Innovation Project Selection Considering Stochastic Weighted Product

Model

Guilherme A. Barucke Marcondes

1 a

and Claudia Barucke Marcondes

2 b

National Institute of Telecommunications, Inatel, Av. Joao de Camargo, 510, Santa Rita do Sapucai, Brazil

Federal Center for Technological Education Celso Suckow da Fonseca, CEFET-RJ,

Av. Maracana, 229, Rio de Janeiro, Brazil

Keywords:

Innovation Project Selection, Multicriteria Decision Methods, WPM, Uncertainty.

Abstract:

Nowadays, organizations and companies are increasingly seeking to innovate in products and processes. In

general, innovation materializes in the form of project execution. However, such projects are complex to

implement, the evaluation of which requires understanding and knowledge of many factors. This makes its

selection also difﬁcult, given that it is necessary to experiment, which may or may not be successful, involving

volatility and uncertainty, which increases when the open approach is implemented (to compensate for a lack

of information, resources and skills). The selection of innovation projects can be supported by appropriate

tools, in order to assist the decision maker in their choices. Multi-criteria decision methods (MCDM) can

provide this support, especially if they take uncertainty into account. This work proposes the application of the

Weighted Product Model (WPM), an MCDM, in the selection of innovation projects. To address uncertainty,

assessments performed by more than one expert are translated into three-point estimates and Monte Carlo

simulation applied for a stochastic approach. The proposed method is applied to the selection in a group of 13

innovation projects, as an example.

1 INTRODUCTION

In boosting the competitiveness and growth of com-

panies, innovation is a fundamental element. One

of its challenges is choosing the “right” projects to

which the necessary resources must be allocated (Si

et al., 2022). Managing innovation is a process that

is strongly linked to the need to choose which ideas

and projects to invest in. This is one of the most im-

portant aspects. Although the selection processes are

part of the daily life of organizations, they involve

people, who use their own forms of calculations or

evaluations, which can lead to subjective conclusions

(Havis, 2020; Basilio et al, 2023).

The resources available for projects, especially

those for innovation, are generally limited and scarce

in organizations, preventing all projects presented or

proposed from being developed simultaneously (Du-

tra et al., 2014; Agapito et al., 2019; Lee et al., 2020).

As a result, decision makers must choose, based on

their pre-deﬁned criteria, which ones will be effec-

tively carried out (Abbassi et al., 2014).

https://orcid.org/0000-0001-8062-4347

https://orcid.org/0000-0001-8002-1968

Some approaches to deal with this situation are

known, project ranking being one of them. It allows

a choice based on structured forms, especially if ob-

jective selection criteria are deﬁned, to better meet

the organization’s desires and marketing positioning

(Perez and Gomez, 2014).

The chances of successful project execution in-

crease when formal selection methods are applied

(Dutra et al., 2014). Eventual waste of scarce re-

sources can be avoided or minimized, when there is

the correct choice of the set of projects to be executed

(Abbassi et al., 2014; Agapito et al., 2019).

The nature of project decisions makes their real-

ization complex, since several criteria must be consid-

ered simultaneously (Tzeng and Huang, 2011). This

is especially true for innovation projects, considering

that unexpected results can negatively impact the fu-

ture of the organization (Lee et al., 2020).

Multicriteria Decision Methods (MCDM) are

tools that help solve complex engineering problems

and can be used for this type of choice. Ranking

the alternatives in order of priority/preference is a

possible solution in some of these methods (Walle-

nius et al., 2008; Mavrotas and Makryvelios, 2021).

Marcondes, G. and Marcondes, C.

Innovation Project Selection Considering Stochastic Weighted Product Model.

DOI: 10.5220/0012270000003639

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 13th International Conference on Operations Research and Enterpr ise Systems (ICORES 2024), pages 207-212

ISBN: 978-989-758-681-1; ISSN: 2184-4372

207

The use of MCDM has grown in academic publica-

tions, some examples of which are listed below (Sadi-

Nezhad, 2017; Martins and Marcondes, 2020; Basilio

et al, 2022):

• Preference Ranking Organization Method for En-

richment Evaluation II (PROMETHEE II);

• VIseKriterijumska Optimizacija I Kompromisno

Resenje (VIKOR);

• Technique for Order of Preference by Similarity

to Ideal Solution (TOPSIS);

• Elimination Et Choix Traduisant la R

ealit

e II

(ELECTRE II);

• Weighted Product Method (WPM).

In turn, every decision about projects to be carried out

must be taken based on estimates, uncertainty being

one of its inherent characteristics (Bohle et al., 2015).

Such uncertainty can inﬂuence the selection result, as

shown in the results of Marcondes et al. (2017); Mar-

condes (2021).

