Mat-2.108 Independent Research Project in Applied Mathematics November 20, 2005

Application of Robust Portfolio Modelling to

the Management of Intellectual Property Rights

Helsinki University of Technology Systems Analysis Laboratory Antti Malava 64705M Department of Engineering Physics and Mathematics

Contents

CONTENTS .....................................................................................................................2

1. INTRODUCTION..........................................................................................................3

2. PATENTS AS INTELLECTUAL PROPERTY...................................................................5

2.1. Background of Patenting ................................................................................5

2.2. Patent Portfolio Valuation Approaches..........................................................6

3. ROBUST PORTFOLIO MODELLING – A THEORETICAL FRAMEWORK......................8

3.1. Representation of Additive Value....................................................................9

3.2. Incomplete Information.................................................................................10

3.3. Additional Constraints ..................................................................................11

3.4. Non-dominated Portfolios.............................................................................11

3.5. Additional Information .................................................................................12

3.6 Robustness......................................................................................................12

4. CASE STUDY ON PATENT PORTFOLIO ....................................................................14

4.1. Problem Statement ........................................................................................14

4.2. Modelling the Problem .................................................................................14

4.3. Experimental Design.....................................................................................15

4.4. Results ...........................................................................................................15

5. DISCUSSION AND CONCLUSIONS .............................................................................18

6. REFERENCES............................................................................................................20

7. APPENDICES.............................................................................................................22

2

1. Introduction

For a company operating in fast-changing, particularly uncertain high-tech market,

systematic management of project portfolio is an important aspect of its strategic

decision-making process. Research and Development (R&D) activities, for example,

represent a typical such environment.

A simple theoretical approach would model the portfolio selection as a single

objective Capital Budgeting Problem that maximises portfolio without violating

resource constraints (e.g. Luenberger 1998). The most used Capital Budgeting

methods include Net Present Value (NPV), Internal Rate of Return (IRR), Discounted

Cash Flow (DCF) and Payback Period (Investopedia, 2005).

In reality, however, this kind of methodology can rarely be applied for several

reasons. Firstly, the value of projects often traces to their performance against several

criteria rather than one (not all of which are necessarily quantitative). Secondly, rather

than considering the portfolio selection as a single objective problem, the company

may have multiple, conflicting and even incommensurate aims (Liesiö et al, 2005)

likewise with their company-wide strategy. Thirdly, and perhaps most importantly, a

standard Capital Budgeting Problem cannot accommodate incomplete information

with regards to criteria weights and criterion-specific performance levels. The

availability of incomplete, uncertain information about project performance against

different criteria, however, is very often a realistic situation – after all, most projects

are novel without reliable historical reference projects to give indication of

performance levels.

Robust Portfolio Modelling (RPM), a recently developed extension of Preference

Programming of the Helsinki University of Technology, takes into account all of the

issues above and provides a flexible framework for mathematical assessment of the

portfolio selection problem. RPM is a decision support framework that makes little

demands on the data and, rather than suggesting a single optimal portfolio, produces a

set of non-dominated (also Pareto-efficient) portfolios and performance measures to

assess the robustness of the portfolio and the proposed projects.

In this paper, RPM methodology is applied to support Intellectual Property Right

(IPR) portfolio management. The study was conducted in co-operation with

Asperation Oy, a joint Research & Development company of Perlos Corporation and

3

Aspocomp Group Oyj1 (Asperation Oy, 2005). Asperation’s innovations concentrate

around audio, optical, radio frequency and other technologies connected to

mechanics, and printed circuit board technology (Perlos Oyj, 2005). Management of

the IPRs related to these innovations are of utmost strategic importance for Asperation

to sustain competitive advantage in future. The purpose of the study is to evaluate the

RPM framework in a real case and to present Asperation a theoretical decision

support tool for patent portfolio optimisation and management. These aims are in line

with Asperations’ larger scope of adapting a more systematic methodology for their

project portfolio management practises.

The rest of this paper is structured as follows. Section 2 Discusses Intellectual

Property Rights background, while Section 3 introduces the theoretical framework of

Robust Portfolio Modelling. In section 4, RPM is applied to the case of IPR portfolio

management. Approach to modelling together with practical issues and results are

discussed. Section 5 draws conclusions from the case study.

1 On September 1st, in the middle of the study, the functions of Asperation were divided between

Aspocomp and Perlos (Perlos Oyj, 2005). The study was continued with Perlos.

