Economists
tell us that pricing strategy is contingent upon the highest level the market
will bear but parallel to the constraints imposed by supply and demand. Conversely,
“the market” is a plural as there are many markets and each market has to
develop a unique pricing strategy, specially, in freight transportation--in
order to endure its distinctive set of constrictions such as routes, traffic,
competition, geography, ports, facilities, capacity, etc.
Specifically,
freight markets are exclusive to each surface domain whether ground, air, water
or a combination thereof. As a result, freight rate optimization must be implemented
within an individual domain not only because the exercise takes place in a
particular environment, but also, because the prerequisites required by the
vehicles used for the implementation of conveyance with many of its variables.
It follows
that a better question to ask when trying to optimize a freight rate would be:
What is the optimal combination for a particular mode of transportation? How
distance and geography affect the calculation after the cost of terminal
facilities at each end are factored in? What about line haul, short haul or
intermodal within or outside of a vehicle’s constraints? Perhaps the most
difficult task to evaluate or measure is the cargo type which comes in many
sizes, flavors and incumbent upon individual vehicle specifications. Cargo in
its many forms can vary from bulk, breakbulk, containerized, liquid, dry,
oversize, overweight, fresh, frozen or hazardous just to mention a few in the catalog.
In addition, commodities have different packaging requirements and unique stowage
factors that influence handling requirements and thus, cost. Moreover, the traditional
economic principles of supply and demand, competition, efficiency, market
specialization and so on are to be concerned with at the end of the day. This universe
of variable can be best expressed with a diagram where a definite integral
depicts a generic market behaving within highs and lows of an average space for
an interval of time.
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This scenario
suggests that a great deal of understanding, knowledge, training and capital is
required for a new enterprise to enter a freight market. This paper suggests the
economic challenge and capital exposure that each method of transportation
represents; and, in order to evaluate revenue and cost based on optimal freight
pricing in a competitive market those fundamental issues need to be address.
One very
significant independent variable responsible for the many headaches in the
industry is dimensional weight
or stowage factor which is
the area to volume ratio cm³/cm²*6 for a cube or 1/6 where 6000cm³=1 Kilo. In
general, if we inscribe a cube Z in a sphere of radius R and
optimize the cube’s volume in relation to the constriction of the sphere’s
radius, then we have an optimization problem in three dimensions.
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In this case the ratio is volume- to- volume within
the constraint of the sphere’s dimensions and the equation isolating one
variable becomes:
Solving with
partial derivatives for (x)
The
maximum volume of a box inscribed in a sphere is therefore =
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The point of
calculating a cube inscribed inside a sphere is that the cube is the figure
that has the most volume per surface area after the sphere. But, in the real
world of transportation vehicles are not practical as spheres or cubes even
though there may be the most efficient geometric surface. Builders must
consider that these vehicles need to transit on roads or over rails. As a result,
rectangular rail box cars and vans are the most common vehicles in use today.
Whereas aircraft and ships are a special cases of SA/V and will be address
later.
Historically,
maximization or minimization became an issue during World War II as British
military leaders asked scientists and engineers to analyze several military
problems which resulted in what is now call Operations Research. Professor Morse at MIT was one of the
pioneers of OR.
In the setting
of linear programming an objective equation model is arranged with a traditional
number of constrictions (as was the case of the cube inscribed in a sphere of
radius R mentioned above). Then, the objective equation is used to solve
the problem. Furthermore, the Objective Equation is a component of the Simplex Method
which is the common way for the numerical solution of linear programming
problems. The Method was created by George B. Dantzig in 1947and John von
Neumann, who independently developed the theory of duality and was the founder
of the modern digital computer. This roundabout will get to freight
optimization after all the recipe ingredients are accounted for.
Another component
of the optimization paradigm is the addition of Freeform Transformations (or topology optimization) the
mathematical approach for determining the optimum material layout for a given
space which takes into account a number of design constraints such as the ratio
of volume to area schemes previously mentioned. Historically, topology began
with the investigation of certain questions in geometry. “Leonhard Euler's 1736
paper on the Seven Bridges of Königsberg is regarded as one of the first
academic treatises in modern topology.” Wikipedia.
