Classifying Ports for Efficiency Benchmarking: A Review and a Frontier-based Clustering Approach

Abstract

Port efficiency and port clustering are two aspects that have received different degrees of attention in the existing literature. While the actual estimation of port efficiency has been extensively studied, the existing literature has paid little attention to developing robust methodologies for port classification. In this paper, we review the literature on classification methods for port efficiency, and present an approach that combines stochastic frontier analysis, clustering and self-organized maps (SOM). Cluster methodologies that build on the estimated cost function parameters could group ports into performance metrics’ categories. This helps when setting improvement targets for ports as a function of their specific cluster. The methodology is applied to a database of Spanish port authorities. The dendrogram features three clusters and five outlier Spanish Port Authorities. SOM are employed to track the temporal evolution of Spanish Port Authorities that are of special interest for some reasons (i.e. outliers). Results show that use of a combination of cost frontier and cluster methods to define robust port typology and SOMs, jointly or in isolation, offers useful information to the decision-makers.

Keywords:

• port benchmarking
• hierarchical clustering
• cost efficiency
• self-organized maps

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Formally, technical efficiency is the capacity of obtaining the maximum amount of output from certain inputs (output orientation). Alternatively, as the capacity of obtaining a given output level using the minimum amount of inputs (input orientation). Also, a company presents efficiencies of scale, if it reaches the maximum productivity with the current technology.

2. One of the advantages of DEA is that the researcher can generate results with relatively small data sets. As a result, DEA has been used extensively in the economic analysis of port efficiency.

3. Note that in our paper, the SOMs are employed to analyse the temporal evolution of ports, and not to produce actual clusters, as Sharma and Yu (2009) and Quaresma-Dias et al. (2009) did. The aim of their application of SOMs was to generate an input-based clustering, which was subsequently combined with a set of efficiency tiers obtained from the DEA.

4. The optimal variable weights which are going to be used for building port clusters come from an SFA model which took unobserved heterogeneity into account.

5. For the sake of brevity, we only summarize the details needed to understand what are we doing here and refer the interested readers to the original paper.

6. They began by following the model proposed by Battese and Coelli (1995), which allows them to specify economic inefficiency in terms of a set of explicative variables that may change with time. This model did not need to recur to second-stage analysis, thus avoiding inconsistency problems; see Wang and Schmidt (2002). However, they proposed the re-estimation of the model within a Fixed Effect Model (FEM) framework, by introducing port authorities dummy variables into the frontier equation; this was done in order to capture possible systematic differences between ports (unobservable heterogeneity), If this heterogeneity exists and it is not explicitly picked up in the model, then a problem of omitted variables exists; consequently, the estimated coefficients of the included variables will be biased. In this way, the FEM model nests the previous pooled model and, on the basis of likelihood ratio tests, the restricted model was rejected; thus, the FEM was found to be a better representation of the technology for the sample. The immediate implication is that a model, which does not account for individual effects, would be misspecified, and therefore provides biased parameter estimates and misleading inference.

7. The estimated cost function fulfils the properties required by the theory; the regularity conditions are satisfied as the outputs are increasing, and the input prices are non-decreasing and quasi-concave.

8. Everitt, Landau, Leese, and Stahl (2011) is a general reference to cluster analysis. Xu and Wunsch (2005) present a comprehensive survey of algorithms for data clustering.

9. Here, we only present their methodology briefly, and we refer the interested readers to the original paper.

10. By using iTOL (Letunic & Bork, 2007), we generated the dendrograms with their branches labelled according to their height.

11. In unsupervised learning, the goal is to describe the associations and patterns among a set of unlabelled samples (Duda, Hart, & Stork, 2000; Hastie, Tibshirani, & Friedman, 2009).

12. On a two-dimensional squared lattice, the Von Neumann neighbourhood comprises the four nodes orthogonally surrounding a central node (Schiff, 2008).

13. To show the advantages of the methodology of combining SFA and hierarchical clustering, we only need to analyse a single year from within the sample. Since we get very similar port cluster for the selected years, we only report results for 2003; moreover, in that year, the Spanish port authorities showed the highest average economic efficiency for the 1993–2007 period.

14. The port authorities clusters mirror the performance indicator because the optimal variable weights used to build them come from a stochastic frontier cost efficiency model.

15. Unobserved heterogeneity is not reflected in measured variables, but it is expressed in the form of effects (Greene, 1993).

16. Although Medal-Bartual & Sala-Garrido classified ports according to multiple characteristics, no variable weights were assigned.

17. For example, Barcelona and Valencia, two out of the three biggest general cargo ports, were merged into the same C1 sub-cluster.

18. Martinez-Budria et al. state that they use the port classification provided by the former General Management of Ports, but the only explanation they offer is “is based on a complexity criterium given by port size and the composition of the output vector”. They offer no reference on where more information about this port classification may be found.

19. Self-Organized Maps were generated using the SOM Toolbox for Matlab: http://www.cis.hut.fi/projects/somtoolbox/.

20. In 2011, Marín-Pontevedra overtook A Coruña as general merchandise port.