4

2. Patents as Intellectual Property

2.1. Background of Patenting

Patents, trade secrets, trademarks and copyrights are all a form of intellectual property

that can be protected. This paper concentrates on patents. Patents are intangible assets,

whose value lies within their right that prohibits others by law to professionally

exploit the underlying invention. Producing, selling, importing or using the patented

method is regarded as professional exploitation (National Board of Patents and

Registration of Finland, 2005). Patents can be granted for inventions that are new,

innovative and industrially practicable. In other words, just an idea cannot be

patented.

Patents and other intellectual property are objects of international co-operation and

corresponding regulation (Ernst & Young, 2000) administered by World Intellectual

Property Organization (WIPO). Patent applications can be filed nationally with the

country’s patent office, or internationally using systems such as Patent Cooperation

Treaty (PCT) or European Patent Convention (EPC). The prohibition law is

applicable within the geographical area it was granted, and it is usually valid for a

maximum of 20 years, subject to yearly payments for keeping the underlying patent

valid.

The statistics show that the number of nation-wide patens granted in Finland has been

decreasing slightly within the last 10 years from about 2400 to about 2100 (National

Board of Patents and Registration of Finland, 2005). At the same time, however, the

number of European patents granted in Finland has increased from zero-level2 to

about 6000. This rapid increase of European and international patents has prompted

companies to find methods to systematically evaluate and manage patent portfolios as

global entities, part of their larger-scope strategies.

The creation, protection and utilisation of intellectual property are recognised as

issues of all stakeholders, including government and industry (Asian Productivity

Organization, 2004), because they directly affect country’s competitiveness in global

markets. Therefore a number of governmental initiatives around the world have been

2 Finland joined the EPC and the EPO in 1996 and is also a member of WIPO.

5

started to not only support the risky process of intellectual property protection, but

also to inform businesses about the importance of systematic management of

intellectual property as part of their strategies. For example, the government of Japan

has established an intellectual property strategic centre that brings together the

government, academia and industry to tackle the problems. Similarly, the Danish

government has addressed the issues of intellectual property in their wider strategy for

improving business development.

2.2. Patent Portfolio Valuation Approaches

The management of tangible assets has a solid basis through many years of research

and the exchange of experience, whereas the management and evaluation of

intangible assets in a strategic way is still not much further than in experimental stage.

Ernst & Young research (2000) revealed, for example, that nine out of ten Danish

companies expected the importance of evaluating the value of their patents and

management of patent portfolio to increase, but only a few could identify actual

methods for doing this. Similarly, although it is estimated that substantially more than

half of the total value of publicly listed US companies arises from intangible assets,

three out of four companies do not assign any value to their intellectual capital (Asian

Productivity Organization, 2004). The core of the problem relates to the difficulties of

valuation, much of which is performed only in connection with purchases, sales,

licensing agreements. The awareness and perceived benefits of IPR are lacking

especially in many small and medium companies that do not see the relevance of IPRs

to their business.

Considering theoretical perspectives, although decision analysis has been widely

accounted for in the literature in connection to different areas of tangible issues such

as healthcare, engineering and project management, very little can be found about

decision analysis methods applied to intangible assets management. Some individual

research contributions exist but there seems to be no clear consensus. The few

mathematical valuation methods used in the field of IPR do come from the field of

decision analysis and relate to evaluating preferences by approximation (such as

PRIME) or through intervals (such as PAIRS) or indirectly by considering

hypothetical alternatives’ value (such as SWING). More quantitative models are some

extensions of Net Present Value or other basic financial methods. Because of the

6

difficulties related to capture uncertainty in mathematical models, subjective methods

of valuation such as Delphi technique, expert opinions and are still widely used and

decisions are often made based on “feeling”.

Patenting institutions have begun to notice the need for companies to develop patent

portfolio management methods. For example, as part of Danish Government’s wider

strategy for improving business development, Danish Patent and Trademark Office

recently addressed this issue by developing a software tool to “identify untapped

business potential” (Nielsen, 2003). The tool, IPscore 2.0, presents a systematic

evaluation – both qualitative and quantitative – in the form of financial forecast

estimating the internal net present value (i.e. not market value) of the evaluated

technology. Input is gathered with questionnaires to ensure comprehensive evaluation

(such as evaluations at various stages during the project lifetime), and output is

provided both numerically and graphically.

