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A Genetic Algorithm approach for Collaborative
Networked Organizations Partners Selection
Lorenzo Tiacci1 , Andrea Cardoni2
1 Università degli Studi di Perugia - Dipartimento di Ingegneria Industriale
Via Duranti, 67 – 06125 Perugia - Italy
2 Università degli Studi di Perugia - Dipartimento di Discipline Giuridiche e Aziendali
Via Pascoli, 20 – 06123 Perugia – Italy
{lorenzo.tiacci, acardoni}@unipg.it
Abstract. In the paper a genetic algorithm approach to form potential
Collaborative Networked Organizations (CNOs) is presented. When analyzing
a set of companies that are potential partners of a CNO, it is possible to collect
specific data from each company through which evaluate, once aggregated, for
which Strategic Objective (SO) the potential aggregation is most suited. At this
purpose a metric, consisting in a set of performance parameters related to
different SO types, has been created. Given a large number of companies,
through a genetic algorithm approach is then possible to set a specific objective
function related to a particular SO (eg. maximize potential creation of new
Business Opportunities), and to find the cluster (or clusters) of companies that
maximizes the objective function.
Keywords: Business Networks Formation, Genetic Algorithm, Strategic
Objectives.
1. Introduction
In the paper a genetic algorithm approach for collaborative networked organizations
partner selection is presented. The perspective adopted in this paper is related to the
framework described and applied by authors in two preceding works [1][2].
In these studies authors defined and applied a framework to analyse a potential
pool of partners and to identify the most appropriate CNOs form that should be
adopted. The choice of the Strategic Objectives (SOs) of the collaborative network is
a crucial analytical phase that determines the most appropriate form of alliance. In
general, when analyzing a pool of companies that wants to collaborate, strategic
network objectives are not defined ‘a priori’, but should be the result of an assessment
of the possible opportunities deriving from the collaboration. This assessment is
conducted by gathering information on several aspects of each company (the so called
‘Analysis Dimensions’). By evaluating and consolidating all the information gathered
from a network perspective it is possible to define which type of Strategic Objective
is achievable by the group, and in turn to identify the most appropriate strategic
mission for the CNO, and the most appropriate strategic form among VBE[4],
VDO[1] and T-Holding[1]. In [2] authors applied the proposed framework to a case
study commissioned by the ICE (the Italian Institute for Foreign Trade) and by a local
industrial association (Confartigianato Terni), whose aim was to investigate how the
companies belonging to an industrial cluster of the metal-mechanic industry in Italy
could be aggregated in an innovative way. A questionnaire through which investigate
the analysis dimensions of each company has been defined. Data provided by this tool
and by economic and financial statements of the companies have been analysed in a
network perspective in a semi-quantitative way. The analysis of the consolidated data
allowed clearly identifying which type of SO was at same time desirable and
achievable by the alliance. This in turn allowed determining the most appropriate type
of CNO. In this paper the above mentioned framework is completed through the
definition of a ‘metric’ that allow to measure in a quantitative way which type of SO
is most suitable for a group of companies that wants to join together. For this purpose,
the metric takes mainly into consideration the so called ‘hard’ factors [5] (e.g.
matching competence, technological fit, etc.), because its scope is limited to the
selection of the SO’s type. An appropriate pattern of the so called ‘soft’ factors (e.g.
reputation, ethical issues, norms, values, trust, etc.) is considered in this context to be
a necessary prerequisite. Thanks to this metric it is possible to extend the usage of the
proposed framework to another interesting context: the selection, from a large number
of companies, of a cluster (or more clusters, here intended as generic business
networks of companies) able to achieve a specific SO. At this scope, a genetic
algorithm approach is presented. The perspective adopted in our work is different
from many interesting studies presented in literature related to partners selection and
evaluation processes [6] that specifically address Virtual Organizations (VOs)
creation process, but not the long term CNO formation process.
The paper is organized as follows: in section 2 the classification of SOs is
reported; in section 3 the metric for measuring which SO is achievable by a group of
companies is presented; in section 4 the genetic algorithm approach is presented.
2. Strategic objectives of primary and secondary type
How illustrated in [1], the strategic objectives (SOs) a generic CNO can pursue have
been classified in SOs of “primary” type and SOs of “secondary” type.
The strategic goals of Primary type represents the ability of the network to
permanently increase the value added related to its business core competencies. To
achieve these goals it is necessary that the alliance is able to create new Business
Opportunities (BOs) and Core Process Opportunities (CPOs):
Business Opportunities: are related to new markets and new products development,
able to increase the network turnover;
Core Process Opportunities: are related to the increase of effectiveness and
efficiency of the core operational activities, able to reduce the network costs.
In the strategic goals of Secondary type we can include all the other synergies that
brings to new Supporting Process Opportunities (SPOs), that are related to increase
the efficiency and effectiveness of all the supporting activities, such as finance,
control, quality, research, administration, education, etc., that are able to emphasize
the benefits of Primary type.
