An Analysis of Shipping Agreements: The Cooperative Container Network

Abstract

The recent economic downturn has intensified the need for cooperation among carriers in the container shipping industry. Indeed, carriers join inter-firm networks for several reasons such as achieving economies of scale, scope, and the search for new markets. In this paper we apply network analysis and construct the Cooperative Container Network in order to study how shipping companies integrate and coordinate their activities and to investigate the topology and hierarchical structure of inter-carrier relationships. Our data set is comprised of 65 carriers that provide 603 container services. The results indicate that the Cooperative Container Network (CCN) belongs to the family of small world networks. This finding suggests that the most cooperative companies are small-to-medium-size carriers that engage in commercial agreements in order to reduce costs and, when in partnership with larger carriers, these cooperative companies are able to compete, especially against the largest carriers. However shipping companies with high capacity engage in cooperation with other carriers by merely looking for local partners in order to increase their local and specialized market penetration.

Appendix

We propose the application of a network community detection analysis in order to identify how carriers cluster together in the container shipping industry.

In this study we present the results of the application of the Spinglass method (Reichardt and Bornholdt 2006). We also test a number of other methods (Table 3), but we propose the partition provided by the Spinglass algorithm because it offers the highest value of modularity Q (Newman and Girvan 2004) among the methods tested. The modularity Q provides a measure to discern if a partition is valid to unfold the community structure in a network.

Table 3 List of community detection methods applied to identify clusters in the CCN

The six methods tested provide us with partitions of similar values of modularity Q, unless the number of clusters provided by each method ranges between 4 and 9. In order to evaluate how similar these partitions look, we propose the application of a quantitative index, the Adjusted Rand Index (ARI) proposed by Hubert and Arabie (1985). The ARI compares two partitions T and W of the same data set. The first partition T is used as a reference partition. Classes in partition W are in turn evaluated according to the following formulation:

$$ ARI=\frac{\left({}_2^n\right)\left(a+d\right)-\left[\left(a+b\right)\left(a+c\right)+\left(c+d\right)\left(b+d\right)\right]}{{\left({}_2^n\right)}^2-\left[\left(a+b\right)\left(a+c\right)+\left(c+d\right)\left(b+d\right)\right]} $$

(4)

Where:

a :

is number of pairs of elements belonging to the same class both in T and W.

b :

is number of pairs of elements belonging to the same class in T and to different clusters in W.

c :

is number of pairs of elements belonging to different classes in T and to the same cluster in W.

d :

is number of pairs of elements belonging to different classes both in T and W.

n :

is number of elements of the partitions.

The ARI ranges between 0 and 1 (perfect similarity). Table 4 shows the level of similarity of the partitions provided by the six methods of community detection. We order the table to have a comparative analysis from the best method (as proved by the modularity function Q) to the lower value. A high level of agreement can be detected among all the partitions (Table 4), thus confirming that apart from small variations, the partition provided by the Spinglass method is reliable.

Table 4 Similarity matrix of the Adjusted Rand Index values between the community detection methods tested on the CCN

By comparing the Spinglass partitioning (Table 5) with the results proposed in Table 4, as well as the composition of official alliances, we can see that community 2 comprises all members of the CKYH alliance. The membership of this cluster appears to be quite heterogeneous, as it is composed of 17 carriers with an average degree k of 11 (standard deviation of 7.9). The other carriers are minor companies, as they do not belong to the first 15 companies in terms of shipped freight volumes. The members of the other official alliance, i.e. G6, are spread over the other clusters.

Table 5 List of cluster carrier membership provided by the Spinglass method. We report the degree k of each carrier in brackets

In order to clarify the relationships between the network structure and the cluster organization of carriers, Table 6 shows some statistics on the average degree and standard deviation of the carriers belonging to each cluster, and the list of the three leading carriers in terms of network connections. Most clusters show similar values of average degree k and standard deviation. There are a few leaders in each group (dominant carriers) while weakly connected carriers compose the remainder of the clusters’ population (high values of standard deviation). Finally, Fig. 7 depicts the cluster membership of the carriers in our sample as provided by the Community Spinglass method. The size of each node is drawn as a function of the number of connections, while the colours correspond to node membership in the five clusters.

Table 6 List of community detection methods applied to identify clusters in the CCN

Fig. 7

A visualisation of the CCN and the partitions detected by the Spinglass algorithm