There are several ways to deal with uncertainty,

the three-point estimate being one of those indicated

in PMI (2021). In this case, instead of estimating by

a single value, three are used (worst case, most likely

and best case). The treatment of such variation can be

done through Monte Carlo simulation or fuzzy num-

bers (Deng, 2014; Wang, 2015; Marcondes, 2021).

Once performed a three-point estimate, each pa-

rameter can be characterized by a triangular proba-

bility distribution, which feeds a Monte Carlo sim-

ulation. At each new round, the parameters receive

random values, based on the deﬁned distribution, al-

lowing, at the end of the simulation, to observe how

the values varied and their conclusions.

The purpose of this work is to consider uncertainty

in the application of an MCDM for the selection of

innovation projects. Each project is evaluated by dif-

ferent experts, considering the various criteria deﬁned

for the choice. These assessments can be charac-

terized in three-point estimation, allowing the Monte

Carlo simulation to be carried out. The MCDM cho-

sen for this work was WPM, since it was used suc-

cessfully in some works for selection and the crite-

ria weights on the decisions outcome is signiﬁcant.

(Goswami et al., 2020; AlAli et al., 2023; Ayan et al,

2022).

The uncertainty addressed in this work is the one

introduced in the estimation process, naturally, due to

the error in values attributed to the decision criteria

for each alternative.

The remaining of this paper is organized as follow:

in Section 2 the characteristics of innovation projects

are summarized; Section 3 presents the principles of

multicriteria decision methods, detailing WPM; the

importance of uncertainty in project selection prob-

lems is presented in Section 4; Section 5 proposes a

method for selecting projects considering uncertainty;

which is exempliﬁed by a real problem in Section 6;

Section 7 concludes the work.

2 INNOVATION PROJECTS

Innovation projects often require the dissemination of

knowledge and its integration to achieve their objec-

tives. As this process is affected by multiple fac-

tors, as a consequence there is high uncertainty. The

integration and dissemination of knowledge during

project implementation is complex (Xu et al, 2023).

The investment decision and selection of innova-

tion projects has become a point of attention and care

in research. Due to their characteristics, innovation

projects require, as much as possible, an assessment

of all factors involved. Its results have great potential

for ﬁnancial return and increased market capillarity

and scale, but require a lot of attention when selecting

which ones to execute (Dong et al, 2023).

The development of new innovative products is es-

sential for sustainable business growth and improved

competitiveness. This means that, annually, many

ﬁnancial resources are invested in the research and

development of new products. It makes innovation

a fundamental element for companies and organiza-

tions (Si et al., 2022).

Due to the characteristics of novelty and change,

innovation projects can be more difﬁcult to control

and, consequently, to be chosen/deﬁned. They bring

with them the need to experiment, succeed or fail, un-

certainty and volatility, adaptation to unforeseen op-

portunities and, above all, creativity. An additional

factor of complexity is the tendency towards open in-

novation, as there is active cooperation with various

actors (internal and external), in order to compensate

for any shortage of information, external and skills.

(Dybal and Wang., 2017).

Once innovation projects are fundamentals for

companies and organizations today, care must be

taken with investments. Generally, innovation is

achieved by carrying out projects. This increases the

importance and responsibility of those who need to

make the selection and deﬁne which ones should be

executed or not.

ICORES 2024 - 13th International Conference on Operations Research and Enterprise Systems

208

3 WEIGHTED PRODUCT MODEL

(WPM)

Structured decisions of choosing between alternatives

must present clear decision criteria. When such a

choice uses only one criterion, for example, choosing

only the lowest price, the decision is simple, just com-

paring the values. However, as more criteria are con-

sidered simultaneously, the decision becomes more

complex. Especially, if there is a conﬂict between the

established criteria (Tzeng and Huang, 2011).

Multicriteria Decision Methods (MCDM) have

been widely used in project selection and signiﬁ-

cant advances in techniques have been made in re-

cent years (Sadi-Nezhad, 2017; Sahoo and Goswami,

2023). Weighted Product Model (WPM) is an easy-

to-apply method that allows the generation of a prior-

itized list (ranking) among the evaluated alternatives,

considering multiple criteria and weights in the deci-

sion.

WPM is an MCDM, based on weighted multipli-

cation of proportions (ratios) between alternative val-

ues. One of its advantages is that it allows the in-

dependent evaluation of the dimensions used in the

different criteria, as the ratios between the values are

always used. The comparison is pair by pair (Tri-

antaphyllou and Sanchez, 1997). The results obtained

from its application allow one to rank the alternatives,

in order of preference.

Considering a selection to be done for m alterna-

tives and n criteria, WPM is performed like following.