Figure 1 show the companies’ analysis dimensions that have to be investigated in
order to evaluate if a potential CNO is able to generate new BOs, CPOs and SPOs,
that is, to fulfill the strategic goals that have been defined in the previous step. The
dimensions identified are: Segments of Business [8], Primary and Supporting
Activities [9], Critical Resources [10], Financial statements analysis [11].
As reported in [2] the proposed framework has been applied to a case study. The
questionnaire is the survey tool that has been utilized to collect information on
qualitative and quantitative variables from each company, and consists of three
distinct sections, each one related to one of the analysis dimensions defined. Data
provided by the questionnaires have then been integrated trough economical and
financial data provided by the companies’ balance sheets.
Figure 1. Analysis dimensions.
3. A Metric for Measuring Strategic Objectives Achievability
The metric proposed herein is applicable to a determined group of company. Data
provided by the questionnaire and balance sheets of each company are used in this
section to calculate a series of performance parameters through which asses the ability
of the potential network to achieve a specific SO.
There are three set of parameters, each one related to one of the three types of
strategic objectives achievable: BOs, CPOs and SPOs parameters. A higher value of a
parameter will indicate that the group has a high probability of achieving the strategic
objective to which the parameter is referred. Due to space limitation, only a part of the
CPOs and BOs parameters that have been defined will be described in the following
paragraphs. The remaining CPOs, BOs and SPOs parameters will be presented in an
extended version of the paper. Each parameter Pk is associated to a weight WPk and to
two vectors of ordered values {x1, ..., xn} and {y1, ..., yn} used to discretize and
normalize the parameter value through the following function:
1
1
0
( ) 2,..., 1
k
k i i k i
n k n
if P x
f P y if x P x i n
y if P x
(1)
Segments of Business
Primary and Supporting
Activities
Critical Resources
Financial statement
analysis
ANALYSIS DIMENSIONS
the capacity to create new
Business Opportunities
the capacity to create new
Core Process Opportunities
and new Supporting Process
Opportunities
Potential competitive
advantages
Economic and
Financial
Performances
to evaluate
to evaluate
to evaluate
to evaluate
The weighted, discretized and normalized value of the parameter is equal to WPk .
f(Pk). The weights and vectors values for some of the BOs and CPOs parameters are
shown in Table 1 and Table 2.
Notation
N = Number of companies in the group
Ti = Turnover of company i
Ei = total external costs (purchases and closing stock + production,
commercial and administrative services)
STOT = total number of industrial sectors (covered by at least one company)
Sij = turnover fraction made in industrial sector j by company i
Sbij = 1 if Sij > 0; = 0 otherwise (=1 if industrial sector j is covered by
company i)
TINi = total expenditures for inbound transportations
TOUTi = total expenditures for outbound transportations
Aij = expenditure fraction on total purchases of company i for product j
Abij = 1 if Aij > 0; = 0 otherwise
A(2-4)j = 1 if 2
ij
iAb
4; = 0 otherwise (=1 if product j is purchased by a
number of company between 2 and 4)
A( 5)j = 1 if
ij
iAb
5; = 0 otherwise (=1 if product j is purchased by more
than 5 companies)
Cij = Turnover fraction of company i made with client j
Cbij = 1 if CLij > 0; = 0 otherwise
C(2-4)j = 1 if 2
ij
iCb
4; = 0 otherwise (=1 if client j is common to a
number of companies between 2 and 4)
C( 5)j = 1 if
ij
iCb
5; = 0 otherwise (=1 if client j is common to more than
5 companies)
MACTOT = total number of machines typologies (used in at least one company)
MACij = number of machines j owned by company i
MACbij = 1 if MACij > 0; = 0 otherwise
TECTOT = Total number of different technologies (adopted by at least one
company)
TECbij = 1 if tecnology j is adopted by company i; = 0 otherwise
Performance Parameters: CPOs, BOs, and SPOs parameters
CPOs parameters measures the potential ability of the group of N companies to
achieve new Core Process Opportunities as a network. The Parameters reported in
Table 1 are the following:
CPO1 = incidence of total inbound transportation costs on total turnover;
CPO2 = incidence of total outbound transportation costs on total turnover;
CPO3 = number of product types purchased by a number of companies
between 2 and 4;
CPO4 = incidence on total turnover of purchasing costs related to products
purchased by a number of companies between 2 and 4;
CPO5 = number of product types purchased by a more than 5 companies;
CPO6 = incidence on total turnover of purchasing costs related to products
purchased by more than 5 companies.
