A methodology to characterise cooperation links for networks of firms

Abstract

Networks of industrial small and medium enterprises are often framed thanks to pre-existing personal relations between managers. This way of building networks is satisfactory in terms of trust between partners, but tends to ignore potential efficient links with other firms. This article provides a methodology to characterise cooperation links objectively and to identify potential ties for enterprise networks. It is based on a theoretical approach combining complementarity of activities and similarity of competences within firms. Activities are modelled with graph theory, and competences with fuzzy sets. This allows plotting cartographies describing potential relationships within a group of firms. The illustration given here is an example of the utilisation of this methodology in the mechanical sector.

Keywords:

• Network of firms
• Coordination
• Activity
• Competence
• Cartography

Acknowledgement

English edited with the help of Christopher Yukna and Igor Konak.

Notes

† Northern Italy has been identified as one of the first places for inter-firm cooperation in the SME’s world. Here, industrial relationships are built between family-owned manufacturing firms thanks to long-lasting ties between people (Pyke et al. 1990).

† These factors are either relating to the market contingency or to the firms’ characteristics. As an example of market contingency, Goyal and Joshi (2003) have shown that incentives to collaborate for R&D projects are intimately related to the nature of market competition and the costs of forming links. However, we will concentrate here on firms’ characteristics for we are interested in manufacturing organisation.

† It differs from the organisational proximity in the way that it does not require organised and coordinated actions. A mental adhesion to institutional values is enough to ensure institutional proximity.

‡ For example, how the SMEs are connected together; which type of organisation is managing the network; how large is the presence of a SME network in its final market.

† In the car industry for instance, this coordination is assumed by inter-enterprise cooperation thanks to extended logistic chains.

† Note that ‘proactive’ and ‘defensive’ are essentially a terminology to identify the nature of the links.

‡ Répertoire Opérationnel des Métiers et de l’Emploi (Operational Directory for Professions and Employment). The ROME dictionary presents an advantage in providing a standard in France, and it describes the savoir faire in an aggregated way, therefore providing a standardised competences dictionary adaptable to the C.L.E. methodology.

† This influence is not symmetrical, that is to say that the influence of A_i on A_j is often different from the influence of A_j on A_i ; hence the graph obtained here is directed.

‡DC = [(0.1 * 0.1) * 3 + (0.05 * 0.1) * 0 + (0.85 * 0.1) * 3 + (0.1 * 0.2) * 2 + (0.05 * 0.2) *2 + (0.85 * 0.2) * 2 + (0.1 * 0.7) * 2 + (0.05 * 0.7) *2 + (0.85 * 0.7) * 3]/3 = 0.9.

† This distance is frequently used when dealing with fuzzy sets (Kaufmann 1973). It is an instance (α = 1) of the distance where α ≥ 1. One way of research is to study the impact of other values of α.

† Definition of transitive closure: Consider a directed graph G = (V, E), where V is the set of vertices and E is the set of edges. The transitive closure of G is a graph G+ = (V, E+) such that for all v, w in V there is an edge (v, w) in G+ if and only if there is a non-null path from v to w in G.

‡ The ‘transitive closure’ of the fuzzy relation is, by definition, the relation: (Note that when card(E) = k, the transitive closure of is obtained after a maximum of k compositions: ).

§ If there is a reciprocal arc of weight under the threshold, then both arcs will be eliminated.

† In this case study, the quality indicator is 0.9 when partitioning the graph into strongly connected components according to Muller (1972), and 0.59 when partitioning via Alpert (1996) algorithm. Furthermore, the obtained sub-groups are less relevant than those obtained with the proposed algorithm.