According to
Hofstra University, “transportation systems are commonly represented using
networks as an analogy for their structure and flows.” Euler treatise has now
been expanded to include other fields such as networks that belong to a wider
category of spatial networks which led to the development of graph theory and
its application to transportation network studies. These new engineering design
challenges are there for improving the cost and fuel efficiency of vehicles
using light weight designs and cost effective materials.
This paper will
now focus on the vehicles currently in use for different modes of freight
transportation and some of the constriction related to the operation of these
vehicles. The ideal vehicle is of course
the one that cost the least and carries the most cargo. The “Greedy Algorithm”
was developed for such purpose. Richard E. Bellman at the RAND Corporation applied
Dynamic Programming to solve the “Knapsack problem” using the “Greedy
Algorithm.”
Biographically,
the “Knapsack problem” has been studied for over one hundred years. It is not
known how the name originated, though
the problem was referred to as such in the early works of mathematician Tobias
Dantzig (1884–1956, father of George Dantzig) suggesting that the name could
have existed as a fable before a mathematical problem had been fully defined.
In reprise
to the account of others, Eric Grimson, Professor of Computer Science and
Engineering at the Massachusetts Institute of Technology states:
“In order to
solve a given problem using a dynamic programming approach, we need to solve
different parts of the problem then combine the solutions of the parts to reach
an overall solution.”
However, the
intent of this paper is to give only a brief historical background of how we
got here and not to go any deeper into the fields of dynamic optimization, networks,
topology, geometry, engineering or physical laws. Nonetheless, there is a need to
describe settings, to compare and contrast some of the vehicles in use today by
carries of freight by air, ground or water surfaces.
The scope of
this paper is not to question why carriers select to enter into a specific mode
of transportation because it would be as speculative as trying to read someone’s
mind or pretending to know the background, knowledge, capital available and
vision of the founder(s).
Besides,
most carriers now days are corporations or capital managers who look at the
fundamentals of a given carrier and purchase the assets for profit. Individual
examples of this market dynamic are Warren Buffet who purchased BNSF rail
transportation or founder of FEDEX, Frederick W. Smith who is now listed in the
stock market as a public company.
At this
juncture, it would be useful to review the basics of performance,
specifications, and financials of the different vehicles that comprise a given
transportation methodology.
Perhaps the
best approach for comparing and contrasting methods and vehicles would be to
use the statistical data available for each mode of transportation starting
with energy efficiency.
Consumption of energy in Proportional
Miles per Gallon (PMPG)
Transport Equipment
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Gross Tonnage
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Average PMPG
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Ratio T/PMPG
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Freight Ship (Handy size)
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24,000
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340.00
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70.58
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Freight Train (60’ Boxcar)
(Unit train 50 cars)
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6,500
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190.50
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34.12
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Plugin Hybrid
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N/A
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N/A
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N/A
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Airplane (Boeing 747-8)
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140
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42.60
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3.29
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18-Wheeler (Truck)
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36
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32.20
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1.12
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Source: (PMPG)
data comes from the U. S. Bureau of
Transportation Statistics.
Ratio data is
provided by the author. All figures are provided in Metric Tons.
Specifications, Costs and Volume to
Area Efficiencies.
RAIL CARS:
60' Standard
Boxcar. (60’ 9”L x 9’ 4" W x 10’10” H). (Metric 18.51 L x 2.84 W x 3.3 H=173.48m³)
Area: (60’
9”x9’ 4”
572’ 4” ft²). (Metric 18.51 x 2.84= 52.57m²)
6,085 ft.
cubic capacity.
6,085/572
10.63
cubic ft. per unit of area. (Metric
173.48/52.57
3.3m³ per unit of area)
Cargo Weight: 100 Metric Tons
Source: CSX.