To take a new, academically orientated approach to patent portfolio valuation and

management, Robust Portfolio Optimisation is presented and applied in this paper.

7

3. Robust Portfolio Modelling – a Theoretical Framework

Multiple Criteria Optimisation (also referred to as Multiple Objective Optimisation)

has been and continues to be a classical field of study in Operational Research (Liesiö

et al, 2004). Over the years this area has evolved, and recently the focus has been to

provide easily applicable, user-friendly methods that accommodate the use of

incomplete information with regards to required data (Liesiö, 2004). In other words,

the methods seem to be developing more and more useful to real problems rather than

offering a theoretical consideration that may be of little value to decision makers.

Preference Programming is one such an area of Multiple Criteria Optimisation that

accommodates incomplete information about criterion-specific performance levels

and criteria weights in the selection of a single alternative (Liesiö et al, 2005).

Incomplete information is captured by set inclusion meaning that the ‘true’ value of a

particular parameter is contained within a feasible set derived from the decision

maker’s preferences.

Robust Portfolio Modelling (RPM) is an extension of Preference Programming to the

problem of project portfolio selection. In RPM, the total value of each project and the

project portfolio are modelled by an additive value tree analysis as a weighted average

of the criterion-specific scores. Linear inequalities are used to capture incomplete

information about criteria weights and criterion-specific performance levels are

modelled by using score intervals (Liesiö et al, 2005). The use of incomplete

information leads to a recommendation of multiple non-dominated portfolios rather

than one. Non-dominated portfolios have an overall value not less than any other

portfolio for any combination of feasible weights and scores. To offer concrete

decision recommendations, measures for individual project and project portfolio

robustness are employed.

A graphical representation of RPM (figure 1) gathers together the main ideas and the

multi-step process of the model application. The first phase includes a choice of the

criteria against which the potential projects are evaluated. Incomplete information is

first modelled by reasonably wide score intervals and loose weight statements in order

to take clearly into account the uncertainties. Computation of non-dominated

portfolios follows, together with gradual analysis of projects and project portfolios by

robustness measures. Once the so-called borderline projects have been identified, the

8

focus moves on to give additional information, i.e. narrow score intervals and give

more precise weight information with respect to these borderline projects. The final

project selection method is left for the decision maker, but by this phase he or she can

concentrate on analysing the set of remaining borderline projects (i.e. the uncertain

zone), which usually is much smaller in number than the original set of potential

projects. The projects identified as core and exterior project require less attention.

Figure 1. RPM framework. Source: http://www.rpm.tkk.fi/

3.1. Representation of Additive Value

Let { }mxxX ,,1 K= denote a set of m available projects that are evaluated against n criteria. A performance score of project j with regards to I:th attribute (criterion) is

represented by . jiv

In addition, each project j is associated with k:th resource consumption , and the

total amount of resource k is limited by a budget B

jkc

k. The overall value of a project is

the weighted average of its criterion-specific scores, i.e.

9

http://www.rpm.tkk.fi/

( ) ∑=

=n

i

jii

j vwxV1

This represents an additive value model in which the weight wi represents the relative

importance of criterion i. The weights of all n criteria form a weight vector

that can be normalised so that it belongs to a set ],,[ 1 nwww K=

⎭⎬⎫

⎩⎨⎧

≥=∈=∈ ∑=

0,1|1

0i

n

ii

nw wwRwSw

that is, weight information is modelled by linear constraints.

3.2. Incomplete Information

One of the most difficult issues of applying mathematical models to support decision-

making is that many of them require complete information in the sense of fixed values

of weights and scores. However, this kind of data is not often available, nor is it

reasonable to always assume that such point estimates are accurate. For example, it is

quite impossible to give a zero-variance point estimate for a completely new project

that has not been started yet. A key feature of RPM methodology is to allow for

incomplete information with regards to weights of the criteria and the criterion-

specific scores of each project.

Incomplete weight information is modelled as a feasible (and convex) weight set

described by linear constraints derived from decision makers’ preference

statements. Incomplete criterion-specific performance information is modelled

through score intervals

0ww SS ⊆

],[ji

ji vv that are assumed to contain the ‘true scores . The

interval for the value of a portfolio p, therefore, is given by

jiv

)],(max),,(min[),,( wpVwpVvwpVww SwSw ∈∈

∈

where

( ) ( )

( ) ( )∑ ∑∑

∑ ∑∑

∈ ∈ =

∈ ∈ =

==

==

px px

n

iiji

j

px px

n

iiji

j

j j

j j

vwwxVwpV

vwwxVwpV

1

1

,,

,,

10

3.3. Additional Constraints

The RPM framework allows taking into account additional information such as:

o minimum budget usage

o project synergies

o balanced allocation of resources

and others that can be modelled by adding relevant logical constraints to the set of

constraints.

