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Production networks and partner selection problem.

1. Introduction

The process of globalization, and recently global economic crisis, are forcing researchers to seek for new flexible business-organizational structures. It is clear that the classical vision of the enterprise and its activities no longer corresponds to economic realities. This fact is especially true when it comes to manufacturing enterprises.

Today's manufacturing enterprises need to have a high degree of specialization in different narrow fields of work, and, at the same time, a flexible manufacturing system that will listen to and adapt to the needs of customers (a very specific ones, and a wide range ones). New manufacturing paradigm called personalized production is taking place (Figure 1).

According to Y. Koren globalization has created a new, unprecedented landscape for the manufacturing industry, one of fierce competition, short windows of market opportunity, frequent product introductions, and rapid changes in product demand (Koren, 2010). Indeed, globalization is challenging, but it presents both threats and opportunities. So the challenge is to succeed in a turbulent business environment where all competitors have similar opportunities, and where customer wants personalized product. There are two types of personalized products (Koren, 2010):

--Product's regional fit--Besides culture and market, regionalization must take into account additional limitations: purchasing power, climate, and legal regulations (e.g., safety, environmental limitations, and driving on the left side of the road). Market research that collects and analyzes information about the habits and needs of customers in the target country is a necessity for the product's success.

--Product personalization--Products that are manufactured to fit the buyer's exact needs are likely to become a new source of revenue in developed countries.

Personalized production creates a new vision of a modern enterprise which needs to unite the somewhat contradictory requirements: specialization vs. flexibility. Traditional flexible manufacturing systems are not able to fulfill those requirements and to be economical in the same time. There is a need of new production systems, like the one presented by Y. Koren: reconfigurable manufacturing system (Koren, 2010). The reconfigurable manufacturing system is much more flexible than flexible manufacturing system. According to Y. Koren there are three main principles of reconfigurable manufacturing system (RMS) (Koren et al., 2010):

1. An reconfigurable manufacturing system providesadjustable production resources to respond to unpredictable market changes and intrinsicsystemevents:

--RMScapacitycanberapidlyscalableinsmallincrements;

--RMSfunctionalitycanberapidlyadaptedtonewproducts;

--RMSbuiltinadjustmentcapabilitiesfacilitaterapidresponsetounexpectedequipmentfailures.

2. A reconfigurable manufacturing system isdesignedaroundaproductfamily, withjustenough customized flexibility to produce all members of that family.

3. The reconfigurable manufacturing system core characteristics should be embedded in thesystem as a whole, as well as in its components (mechanical, communicationsandcontrol).

For instance, the environment of many manufacturing enterprises is characterized by unpredictable market changes. Reconfigurable manufacturing system meets these requirements by rapidly adapting capacity and functionality to new situation. Implementing RMS characteristics and principles in the system design leads to achieving the ultimate goal: "living factory" (Koren et al., 2010). The "living factory" can rapidly adjust its production capacity while maintaining high levels of quality.

However, such a reconfigurable structure as "living factory" can be also achieved by networking small and medium-sized enterprises (SMEs) into production networks. It is only important that every SME of production network is capable and wiling to be part of special cooperation inside network called virtual enterprise (VE) (Camarinha-Matos et al., 2001). For each new product a new virtual enterprise is formed from different SMEs (Figure 2).

According to L.M. Camarinha-Matos (Camarinha-Matos et al., 2007)virtual enterprise is a temporary alliance of enterprises that come together to share skills or core competencies and resources in order to better respond to business opportunities, and whose cooperation is supported by computer networks. Two key elements in this definition are the networking and cooperation, as most important part (Schermerhorn et al., 2002). Clearly, there is a tendency to describe a virtual enterprise as a network of cooperating enterprises. A number of pre-existing enterprises or organizations with some common goals come together, forming an interoperable network that acts as a single (temporary) organization without forming a new legal entity nor establishing a physical headquarter. In other words, virtual enterprises materialize through the integration of skills and assets from different firms into a single business entity. The idea of virtual enterprise compared to other types of virtual organization is shown on the following figure (Figure 3).

So, in production network each SME has its autonomy, because this network is non-hierarchical. Such a network contains elements of a holistic system, such as for example: ants in nature. Each ant is an autonomous, but all the ants communicate with each other and cooperate for the benefit of the entire anthill. This is the basic idea of production network. Which means, all enterprises in the network, in addition to already existing cooperation, are willing and able to develop new cooperation on new projects forming a new virtual enterprise?

