1/5

1/5

Profit (US$)

5

1

1

Net Present Value

5

1

1

Strategic Criteria

Compete in International Markets

Internal Processes

Reputation

Compete in Intern. Markets

1

7

3

Internal Processes

1/7

1

1/5

Reputation

1/3

5

1

Other Criteria

Lower Risks for the Organization

Urgency

Internal Technical Knowledge

Lower Risks for the Organization

1

5

1/3

Urgency

1/5

1

1/7

Internal Technical Knowledge

3

7

1

The following charts (Figure 20 to 23) demonstrate the priority results for the sub-criteria for each one of the criteria groups2

2 The data have been simulated and calculated using ExpertChoice 11.5 for Windows, available at
www.expertchoice.com

and their respective inconsistency indices. We can observe that none of the criterion demonstrates any inconsistency above tolerable limits.

image014.pngFigure 6 – Priority results for the Stakeholder Commitment Criteria

image016.pngFigure 7 – Priority results for the Financial Criteria

image018.pngFigure 8 – Priority results for the Strategic Criteria

image020.pngFigure 9 – Priority results for the Other Criteria

The global priority for each criterion is determined by the result of the multiplication of each priority on the first level by its respective priority on the second level. The results are shown on the hierarchy depicted on Figure 10. We can also see that the sum of the weights of all twelve (12) factors is equal to 1.

image022.pngFigure 10 – Hierarchy of criteria for the fictitious ACME organization with global priorities for each criterion

Evaluating candidate projects for the portfolio

After having structured the tree and established the priority criteria, it is now possible to determine how each one of the candidate projects fits the chosen criteria. In the same manner that the criteria prioritization has been made, the candidate projects are pair-wisely compared considering every established criteria.

For our ACME organization, six (6) different projects have been identified and must then be prioritized. The fictitious projects are:

  • Move to a new office facility
  • New ERP system
  • Opening of an office in China
  • Development of a new Product aiming at the International Market
  • IT infrastructure Outsourcing
  • New local Marketing Campaign
  • In order to apply AHP, the decision makers from ACME organization have compared six (6) projects taking into consideration every one of the twelve (12) established criteria. The results are shown in the following twelve (12) tables.

Team Commitment

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

5

3

1/3

9

7

ERP Implementation

1/5

1

1/5

1/7

1

1/3

Chinese Office

1/3

5

1

1/3

7

3

International Product

3

7

3

1

5

5

IT Outsourcing

1/9

1

1/7

1/5

1

1/3

New Local Campaign

1/7

3

1/3

1/5

3

1

Organizational Commitment

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

3

1/9

1/5

5

3

ERP Implementation

1/3

1

1/9

1/7

1

1/3

Chinese Office

9

9

1

3

7

7

International Product

5

7

1/3

1

9

7

IT Outsourcing

1/5

1

1/7

1/9

1

1/3

New Local Campaign

1/3

3

1/7

1/7

3

1

Project Manager Commitment

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

7

1/3

1/3

5

3

ERP Implementation

1/7

1

1/9

1/7

3

1/3

Chinese Office

3

9

1

1

7

7

International Product

3

7

1

1

7

9

IT Outsourcing

1/5

1/3

1/7

1/7

1

1/5

New Local Campaign

1/3

3

1/7

1/9

5

1

Return on Investment

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

1/3

1/7

1/9

1/3

1/3

ERP Implementation

3

1

1/9

1/9

1/3

1/3

Chinese Office

7

9

1

1/3

7

5

International Product

9

9

3

1

7

5

IT Outsourcing

3

3

1/7

1/7

1

1/3

New Local Campaign

3

3

1/5

1/5

3

1

Profit (US$)

