**Logistics and Algorithms for Networks**

Social networks and transportation networks share many of the same properties, although, there are some unique differences. Social networks are about people in diverse geographic locations linked to each other who link to other people on so on and on. A transportation network shares some of the same interconnections; some are mobile and others are fixed on geographic locations: i.e., seaports, airports, depots, and cities. However, ships, trucks, trains and airplanes are mobile in and out of the fixed networks and sometimes with nodes in between because of geography. In contrast, airplanes are free to move in a Euclidean space because they are not Earthbound.

Scale varies with mode of transportation i.e., commercial ports on the waterfront of countries are distinct from other ports such as fishing ports and marinas which are not included in this network. Nonetheless, a transportation network has a couple more unique properties: Nodes and edges are established “between” countries and “within” countries for all modes of transportation which generates another network known in the industry as inter-modal or multi-modal where one or more modes of transport are combined to complete a shipping transaction.

In this scenario nodes and edges must have attributes for each mode of transport such as distance, geography, freight rates, loops, links, all in a topological space. Once the network is put together it must fulfill the functions and run with the properties of a network.

To be useful this kind of network must be able to locate the most efficient route within the network. Dijkstra’s algorithm can be used for finding the shortest paths between nodes in a transportation network graph. This method was originally published by Dutch computer scientist Edsger W. Dijkstra in 1956. The algorithm exists in many variants: The original variant was conceived for finding the shortest path between two nodes; however, a more common variant selects a single node as the fixed node and finds shortest paths from this node source to all other nodes in the graph, generating a shortest path tree.

For a given fixed node in the graph, the algorithm finds the shortest path between that node and every other node but it can also be used for finding the shortest paths from a single node to a single destination node by stopping the algorithm as soon as the shortest path to the destination node has been located. As an example, if the nodes of the graph represent ports and the edges path are weighted with cost values then cost is represent by the distances between pairs of ports and a direct routing protocol. Dijkstra’s algorithm can also be used to find the shortest route between one city and all other cities.

For theoretical computer science and network routing, Suurballe’s algorithm is used for finding two unconnected paths in a non- negatively-weighted directed graph, so that both paths connect the same pair of vertices with a total length. The algorithm was conceived by Danish J. W. Suurballe and published in 1974. The principal idea of Suurballe was to use Dijkstra’s algorithm to find one path, then modify the weights of the graph edges, and run Dijkstra’s algorithm a second time. A similar method, which allows negative edges in the network, was developed by American scientist Donald b. Johnson who published his algorithm in 1977. The objective is to suggest the minimum cost directional algorithms, where in this case there are two bidirectional edges connected and nodes that have units of weight… or values, time, distance, etc.

Shipping statistics indicate that ninety per cent of world trade by weight is carried by ocean going vessels and high shipping costs can significantly impede trade participation for some countries.

Transport costs also vary significantly among commodities and finished products. These transport costs are strong determinants of which countries can enter the market with the same kind of merchandise and pricing if these countries are not located on the trade routes; don’t have safe harbors with sufficient water depth or lack port infrastructure.

Shipping Economics. The cost of transportation tends to be lower as distance increases and although it sounds counter-intuitive what happens is that the cost per-ton-mile decreases as the denominator gets larger. I,e., 1 ton/1 mile — 1 ton/1000 miles which becomes the effect of distance on freight rates.

Another economics principle that applies is the 80–20 Pareto rule, where 80% of the cost is derived from 20% of the factors such as capital, energy and time which, can be depicted in a curve of central tendency if statistical analysis is used.

Port Infrastructure. The efficiency and capacity of transport modes and terminals has a direct effect on the landed cost of a commodity. These efficiencies include storage areas either open or enclosed, access roads and rail spurs to the docks, mechanical equipment like cranes and loaders, turn around basins for ships and sufficient dock space proportional to ship traffic and invariably, availability of dredging when more water depth is needed.

Geography of Transport. Its impacts mainly involve distance and accessibility. Distance is commonly the most basic condition affecting transport costs in a time-cost equation. However, the geography of the terminal is heavily influential on logistics of a transportation network.

Tanya Latty , Kai Ramsc, et als published in 2011 a study of transportation networks built by ants in a non-Euclidian topological spaces. “Structure and formation of ant transportation networks.”

The work of these authors establishes that “many biological systems use extensive networks for the transport of resources and information.” In essence, one can observe from the study that biological transportation networks are not unique to humans with advanced technology for a primitive natural system can create an efficient transportation and logistics network instinctually.

Commodities and Products. Bulk, semi-manufactured and manufacture goods require packaging, special handling, are bulky or perishable and thus, must treated as independent units of cost for any kind of analysis. The general rule to apply here is that the higher the value of the item the lower the percentage of transportation cost. i.e., a $1000 TV set will probably have cost of .01 of the unit value or $10 while $1000 worth of coffee beans will probably have a cost of .07 or $70. A TV set can fit in a box while coffee beans will require a much larger space which translates as the stowage factor of the merchandise.

A big issue for ocean container carriers is the asymmetry of trade because the trade imbalance implies the repositioning of empty containers that have to be taken into account in the total transport costs. Tramp carriers on the other hand, are on a better position to provide better rates since they don’t have to worry about positioning containers. However, most of these carriers operate without established routes or schedules and just go where the cargo is which makes it difficult for shippers to plan ahead on the inherently uncertainty of tramp carriers and bidding on spot movements and rates.