SMEs, which primarily apply new technologies with ease, were recognized by the European Union as the key factors of transformation of the European "knowledge-based economy" (KPMG Special Services, 2003). According to the EU, the enterprise is classified as SME if: it's independent, have fewer than 250 employees and balance sheet total not exceeding 43 million[euro]. In addition, SMEs can be parsed to very small (micro) enterprises having fewer than 10 employees. A further reason of EU investment in SMEs is their share in the total number of enterprises: 99.8% (Figure 4).

A particular potential are micro enterprises that have the productivity level of 62% which is up to 25% less than productivity of SMEs (Muller, 2006). This lack of productivity is primarily classified as unused capacity or lack of work. When it comes to the Republic of Croatia, the structure of industrial enterprises is similar (Figure 5).

The only difference is that in the Republic of Croatia half of employees in the industrial sector are in LEs, while in the EU about a third of employees are in LEs.However, trends in the period 2004-2007 show an increase in the number of SMEs by 39.6% (Table 1) and an increase in number of employees by 22.6% (Table 2) (Mladineo et al., 2011). While in the same period the number of LEs remained the same, and number of their employees declined by 2.1%.

The general conclusion is that the Republic of Croatia is catching up with EU trends in the structure of industrial enterprises, as well as in the structure of their employees. Therefore, the EU strategy for the development of SMEs should begin to apply in Croatia.

I Similar structure of SMEs can be found in country with some of the world's best production systems: in Japan (Figure 6) (Mladineo et al., 2011). That clearly shows that networking of SMEs has a global potential and it represents a future of production systems.

In 2011, to stimulate research and development of SMEs production networks, European Union has funded six FP7 projects with more than 37 million [euro] budget: ADVENTURE, BIVEE, ComVantage, GloNet, IMAGINE, and VENIS. It appears that one of the key strategies of development of SMEs is their networking in regional production networks

2. Production Network Models

Concept of production networks is a research field of scientists all over the world. In EU: Germany (Bolt et al., 2000; Gerber et al., 2004; Neuberta et al., 2004; Roth et al., 2005; Jahn et al., 2006; Muller et al., 2006; Ackermann, 2007; Jaehne et al., 2009; Kampker et al., 2010; Ganss et al., 2011; Lau et al., 2011), Belgium (Vancza et al., 2011), Hungary (Schuh et al., 2008), Portugal (Camarinha-Matos et al., 2001; Pinto Leitao, 2004), Netherlands(Camarinha-Matos et al., 2007), Spain (Giret et al., 2009), Italy (Villa et al., 1998; Corvello et al., 2007; Manzini et al., 2011), Greece (Assimakopoulos et al., 2003) and Croatia (Mladineo et al., 2011); in USA (Leigh Reid et al., 1996; Sturgeon et al., 2002); in China (Hongzhao et al., 2005), Japan (Yamawaki, 2002) and South Korea (Choi, 2005); in Columbia (Mican et al., 2011) and Brasil (Lima et al., 2011). However, only few concepts (models) have been completely developed to be implemented in practice. These three models are: competence-cell-based network, complexity-based model, and core competence cell model.

2.1. Competence-cell-based Network

According to E. Muller et al. (Muller et al., 2006) the current mode of cooperation is mostly hierarchical. In most cases, the two components of cooperation, operation and communication, are delegated to different hierarchical levels: operation to the shop floor level and the inter-organizational communication to the management level. The "redirection" of communication regarding the cooperative production process, produces process losses and prevents direct feedback from shop floor to shop floor.

So the idea was to seek for the non-hierarchical cooperation concept of networking of small and medium-sized enterprises. Such a network is called competence-cell-based network (Muller et al., 2006). Each enterprise represents a single competence-cell, since the employees of each company have a specific set of competencies. However, each competence-cell retains its autonomy, because this network is non-hierarchical.

This concept is particularly interesting for application in Croatia, since the economy of Croatia has very similar problems with slow recovery from real-socialist production system, like ex-Eastern Germany.

2.1.1. Competence cell

A competence cell (Muller et al., 2006) is considered as smallest autonomous indivisible performance unit of value adding. The human competences of each cell are obtaining crucial importance, so the human is in the centre of the competence cell. There are different types of competence cells, covering the whole value adding process: marketing competence cells, product development competence cells, production planning competence cells, manufacturing competence cells, assembly competence cells and quality control/service competence cells. E. Muller et al. developed generic model of the competence cell (Muller et al., 2006) (Figure 7) based on general production theory, specific networking requirements and investigations into the business processes of marketing, product development, production planning, manufacturing & assembly, logistics and quality control & service. The generic model consists of (Muller et al., 2006):

--the competence of humans, arranged according to professional, methodical, social and personnel competences;

--available resources;

--the fulfilled task or executed function.