3.4. Non-dominated Portfolios

Because of using incomplete information, the model does not suggest a single optimal

portfolio but offers a number of non-dominated portfolios that lie within a feasible

information set. Non-dominated portfolios are feasible (i.e. constraint-satisfying)

portfolios whose overall values are higher than any other portfolios’ values for any

combination of feasible weights and scores.

Definition. Portfolio p dominates p’ with regards to information set S if and only if

V(p,w,v) ≥ V(p’,w,v) for all (w,v) ∈ S, (p,p’) ∈ P and

V(p,w,v) > V(p’,w,v) for some (w,v) ∈ S, (p,p’) ∈ P.

Non-dominated portfolios are therefore optimal solutions in some parts of the

information space. A thorough discussion of theory behind dominance structures and

the computation of non-dominated portfolios can be found in Liesiö et al, 2005.

To illustrate the effect of incomplete weight information on non-dominated portfolios,

consider figure 2. It depicts a situation where three portfolios are evaluated against

two criteria of which criterion 1 is more important than criterion 2 (i.e. w1 > w2). The

feasible weight area is therefore delimited to the left-hand side of vertical dotted line,

which means that portfolio 3 can be excluded from the set of non-dominated

portfolios with regards to given information set.

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Figure 2. Additive value of portfolios with preference information w1 > w2

3.5. Additional Information

Should the number of non-dominated portfolios be too large, decision makers can be

asked to reduce the information set by proving narrower score intervals and/or further

weight constraints. It should be noted that while these actions are likely to reduce the

number of non-dominated portfolios, they do not add any new portfolios to it.

3.6 Robustness

The set of non-dominated portfolios itself does not give the decision maker any

straight recommendation about which projects should be included in the chosen

portfolio – after all, there may be a large number of different non-dominated

portfolios. However, one can calculate a core index for each individual project. The

core index simply measures in how many of the non-dominated portfolios each

project was contained. A core index of 100% implies that no matter what the ‘true’

weights and scores are, as long as they lie within the given limits, this project would

be included in all of the non-dominated portfolios and should therefore be selected by

the decision maker in any case. These projects are called core projects. Using the

same logic, a project with 0% core index is not included in any of the non-dominated

portfolios and should therefore be discarded. These projects are referred to as exterior

projects. The projects whose core index lies between these two extremes are so-called

borderline projects.

12

The identification of core, exterior and borderline projects facilitates the work of

decision maker greatly because s/he can concentrate on evaluating further the

borderline projects that belong to optimal portfolios for some but not all weight and

score regions. This narrowing of the scope of analysis and further investigation is the

real value of RPM methodology. Even though the computation of non-dominated

portfolios requires a complicated algorithm, the end results are clearly understandable

even without mathematical background and can therefore be easily communicated.

The robustness of a non-dominated portfolio can be measured by maximin and

minimax-regret rules that are employed in Preference Programming (Salo and

Hämäläinen, 2001). Maximin rule by definition recommends the portfolio that

performs the best in the worst-case scenario (i.e. the lower bound of its value defined

by feasible weights and scores). The recommendation is therefore

( )wpVPwn SwPp

,minmaxargmin ∈∈=

Minimax-regret on the other hand recommends a portfolio whose greatest possible

loss of value with regards to some other portfolio over the information set is smallest.

The recommendation is therefore

( ) ( )[ ]wppVwppVPwNn SwPpPp

regret ,'/,/'maxminarg,

maxmin '−=

∈∈∈−

It should be noted that maximin and minimax-regret rules may recommend different

portfolios.

13

4. Case Study on Patent Portfolio

4.1. Problem Statement

For a company whose success is closely tight to the innovative Research &

Development activities, systematic managing of Intellectual Property Rights (IPR)

related to these new technologies is vital to ensure positive future perspectives. The

problem is twofold. On micro level, the company needs a methodology to value IPR

in order to assess whether it is profitable to patent a particular IPR in some possible

technological and/or geographical extent. Secondly, because of limited (financial)

resources, not all IPRs can be patented – at least in global scale. Therefore the

company needs a methodology to recommend a selection of individual projects to

form an efficient patent portfolio.

