By Alfonso Llanes
September 1, 2016
Abstract
In order to accommodate all concerning materials and still
keep this paper length-readable it is made available in two parts.
Freight rates in nodal format based on origin-destination
published by carriers; leave out minor ports in the network. Using a minimal approach of 50 nodal points
to cover the entire world, carriers can reduce the number of individual rates
to (50)²= 2,500 for each service type that can easily be kept and updated in a
data base thus, avoiding storage and updates of millions of rates. It fallows
that with this recipe, carriers can use algorithms for covering the ports in
the network not included in the nodes. The balancing act relies in developing
an algorithm that works across all service types within the 50 nodes. For
instance, if 4 service types are considered it would render 4*2,500= 10,000
rates with all its attributes.
Even though this method can work for carriers, how does a
freight broker keep track of all the possible combinations of routes and rates?
How does a manufacturer find out about a particular freight rate before
committing to a production-delivery contract? The list goes on to include
traders, bankers, governments and individuals who need to know freight rates as
accurately as possible in any part of the world in the age of the Internet with
instantaneous response for a management board in session?
Introduction
Over the
years many methods, theories and models have been introduced by many
researchers in various fields of study such as economic geography, transportation
economics, economics, theoretical dynamic system analysis and fractals applied to
transportation studies. This paper makes a collection of many of the methods
and models developed by academics. The
most prevalent models will be cited here with the intent of making the reader
familiar with the contribution made over the years by many scholars. This paper
will introduce a model developed by the Barcelona Field Studies adapted to fit
an ocean transportation model and conclude with a new model proposed by the
author of this paper as a contribution to the field. The narrative of the adapted
Barcelona model will be derived from Dijkstra’s algorithm. By constructing Dijkstra’s “closest neighbor”
algorithm and the Barcelona “alternative nearest neighbor” a new model can be developed.
Distance and density variables functions model
Elvira
Kurmanalieva in her paper Transport Costs in International Trade, 2006 writes
about a transport density that can be “broadly interpreted as an efficiency of
transportation network and infrastructure”.
In her paper she states that inspiration came from the
“shortest-path-problem” Adding that the number of shortest paths between two
countries is an approximate estimation of transport density and therefore, the
model is estimated as a function of distance and density variables.
FOB/CIF model ratio
This model is used by the International Monetary Fund----“If
something is being transported from two international markets then the FOB and
CIF prices must differ only by transport costs between one country and another
wherein CIF-FOB equals the transport factor”. The problem with this approach is
that it depends on shipper’s declaration of value and Custom entry form that
more often than not, are not accurate. As a result a unit percent
[(CIF/FOB)]-1*100% is only an academic exercise if declared and entry values
are not dependable.
Iceberg Theory
The Iceberg Theory (Samuelson 1952) bases the cost of
shipping on a relative price rather than relative quantity. In the words of David
Hummels traditional “iceberg” formulation, transport is treated as an exogenous
friction (r) that is fixed and proportional to the value shipped, with the
value‐added of transportation services treated as pure waste, or “melt”. Krugman--
(1991a, 1991b) formulation of the iceberg transport of costs is: T (d) = e rd
economic geography where d= distance and r = is the melt.
Static theory
This theory treats shipping markets as a static mechanism
where a system of variables must link together supply and demand into balance. According
to Hofstra University this model represent a well-functioning transport markets
where supply meets transport demand. Most
theories, which were dedicated in market’s equilibrium, come from this static
notion about shipping economy. A “stochastic process” is a random process changing
with time. Directly, in probability theory, a stochastic process is a time-sequence
representing the progression of some system characterized by a variable that varies
as a subject of a random difference.
Additive and multiplicative
trade costs theory
In 2011 Alfonso Irarrazabal, Andreas Moxnes, and Luca David
Opromolla published a paper that introduces the idea of additive costs as a
constant monetary cost per unit which departs from Samuelson’s framework. This
model incorporates variable trade costs as comprising both a multiplicative
(iceberg) and an additive part. Multiplicative costs are defined as a constant
percentage of the producer price per unit traded. With data collected from Norwegian Customs
these authors built a model of international trade with heterogeneous firms.