With this function a business entity is transformed and a certain performance is achieved. For a complete technical description the aspects of dimension and structure were supplemented. Function, competence, resource and marketable performance serve as criteria to further operationalise the required decomposition of the competence cell. Although E. Muller et al. differ several types of competence-cells, this paper will be limited only to the competence-cells for manufacturing and assembly.

2.1.2. Networking of competence cells

The vision of competence-cell-based networking is based on the model consisting of three levels (Figure 8) (Roth et al., 2005; Ackermann et al., 2007). From loose infrastructural and mental relations in a regional network (level I) there initially emerges an institutionalized competence network, based on competence cells (level II). The actual creation of value takes place in a production network (level Ill), and the production network in this model represents virtual enterprise. It is initiated by customer needs transformed into business request.

2.2 Complexity-based Model

According to G. Schuh et al. (Schuh et al., 2008) it is possible to manage dynamic reconfigurable collaborations in industry by defining generic model of complexity. Reconfigurable collaboration is a type of production network. There are several abstract complexity drivers that can cause problems in collaboration networks. The main drivers are as follows:

--uncertainty (e.g., limited information);

--dynamics (e.g., dynamic changes);

--multiplicity (e.g., a large number of participating elements and influencing factors);

--variety (e.g., many types of elements);

--interactions (e.g., communication loads);

--interdependencies (e.g., feedback loops).

G. Schuh et al. suggest modeling the dynamic behavior of a production network as a Complex Adaptive Systems (CAS) (Schuh et al., 2008). A CAS can be considered a multi-agent system with seven basic elements in which "a major part of the environment of any given adaptive agent consists of other adaptive agents, so that a portion of any agent's efforts at adaptation is spent adapting to other adaptive agents". Agents may represent any entity with self-orientation, such as cells, species, individuals, enterprises or nations. Environmental conditions change, due to the agents' interactions as they compete and cooperate for the same resources or for achieving a given goal. This, in turn, changes the behavior of the agents themselves.

Furthermore, computer-based simulations can be applied to evaluate these systems. Simulations can help observing and investigating, e.g., how (potentially simple) individual behavior rules may emerge and give rise to complex (and often unpredictable) collective behavior. Additionally, the stability of these kinds of systems together with the effects of uncertainties (such as the lack of precise market forecasts as well as personal contacts) could also be evaluated by simulations.

2.3. Core Competence Cell Model

D. T. Matt (Matt, 2007), like G. Schuh (Schuh et al., 2008), is dealing with problem he structural complexity of growing organizational systems like production networks. To reduce structural complexity he reduces cells (enterprises) to three basic types: core competence cells (3C). The core competence cells are defined as:

--dealer (DL) is defined as a person or a company that buys and sells goods or services;

--producer (PR) aims at the minimization of manufacturing costs and the optimization of flexibility;

--service provider (SP) aims at "selling" his collaborators most profitably.

The central success factor of a network cell is to strictly focus on one core competence type and to force and professionalize it by entrepreneurial incentives. The different success mechanisms of DL, PR, and SP show once again that their mixing increases complexity and causes losses in efficiency. To maintain the strict core competence type focus means to inherit a cell's "success DNA" to its spin-off in the case of a cell division.

According to D. T. Matt (Matt, 2007), it can be stated that the proposed 3C model helps to reduce the entire organizational complexity from a structure perspective. It allows an organization to flexibly adapt to changing environmental conditions and thus promotes sustainable business growth within an organizational network.

3. Production Network Lifecycle

As it was mentioned, the idea of virtual enterprise differs from other types of virtual organization (Figure 3). According to L. M. Camarinha-Matos virtual organizations can be described as (Camarinha-Matos et al., 2001):

--extended enterprise is the closest to virtual enterprise, however it is better applied to an organization in which a dominant enterprise extends its boundaries to all or some of its suppliers (automotive industry);

--virtual enterprise can be seen as a more general concept including other types of organizations, namely a more democratic structure in which the cooperation is peer to peer (i.e. extended enterprise can be seen as a particular case of virtual enterprises);

--virtual organization is a concept similar to a virtual enterprise, comprising a network of organizations that share resources and skills to achieve its mission/goal, but not limited to an alliance of enterprises, for example virtual organization could be a virtual municipality organization, associating via a computer network, all the organizations involved in a municipality (city hall, municipal water distribution services, internal revenue services, public leisure facilities, cadastre services, etc.);

--networked organization is the most general term referring to any group of organizations inter-linked by a computer network, but without necessarily sharing skills or resources, or having a common goal.