Cost per
km: $9.1 million. (2015)
Cost per Vehicle,
Diesel-electric locomotives: $7.5 million. (2015)
Cost per
Vehicle Standard 60’ Boxcar: $135,000. (2015)
Source: Market Watch.
FINANCIALS
Revenue/Cost Ratios: 1.47 (2015)
From Financial Statements
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Source: Securities and Exchange
Commission (SEC)
TRACTOR TRAILER DIMENSIONS 18 WHEELER:
Area: (52’x
8’25”
429’). (Metric
15.84 L x 3.07 W)=48.63m²
4050 ft.
cubic capacity= (52’ L x 8’25” W x 9’17”H). (Metric
15.84 L x 3.07 W x 3.17 H=151.23m³)
(4050/429
9.44
cubic ft. per unit of area). (Metric
151.23/48.63
3.11m³ per unit of area).
Cargo Weight: 36 Metric Tons
Source: Wikipedia
Cost per
Vehicle Cab: $80,000 (2015)
Cost per
Vehicle Van: $30,000 (2015)
Source: Freight liner trucks
FINANCIALS
Revenue/Cost Ratios: 1.55 (2015)
From Financial Statements
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Source: Securities
and Exchange Commission (SEC)
AIRCRAFT FREIGHTER:
Make-Model Payload MT CBM Cargo hold
meters
Boeing 747-8 140 upper 692.7 hold (L 2.40 x W 3.20)34 x H 3.00
---------------- -------- Lower 165.7 hold
(L 3.20 x W 2.40)12
Total 858.4 CBM
(2.4x3.20)34
+ (3.2x2.4)12= 353.28m²
(692.7+165.7)/353.28=
2.43 CBM³ per unit of area.
Cargo Weight: 140 Metric Tons
Cost per Aircraft:
$357.5 million (2015)
Source: Boeing 747-8 Freighter
FINANCIALS
Revenue/Cost Ratios: 1.92 (2015)
From Financial Statements
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Source: Securities
and Exchange Commission (SEC)
International
Convention on Tonnage Measurement of Ships
International Maritime Organization:
Adopted 23 June 1969; Entry into force: 18 July 1982
Regulation 3
is based on two variables:
The gross tonnage (GT) of a ship
shall be determined by the following formula: GT = K1V
Where: V = Total volume of all
enclosed spaces of the ship in cubic meters,
K1 = 0.2 + 0.02log10V It is
calculated by using the formula:
where V = total volume in m³ and
K = a figure from 0.22 up to 0.32, depending on the ship’s size so that, for a
ship of 10,000 m³ total volume, the gross tonnage would be 0.28 × 10,000 =
2,800. GT is consequently a measure of the overall size of the ship. For a ship
of 80,000 m³ total volume the gross tonnage would be 0.2980617 × 80,000 =
23,844.94 GT or 23,844.94/.2980617=80,000 m³.
80,000/150x26=
20.51 CBM³ per unit of area.
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CLASS: BV Bureau Veritas in Metric Tons
LBP: Length between perpendiculars150.00 L.
BREADTH: 26.00 W
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Cost per Handy
Size ship of 24,000 dwt Metric Tons: $25 million (2015)
Source:
Lloyd’s Register
FINANCIALS
Revenue/Cost Ratios: 1.65 (2015)
From Financial Statements
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Source: Securities
and Exchange Commission (SEC)
In closing, transportation network efficiency is a measure
that can be used to assess the performance of the network in that it captures
flows, costs, and mobility behavior information, along with its topology. Each
mode of transportation network has its own particulars for efficiency analysis
but in general:
The characteristic path length of a network is defined as
the average of the shortest path lengths between any two nodes: where D I,
j is the shortest path length between i
and j defined as the minimum number
of links traversed to get from node i
to node j.
Source:
Analysis of Networks
I. E. Antoniou and E. T. Tsompa
Finally, the conclusions remarks of this paper are about
the most efficient rates for each method of transportation in terms of
volume/area and energy efficiency are given in the table below:
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