By Alfonso Llanes
October 10, 2016
Abstract
Different transportation theories were
covered in part one of these papers, therefore,
part two will propose a new theory based on “waterways corridor” method to analyze
freight rates and how these freight rates can be established by carriers. The
principle proposed here is based on routing traffic through ocean, air, or
ground corridors each with a “toll” at each segment the route either from the
applicable international water corridors or the domestic traffic lanes to a final
destination. This paper focus on ocean freight only and will derive a
corresponding equation based on the “tolling” of traffic corridors and the fact
that all carriers must use the same trade lanes. This argument can be reduced
to a numerical expression with two parameters: Knowns and unknowns where every ship
entering the trade corridor has a “toll” known factor of distance-cost no matter
what the size of the ship is. It follows that domestic sea-lanes are the next “toll”
to be added which is also a known quantity, so, the remaining unknowns are the variable
quantities of canal crossings and destination seaboard ports-costs. Therefore,
this argument simplifies the equation to the problem of finding the marginal
cost with one dependent and one independent variable based on the following
facts:
1.
Ocean routes have an established transit
time or “toll” for all carriers.
2.
Sea Lanes have an established transit time
or “toll” for all carriers.
3.
Straits have an established transit time or
“toll” for all carriers.
4.
Canals have variable costs according to the
size of the ship.
5.
Ports in the coastal waterways have variable
costs according to the size of the ship.
Graphic depiction of waterways, geographic obstacles and
location of ”tolls” to navigation.
Photo-depiction
of geographic elements of water passages and port terminals feeds.
However, this model can only
be used to solve individual rates per unit of cargo. It follows that a second
model is needed to exact a proportional assessment of port costs or canal
crossings for varying ship sizes and whether this proportion varies directly or
inversely with a new ship size. The advantage of this analysis is that
technical innovation of ships can be included in a proportional matrix and a scalar.
Economic pricing theory is based on the equilibrium price
calculated when supply and demand is in balance. This price does not exist in
actual trading processes except in special and rare cases; it is only an ideal
or theoretical price level, which at best is only approximated in the real
world.
The Principle of "Charge What the Traffic Can Bear” tell
us that freight rates for different commodities are determined on the basis of
the capacity of an individual commodity to bear the burden of freight.
In formal economic terms, the law of diminishing marginal
returns states that as the number of new inputs, the marginal product of an
additional input will at some point be less than the marginal product of the
previous input. Neoclassical economists assume that each "unit" of input
is identical. Diminishing returns are due to the disruption of the entire
productive process as additional inputs are added to a fixed amount of capital.
(Same size port and facilities but more ships to attend)
David Hummels, Georg Schaur (2012) argue that delays to shipping
navigation of one day in transit or port is equivalent to an ad-valorem tariff
of 0.6 to 2.3 percent. They continue with the comparison of transportation
cost-benefit analysis between airplanes for fast time-sensitive- delivery and
the slower but larger weight ships can carry as components of trade.
They provide the following relationships in the
comparison between Air Premium Value =fa −fo = (1+air charge/air
value)-(1+vessel charge/vessel value). Air Premium Weight =ga/go = (air
charge/air weight)/ (vessel charge/vessel weight).
One concern for carriers is whether regulatory incentives will continue to
encourage individual owners to invest in modernization of the fleets, however,
older ships need to be demolished or else it would lead to increases in global
capacity, clogging ports of origin-destination and putting downward pressure on
freight and charter rates.
Strategies for hybrid-transportation and tactics for
leaning inventories.
A number of techniques corresponding to this shift have
emerged such as consolidation of merchandise along shared routes. Shippers are also finding ways to consolidate
in multi product containers, pallets, or cartons to optimize capacity
utilization. Finally, finding and evaluating alternative modes of transportation
by using intermodal rail services, instead of canal crossings or trucking services,
for long-haul freight for instance, going across the US or Canada by rail
rather than the Panama Canal.
Surface carriers on the other hand, are focusing more on
critical mass costing, marginal costs delivery patterns, time of day mileage
user fees and the various ratios size-weight, time-distance and tracking costs
by either GPS tolling or cellphone text communication where available.
Many developing countries mainly in Africa and Oceania,
pay 40-60% more on average for international transport of imported goods than
developed countries do. The main reasons for this situation are to be found in
these regions’ trade imbalances, pending port and trade facilities legal reform,
as well as lower trade volumes and shipping to/from connectivity. Legislators
in these countries could partly help the situation with investments in
infrastructure and legal framework reforms, especially, in shipping systems and
Customs’ clearance and administrations.
On many shipping routes,
especially for most bulk cargoes, ships sail full in one direction and return
almost empty as round trip freight is charge to the shipper. Having spare
capacity, carriers can offer backhaul cargoes at a much lower freight rate than
front haul rates. For instance, freight rates from China to North America are higher
than on back haul for North American exports to China.
UNCTAD analysts estimate that global seaborne shipments
have increased by 3.4 per cent in 2014 which is the same rate as in 2013. These
volumes exceeded 300 million tons bringing the total of maritime trade
to 9.84 billion tons per year. The total seaborne capacity at the
beginning of the year for the commercial fleet consisted of 89,464 vessels,
with a total tonnage of 1.75 billion dwt.
The distribution of percentage by product is as follows:
Greece still is the largest ship-owning-country, next to
Japan, China, Germany and Singapore.
Together, the top five ship-owning countries control more
than 50% of the world tonnage.
Five of the top 10 ship-owning-countries are in Asia,
four are European and one is from the Americas.