Since the virtual enterprise has been defined as a something non-hierarchical and temporary, it is important to analyze lifecycle of virtual enterprise, i.e. lifecycle of production network. Few researches have made phenomenological research of virtual enterprise lifecycle. In literature can be found virtual enterprise lifecycle of L. M. Camarinha-Matos et al. (Camarinha-Matos et al., 2001) and R. Leigh Reid et al. (Leigh Reid et al., 1996). Generally, virtual enterprise lifecycle consists of: customer request which triggers the creation of virtual enterprise, creation process, operation process and dissolution process. This generic concept of virtual enterprise lifecycle is compared to the concepts from literature (Figure 9).

In the following table virtual enterprise lifecycle of L. M. Camarinha-Matos et al. and R. Leigh Reid et al. are mutually compared (Table 3).

4. Partner Selection Problem

The problem of the selection of enterprises in production network, also known as partner selection problem (Wu et al., 1999; Fischer et al., 2004; Wu et al., 2005; Mourtzis, 2010; Ma et al., 2012; Mourtzis et al., 2010), arises when the production process is parsed to technological operations that need to be completed to produce a product. In fact it is very likely that the same technological operations can be done by two or more different cells (enterprises) in the network. The question is: which enterprise to choose? Therefore, it is obvious that, before the selection process, enterprises need to be evaluated (on the basis of their performances and competences)(Fischer et al., 2004; Mladineo et al., 2011). In this way, enterprises with the highest ratings will be selected and they will form new virtual enterprise.

Figure 10 shows a production problem, i.e. a production process with possible alternatives, and its optimal solution (Mladineo et al., 2013). The problem can be presented as a network graph that has a beginning or source (order) and end or drain (delivery). The network is formed of competence-cells (enterprises), and each technological operation is presented by cells that can perform it. Each enterprise has its rating. Higher rating is better.

According to Figure 10, for each technological operation (turning, milling or assembly) a cell (enterprise) with higher rating is selected. Hence, the production process will be realized using best combination of enterprises. The combination of enterprises is one new virtual enterprise.However, the evaluation of enterprises performances is needed to solve the problem of the selection of enterprises in production network, or partner selection problem.

Since, the partner selection problem is multicriteriaproblem, in this chapter a special multiple criteria decision analysis (MCDA) method is used: PROMETHEE method. However, to completely solve partner selection problem a combination of metaheurstic optimization algorithms and MCDA methods must be used. In the literature different approaches using different multicriteria methods or metaheuristics can be found: M. Fischer et al. (Fischer et al., 2004) and H. Jung (Jung et al., 2011) are using AHP (Analytic Hierarchy Process) method; G. Lanza et al. (Lanza et al., 2010) and M. Mladineo et al. (Mladineo et al., 2013) are using PROMETHEE (Preference Ranking OrganisationMETHod for Enrichment Evaluations) method; F. Gao et al. (Gao et al., 2006) are using Particle swarm algorithm; C. X. Yu et al. (Yu et al., 2011) are using TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method; C. L. Chuanga et al. (Chuanga et al., 2009) F. Zhao et al. (Zhao et al., 2006) are using combination of DEA (Data Envelopment Analysis) and Genetic algorithm, and many others are using different evolutionary or multi-agent approaches (Choi et al., 2007; Wang et al., 2009; Nayak et al., 2010; Tao et al., 2010; Lanza et al., 2011; Zhang et al., 2012). It is also important to highlight the partner selection problem is more complex than similar optimization problems like the assignment problem (Wikipedia, 2013) and the job-shop problem (Wikipedia, 2013), therefore same algorithms can not be used.

4.1. PROMETHEE Method

The problem of the selection or the ranking of alternatives submitted to a multicriteria evaluation is not an easy problem, neither economically nor mathematically. Usually there is no optimal solution; no alternative is the best one on each criterion. In the recent years several decision aid methods or decision support systems have been proposed to help in the selection of the best compromise alternatives. In this chapter the PROMETHEE (Preference Ranking OrganisationMETHod for Enrichment Evaluations) methodwas chosen for treating multicriteria problem(Brans et al., 1984; 1986; 1994). This method is known as one of the most efficient but also one of the easiest in the field. PROMETHEE method is well accepted by decision-makers because it is comprehensive and has the ability to present results using simple ranking(Brans et al., 1984).

An input for PROMETHEE method is a matrix consisting of set of potential alternatives (actions) A, where each a element of A has its f(a) which represents evaluation of one criteria (Figure 11). Each evaluation fj(ai) must be a real number.