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

1

1/7

1/9

1/5

1/3

ERP Implementation

1

1

1/7

1/9

1/3

1/5

Chinese Office

7

7

1

1/3

7

5

International Product

9

9

3

1

9

5

IT Outsourcing

5

3

1/7

1/9

1

1/3

New Local Campaign

3

5

1/5

1/5

3

1

Net Present Value

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

1/3

1/5

1/7

1/3

1/3

ERP Implementation

3

1

1/5

1/7

1

1/3

Chinese Office

5

5

1

1/3

5

3

International Product

7

7

3

1

5

7

IT Outsourcing

3

1

1/5

1/5

1

1/3

New Local Campaign

3

3

1/3

1/7

3

1

Improves Ability to Compete in International Markets

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

3

1/9

1/7

5

5

ERP Implementation

1/3

1

1/9

1/9

1/3

3

Chinese Office

9

9

1

1

9

9

International Product

7

9

1

1

9

9

IT Outsourcing

1/5

3

1/9

1/9

1

3

New Local Campaign

1/5

1/3

1/9

1/9

1/3

1

Improves Internal Processes

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

1/5

3

5

1

7

ERP Implementation

5

1

7

7

1

7

Chinese Office

1/3

1/7

1

1

1/7

1

International Product

1/5

1/7

1

1

1/7

1/3

IT Outsourcing

1

1

7

7

1

7

New Local Campaign

1/7

1/7

1

3

1/7

1

Improves Reputation

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

1/3

1/7

1/5

3

1/7

ERP Implementation

3

1

1/9

1/5

5

1/7

Chinese Office

7

9

1

3

7

1

International Product

5

5

1/3

1

7

1/3

IT Outsourcing

1/3

1/5

1/7

1/7

1

1/9

New Local Campaign

7

7

1

3

9

1

Lower Risks (Threats) for the Organization

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

5

7

3

5

1

ERP Implementation

1/5

1

5

3

3

1/7

Chinese Office

1/7

1/5

1

1/3

1/3

1/9

International Product

1/3

1/3

3

1

5

1/7

IT Outsourcing

1/5

1/3

3

1/5

1

1/9

New Local Campaign

1

7

9

7

9

1

Urgency

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

1/3

1/5

1/7

3

1

ERP Implementation

3

1

1/7

1/9

3

3

Chinese Office

5

7

1

1/3

5

7

International Product

7

9

3

1

7

7

IT Outsourcing

1/3

1/3

1/5

1/7

1

1/3

New Local Campaign

1

1/3

1/7

1/7

3

1

Internal Technical Knowledge

New Office

ERP Implem.

Chinese Office

Intern. Product

IT Outsourc.

Local Campaign

New Office

1

9

9

9

9

3

ERP Implementation

1/9

1

1/3

1/3

1/5

1/9

Chinese Office

1/9

3

1

3

1

1/9

International Product

1/9

3

1/3

1

1/3

1/9

IT Outsourcing

1/9

5

1

3

1

1/9

New Local Campaign

1/3

9

9

9

9

1

After calculating all priorities and inconsistency indices, it is possible to determine the relative weight of each project for each criterion, as we can see in the following twelve (12) charts (one chart for each criterion).

image024.pngFigure 11 – Priority results for the projects according to the Team Commitment Criterion

image026.pngFigure 12 – Priority results for the projects according to the Organization Commitment Criterion

image028.pngFigure 13 – Priority results for the projects according to the Project Manager Commitment Criterion

image030.pngFigure 14 – Priority results for the projects according to the Return On Investment Criterion

image032.pngFigure 15 – Priority results for the projects according to the Profit (US$) Criterion

image034.pngFigure 16 – Priority results for the projects according to the Net Present Value Criterion

image036.pngFigure 17 – Priority results for the projects according to the Ability to compete in International Markets Criterion

image038.pngFigure 18 – Priority results for the projects according to the Improves Internal Processes Criterion

image040.pngFigure 19 –Priority results for the projects according to the Improves Reputation Criterion

image042.pngFigure 20 – Priority results for the projects according to the Lower Organizational Risks (Threats) Criterion

image044.pngFigure 21 – Priority results for the projects according to the Urgency Criterion

image046.pngFigure 22 – Priority results for the projects according to the Internal Technical Knowledge Criterion

The crossing product of all project evaluations using all criteria determines the final priority for each project in relation to the desired goal.

The mechanism for calculating the final priority is to sum the products of the multiplication of each criterion’s priority weight by its alternative weight.

