TRANSPORTATION NETWORK PROBLEM SOLVING

The Federal Maritime Commission was in the past, the repository government agency of common carrier rates until the Shipping Act of 1998 stopped the official requirement of filing freight rates. Moreover, the same Act mandates carriers to publish rates in private networks open to the public. However, these "open" networks charge a user time-fee for access to diversified number of rate publishing services,  resulting in more confusion to the public rather than clarity i.e., a manufacturer, exporter, trader, or consultant needing to quote the landed price of a product would need to subscribe to all publishing services and spend the time looking for a specific rate!

There are other choices of course and those are: Joining one of the carriers' conferences for access to their particular logistics network which makes users captive of a particular conference in addition of not being able to shop for rates from other conferences or independent carriers.

This business model addresses these issues making our international world rating system for all modes of transportation a very useful tool accessible to anyone without being captive to anyone service and at a reasonable access fee.

This is a highly competitive market and somewhat a monopoly at the same time. The large capital amount required for entry keeps the competition in check and national governments have to monitor rate setting practices to prevent unfair competition, therefore, it is against carrier’s interest to have rates open to the public for shopping.  National legislators require common schedule carriers to make rates available to the public in order to exploit a given route. Carriers however get around regulations by publishing rates in private networks they control in such a way that a user would need to pay for access to all of the existing networks in order to find a specific rate. Moreover, the rates are listed at the high end of the spectrum so that carriers can offer discounts to large brokers, and other third part service providers, while at the same the same, carriers can enter confidential service agreements with preferred customers. At the end of the day keeping rates away from shoppers is the name of the game.

So who needs to participate in such regressive system?

a)      Anybody in the world who needs to ship something needs to find the best rate for the landed price of a product in order to take part in international merchandise trade. Mainly, manufacturers, wholesalers, retailers and merchandise traders in general who have a need for competitive rates in order to participate in global trade. Whether bulk commodities, semi-manufactured products and consumer merchandise must have a choice for the best option in order to enter or stay in a particular international market.

b)      ) In this scenario, carriers of goods can manipulate the market to their advantage, specially, when a country does not have a merchant marine and must depend on foreign flag carriers that can co-join routes with other carriers and set prices at will as fewer choices are globalized. The World Bank and the International Monetary Fund follow these markets and report to national governments its findings so that better trade agreements can be negotiated among countries.

This asymmetry of international trade is also monitor by custom unions as each country has a Customs organization at the ports of entry or exit of imports and exports. This monitoring tool is as accurate as the information provided to Customs by the importing or exporting party. The issue comes down to the difference between free on board (FOB) and cost insurance-freight (CIF).  As a result, the variation in the cost of imported and exported merchandise at the port of entry or exit is the cost of transportation. However, declared value or merchandise for insurance or Customs can vary among individuals shipping the same or similar merchandise.

By calling freight forwarders, brokers, carriers, and more recently with the Internet many sites offer freight services but their model is to obtain shipping information from the user and then go shopping for a carrier that can provide such service after a fee has been added. Others work on commission with/or for brokers but this requires licensing from regulators which is a deterrent for many. In conclusion, obtaining independent freight rates for a given trade lane is the best option for the existing order where carriers can make or break a business deal or keep a party from entering the market.

Curiously enough commodity pricing is not set for the most, part at the origin, but in financial markets.

Selected samples:

Price Specifications Point

Crude Palm Oil Futures Bursa Malaysian                                                              

Peru Fish meal/pellets, 65% protein, CIF United Kingdom                                                                                          

United Kingdom ex-tanker prices, crude extra virgin olive oil,                                                  

Ground nuts 40/50 (40 to 50 count per ounce), in-shell, CIF Argentina                                                   

Rapeseed oil crude, fob Rotterdam                                                                                                                       

Lamb New Zealand, PL, frozen, wholesale price at Smithfield Market, London                                                 

Coffee, Sugar and Cocoa Exchange, New York Board of Trade.                                                   

EU import price, unpacked sugar, CIF European ports.                                                                                   

International Coffee Organization, Other Mild Arabicas New York cash price.                                                   

Cotton Middling 1-3/32 inch staple, Liverpool Index "A" Cts/lb five of fourteen styles, CIF Liverpool

Singapore Commodity Exchange, No. 3 Rubber Smoked Sheets.                                                                                              