4.1.1. Preference function

The preference structure of PROMETHEE method is based on pairwise comparisons(Brans et al., 1984; 1986; 1994). The deviation between the evaluations of two alternatives on a particular criterion is considered. For small deviations, the decision-maker will allocate a small preference to the best alternative and even possibly no preference if he considers that this deviation is negligible. The larger the deviation is, the larger the preference is. There is no objection to consider that these preferences are real numbers varying between 0 and 1. This means that for each criterion the decision-maker has in mind a function:

[P.sub.j](a, b) = [F.sub.j][[d.sub.j](a, b)] (1)

where:

[d.sub.j](a, b) = [f.sub.j] (a) - [f.sub.j](b) (2)

and for which:

0 [less than or equal to] [P.sub.j] (a, b) [less than or equal to] 1 (3)

In case of a criterion to be maximized, this function is giving the preference of a over b for observed deviations between their evaluations on criterion [f.sub.j]. It should have the following shape (Figure 12).

The preferences equal 0 when the deviations are negative. The following property holds:

[P.sub.j](a, b) > 0 [??] [P.sub.j] (b, a) = 0 (4)

For criteria to be minimized, the preference function should be reversed oralternatively given by:

[P.sub.j](a, b) = [F.sub.j][-[d.sub.j](a, b)] (5)

The pair{[f.sub.j](), [P.sub.j](a,b}) is thegeneralized criterionassociatedto criterion [f.sub.j](). Such ageneralized criterion hasto be defined foreach criterion.In order to facilitate the identification six types of particular preference functionshave been proposed (Table 4)(Brans et al., 1984; 1986; 1994).

4.1.2. PROMETHEE I and PROMETHEE II

First, method PROMETHEE I ranks actions by a partial pre-order, with the following dominance flows (Figure 13) (Brans et al., 1984; 1986; 1994):

leaving flow: [[PHI].sup.+](a) = 1/[n - 1] [[summation].sub.x[member of]A] [product](a,x) (6)

entering flow: [[PHI].sup.-](a) = 1/[n - 1] [[summation].sub.x[member of]A] [product](x,a) (7)

wherea denotes a set of actions, n is the number of actions and [product] is the aggregated preference index defined for each couple of actions. The PROMETHEE I method gives the partial relation.

Then, a net outranking flow is obtained from PROMETHEE II method which ranks the actions by total pre-order (Figure 14) (Brans et al., 1984; 1986; 1994):

net flow: [PHI](a) = [[PHI].sup.+] (a) - [[PHI].sup.-](a) (8)

In the sense of priority assessment net outranking flow represents the synthetic parameter based on defined criteria and priorities among criteria. Usually, criteria are weighted using criteria weights wj and usual pondering technique:

[product](a,b) = [summation][w.sub.j][P.sub.j](a,b)/[summation][w.sub.j] (9)

Furthermore, different sets of criteria weights can be used and then each set represents one scenario. And usually MCDA problems have more than one scenario.

4.1.3. Example of usage of PROMETHEE method

Here the PROMETHEE method is demonstrated on the problem of selection of location for new power plant. There are 6 different locations (alternatives) and there are 3 criteria: manpower (number of personnel), power of power plant (MW) and cost of construction (M[euro]). For each criterion preference function and all parameters are chosen (Figure 15). Problem is solved by PROMETHEE I method (Figure 16) and PROMETHEE II method (Figure 17) using special software called Visual PROMETHEE(http://www.promethee-gaia.net/). The weight for each criteria is determined by group of experts.

5. Solving Partner Selection Problem

Special case of virtual enterprise evaluation occurs when partners are a prioriselected(Mladineo et al, 2013), i.e. some of enterprises are willing to be part of new virtual enterprise, and some are not. In this special case it is possible to have small number of different combinations of partners of new virtual enterprise. So there is need to mutually compare couple of virtual enterprises. It rises following questions: Which virtual enterprise is the best one? How much is one virtual enterprise better than others? The first question is ranking problem, and the second question is sorting problem(Mladineo et al, 2013). However, pre-requisition of virtual enterprise evaluation is the evaluation of enterprises that can be part of new virtual enterprise.

5.1. Enterprise Evaluation

To evaluate and rank enterprises it is necessary to design a set of criteria that will represent all the important parameters which need to be taken into account when performing ranking. It should be primarily taken into account that there are parameters that change each time when a new production network is formed for a new product, and there are parameters that do not change so often. Therefore, a set of criteria which will be used can be divided into two sets (Mladineo et al, 2011),:

--dynamic criteria: criteria whose values change for each enterprise depending upon the offer for particular product production or development (an example of such criteria is the price of the product);

--static criteria: criteria whose values do not change so often, or at most a few times a year (an example of such criteria is a technology of enterprise).