A recent academic study on IPR valuation concentrated on building a methodology

for valuing individual projects (Antila et al, 2005). In this section, RPM methodology

is applied to a problem of supporting patent portfolio management, whereby patents

are considered as projects. Previously Asperation Oy had chosen individual patents to

project portfolio so that they fit within the budget. One of the objectives of this study

is provide comparison for the previous heuristic.

4.2. Modelling the Problem

In the studied case, there are 21 available projects, each of which is evaluated against

5 criteria that are most important to the company. With regards to ordinal preference

order, these criteria are Primary Business Potential, Necessity, Technical Coverage,

Strategic Fit and Secondary Business Potential, respectively. The resource usage cj

represents the cost of securing the patent and the total cost is constrained by a budget

B that is not to be exceeded. The patent-specific costs are constructed so that they

represent the “useful” geographical patenting area for each patent (project). In other

words, for the given cost (i.e. geographical area) of each patent it is profitable to

secure the patent if it is decided to be included in the portfolio. This kind of

formulation helped to keep the number of projects reasonable with regards to

computational time (if patents in different geographical extent were modelled as

mutually exclusive projects, with 5 extents the number of projects would have been

already 105). The criteria weights were obtained both as ordinary preference

14

statements (most important, second most important etc) and precise point estimates.

This allowed testing the model with different set-ups to see if and how the results are

affected.

The criterion-specific score estimate intervals were obtained after careful

consideration by the decision makers. The intervals represent an area of assumable

but tolerable variation about uncertain future performances. In other words, from

strategic perspective, it is unrealistic to imagine that a project’s performance with

regards to given criteria would not lie within the suggested interval.

4.3. Experimental Design

A computational study of case was performed with RPM-Solver – a software

developed at the Systems Analysis Laboratory in Helsinki University that uses RPM

framework to calculate non-dominated portfolios and different robustness measures

for individual portfolios. A short description of the software is presented in

www.rpm.tkk.fi.

The first test run was conducted with the data in the exact form it was given (see

appendices, table 1). However, given that the score intervals were rather

homogeneous in width and that levels of scores did not vary much, the computational

time grew unrealistic. Therefore several slightly simplifying experimental designs

were developed to analyse the case in numerical terms. Three different score intervals

representing criterion-specific variation (that is, uncertainty) of 5% (low), 10%

(medium) and 15% (high) were constructed. All cases were run with three different

budgets (low, medium, high). Criteria weights were modelled as ordinary preference

statements (RICH-method), with the restriction that all of the weights were at least

one fifth of the average of the weights.

4.4. Results

The results are analysed mainly by comparing core indices. Although some test runs

produce promising results, in general the recommendations are not so obvious. In fact,

in most cases almost all projects fall into borderline category meaning that the model

is not able to produce many core or exterior projects that would reduce the amount of

further consideration. For example, the results of a “middle case” test run (medium

15

http://www.rpm.tkk.fi/

score variation and budget) are presented in figure 2. Only one project appears as so-

called core project and another as exterior project.

Figure 2. Core indeces with a score interval of 10% and a budget constraint of 107.5

In general the projects 23, 26 and 37 perform very well in most of the test runs.

Similarly, projects 13 and 33 fall into exterior project class in most cases. The model

therefore helps to reduce the amount of further investigation by about 25% in general.

Effect of budget constraint

Changing the budget constraint does not seem to change the number of core and

exterior projects meaningfully (see appendices, figures 2 and 3). On the other hand,

borderline projects’ core indices get bigger when increasing the budget.

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Effect of score intervals

Increasing the score intervals seems to have a dramatic effect in not only decreasing

the number of exterior projects but also decreasing the number of core projects. In

fact, regardless of the budget constraint, a score variation of 15% yields neither core

nor exterior projects, (see appendices, figure 3) whereas a score variation of 5%

produces both core and exterior projects (see appendices, figure 4). The reason

translates back to the data being quite homogeneous. For more variable data a 15%

score interval would produce clearly better results.