London Metal Exchange, grade A cathodes, spot price, CIF European ports                                                         

London Metal Exchange, standard grade, spot price, minimum purity 99.5 percent, CIF U.K. ports                           

China import Iron Ore Fines 62% FE spot CFR Tianjin port;                                                           

Malaysian, straits, minimum 99.85 percent purity, Kuala Lumpur Tin Market                                                      

London Metal Exchange, melting grade, spot price, CIF Northern European ports                                                            

London Metal Exchange, high grade 98 percent pure, spot price, CIF U.K.                                                            

London Metal Exchange, 99.97 percent pure, spot price, CIF European ports.                                                     

Metal Bulletin Nuexco Exchange Uranium (U3O8 restricted) price.

Statistical Freight Rates Predictions

The question that this paper intends to answer is whether freight rates can be predicted accurately applying statistical and network methods?

I had the pleasure of watching an online video lecture in Computer Science by Professor, John Guttag, at the Massachusetts Institute of Technology: “Using Randomness to Solve Non-random Problems”. He wrote a small program in Python to obtain the ratio of Pi using the old problem of randomly dropping needles on a drawing of a circle inside a square to obtain the ratio between the two drawings. This experimental geometric probability problem was first proposed in 1777 by Georges-Louis Leclerc, Comte de Buffon. He never obtained a good answer because his sample of trials wasn’t big enough or his method of dropping needles was poorly designed. A correct solution was given by Laplace in 1783 using binomial distribution: np (1-p) and sqrt (np (1-p).

Professor’s Guttag Python model simulated 20 trials starting with 1000 needles and doubling the number of needles each time to obtain a Gaussian distribution. As it turned out 16,000 needles provided a Pi ratio of 3.1413875, however, with 32,000 needles the ratio was 3.1457. While the program continued to double the number of trials, the trial ratio did not improve its variance. On the other hand, the standard deviation became smaller with each doubling of the needles from .012 and 16,000 needles to .008 with 32,000 needles. So, even when there was variance in the trial ratios throughout the trials the standard deviation got smaller every time where two standard deviations would be a very small fraction and a confidence level of 99% could be attained.

As stated by Lancaster University, UK: “In the 1940’s Ulam and Von Neumann suggested that aspects of research into nuclear fission at Los Alamos could be aided by use of computer experiments based on chance. The project was top secret so Von Neumann chose the name Monte Carlo in reference to the Casino in Monaco”. And so, experiments with randomness became better known as Monte Carlo simulations.

This begs the question of whether building a model of normal distribution using published liner shipping rates and comparing it with a model of random rates is accurate. The answer should be yes. We know from statistics that real life events have a normal distribution and when compared with a model of virtual reality there is only negligible variance between the two models.

With this in mind can freight prediction be made and plugged into a transportation network of nodes and edges where the nodes have all the attributes embedded or extracted from databases? This, of course, would be a challenging coding task but this paper proposes that such project is doable!

To begin with and in order to simplify building a model, only known variables in a rate structure should be considered. For example, a typical freight rate structure contains distance, dimensional weight and the rate per unit of cargo to be shipped. This model will not include the occasional variables of weather, accidents, labor strikes, port congestions and consider them as out layers. Also, a stable model is assumed for a length of time (one year) where fuel prices, route competition, crewing cost remain steady and there is fair play in the market between shippers and carriers.

Fair play in the market is the most difficult variable to predict because of its numerous components. Just as in financial markets the better informed party wins the day bearing in mind that better information empowers consumers in an impartial market.

Estimating the actual value of trade between countries is a strenuous effort not only for regulators but also for national institutions responsible for measuring the behavior of international trade and its effects on local economies. Among these institutions are the UN, OECD, The World Bank, The IMF and others but they all get their values as quantified by national governments, trade banks and others such as Global Insight, Platts etc.

The task of estimating the value of trade would easy if the same factors were applied globally in a linear relationship. However, this not the case, as the same unit of cargo will have a higher transportation cost from a landlocked country than from a developed country with multiple port facilities.  Also, asymmetry of trade must be factored in; in addition, competition in the route or the lack thereof injects itself between nominal and real prices.

One general measurement assessed by Custom Unions is the difference existing between clearance values from origin and destination countries. The problem with this measure is that Customs depends on declared invoice value to make the assessment of duties after discounting transportation costs. So, if a commodity is purchased Free on Board basis (FOB) or Cost and Freight basis (C&F) the difference between the two values most be transportation. Unfortunately, this is not the case as declared values are manipulated by buyers, sellers and carriers while Customs use tariffs to determine duties--transportation tariffs can be ambiguous in a deregulated market. And so, the real cost of transportation is at best, an estimated value for reporting institutions.