A set of dynamic criteria includes offer that enterprise offered when a new production network for a new product is formed. That offer is usually made up of two elements: the price per piece and the day of delivery. Static set of criteria can be further divided onto :

--competence criteria: criteria covering all the competencies of the enterprise: technical, organizational and human competence;

--economic criteria: criteria that consider economic feasibility or risk of involving enterprise into production network;

--sociological criteria: criteria which analyze sociological impact of involving certain enterprise in the production network.

After criteria and theirs parameters have been determined, an input matrix for PROMETHEE method, i.e. criteria evaluation for each action (enterprise), is made using data gathered in special questionnaire. This questionnaire was sent to the production enterprises of Split-Dalmatia County. In the following figures (Figure 18 and Figure 19) an input matrix for 7 enterprises is shown. However, star names are used instead of real names of enterprises.

PROMETHEE method was performed using 4 different predefined scenarios (Figure 20). A set of weights for each scenario was determined by experts. Criteria preference function type and preference thresholds where obtained using in-built function "Preference Function Assistant" of Visual PROMETHEE software. Following results where obtained (Figure 21 and Figure 21).

This analysis showed that 3 enterprises (Beta UrsaeMinoris, Alpha Ophiuchi and Beta Aquarii) are dominant in comparison with other enterprises. However, in different scenarios these 3 enterprises are taking turns at the top. For example: for simple product and small series the best enterprise to realize that production process is Alpha Ophiuchi. However, for complex product and large series the best enterprise to realize that production process is Beta UrsaeMinoris.

5.2. Virtual Enterprise Evaluation

Special case of virtual enterprise evaluation, when partners are a priori selected, will be analyzed on example of virtual enterprise for simple production process. For analysis and discussion a partner selection problem presented on Figure 23 will be used. Data on enterprises used in this problem are presented on Figure 24.

For production process presented on Figure 23 following virtual enterprises are a priori formed (Figure 25 and Table 5).

For each enterprise criteria evaluations are made depending on bid (i.e. cost) and rating (quality level) of every enterprise (Table 6).

Finally, criteria evaluations for each virtual enterprise are calculated using sum for cost and transport criteria, and average for rating criteria (Table 7).

These three virtual enterprises were compared using PROMETHEE method. A weight for each criterion was determined by experts. Criteria preference function type and preference thresholds were obtained using in-built function "Preference Function Assistant" of Visual PROMETHEE software. Following results were obtained (Figure 26).

From Figure 26 it is clear that the best virtual enterprise is VE-2. However, how much better is VE-2 than VE-3 and VE-1?

It is a problem of sorting, not just ranking. To calculate how much is VE-2 really better, it is important to compare all three virtual enterprises with optimal and anti-optimal solution of production process presented on Figure 3. It is similar to ideal and anti-ideal alternative used in TOPSIS method (Yu et al., 2011). However, in TOPSIS method ideal and anti-ideal alternative are fictional, but optimal and antioptimal solution of production process are real alternatives (Table 8 and Figure 27).

Now, final virtual enterprise evaluation matrix can be made (Table 9).

Again, these virtual enterprises were compared using PROMETHEE method. Same criteria weights, type of preference function and preference thresholds were used. Following results were obtained (Figure 28 and Figure 29).

After sorting virtual enterprises (Figure 29), it is clear that all three virtual enterprises mutually compared are very similar, and they are all much closer to the optimal alternative than the anti-optimal alternative. VE-2 and VE-3 are especially very similar alternatives (Figure 28), and only after sorting it was possible to clearly see that fact.

6. Conclusion

In this chapter the optimization of selection of enterprises in production network was achieved using multi criteria decision analysis: PROMETHEE method. An evaluation and comparison of enterprises has been achieved. It is clearly shown that, using PROMETHEE method, enterprises can be evaluated taking into account their competences, i.e. what enterprise posses in the terms of technology, references, information system, etc. Hence, economic and sociological criteria can also be added into analysis. A special scenario portfolio was created for different complexity of product and/or production process. On the case study with real enterprises, it is shown that different scenarios will produce different enterprise as the best one. So it is very important for production network manager to carefully choose criteria weights and form proper scenarios. This could be done by interviewing experts. The evaluation and comparison of enterprises was pre-requisition to evaluate, compare andrank virtual enterprise.

A special case of virtual enterprise evaluation, when partners are a priori selected, has been analyzed. The difference between ranking and sorting is demonstrated on the example. It has been shown that sorting of alternatives is very important to get clear picture about real difference between alternatives (virtual enterprises).