In order to exemplify this process, Table 25 shows the calculation process for the alternative “Move to a New Office”

Criteria

Priority Weight

Alternative Weight

Product

Team Commitment

0,0122

0,2968

0,0036

Organizational Commitment

0,0048

0,0993

0,0005

Project Manager Commitment

0,0514

0,1586

0,0082

Return on Investment (ROI)

0,0357

0,0296

0,0011

Profit (US$)

0,1785

0,0315

0,0056

Net Present Value

0,1785

0,0366

0,0065

Improves Ability to Compete in International Markets

0,2988

0,1033

0,0309

Improves Internal Processes

0,0331

0,1903

0,0063

Improves Reputation

0,1284

0,0421

0,0054

Lower Risks (Threats) for the Organization

0,0219

0,2994

0,0066

Urgency

0,0056

0,0553

0,0003

Internal Technical Knowledge

0,0510

0,4796

0,0243

Results

0,0992

The same process should be repeated for the other five (5) projects. The final results for all projects are shown in Figure 23.

image048.pngFigure 23 – Final priority results for the for ACME’s portfolio of projects

Figure 23 shows that the project with the highest level of adherence to the defined goal is “Development of a New Product for the International Market”. It contributes with 34.39% (0.3439). In order to better illustrate the importance of the difference between the weights and priorities of each project, this project contributes with about three (3) times more to the goal than the New Local Marketing Campaign project, which contributes with only 13.1% (0.131) to the global goal.

Conclusion

AHP has been attracting the interest of many researchers mainly due to the mathematical features of the method and the fact that data entry is fairly simple to be produced (TRIANTAPHYLLOU & MANN, 1995). Its simplicity is characterized by the pair-wise comparison of the alternatives according to specific criteria (VARGAS, 1990).

Its application to select projects for the portfolio allows the decision makers to have a specific and mathematical decision support tool. This tool not only supports and qualifies the decisions, but also enables the decision makers to justify their choices, as well as simulate possible results.

The use of AHP also presumes the utilization of a software application tailored specifically to perform the mathematical calculations. In this paper, the intention has been to show the main calculations performed during the analysis, enabling project managers to have an adequate understanding of the technique, as well as the complexity involved to make the calculations by hand (in case software applications can’t be used).

Another important aspect is the quality of the evaluations made by the decision makers (COYLE, 2004). For a decision to be the most adequate possible, it must be consistent and coherent with organizational results. We saw that the coherence of the results can be calculated by the inconsistency index. However, the inconsistency index allows only the evaluation of the consistency and regularity of the opinions from the decision makers, and not whether these opinions are the most adequate for a specific organizational context.

Finally, it is important to emphasize that decision making presumes a broader and more complex understanding of the context than the use of any specific technique. It predicates that a decision about a portfolio is a fruit of negotiation, human aspects and strategic analysis, where methods like AHP favor and guide the execution of the work, but they cannot and must not be used as a universal criteria.

References

BHUSHAN, N. & RAI, K. (2004). Strategic Decision Making: Applying the Analytic Hierarchy Process. New York: Springer.

COYLE, G. (2004). The Analytic Hierarchy Process. New York: Pearson Educational.

HAAS, R. & MEIXNER, O. (2005). An Illustrated Guide To Analytic Hierarchy Process. Vienna: University of Natural Resources and Applied Life Sciences.

KOSTLAN, E. (1991). Statistical Complexity of Dominant Eigenvector Calculation. Hawaii: Journal of Complexity Volume 7, Issue 4, December 1991, Pages 371-379. Available at http://www.developmentserver.com/randompolynomials/scdec/paper.pdf

HILLSON, D. (2002). Use a Risk Breakdown Structure (RBS) to Understand Your Risks. San Antonio: PMI Global Congress and Symposium.

PMI (2008). The Standard for Portfolio Management: Second Edition. Newtown Square: Project Management Institute.

SAATY, T. L (1980). The Analytic Hierarchy Process. New York: McGraw-Hill International.

SAATY, T. L. (2005). Theory and Applications of the Analytic Network Process: Decision Making with Benefits, Opportunities, Costs, and Risks. Pittsburgh: RWS Publications.

