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Conceptually, the origin of delivery route planning can be traced to a mathematical problem known as the seven bridges of Konigsberg (now called Kalingrad located in European Russia, near the border with Lithuania). The problem was to devise a course that enabled a person to travel through the entire city by crossing each of the seven bridges once only. In 1735, the problem was solved by a Swiss physicist and mathematician called Leonhard Euler and facilitated the generation of advanced strands of mathematics known as graph theory and topology, which is not be confused with the subdiscipline of geography known as topography. The pre-requisites to solving the problem where that each bridge had to be completely traversed and the islands in the river Pregolya, which bisects the city could only be reached by crossing the bridges. The solution is that there is no solution such that the pre-requisites cannot be met so the next best option was to develop the optimal route. It is from this position that all the algorithms, code and software that allow efficient vehicle route planning is derived.
Topology and graph theory
Topology is the study of relationships and connectivity between objects and was first coined by the German mathematician Johann Benedict Listing. When route planning software programs show the possible transport options, there is a spatial relationship between the destinations on the route. These displays are derived from graph theory that is concerned with the study of graphs as mathematical structures, not as a visual data display. The graph is made up of destination points (the nodes) and the lines (the edges) which connect them. In applications such as multi-drop route planning software, the edges and nodes are directed such that the optimal path between them is found.
The development of this graph search algorithm by its namesake a Dutch computer scientist in 1959 is in many ways the bedrock of modern route planning software. It set to find the shortest path between different locations and is commonly used to find the best route between a central node, for example a city or distribution centre and multiple destinations along a direct route. The Dijkstras algorithm has application in distribution logistics ranging from courier route planning software and across dynamic route planning protocols in general. By the turn of the 21st century, vehicle route planning software had moved from the strict preserve of booking systems for leisure and public transport into an essential component for the organisation and distribution of goods by logistics companies. Goods can today be moved rapidly by intermodal means and this is only possible due to the sophisticated software used to display optimal routes between various destinations.
Overall journey planning search engines and the delivery route planning software they use are absolutely central to successful route planning. The seven bridges of Konigsberg and Dijkstra algorithm are the principle mathematical constructs behind the successful global distribution of commodities and associated goods.