7. Future Challenges

Production networks represent future of manufacturing; especially they represent possible solution for the new production-organizational paradigm "Production as a Service". This new paradigm intends to fulfill very specific needs and requirements of modern customer, i.e. to produce one piece of specific product for only one customer.

For instance, if a customer needs a special custom made motorcycle (Figure 30), he can buy only a similar motorcycle from motorcycle producer for reasonable price. If the customer wants exactly the same motorcycle as imagined one, he needs to buy it from custom made motorcycle producer. However, the price will not be reasonable, it will be very expensive. A custom made motorcycle for reasonable price is something that only production network can produce. And it represents main competitive advantage of production networks. But it also shows that production networks can function like "Production as a Service".

However, production networks are virtual organizations and there is a problem of stability of such an organizational formation. So the key challenge is to have production network formed of good and trustful enterprises, i.e. partners. And that is the reason why is solving of partner selection problems is one of the key challenges for successful management of production networks.

In further researches focus will be on solving more complex production processes, and on determination of criteria weights and other criteria parameters, usage of criteria weights stability intervals analysis, etc. Focus will also be on the design of fast and accurate algorithms for solving partner selection problems. Today's algorithms are taking lot of time to solve complex production processes. In the future this needs to be solved to be as fast as a web service used in web application for management of production network.

It is also important to highlight that the management of production networks requires knowledge about information technology ant it also requires knowledge about some management tools like multiple criteria decision analysis. All these issues need to be taken into account when drawing a path into the research area of production networks.

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Authors' data: Prof. Veza, I[vica]; Mladineo, M[arko]; Gjeldum, N[ikola], University of Split, Faculty of electrical engineering, mechanical engineering and naval architecture, R. Boskovica 32, 21000 Split, Croatia, iveza@fesb.hr, marko.mladineo@fesb.hr, ngjeldum@fesb.hr

DOI: 10.2507/daaam.scibook.2013.28

Tab. 1. Number of industrial enterprises in the period
2004-2007 (DZS)

            Large   Small and    Micro
                    medium       (Very small)

2004        210     2.108        4.133
2007        210     2.942        4.523
Increment   0,0%    39,6%        9,4%

Tab. 2. Number of employees in industrial enterprises in the
period 2004-2007 (DZS)

            Large     Small and    Micro
                      medium       (Very small)

2004        155.181   105.874      14.927
2007        151.867   129.819      16.862
Increment   -2,1%     22,6%        13,0%

Tab. 3. Virtual enterprise lifecycles comparison

Leigh Reid virtual          Camarinha-Matos virtual enterprise
enterprise lifecycle        liiecycle (Camarinha-Matos et al., 2001)
(Leigh Reid et al., 1996)

A virtual enterprise is     Creation: this is the initial phase when
conceived when a need is    the virtual enterprise is created /
recognized in the           configured and for which some of the
marketplace and an          major required functionalities are:
objective (or set of        Partners search and selection, Contract
objectives) is              Negotiation, Definition of access rights
established. This step      and sharing level, Join /Leave
requires understanding of   procedures definition, Infrastructure
the customers'              configuration, etc.
expectations/needs and
what it will take to
satisfy them. The
enterprise that is
required to meet the need
is visualized, and a
transformation/migration
strategy is articulated.
This activity can be
accomplished by a single
firm or by an existing
virtual enterprise. This
step is essentially the
conceptual design of a
new enterprise.

The enterprise is created   Operation: this is     Evolution:
when relationships are      the phase when the     evolutions might
established that will       virtual enterprise     be necessary
eventually bring together   is performing its      during the
the requisite               business process(es)   operation of a
competencies, when a        in order to achieve    virtual enterprise
strategy is crafted and a   its common goal(s),    when it is
"product" is "designed"     and which requires     necessary to add
to meet the identified      functionalities such   and /or replace a
need. At this stage, the    as: Basic secure       partner, or change
firms that comprise the     data exchange          roles of partners.
enterprise will likely      mechanisms,            This need might be
develop and implement new   Information            due to some
or improved processes and   sharing and            exceptional event,
systems to prepare for      visibility rights      such as
the next stages of the      support, Orders        (temporary)
cycle. Activities in this   management,            incapacity of a
stage constitute detailed   Distributed and        partner, changes
design of the new virtual   dynamic planning       in the business
enterprise and complete     and scheduling,        goal, etc.
preparation for             Distributed task       Functionalities
implementation.             management, High       similar to the
                            levels of task         ones specified for
The virtual enterprise      coordination,          the creation phase
competes when the           Collaborative          are necessary to
"product" is offered in     engineering            also be supported
the marketplace. This       support, etc.          here.
activity may be

accomplished in several
ways. The enterprise may
offer new or alternative
solutions to previously
unmet need, or it could
identify, pursue and
capture a defined
opportunity to produce
and deliver its product.
Finally, the enterprise
could secure new
customers for existing
products.