Moreover, Customs looks to documentation provided by the shipping company, as opposed to the documentation between the buyer and the seller. Information from the buyer and seller often contains estimated transportation costs or charges, while documentation from the shipping company contains the cost for the shipment. Notwithstanding, there is no precedent which specifically address the issue of whether terminal handling charges or other surcharges like fuel adjustment factor and value added services are to be taken into account when determining the actual amount paid for international transportation. The reason is that this additional cost factors sometimes are included in the basic freight rate tariff and other times is not as a way to achieve pricing differentiation between carriers.

One method used by some NGOs for estimating transportation cost in international trade is to fix a point for both origin and destination and assess the average increase or decrease in cost of commodities going through the fixed point in multiple directions. The Strait of Malacca has been used as a fixed point of reference for this purpose.

In conclusion, predicting freight rates using a combination of statistics and networks based on published rates should provide a probability confidence of 95% with one standard deviation from the mean in a basket of rates offered by other carriers in compatible routes is doable.

Alfonso Llanes

July 4, 2015

References:

John Guttag. 6.00SC Introduction to Computer Science and Programming, Spring 2011. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu

Kady Schneiter Utah State University Kady.schneiter@usu.edu. Exploring Geometric Probabilities with Buffon’s Coin Problem. Fall 2014.

Monte Carlo Simulation - A Brief History - Lancaster University www.lancaster.ac.uk/pg/jamest/Group/intro2.html

https://www.ihs.com/industry/maritime.html

Maritime Operations and Logistics Data and Analysis

METHODOLOGY AND SPECIFICATIONS GUIDE https://www.platts.com/IM.Platts.Content/MethodologyReferences/MethodologySpecs/Freight-methodology.pdf June 2015.

The World Customs Organization (WCO), established in 1952 as the Customs Co-operation Council (CCC) is an independent intergovernmental body whose mission is to enhance the effectiveness and efficiency of Customs administrations.

http://www.wcoomd.org/en.aspx

Optimizing Freight Rate Functions

Using discrete mathematics to describe the behavior of transportation networks has to include Riemannian geometry in consideration of geographical curved space and gradients. This issue alone can represent an immense challenge for developers who may be very competitive in computer science but not in the business side of transportation networks. Specially, when defining which method and what set of metrics are to be used for taking measurements across the entire spectrum of the system being developed.

Freight managers recognize that they need to allocate in separate sets direct and indirect costs for the vehicles, the routes, as well as the size, and capacity, for determining the unique transportation platform’s weight and cubic space available for the market at a price that defines the break-even point for a specific case in question.

The short cut for calculating a freight rate is of course to add all the fixed and variable costs and divide them by the vehicle’s capacity on either weight or space in order to establish a freight rate per unit of cost. Intuitively, this is a reasonable argument but other hidden costs can upset the balance in unexpected ways.

A more labored approach is to use a tool such as a modified Cobb-Douglas  production function used in economics to determine the marginal product of capital (K) and the marginal product of labor (L) and replace them with applicable variables for freight transportation. The method prosed here is to use a theoretical freight rate divided with fractional exponents that can result in a model that can measure  returns of scale with a given set of variables and within a specific route or market.

For example, if a freight vehicle makes a round trip but only carries cargo one way then the utilization factor is ½ its capacity. In this case, the backhaul is negative but the round trip cost is positive. So, if no backhaul cargo is available a round trip charge would need to be applied, however, this may not be possible because route competition or some other market condition don’t allow it. Freight component can be represented with a fractional exponent representing the utilization factor as it is applied to the theoretical model.

 The next problem to be assign a solution is stowage factor and freight managers will try to maximize the amount of cargo that can be carried for either weight or volume.  Under these circumstances, vehicle capacity becomes an issue of dimensional weight factoring. That is the factor at which the unit platform arrives at its weight or volume capacity for a given freight rate. So, another fractional exponent can be inserted into the cost function.