SAATY, T. L. (2008). Relative Measurement and its Generalization in Decision Making: Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors – The Analytic Hierarchy/Network Process. Madrid: Review of the Royal Spanish Academy of Sciences, Series A, Mathematics. Available at http://www.rac.es/ficheros/doc/00576.PDF

SAATY, T. L. (2009). Extending the Measurement of Tangibles to Intangibles. International Journal of Information Technology & Decision Making, Vol. 8, No. 1, pp. 7-27, 2009. Available at SSRN: http://ssrn.com/abstract=1483438

TEKNOMO, K. (2006). Analytic Hierarchy Process (AHP) Tutorial. Available at http://people.revoledu.com/kardi/tutorial/ahp/

TRIANTAPHYLLOU, E. & MANN S. H. (1995). Using The Analytic Hierarchy Process For Decision Making in Engineering Applications: Some Challenges. International Journal of Industrial Engineering: Applications and Practice, Vol. 2, No. 1, pp. 35-44, 1995. Available at http://www.csc.lsu.edu/trianta/Journal_PAPERS1/AHPapls1.pdf

TRIANTAPHYLLOU, E. (2002). Multi-Criteria Decision Making Methods: A comparative Study. New York: Springer.

VARGAS, L.G. (1990). An Overview of the Analytic Hierarchy Process and its Applications. European Journal of Operational Research, 48, 2-8.

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  1. Nice article Ricardo! You’ve done a great job of demonstrating the efficacy of the AHP methodology, and the use of the Expert Choice software. You may wish to consider the use of optimization after the projects are prioritized, to determine the best mix of alternatives that will create the best bang for the buck in the portfolio. It would also allow you to model constraints such as FTEs (full time equivalencies), risks, dependencies, and other constraints.

  2. ibrahim says:

    Very systematic and clear approach for priorization ,founded very useful.Any advice to road the best practice into Select and Prioritize Projects!

  3. Fine work.
    I have however an question regarding the financial criteria. You seem to treat them as “independent” criteria, or at least as “good to have them all”. Assuming the banking system works, there is a lot of “overlapping” here. What extra information does one gain by the NPV if one has the RoI and the initial investment? Or, if one has the B/C ratio? Again, assuming the banking system works as it is supposed to.
    Moreover, when the initially required investment sums are grossly different for different alternatives(e.g. 1000 and 600), then, accepting the 1000 as an alternative essentially says that you do have 1000 available (or at least you can borrow that sum). Thus, there is really no 600 alternative by itself. What you have is a combination of 600 invested in the corresponding project and 400 left where they are or invested elsewhere (the a priori opportunity cost being a measure of its “profitability”).

    All this, iff the banking system works. If it doesn’t, the whole financial analysis breaks down.

  4. […] Using the Analytic Hierarchy Process (AHP) to Select and Prioritize Projects in a Portfolio […]

  5. I’m stack how to compare criterias which contain financial value, let say capital invesment, management fee, royalti fee, roi and bep.

    I assumme people more preferrable with the high benefit with low cost
    If compare about roi and bep with other criterias, people will choose high value, let say 9
    then if compare about capital invesment, management fee, royalti fee with other criterias, people will choose repriocial, let say 1/9

    If people do comparation like that, is that Consistent ?

    Your reply very helpfull

  6. Ricardo Toloimei Costa says:

    Boa tarde, Ricardo!

    Trabalho na Suzano Papel e Celulose em Sao Paulo,como Gerente PMO Corporativo na área de Estratégia e Novos Negócios.
    Toda minha formação foi sempre estudando processos, métodos e ferramentas para selecionar e priorizar os melhores projetos e procurar alinhar os objetivos estratégicos com a carteira de projetos , entre eles o método AHP foi bastante estudado por mim. Ao ler seu artigo sobre este método percebi que no momento de realizar a comparacao par a par entre os critérios você realiza inicialmente a comparação entre as \”dimensões\” (dedicação da direção, financeiro, estratégicos e outros critérios), depois você realiza a comparação entre critérios par a par de cada dimensão. Por fim, voce compara os projetos par a par por critério. Tive uma dúvida e gostaria que você me posicionasse se tem diferença eu realizar a comparação par a par entre todos critérios. Isto me resultaria em apenas 1 matriz de comparação par a par para os critérios.
    Inicialmente, identifico algumas vantagens e desvantafens:

    Vantagem:
    – 1 única matriz de comparação;
    – Resultado das dimensões seria o somatório dos % dos critérios;
    – Comparação mais detalhada;

    Desvantagem:
    – Mais dificil para fazer os julgamentos
    – Leva mais tempo

    O ponto levantei questões muito mais qualitativas do que quantitativas. Você conseguiria identificar se existe erro no método em fazer da maneira que falei?