17

5. Discussion and Conclusions

Although the numerical results appear somewhat inconclusive, it should be kept in

mind that the model in this study was somewhat simplified, partly because of lack of

available data and resources needed with regards to the scope of the course. In

addition, the data was perhaps not gathered in the way that would benefit the model

best (that is, the data was not enough variable). Therefore more important than

concentrating on the results of the test runs is to consider how to improve and extend

the model. Some ideas of these ideas are discussed below.

Firstly, the applied model in this paper simplifies the problem from a geographical

perspective. The patent-specific costs (annual payments) were formed to represent a

“useful” patenting area. In other words, the cost of a particular patent, i.e. the sum for

the useful patenting area, is such it that guarantees profitable protection of the patent

should it be patented. In reality, each patent has different cost and criterion-specific

performance level depending on geographically how widely the patent is protected. A

full examination of the geographical issue would be to treat each project in each

geographical area independently and model them as mutually exclusive projects. For

example, if projects 1,2,3,4 and 5 represent the same patent in different geographical

extent, an additional logical constraint tells that only one of these 5 projects can be

selected for any portfolio. However, because this approach would require the

collection of many times the original data it was decided to leave it outside this study.

Another curiosity to consider is the assumption of the applied model that there are no

interdepencies between the individual projects. However, in reality such

interdepencies exist. For example, it is quite likely that two related projects, if both

started, produce together greater overall value than the sum of their individual values.

In other words, these projects have positive synergies. In RPM framework, synergies

can be modelled by adding aditional project for which there are no costs but a value

equal to the supplemental synergy value of the two projects if both started. This

additional “synergy project” is thus started if and only if both (or all) of the

underlying projects are started.

Even further modelling challenge arises from the issue that R&D company may have

rights to patents that they do not own. In other words, one company owns the patents

and another uses them for some cost, and vice versa.

18

With regards to numerical results, the study shows that although there is no need to

provide accurate data, too homogenous data leads to results that do not say much.

Emphasising the fact that preference statements about weights and score intervals for

criterion-specific performance levels are enough may lead to a situation where the

given information is not diverse enough. For example, if the score intervals are close

to the same width for many project-criterion combinations, even though the levels of

the intervals vary, the model is not able to find a clear set of core or exterior projects.

This finding is important when communicating how the decision maker should gather

the information needed.

In conclusion, RPM framework provides a flexible, easily understandable but process-

wise challenging framework for portfolio analysis. The real merits of RPM seem to be

its low demand on data and the ability to simply communicate all phases of the

modelling process to all decision makers. The implementation of RPM is a multi-step

challenge that requires careful planning. The study proved a useful introduction to

these challenges and opportunities in applying RPM to real cases.

19

6. References

1 Antila, M., Beletski, A., Isola, T., Janhonen, H., Leino, L., (2005). Seminar on

Case Studies in Operational Research, Final Report, Systems Analysis Laboratory,

Helsinki University of Technology, http://www.sal.tkk.fi/Opinnot/Mat-

2.177/projektit2005/Loppuraportti_Asperation.pdf

2 Asian Productivity Organization, (2004). Intellectual Property Rights, Report of

the APO Symposium Intellectual Property Rights 11-14 November 2003,

Bangkok, Thailand, ISBN: 92-833-7020-1.

3 Asperation Oy website, (2005), http://www.asperation.com/.

4 Ernst & Young and Ementor Management Consulting, (2000). Management and

evaluation of patents and trademarks, Consultant’s Analysis Report for the Danish

Patent and Trademark Office.

5 Investopedia website, (2005),

http://www.investopedia.com/terms/c/capitalbudgeting.asp.

6 Liesiö, J., (2004). Robust Multicriteria Optimization of Project Portfolios,

Master’s Thesis, Systems Analysis Laboratory, Helsinki University of

Technology.

7 Liesiö, J., Mild, P., Salminen, L., Ikonen, L., (2004). Final Report, Seminar on

Case Studies in Operational Research, Systems Analysis Laboratory, Helsinki

University of Technology, http://www.sal.tkk.fi/Opinnot/Mat-

2.177/projektit2004/Loppuraportti_Inframan.pdf.

8 Liesiö, J., Mild, P., Salo, A., (2006). Preference Programming for Robust

Portfolio Modeling and Project Selection, manuscript, European Journal of

Operational Research (forthcoming).

9 Luenberger, D., (1998). Investment Science, Oxford University Press.

10 Multiple Criteria Portfolio Analysis research project’s website (2005),

http://www.rpm.tkk.fi/.