Determining maximum carrying value on a limited transportation platform by either weight or volume is an issue that can, in many cases, determine success or failure of a transportation company. The theory behind the problem has been endlessly studied with “the knapsack problem” which, relates to combinatorial optimization between weight, space and value.  Given a set of cargoes, each with a weight, a volume and value, freight managers must determine the number of each unit that can be included in a collection of items equal to a given limit where the total commodity-freight-value is as large as possible. Thus, the problem becomes an issue of optimizing a vehicle utilization factor for any given trip. As a result, another fractional exponent representing commodity value can be added to the function.

Distance from origin to destination can be a constant for a route but not for off route trips and must be considered accordingly as yet another exponential fraction that can be added to the overall equation. Once all the exponents have been determined the function should provide a theoretical optimized approximation to an original set previously defined by capital, labor and energy at a break-even of the function.

It follows that if a freight manager who targets optimization based using the modified Cobb-Douglas can assign random values to the function to perform an initial evaluation between the break-even and marginal cost incremental  for Utilization, Stowage, Commodity Value and  Distance. This ca be abbreviated as: Freight where (F)=   a fractional exponent like 1/n taken to the nth root and expressed on its decimal exponent equivalent of F= (  U^.25 S^.25 C^.25 D^.25   ).

If we make the assumption that this equation will hold for 90% of the rate optimization cases and the remaining 10% is treated as extraneous freight components that only apply to very few cases. For instance, where berthing facilities are poor, port infrastructure is inadequate and/or terminal expenses are not competitive with the rest of the world because of inefficiencies or corruption.

Under these circumstances, freight managers can assess the marginal effect of cost on freight rates when one or more of the factors of the proposed freight equation domain is increased or decreased from an initially evenly divided cost-freight-factors set at  1/4+1/4+1/4+1/4.

The following exercise using a generic freight rate of $12 for weight or measure per metric ton constrained by market rates in a given route is found to have a $4 utilization rate cost component. If the marginal cost needs to be measured in order to define if any rate flexibility exist on the intended route using the proposed equation, then, a freight manager must proceed as follows: 12/4=3 as the freight initial constant of cost in its decimal equivalent of F= (U^.25 S^.25 C^.25 D^.25).

= .25 ( ) ·²⁵ =    .27 so that the original cost component of $4 has a marginal increase/decrease of 4/1.27 3.15. In other words, the rate component could be dropped $0.85 cents per ton with little effect on the profit of the rate because the marginal utilization cost factor can be set at a smaller cost.

This equation can be applied not just to obtain marginal return on each freight cost component but also, to measure profit margin and overall productivity by replacing the corresponding exponent(s) with different testing values for the model.

 Comparing values obtained between the model and those calculated based on break-even point, rate per ton mile, rate per trip, rate per day and so on can vary with each method of calculation but once the factors are obtained and entered in a computer or interactive worksheet it can become a very useful tool for improving productivity.

Arguably, optimization can also be accomplish using LaGrange multipliers, although, it requires a lot more algebraic manipulation which makes its handling weighty,  moreover, with the proposed method individual variables can be isolate and evaluated and this feature cannot be replicated using the LaGrange multipliers.

Alfonso Llanes

May 20, 2016

References

MATHEMATICAL MODELS OF TRANSPORTATION AND NETWORKS, (2007). Anna Nagurney John F. Smith Memorial Professor Department of Finance and Operations Management Isenberg School of Management University of Massachusetts

Amherst, Massachusetts.

Mathematical Models in Economics (2007)

Filipe, Jesus; Adams, F. Gerard (2005). "The Estimation of the Cobb-Douglas Function: A Retrospective View". Eastern Economic Journal 31 (3): 427–445.

Optimization Methods in Economics (2001). John Baxley Department of Mathematics

Wake Forest University. Winston-Salem NC.

Discrete Optimization Algorithms (1983). Maciej M. Syslo, Narsingh Deo, and Janusz S. Kowalik.

 Prentice-Hall, Inc., Englewood Cliffs, NJ.

Calculus: Early Transcendentals (2008). Sixth edition. Stewart, James).. McMaster University, Ontario, Canada.

Maritime Economics, Third Edition2009. Stopford, Martin. Roudledge, Keble College Oxford, England.

Where are the hard knapsack problems?. Technical Report (2003/08). Pisinger, David. Department of Computer Science, University of Copenhagen, Copenhagen, Denmark.

"Lagrangian relaxation".  Lemaréchal, Claude (2001). In Michael Jünger and Denis Naddef. Computational combinatorial optimization: Lecture Notes in Computer Science 2241. Berlin.