Step 1 - Calculate the product P for each alternative

related to all other alternatives(Triantaphyllou and

Sanchez, 1997):

P(A

) =

∏

k=1





(1)

where:

i and j are the alternatives (i = 1,...,m and

j = 1, ..., m)

k is the selection criteria (k = 1,...,n)

and a

are the values for alternatives i and j,

respectively, for the criterion k

is the the weight for the criterion k

After this step, one has m P values for each alter-

native.

Step 2 - Calculate wpm value for each alternative (ge-

ometric mean of values):

wpm

∏

j=1

P(A

) (2)

for ∀ j.

Step 3 - Organize alternatives in descending order of

wpm values. It is feasible to determine the best alter-

natives using this ranking of preferences.

4 UNCERTAINTY TREATMENT

The application of MCDM requires a decision maker,

or several ones, to estimate the value to be assigned,

for each alternative and in each criterion. Estimation

and forecasting bring with them uncertainty (Bohle

et al., 2015; Marcondes et al., 2017).

When estimating a certain value for a parameter,

within his best evaluation and understanding, the de-

cision maker assigns what he understands to be the

best. However, there may be inaccuracy in this esti-

mate. Such inaccuracy can increase if more than one

person estimates values for the same parameters.

To exemplify this situation, one can imagine a

group of several evaluators estimating the values for

the same parameters. The most likely thing to hap-

pen is, instead of a single value for each parameter, a

range of values should be obtained for each one.

To deal with uncertainty, one can apply three-

point estimates and Monte Carlo simulation. In three-

point estimation, each parameter to be estimated must

have three values: most likely estimate, optimistic es-

timate, and pessimistic estimate. Optimistic and pes-

simistic estimates should reﬂect, in the estimator’s

view, the best and worst case scenarios, respectively.

The most likely estimate should reﬂect the estimator’s

view of which scenario is most likely to occur (PMI,

2021).

In order to indicate how to generate random values

in the Monte Carlo simulation, the three values for

each parameter allow the construction of a triangular

probability distribution, as indicated in Figure 1 (PMI,

2021):

• parameter a is equal to worst-case estimation;

• parameter b is equal to best-case estimation;

• parameter c is equal to most likely estimation.

Thus, at each new round of the Monte Carlo simu-

lation, random values following this deﬁned distribu-

tion can be generated. Rounds can be repeated and

their results recorded. At the end, there is a set of re-

sults obtained randomly, which allow to conclude the

simulation.

5 PROPOSED METHOD

The ﬁnal objective is to achieve a ranking of projects

to support the selection. The method proposed in this

Innovation Project Selection Considering Stochastic Weighted Product Model

209

Probability Density Function

Random Variable

a bc

Figure 1: Triangular distribution based on three point esti-

mation.

work follows the steps described following.

• Step 1: A group of specialists estimates the value

for each of m projects considering all n criteria. It

is better they use the same range of values (for in-

stance, from 1 to 10). Otherwise, the estimations

must be normalized before proceeding. The esti-

mated values for each parameter lead to the deﬁ-

nition of a three-point estimate.

• Step 2: The three-point estimate from Step

1 allows to deﬁne a triangular distribution for

each parameter (each criterion evaluation for each

project). It allows the stochastic approach to be

applied.

• Step 3: Monte Carlo simulation is proceeded. For

every run, a new random value is generated for

each parameter, based on the triangular distribu-

tion respectively deﬁned. wpm values are calcu-

lated and stored for the ﬁnal evaluation.

• Step 4: After all runs of simulation, it is calcu-

lated a mean of wpm values. These means values

allows one to prepare a ﬁnal ranking, of descend-

ing values, considering the stochastic approach.

Uncertainty is treated in this proposed model by the

three-point estimate performed, its respective conver-

sion into a triangular distribution and the subsequent

application of Monte Carlo simulation for a stochastic

approach.

6 NUMERICAL EXAMPLE

As an example, the proposed method in Section 5

was applied in the selection carried out by a scien-

tiﬁc and technological institution, for a call to ﬁnance

three innovative projects with a pre-deﬁned maximum

budget. All proposals were evaluated by three ex-

perts, who indicated, according to their experience,

Table 1: Projects Parameters Estimates C1/C2/C3.

