Parcel Size Distribution (PSD)

By David Restrepo G.


The Parcel Size distribution function (PSD) is a fundamental factor in the international maritime trade. There is an extensive commodities diversity, manufactured semi-finished and finished products that must be mobilized along the supply chain to meet the demands of the global market. Therefore, it is essential to understand some variables that affect the way in which the maritime industry transports these products (Spopford, 2009. p.58) and the type of vessels that are used to achieve the optimization of resources.

Parcel Size Distribution (PSD) is defined by Stopford (2009) as “… the consolidated individual charge for one (01) shipment …” (page 59). It describes the interdependence between the products to be transported (production, inventories/demand), the characteristics of the ships used for transport, and the capacity of the ports that receive this cargo.

Variables interaction in parcel size distribution function:
The graphs below show visually the interaction of the variables that are part of the PSD. Each of the products that are transported by sea handled a particular PSD function. In Figure 1, adapted from Stopford (2009), the shape of the load-size distribution of products such as coal, grains (soybeans, cereal, wheat), iron ore and sugar are shown. The grouping and size of the parcels and, therefore, the necessary capacity of the ships to transport them. Additionally, it has the information of the ports with a high flow of mentioned products, allowing to support the normal distribution of the sample.

In Figure 1 (a): Coal transport handles a range of parcels between 20,000 tons to 160,000 tons, with two clusters and an average between 65,000 tons and 155,000 tons each. This indicates the use of Handy, Handymax and Panamax vessels for ports with smaller scales of export and import for the first group and average use of Post-Panamax vessels, Capesize and VLOC, in the routes between the leading exporting countries and consumers. In Colombia, in particular, Puerto Bolívar, Port of the transnational company Drummond Ltda. Moreover, the Sociedad Portuaria Puerto Nuevo (Prodeco), handle an average PSD function of 114,404 DWT; Gladstone Port in Australia uses Post-Panamax vessels, Capesize and Very Large Ore Carriers VLOC, for 57.72% of its exports.Parcel size distribution - Coal

For grains, the load size distribution function has different performance, with the size of the plots concentrated in 30,000 tons and the second group of 55,000 tons. In Rosario port, Argentina, figure 1 (b), contemplating the four (04) ships in port on May 8, and four (04) expected arrivals, the PSD function showed an average of 65,879 DTW, being the Supramax and Panamax the most recurrent for this service.

Parcel Size Distribution - GarinFinally, in Figure 1 (c), there is a significant difference between the load size distribution function of iron ore and sugar, the first product shows a normal distribution with an average of 150,000 tons, being very close to the average thrown in the port of Tubarao, Brazil, where six (06) ships in port on May 8 and six (06) expected arrivals averaged 157,046 DWT. However, sugar handles a much smaller function close to 25,000 tons.

Parcel Size distribution - Iron ore & Sugar by David RestrepoIn conclusion, to carry out a practical application of the parcel size distribution function, three factors must be considered: First, the logistics chain in charge of handling inventories of primary, semi-finished and finished products. Second, the physical characteristics of the ports where these products are transported (capacity of a port to receive vessels of specific draft, beam, length, and DWT). Also, third, the need to achieve the effects of the economy of scale, considering the ship’s capacity and the size of the parcels that allow reduction of transport costs. The analysis and evaluation of the three factors allow determining the parcel of the cargo and the ships that will be ordered in the future, to consolidate the export and import processes.

David A. Restrepo G.


Stopford, M (2009) Maritime Economics – Chapter 2 The organization of the shipping market – Characteristics of sea transport demand (3 ed., Pp. 53-65). London Routledge.

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