    Usando o exemplo do seu artigo criaria uma matriz com os critérios:
    – Team Commitment
    – Organizational Commitment
    – project manager Commitment
    – ROI
    – Profit
    – NPV
    – Improves ability to compete
    – Improves internal process
    – Improves reputation
    – Lower risks
    – Urgency
    – Internal technical Knowledge

    E realizaria a comparacao par a par entre eles.

    • Ei Ricardo

      Legal demais sua pergunta e suas colocações.

      Não existe tecnicamente um impeditivo entre comparar os 12 critérios 2 a 2 não. No entanto o objetivo de comparar a importância das dimensões primeiro facilita o processo do AHP e também dá uma capacidade de julgamento melhor entre os fatores. Eu lembro que nesse caso do paper usamos um conjunto super simples. Podemos ter um conjunto com 5 dimensões e 10 critérios em cada um. Ao usar a dimensão inicialmente teremos a comparação de 5 (2 a 2)e 5 comparações de 10 (2 a 2). Se não fizermos isso teremos uma comparação 50 x 50 o que seria do ponto de vista de trabalho um esforço praticamente inviável.

      Uma outra coisa que precisa ser avaliada é que esse é um trabalho em equipe. Muitas vezes as dimensões facilitam violentamente o entendimento do grupo e a condução da sessão. Por isso acaba sendo uma melhor prática. Atualmente praticamente todos os programas de AHP colocam essas dimensões como melhores práticas.

      Espero ter ajudado no seu entendimento. Muito sucesso e obrigado pelo retorno.

    • Célio Caruso Gomes says:

      Ricardo Toloimei Costa

      Sou aluno do Instituto Tecnológico de Aeronáutica e na minha especialização concluída há pouco, em gerenciamento de projetos, foquei em métodos para seleção e priorização de projetos, com ênfase no método AHP.

      Gostaria de complementar a ótima resposta dada pelo Ricardo Vargas, com mais alguns detalhes.

      O método AHP (Analytic Hierarchy Process), como o nome já diz, pressupõe a estruturação do problema de forma hierárquica. Essa estruturação permite entre outras:
      – maior e melhor visibilidade do problema em questão;
      – a comparação de critérios de mesma natureza – critérios financeiros entre si, critérios de risco entre si, etc.
      – permite reduzir a quantidade de comparações em cada matriz – essa redução é particularmente importante, pois existem estudos que demonstram que o cérebro humano tem dificuldade de realizar comparações de uma quantidade grande de critérios ou itens, sendo que o próprio Saaty recomenda a quantidade de 7 + ou – 2 comparações (o principal artigo que fala sobre isso é “The Magic 7 Plus or Minus 2″ de George A. Mille, 1956).

      Ou seja, caso se tenha mais de 9 comparações, Saaty recomenda que esses sejam separados abaixo de subcritérios, para que se reduzam as comparações até a quantidade de 7 +-2.

      Ao estruturar seu problema na forma hierárquica, você compara os critérios principais entre si, cada grupo de subcritério entre si (como realizado pelo Ricardo em seu artigo), nível a nível (no caso de haver mais de um subnível de subcritérios) e então multiplicam-se os valores dos vetores resultantes obtidos pelas matrizes de decisão, pelo critério principal acima, para se obter o vetor final de cada subcritério (nível mais inferir da árvore de decisão).