Time in transit theory
Kiyoyasu Tanaka 2010. Tanaka concentrates his argument
around the issue of tradeoff between freight- cost-time and timely delivery to
build this model. Using the Japanese Census of Logistics, his paper examines
the cost influence of distance and time across shipping modes. Tanaka states that he found the results
“puzzling because business enterprises are likely to pay more for
shout-distance shipments by truck, ship and railroad transportation”. Tanaka’s statement is in itself puzzling
because the effect of
short distances on rates as per-mile freight rates tend
to decline with distance as the ratio decreases.
Effect of distance on rates.
System Dynamics Theory
In
2010 M. Jurčević, F. Mitrović, M. Nadrljanski introduced the concept of System
dynamics and Theory of Chaos in Freight Rate Forming in Shipping with
significant fractal characteristic as
self-resemblance. Fractal organization is already known in literature. The
biggest impediment to the building blocks of a system is not an engineering
problem but a managerial one. That is because management must deal with social
issues which are harder to understand and administer. Jay W. Forrester, 1992 and the history of
system dynamics In the logistics and supply chain context between fractals and
feedback models examines a simple reinforcing and balancing loop in a system.
These collections of theories should give the reader a good
idea of the different approaches that have been tried over the years.
At this juncture we
need to retake the narrative of the adapted Barcelona model and the derivation
of the Dijkstra’s algorithm. It follows
that the graphic/photo representation of these ideas will provide a better
understanding of “closest neighbor” algorithm the description and the Barcelona
“alternative nearest neighbor” as new models.
Below is an example of a generic system of
origin-destinations nodes and its geographic structure for world coverage
constructed with 48 nodes or (48)²= 2,304 combinations.
The “alternative nearest neighbor”
used by the Barcelona Field Studies applied to forest distribution studies can
also be applied to transportation nodes for we already know the distribution of
ports around the world.
This algorithm measures the
distributions according to whether they are clustered, random or regular. The
nearest neighbor formula will produce the following distribution patterns from
a continuum:
The formula used by the Barcelona Field
Studies is as follows:
Methodology
1. Select an
area using random points in a quadrant. This should be sufficient to obtain a
minimum number of points with the corresponding values.
2. Measuring
the coordinate’s distance of each point within the quadrant to its nearest
neighbor and assigning a corresponding value based on the statistical average
distribution of points and values.
The following
alternate model of the “nearest neighbor” is measured from Adak to the
destination port of the Vladivostok, Russia quadrant using Google Earth. This
particular port is chosen because is not located in the node for Russia, for
the country has three different water outlets: The Baltic Sea, the Black Sea
and its Eastern Seaboard where these ports need to be calculated independently
from the Russian node in the western part of the country. In this case, neither
the bound Barcelona method nor the Dijkstra’s are favored over other closest
neighbor techniques available. Either technique can be placed on a graph and be
analyzed with discrete mathematics.
REFERENCES
Samuelson, P. A., 1952. "The Transfer
Problem and Transport Costs: The Terms of Trade When Impediments are
Absent," The Economic Journal, Vol. 62, No.246 (Jun., 1952), pp. 278-304.
Irarrazabal, Alfonso Moxnes, Andreas Opromolla, Luca David(2010). The
Tip of the Iceberg: Modeling Trade Costs and Implications for Intra-Industry
Reallocation.
Engelen, S., Meersman, H., Van der Voorde,
E.: Using system dynamics in maritime economics Maritime Policy Management, 33
(2), 2006.
Abbas, K.A., and Bell, M.G.H. (1994).
System dynamics applicability to transportation modeling.
Randers, J. and Göluke, U. (2007) Forecasting turning
points in shipping freight rates: lessons from
30 years of practical effort. System Dynamics Review Vol.
23, No. 2/3, (Summer/Fall 2007): 253–284.
Aizenman, Joshua (2004), ‘Endogeneous
pricing to market and financing cost’, Journal of Monetary Economics 51(4),
691–712.
Evans, Carolyn and Harrigan James (2005), “Distance,
Time, and Specialization” American Economic
Review.
Barcelona Field Studies Center