11 National Board of Patents and Registration of Finland, (2005), http://www.prh.fi/.

12 Nielsen, P.-E., (2004). Evaluating patent portfolios – a Danish initiative, World

Patent Information, Vol. 26, Issue 2.

20

http://www.sal.tkk.fi/Opinnot/Mat-2.177/projektit2005/Loppuraportti_Asperation.pdfhttp://www.sal.tkk.fi/Opinnot/Mat-2.177/projektit2005/Loppuraportti_Asperation.pdfhttp://www.asperation.com/http://www.investopedia.com/terms/c/capitalbudgeting.asphttp://www.sal.tkk.fi/Opinnot/Mat-2.177/projektit2004/Loppuraportti_Inframan.pdfhttp://www.sal.tkk.fi/Opinnot/Mat-2.177/projektit2004/Loppuraportti_Inframan.pdfhttp://www.rpm.tkk.fi/http://www.prh.fi/

13 Perlos Oyj website (2005), http://www.perlos.com/.

14 Salo, A., Hämäläinen, R.P, (2001). Preference Ratios in Multiattribute Evaluation

(PRIME) – Elicitation and Decision Procedures under Incomplete Information,

IEEE Transactions on Systems, Man, and Cybernetics, Vol. 31, pp. 553 – 545.

21

http://www.perlos.com/

7. Appendices

Budget limits Importance 80 65 100 50 70 90 125 2 4 1 5 3

Project Annual payment Necessity Strategic fit

Primary business potential

Secondary business potential

Technical coverage

002ab 10 4 4,5 3,5 4,5 3 4,5 3 4 2,5 3,5 007 7,5 4 5 2,5 3,5 2 3 3 4 2 3 011 7,5 3,5 4,5 3 4 2 3 1,5 2 3 4 012 7,5 3,5 4,5 3 4 2 3 1,5 2 3 4 013 10 4 4,5 2,5 3,5 2,5 3,5 2,5 3,5 1,5 2,5 014 10 4 4,5 2,5 3,5 3,5 4,5 3 4 1,5 2,5 020 7,5 4 4,5 3,5 4,5 2 2,5 2 3 1,5 2,5 021 7,5 2 3 3 4 2 3 1,5 2 1,5 2,5 022 5 2,5 3,5 2,5 3,5 2 2,5 1,5 2,5 3,5 4,5 023 7,5 3 4 3 4 3,5 4,5 3 4 2,5 3,5 026 7,5 3 4 3,5 4,5 3 4 1,5 2,5 3 4 027 7,5 4 4,5 3,5 4,5 1,5 2,5 1,5 2,5 3,5 4,5 028 10 4 5 4 4,5 3,5 4,5 3 4 2 3 029 10 4 5 4 4,5 3 4 2,5 3,5 2 3 030 10 4 5 3,5 4,5 2,5 5 2 4,5 3 3,5 033 10 4 4,5 4 4,5 1,5 4,5 2 3 1,5 3 034 5 1,5 2,5 2,5 3,5 1 3,5 1 3,5 1,5 3,5 035 10 4 4,5 2,5 3,5 3 4 3,5 5 3,5 4,5 036 10 4 4,5 3,5 4,5 3,5 4,5 3 4 3,5 4,5 037 5 3 4 2,5 3,5 2 3 2 3 3,5 4,5 038 10 3,5 4,5 3,5 4,5 3 4 2,5 3,5 3,5 4,5

Table 1. Original data. Note that the data was modified for test runs

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Figure 1. Core indeces with a score interval of 5% and a budget constraint of 90

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Figure 2. Core indeces with a score interval of 5% and a budget constraint of 125

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Figure 3. Core indeces with a score interval of 5% and a budget constraint of 107.5

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Figure 4. Core indeces with a score interval of 15% and a budget of 107.5

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Contents1. Introduction2. Patents as Intellectual Property2.1. Background of Patenting2.2. Patent Portfolio Valuation Approaches

3. Robust Portfolio Modelling – a Theoretical Framework3.1. Representation of Additive Value3.2. Incomplete Information3.3. Additional Constraints3.4. Non-dominated PortfoliosV\(p,w,v\) \( V\(p’,w,v\) for all \

3.5. Additional Information3.6 Robustness

4. Case Study on Patent Portfolio4.1. Problem Statement4.2. Modelling the Problem4.3. Experimental Design4.4. ResultsEffect of score intervals

5. Discussion and Conclusions6. References7. Appendices