      O mesmo conceito deve ser lembrado para o caso de o problema apresentar uma quantidade grande de alternativas, nesse caso, de projetos. Deve-se lembrar da regra do 7 +-2 também, e caso sua priorização envolva mais de 9 projetos, deve-se escolher um particular do AHP, o AHP com utilização de Ratings. Esse método faz com que a quantidade de comparações seja consideravelmente reduzida e torna problemas complexo mais simples de serem resolvidos. (você pode eventualmente utilizar AHP com Ratings para problemas com menos de 9 alternativas também).
      Tenho um artigo publicado no anais do XVII SIMPEP que ilustra esse método, apesar de sua aplicação ter sido desenvolvida para um outro problema, é possível ter ideia do método e do tipo de formulação. Caso queira consultá-lo, o título do artigo é “APLICAÇÃO DO MÉTODO AHP COM ABORDAGEM RATINGS PARA A ORDENAÇÃO DAS LOJAS DE UMA REDE DE VAREJO EM FUNÇÃO DO RISCO DE CRÉDITO”.

      Espero ter contribuído um pouco mais, complementando a resposta do Mestre Vargas, e assim tê-lo ajudado com subsídios para que utilize o método da melhor forma possível.

      • Ana Cevigni Guerra says:

        Nao acho seu artigo….
        “APLICAÇÃO DO MÉTODO AHP COM ABORDAGEM RATINGS PARA A ORDENAÇÃO DAS LOJAS DE UMA REDE DE VAREJO EM FUNÇÃO DO RISCO DE CRÉDITO”.

  7. Lucas Luz says:

    Olá seu artigo foi muito instrutivo para mim. Eu estou fazendo o meu Trabalho de Conclusão de Curso, do curso da Administração da UEPB e fiz uma pesquisa. Para analisar os questionários (142) eu achei esse método bastante atrativo. Só que me surgiu uma dúvida: Como eu construo a matriz de decisão com os dados dos questionários?

  8. Lucas Luz says:

    Tenho outra pergunta que esqueci de fazer:
    Como calculo os “exact value for the Eigenvector” (tabela 6)?

    Eu posso calcular o λ_Max pelos “approximate value for the Eigenvector”? Se eu utilizar eles a minha pesquisa fica errada?

    • Ricardo Vargas says:

      Lucas

      O processo é ultra complicado mesmo. Consiste em elevar ao quadrado a matriz até que a diferença entre os números de Eigen seja desprezível. Sugiro fortemente que vc veja o livro do Thomas Saaty de AHP. Ele tem umas 30 páginas só explicando esse processo. Abraços.

      • Ana Cevigni Guerra says:

        O livro que vc recomenda para encontrar os autovetores é:

        Models, Methods, Concepts and Applications of the Analytic
        Hierarchy Process? de 2000 ou

        The Analytic Hierarchy Process, New York: McGraw Hill. International, Translated to Russian, Portuguese, and Chinese, Revised editions, Paperback (1996, 2000),
        Pittsburgh: RWS Publications.

  9. Abel Jiménez says:

    The AHP has demonstrated its application to any kind of problem or decision at hand no matter how complex. That is, the logical structure and math work well.

    Only, the selection of criteria could be improved incorporating Value Science, in which Intrinsic, Extrinsic and Systemic values can be compared with logic fundamentals.
    Axiology and AHP is something I am working on.

  10. Caio Azevedo says:

    Ótimo trabalho, Ricardo.

    Cheguei até aqui depois de ler um artigo sobre a utilização de Data Envelopment Analysis (DEA) para a exata função que teve o Analytic Hierarchy Process (AHC) nesse artigo.

    Acredito que a opção pelo segundo método é muito mais indicado quando a empresa possui noção exata de qual é a sua estratégica (situação comum para empresas de grande porte, que possuem Planejamento Estratégico bem definido). Em contra partida, acredito que para empresas pequenas e sem estratégias previamente definidas de maneira sólida – que provavelmente teriam dificuldade em priorizar suas necessidades comparando-as umas às outras – a opção pelo primeiro método é muito mais indicado, já que usa Programação Linear para determinar os “pesos” dos critérios de seleção de projetos.

    Forte abraço!

  11. João Salgado says:

    Ricardo, boa noite.

    Parabéns pelo artigo, muito didático e ilustrativo.

    Fiquei com três dúvidas sobre o exemplo apresentado e ficarei muito grato se dirimi-las.