Project

C1 C2 C3

WC ML BC WC ML BC WC ML BC

A 2 3 5 8 9 10 4 5 7

B 8 9 10 6 7 8 6 7 8

C 3 3 4 1 1 2 8 9 10

D 1 1 2 6 7 7 1 2 2

E 4 5 7 1 1 3 2 3 5

F 8 9 10 4 6 7 1 1 2

G 9 9 10 7 7 8 8 8 9

H 5 6 6 5 7 7 6 8 8

I 5 6 8 1 2 4 4 5 7

J 8 10 10 8 10 11 4 6 7

K 1 2 2 3 3 4 5 6 6

L 3 4 5 7 8 8 1 2 4

M 3 4 4 5 6 6 6 8 9

the grades for each criterion. The values indicated by

the evaluators allowed the composition of the three-

point estimate.

The criteria used in the evaluation are listed in the

sequence. And the evaluations carried out, already in

the three-point estimation format, are presented in Ta-

bles 1 and 2 (WC is the acronym for worst-case, ML

is the acronym for most likely and BC is the acronym

for best-case).

• C1 - Feasibility of technical execution (weight

- 0,2): Evaluating the proposal presented, it must

be veriﬁed whether the project has technical fea-

sibility. (from 1 - the worst to 10 - the best);

• C2 - Feasibility of execution within the pro-

posed deadline (weight - 0,2): Evaluating the

proposal presented, it must be veriﬁed whether the

project is feasible within the indicated deadline.

(from 1 - the worst to 10 - the best);

• C3 - Expected ﬁnancial return (weight - 0,2):

Evaluate the expected ﬁnancial return for the pro-

posed project. (from 1 - the lowest to 10 - the

highest);

• C4 - Degree of innovation (weight - 0,2): How

innovative the project is (from 1 - the worst to 10

- the best).

• C5 - Team’s ability to execute the project

(weight - 0,2): Considering the team presented

in the project proposal, evaluate whether it is ca-

pable of carrying out its execution. (from 1 - the

worst to 10 - the best).

The application of the method aimed at a ﬁnal rank-

ing, indicating the projects to be selected in order of

preference.

The ranking obtained by executing the stochastic

WPM method can be seen in the bar graph in Figure

2. It indicates that projects G, B and H should be se-

lected, as they had the best results after the simulation

carried out. It is important to highlight that, applying

the WPM method in a deterministic way (using the

ICORES 2024 - 13th International Conference on Operations Research and Enterprise Systems

210

Table 2: Projects Parameters Estimates C4/C5.

Project

C4 C5

WC ML BC WC ML BC

A 2 3 5 2 3 5

B 2 3 4 8 9 10

C 5 5 6 7 7 8

D 5 6 6 5 6 6

E 6 7 9 1 2 4

F 8 10 10 5 7 8

G 6 6 7 5 5 6

H 2 4 4 8 10 10

I 8 9 10 4 5 7

J 2 4 5 1 2 3

K 9 9 10 3 3 4

L 1 1 2 5 6 6

M 2 3 3 1 2 2

most likely estimate) the same three projects were in-

dicated, however with a reversal of order in the rank-

ing between projects B and H (in the deterministic

values execution H was second and B the third).

Figure 2: Projects Ranking - With Uncertainty - Stochastic

WPM.

7 CONCLUSIONS

Innovation has been pursued by companies and orga-

nizations as a way of gaining market share and im-

proving competitiveness. These types of projects are

characterized by complex management and selection,

as many factors must be evaluated simultaneously. In

addition, they must consider the inherent risks of suc-

cess and failure in results, given the need for experi-

mentation, which increase the uncertainty of their re-

sults.

On the other hand, the scarcity of resources does

not allow investing in all proposed or identiﬁed inno-

vation projects. A selection is necessary as a way of

optimizing ﬁnancial, material and human resources.

Which can be difﬁcult for the decision maker.

This work proposes a method for selecting innova-

tion projects based on WPM, an MCDM that is easy

to apply and understand. Uncertainty, inherent in the

selection process, is addressed using three-point esti-

mates and Monte Carlo simulation for the stochastic

approach.

As an example, the proposed method was applied

to a set of 13 innovation projects, in a process that

aimed to select three for execution. The result was

a ranking of the projects to be carried out, in or-

der of preference, indicating the three most suitable.

This result, compared with the application of the same

method in a deterministic way, indicated the same

three projects, however, with a change in the rank-

ing order, conﬁrming the impact of uncertainty and

stochastic approach in the selection. The results high-

light the importance of considering the stochastic ap-

proach in selection, when there is uncertainty in the

estimate, given its impact on the ﬁnal selection.

As a proposal for future work, a comparison can

be made between the results obtained with the WPM

method with those of other MCDMs known in the

literature (PROMETHEE, TOPSIS, ELECTRE and

VIKOR, for example), when using the stochastic ap-

proach. Furthermore, a new method could be studied,

combining WPM with the others, for a broader evalu-

ation of the ranking. Another line of work could also

be the application of the fuzzy approach to deal with

uncertainty.

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