After competing, the
enterprise is configured
as assets and
competencies are acquired
and the requisite
processes and
infrastructure are
deployed to accomplish
the objectives of the
enterprise. The assets,
processes, and procedures
are acquired or
developed, and integrated
as specified by the
enterprise design to
produce and deliver the
required product. These
activities comprise the
actual implementation
step for the new virtual
enterprise.

The virtual enterprise
then conducts operations
to produce, deliver and
support the "product" and
to maximize stakeholder
value.

It concludes operations     Dissolution: this is the phase when the
when the objectives of      virtual enterprise finishes its business
the enterprise are          processes and dismantles itself. Two
satisfied, by terminating   situations may be the cause for virtual
the relationships and by    enterprise dissolution, either the
re/deploying and/or         successful achievement of all its goals,
disacquiring assets.        or by the decision of involved partners
                            to stop the operation of the virtual
                            enterprise. The definition of
                            liabilities for all involved partners is
                            an important aspect that needs to be
                            negotiated. For instance, the
                            responsibility of a manufacturer more
                            and more remains during the life cycle
                            of the produced product till its
                            disassembly and recycling.

Tab. 5. Virtual enterprises formed a priori

Name of VE   Milling   Drilling   Counter-sinking   Threading

VE-1         E1        E1         E5                E5
VE-2         E10       E7         E8                E8
VE-3         E4        E9         E5                E9

Tab. 6. Criteria evaluations for enterprises

Enterprise ID   C1           C2
                Cost         Rating

E1              32 k[euro]   60 %
E2              34 k[euro]   81 %
E3              29 k[euro]   87 %
E4              31 k[euro]   77 %
E5              27 k[euro]   54 %
E6              33 k[euro]   49 %
E7              30 k[euro]   68 %
E8              29 k[euro]   44 %
E9              28 k[euro]   57 %
E10             31 k[euro]   91 %
E11             33 k[euro]   63 %
E12             30 k[euro]   72 %

Tab. 7. Criteria evaluations for virtual enterprises

             C1            C2       C3
Name of VE   Cost          Rating   Transport
             (Min)         (Max)    (Min)

VE-1         118 k[euro]   57,0 %   67 km
VE-2         119 k[euro]   61,8 %   74 km
VE-3         114 k[euro]   61,3 %   89 km

Tab. 8. Optimal (optimum) and anti-optimal (pessimum) alternative

Name of VE    Milling   Drilling   Counter-   Threading
                                   sinking

VE-Optimum    E10       E9         E5         E5
VE-Pessimum   E6        E11        E6         E6

Tab. 9. Final virtual enterprise evaluation matrix

              C1            C2       C3
Name of VE    Cost          Rating   Transport
              (Min)         (Max)    (Min)

VE-Optimum    113 k[euro]   64,0 %   48 km
VE-1          118 k[euro]   57,0 %   67 km
VE-2          119 k[euro]   61,8 %   74 km
VE-3          114 k[euro]   61,3 %   89 km
              132 k[euro]   52,5 %   120 km

Fig. 4. Structure of industrial enterprises in the EU

ENTERPRISES STRUCTURE (TU Chemnitz 2007)

Small and Medium             7,5%
Micro                       92,3%
Large                        0,2%

EMPLOYEES STRUCTURE (TU Chemnitz 2007)

Large                       30,3%
Small and Medium            30,3%
Micro                       39,4%

Note: Table made from pie chart.

Fig. 5. Structure of industrial enterprises in the Republic of Croatia

ENTERPRISES STRUCTURE (DZS 2007)

Large                        2,7%
Small and Medium            38,3%
Micro                       58,9%

EMPLOYEES STRUCTURE (DZS 2007)

Large                       50,9%
Small and Medium            43,5%
Micro                        5,6%

Note: Table made from pie chart.

Fig. 6. Structure of industrial enterprises in Japan

ENTERPRISES STRUCTURE (SMBA 2000)

LE           0,7%
SME         99,3%

EMPLOYEES STRUCTURE (SMBA 2000)

LE           26,0%
SME          74,0%

Note: Table made from pie chart.
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Author:Veza, I.; Mladineo, M.; Gjeldum, N.
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