    1 – Existe alguma técnica/dinâmica recomendada para realizar a comparação par a par dos critérios e dos projetos levantando os valores das matrizes?

    2 – Na Figura 17 o índice de inconsistência (CI) ficou maior que 10%, neste caso não deveria ter sido realizada uma revisão da avaliação deste critério trazendo o CI para dentro do tolerável?

    3 – Qual foi a função utilizada para chegar no valor da inconsistência global (0,05)?

    Muito obrigado antecipadamente.

    • Oi João

      Comentários rápidos

      1. Existem várias técnicas vc pode usar. Tem um paper legal que discute isso http://rvarg.as/a8

      2. Você está falando da Figura 16 (Net Present Value Criterion), confere. Ela deu 0,11 (11%). Eu decidi manter mesmo com a inconsistência acima de 10% pq era apenas 1% a mais. Eu poderia ter refeito a análise mas achei isso dispensável pq todas as outras estavam consistentes.

      3. A função é CR=CI/RI<0.1 ~ 10% onde RI é fixo e está dado na Tabela 8 (SAATY, 2005).

      Grande abraço

  12. Oi João

    Comentários rápidos

    1. Existem várias técnicas vc pode usar. Tem um paper legal que discute isso http://rvarg.as/a8

    2. Você está falando da Figura 16 (Net Present Value Criterion), confere. Ela deu 0,11 (11%). Eu decidi manter mesmo com a inconsistência acima de 10% pq era apenas 1% a mais. Eu poderia ter refeito a análise mas achei isso dispensável pq todas as outras estavam consistentes.

    3. A função é CR=CI/RI<0.1 ~ 10% onde RI é fixo e está dado na Tabela 8 (SAATY, 2005).

    Grande abraço

  13. Eduardo Rodrigues says:

    Ricardo, boa noite.
    Gostei muito do artigo e estou lendo o livro indicado (Saaty, 1991). Trabalho com avaliações de desempenho de empresas a partir de índices financeiros.
    Já encontrei alguns artigos aplicando a técnica AHP, mas uma dúvida permanece.
    É possível estabelecer, através de alguma medida estatística, os pesos (importância) entre os critérios sem os especialistas? Essa dúvida persiste, pois há muita subjetividade nessas avaliações.
    Um abraço

  14. Eduardo Rodrigues says:

    Oi Ricardo, apenas complementando.
    No seu artigo percebi essa mesma necessidade quando comparou diferentes sub critérios dentro do critério financeiro. Se a analise fosse feita dentro da empresa a avaliação, mesmo que subjetiva, refletiria as intenções do conselho de administração (CA). No meu caso é diferente, pois avalio de “fora”, portanto ao priorizar um indicador financeiro não conheço as intenções de cada CA.

  15. Hélio Costa says:

    Olá Ricardo,
    OK, o AHP prioriza projetos, mas isso forma o melhor portfólio?
    Nem sempre os melhores projetos formam o melhor portfólio, pois apenas a priorização trata os projetos de forma isolada e não analisa a interdependência entre os projetos.
    No meu entender, o melhor portfólio é o que possui a melhor combinação entre os projetos.
    O que você tem a dizer?

    • Ei Hélio

      Muito pertinente sua colocação. No caso de projetos interdependentes eu faço 2 abordagens. A primeira é agrupar os projetos interdependentes em “clusters” e comparar os clusters usando AHP. A segunda é usar uma matriz de interferência onde os projetos candidatos são listados nas linhas e colunas e comparados entre si. Uma interdependência positiva é evidenciada por um + e uma interferência é dada como um -. Ao finalizar o AHP vc verifica essa sinergia ou interferência para apoiar a decisão.

      É importante ressaltar que o AHP apoia o processo mas não pode ser considerado isoladamente sob o risco de apresentar uma visão míope da situação.

      Espero ter esclarecido. Abraços

      Ricardo.

  16. […] 1. Vargas, Ricardo; Utilizando a Programação Multicritério (Analytic Hierarchy Process – AHP) para Selecionar e Priorizar Projetos na Gestão de Portfólio., out. 2010. http://www.ricardo-vargas.com/pt/articles/analytic-hierarchy-process/ […]

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