According to UNCTAD, Maritime Review, (2015) the
container-carrying-capacity per carrier-country tripled between 2004 and 2015,
but the average number of companies that provide services from/to voyages
decreased by 29%. Both trends illustrate two sides of the same issue: as ships
get bigger and companies’ objective is to achieve economies of scale, there are
fewer remaining companies in individual markets.
CONCLUSION
The defining feature of diminishing marginal returns is
that as total investment increases, the total return on investment as a
proportion of the total investment (the average product or return) decreases. For
example, 1 docked ship can deliver merchandise to a port that adds 1 unit of
economic gain to the area. A second ship docked
would add 1.5 units and a 3rd ship would produce 1.75 units of economic
gain.
In numeric terms, the i th produce
additional economic gains to the area.
The return from the first ship is 1 s/unit. When
2 ships dock, the return is 1.5/2 = 0.75 s/unit, and when 3 ships are
docked, the return is 1.75/3 = 0.58 s/unit, as the same amount of dock space is
shared by additional ships.
It follows that as dock space remains constant and more
ships are added delays to unloading arise and as a consequence, a diminished
marginal return occurs as the fixed dock space is being shared:
Another way to measure the best route to
a port is applying Dijkstra’s algorithm in graph theory:
Finding
Shortest Path with Dijkstra’s Algorithm
Initial
Condition
Probing For
Shortest Route
Transportation modeling in general, was formalized by French
mathematician Gaspard Monge in 1781. Since then many others have contributed to
the theory and its economic implications. Below is the original formalized
expression by Monge.
It corresponds to finding an optimal matching between the source
points and the target points from
R---R² in Euclidean
space. Russian Leonid Kantorovich improved on Monge’s model 150 years later by
introducing his duality principle in set theory. The informal way of interpreting Kantorovich
and his duality principle is explained by Caffarelli as:
A shipper needs to move and pay for a certain amount of sand c(x; y)
which is transported from place x to place y. Both the amount of excavated sand
and the amount of sand pile are equal and at fixed points of
origin-destination.
Kantorovich expanded this model by liberalizing the origin-destination
and transportation of the sand without regard to order. Where the cost of
loading ϕ(x) of one ton of sand at place x, and a cost ψ(y) for unloading it at
destination y will be the same no matter the order the loads are taken or delivered
in the given space R---R².
In 1965 Lotfi A. Zadeh introduced the idea of Fuzzy Sets
but it wasn’t until Hans-Jiirgen, Zimmermann in 1985 introduced the application
of fuzzy logic to many human endeavors including transportation. In the three
decades since its inception, the theory has matured into a wide range of
concepts and techniques for dealing with complex phenomena that do not lend
themselves to analysis by classical methods based on probability theory and”
fuzzy” logic. This novel idea is opposed to the principle of a conventional sets
for which an element is either a member of the set or not as 0 or 1. A fuzzy
set can be anywhere between 0 and 1 or what is called approximate reasoning and
also, where probability theory plays a major role in the distribution values
between 0 and 1.
Source: Applied Mathematical Sciences, Vol. 6,
2012, no. 11, 525 – 532
This mathematical modeling applied to transportation can
be structured applying fuzzy logic to common crisp numerical methods as
regression analysis, matrices, probability, and statistics and so on. In simple
terms, fuzzy values are to be found between and within a given
range in a closed interval for a given set, i.e., 1000 freight rates. It
follows that we can get the constant of proportionality k in a boundary of values
in a 6 month period-interval if we assign a value for
at
time 0 and then solve for a separable differential equation in a closed
interval. i.e., at
REFERENCES
David Hummels, Georg Schaur January 2012, TIME AS A TRADE
BARRIER. NATIONAL BUREAU OF ECONOMIC RESEARCH .Cambridge, MA 02138.
Krugman, Paul(1991) 'Increasing returns and economic
geography'. Journal of Political Economy
Vol. 99, No. 3 (Jun., 1991), pp. 483–99.
C. Broda and D. Weinstein. 2006. "Globalization and
the Gains from Variety,"
Quarterly Journal of Economics, Volume 121, Issue 2
Eaton, Jonathan and Samuel Kortum. 2002.
"Technology, Geography, and
Trade." Econometrica, 70 (September): 1741-1779.
Lugovskyy, V. and Skiba, A., 2009. "Quality Choice: Effects
of Trade, Transportation Cost, and Relative Country Size,"
Berthelon, Matias and Freund, Caroline L., "On the
Conservation of Distance in International Trade" (May 6, 2004). World Bank
Policy Research Working Paper No. 3293.
Gilman, Sidney (1983), The Competitive Dynamics of
Container Shipping, University of Liverpool Marine
Transport Center.
Harley, C. Knick, (1988) “Ocean Freight Rates and
Productivity, 1740-1913: The Primacy of Mechanical Invention Reaffirmed”,
Journal of Economic History, 48, 851-876.
Mohammed, Saif I. and Jeffrey G. Williamson.
"Freight Rates And Productivity Gains In British Tramp Shipping
1869-1950," Explorations in Economic History, 2004, v41(2,Apr), 172-203.
Combes, P., Lafourcade, M. (2002) Transport costs,
geography, and regional inequalities. 2894, C.E.P.R. Discussion Papers.
Oyama, T., Taguchi, A. (1991) On some results of the
shortest path counting problem. Abstracts of the OR Society Meeting
(Kitakyushu): 102-103.
UNCTAD (2015) Review of maritime transport. United
Nations Conference on Trade and Development,
Geneva.
Pedrycz, W. [1989] . Fuzzy Control and Fuzzy Systems. New
York, Chichester, Toronto .
Hadi Basirzadeh . An Approach for Solving Fuzzy
Transportation Problem (2011) Shahid Chamran University Ahvaz, Iran.