The higher the value of these parameters, the higher the possibility to achieve so me
core process opportunities such as synergies in transportations activities (CPO1 and
CPO2) or collaborative procurement opportunities (CPO3 to CPO6). In order to
evaluate through a unique parameter the ability to achieve generic CPOs, an overall
parameter, FC PO , is defined by summing the discretized, weighted and normalized
values of all the considered CPOs parameters:
()
CPO CPOp p
p
F W f CPO
(2)
Table 1. CPOs Parameters.
CPOp Parameter
WCPOp
{x1, ..., xn}
{y1, ..., yn}
1INi i
ii
CPO T T
3
{0.33, 0.66}
{5, 10}
2OUTi i
ii
CPO T T
3
{0.05, 0.2, 0.3}
{2, 5, 10}
3 (2 4) j
j
CPO A
2
{2, 5, 10}
{2, 5, 10}
4 (2 4)ij j i i
i j i
CPO A A E T
2
{0.05, 0.1, 0.2}
{2, 5, 10}
5 ( 5) j
j
CPO A
5
{2, 5, 10}
{2, 5, 10}
6 ( 5)ij j i i
i j i
CPO A A E T
5
{0.05, 0.1, 0.2}
{2, 5, 10}
BOs parameters measures the potential ability of the group to find new Business
Opportunities as a network. The parameters reported in Table 2 the following:
BO1 = degree of diversification of industrial technologies;
BO2 = degree of diversification of machines types;
BO3 = degree of diversification of industrial sectors;
BO4 = number of clients common to a number of companies between 2 and 4;
BO5 = incidence on total turnover of clients common to a number between 2
and 4 companies;
BO6 = number of clients common to more than 5 companies;
BO7 = incidence on total turnover of clients common to more than 5
companies.
The higher the value of this parameters, the higher the possibility to create new
Business Opportunities by exploiting complementarities in technologies, machines,
and industrial sectors (BO1 to BO3) or by supplying integrated products/services to
common clients (BO4 to BO7). As in the previous case, to evaluate through a unique
parameter the ability to achieve generic BOs, an overall parameter, FBO , is defined by
summing the discretized, weighted and normalized values of all the considered BOs
parameters:
()
BO BOp p
p
F W f BO
(3)
In an analogous way, a series of SPOs parameters are defined (not reported due to
space limitation), and the ability to achieve generic SPOs can be measured by a
unique parameter FSPO obtained by weighting, discretizing, normalizing and finally
summing all the SPOs parameters.
Table 2. BOs Parameters
BOp Parameter
WBOp
{x1,…,xn}
{y1, …, yn}
11
11
TOT
TEC
N
ij
ij
TOT
TECb
BO N TEC
5
{0.6, 0.8}
{5, 10}
11
21
TOT
MAC
N
ij
ij
TOT
MACb
BO N MAC
5
{0.6, 0.8}
{5, 10}
311
1TOT
S
N
ij TOT
ij
BO Sb N S
5
{0.6, 0.8}
{5, 10}
4 (2 4) j
j
BO C
2
{2, 5}
{5,10}
5 (2 4)ij j i i
i j i
BO C C T T
2
{0.05, 0.1}
{4, 10}
6 ( 5) j
j
BO C
5
{2, 5}
{5,10}
7 ( 5)ij j i i
i j i
BO C C T T
5
{0.05, 0.1}
{4, 10}
4. A Genetic Algorithm Approach
The proposed metric can be applied to a group of potential partners. Given a large
number of companies, the metric makes also possible to set a specific objective
function related to a particular SO (eg. maximize potential creation of new Business
Opportunities), and to find the cluster (or more clusters) of companies that maximizes
the objective function. In order to define the desired solution features, three possible
input parameters, that define the constraints that a feasible solution must respect, are
taken into consideration:
NC = the desired number of clusters that has to be find;
minC = minimum number of companies in each cluster;
maxC = maximum number of companies in each cluster.
From an initial set of M companies, the algorithm will give as output NC clusters
of companies, each containing a number of companies between minC and maxC. The
genetic algorithm approach seems to be particular suited to explore the space of this
combinatorial problem, in which companies cannot be evaluated singularly. In fact,
the contribution of each company to many of the performance parameters above
described is dependent by which other companies are in the same cluster.
