# Representations of Distance

Three major representations of the friction that distance imposes on transportation can be considered:

• Euclidean distance. The most basic manner to represent distance as a simple function of a straight line between two locations where distance is expressed in geographical units such as kilometers. Commonly used to provide an approximation of distance, but rarely has a practical use.
• Transport distance. A more complex representation that accounts for the existing structure of the transport network. A simple form involving only one mode is a routing exercise that considers the shortest path between two points. In a more complex form, it concerns the set of physical activities related to transportation, such as loading, unloading, and transshipment. In the above figure, the transport distance between locations A and B includes pickup, travel by mode 1, transshipment, travel by mode 2, and delivery. The same applies to the circulation of people, although the involved activities will be different. For instance, air travel between two locations requires going to an airport, the potential transit through an intermediate hub airport, and finally, the need to reach a destination from the airport terminal. Transport distance is jointly expressed in geographical units, cost, and time.
• Logistical distance. A complex representation that encompasses all the tasks required for a movement to take place between two locations. Logistical distance includes physical flows and activities necessary for managing these flows. Among the most significant tasks for freight movements are order processing, packing, sorting, and inventory management. Geographical distance units are less relevant in this assessment, but the costs and time factors are significant. Time not only involves the delay related to management and circulation but also how it is used to service the transport demand, namely the scheduling of pickups and deliveries. In the above figure, the logistical distance between locations A and B includes an order from B, which is processed, packed, and scheduled to be picked up. At the intermediate transshipment location, sorting and warehousing are performed, and finally, at the destination, the delivery will be unpacked and used. For the transportation of passengers, the logistical distance also concerns an array of tasks. Using air travel as an example, a ticket would first need to be purchased, commonly several weeks in advance, which requires advance planning. Other common time and cost tasks concern checking in, security checks, boarding and disembarking, and picking up luggage. Thus, a three-hour flight often requires to be planned several weeks in advance, and its full realization can take twice as much time if all the related logistical activities are considered.