Representation, decoding and fitness functions. In a genetic algorithm approach,
each Individual represents a possible solution of the problem. Thus, the individual is
formed by one or more clusters of companies. The algorithm has been implemented in
Java, and the representation of an individual has been made using an object oriented
approach. Each Individual k contains a List of Ik clusters Cki, i = 1,…,Ik. Each cluster
Cki contains a certain number of companies ni, so that the total number of companies
contained in all the clusters Cki is equal to the initial set of M companies. However,
when decoding an individual, only the feasible clusters (i.e. respecting the relation
minC ≤ ni ≤ maxC) have to be taken into consideration for calculating the fitness
function. So Fk, the set of feasible clusters of individual Ik, is sorted in descending
order with respect to the selected fitness function, and only its first NC clusters are
considered when decoding the individual. Thus the individual fitness is calculated by
considering only Cki Fk for i ≤ NC. This set of clusters is the output of the decoding
phase of an individual. It is noteworthy that, depending from the number of clusters to
find and the minimum and maximum number of companies per cluster, one or more
companies of the initial set of M companies could not be selected to be part of this
final set of clusters generated by the individual decoding. Four possible fitness
functions, shown in Table 3, can be selected. By selecting one of the fitness functions
defined in Table 3, it is possible to search for potential cluster(s) able to achieve
specific SOs. Through the FALLO fitness function the type of SO is not specified ‘a
priori’ for all the clusters, but the algorithm will search for the best combination of
clusters able to achieve different SOs.
Table 3. Fitness functions
Find clusters that maximize:
Fitness function
CPOs
1
NC
CPO CPOi
i
FF
BOs
1
NC
BO BOi
i
FF
SPOs
1
NC
SPO SPOi
i
FF
indifferently CPOs, BOs, or SPOs:
max{ , , }
NC
ALLO CPOi BOi SPOi
ki
F F F F
Initial population. An initial population is created by randomly generating a number
P of individual. Each individual is created by iteratively forming clusters; each cluster
has number of companies, randomly chosen from the initial set, between minC and
maxC. Each time a cluster is formed, the set of companies belonging to the cluster is
removed from the initial set. The procedure continues until the initial set is empty or it
contains less than minC companies. In the latter case, the last cluster is formed
including the remaining companies, although their number is out of the feasibility
range.
Reproduction and mutation. Each generation of the genetic algorithm provides
reproduction and mutation phases. In the reproduction phase, all the individuals of the
population are coupled through a binary tournament selection procedure[12]. Then
each couple of parents p1 and p2 generates two children, c1 and c2. For example, child
c1 is generated in this way: a cluster C belonging to p1 is randomly chosen; then the
companies belonging to C are removed from clusters belonging to p2; finally C is
added to p2. The resulting individual is c1. Child c2 is obtained inverting p1 and p2
roles. In this way, after the reproduction phase, the population size is equal to 2P.
Each individual of this population has now a certain probability m to undergo the
mutation phase. Each mutated individual is added to the population, but the original
one is also maintained in the population. There are three possible types of mutation,
randomly selected with probability m1, m2, and m3 respectively. In the first type of
mutation two clusters are randomly selected and are joint together. In the second type
a cluster, randomly selected among clusters with a number of companies higher than
2 . minC, is halved, generating 2 clusters. In the third type, two companies, belonging
to different clusters, are swapped. Note that the first type of mutation can generate
clusters with a number of companies out of the feasible range. The mutation phase is
responsible (together with the initial population creation phase) of the heterogeneity
of the number of clusters Ik in each individual k. The population now is sorted,
following one of the four fitness function proposed, and only the first P individuals
survive and pass to the next generation. After a number of generation G, the algorithm
stops, and the individual with the highest fitness is considered the final solution.
5. Discussion and Conclusions
The proposed metric has been validated by calculating the three performance
parameters FBO, FCPO and FSPO for the cluster of companies considered in the case
study described in [2]. The study was commissioned by ‘Confartigianato Terni’, a
local agency of 'Confartigianato', the main Italian industrial Association of SMEs,
with about 700000 associated companies, and 120 local agencies spread over the
territory. The resulting values (FBO=265, FCPO=45, FSPO=35) are consistent with the
qualitative analysis of results described in [2], that indicated the creation of new BOs
as the most suited SO for the cluster. They are also consistent with the evolution of
the cluster that, after the understanding of the basic characteristic of the proposed
network model and the strategic logic of the collaboration, manifested a successfully
capability to explore and catch new BOs, f.e. providing integrated products/services
in the renewable energies plants sector. Confartigianato is currently considering the
development of a software based on the metric and the algorithm presented in the
paper, that, after a testing and validating phase through real data from the field, could
be used by the local agencies as a decision supporting tool for networks formation.
The genetic algorithm approach presented here in is a supporting decision tool to
individuate, among an extensive number of companies, potential clusters of
companies that can achieve specific strategic objectives. Through the proposed
approach it is be possible to find out which companies, among the associated partners,
could joint together to fulfill a specific mission. In particular the associations could
suggest not only the cluster(s) composition, but also the type of strategic objective the
cluster(s) should/could pursue. Furthermore, by analyzing the values of each
performance parameters related to a determined cluster, and selecting the parameters
that give the major contribute to the total fitness, it is also possible to indicate the
particular opportunity that can be caught. For example, a high value of BO6 indicates
that there are some clients common to more than 5 companies. This suggests the
possibility, for a network, to offer a new integrated product/service to that clients,
given by the combination of products/services provided by the single companies.
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