The classic transportation problem concerns minimizing the cost of transporting a product from sources/supplies to destinations/demands. It is a network-flow problem that arises in industrial logistics and is often solved by linear programming (LP). The three inputs of the model are total units produced at each source, total units needed at each destination, and the cost to transport one unit from each source to each destination. And the objective is to minimize the total cost of transporting all units produced at sources to meet the demands at destinations. The problem solution includes three basic steps: 1) finding an initial basic feasible solution, 2) checking if the current solution is optimal (with the lowest costs), and improving the current solution through iteration. Solving such a problem relies strongly on the network data models, least-cost path algorithms, other functionalities in GIS. And an integrated framework is often adopted to utilize both GIS and non-GIS linear programming solvers to search for the optimal solution.
Spatial network modeling has started with quantitative geography and its integration into GIS for analyzing transport and material flows. Concepts from graph theory were combined with spatio-temporal concepts to model spatial relationships. As GIS evolved, it established close links to transportation science and graph-based complexity models. Spatial networks thus provide a way to measure relationships between geo-located entities. Yet, though spatial networks are often modeled as spatially embedded graphs, the concepts involved are more specific: nodes can be locations or spatial objects with possibly changing locations, potentials or attractiveness scores, and edges can measure diverse quantified (extensive or intensive) relationships, such as distances, interactions, or flows. A primary example are transport networks. Here, key tasks include constructing distance networks based on road infrastructure, modeling potential interactions within defined distances, measuring accessibility by identifying proximity to services like schools, and measuring network centrality. Spatial networks also can be used to estimate flows between objects using gravity models, based on spatial interactions between the potential of origins and the attractiveness of destinations and their distance. Distances can thereby be modeled in various manners, including metric, topological or angular distances.
The idea of networks has become popular in GIS since the early 1990s. There are several applications of network analyses that could be solved with the use of GIS but the first and foremost context that comes to mind is that of city planning. A network structure emphasizes the connectivity between infrastructure, essential amenities, and green spaces in a city. If we assume each amenity to be a single node then the interconnections among these nodes via street networks become the underlying network structure that defines the city’s accessibility. Such an assumption of the city’s structure has been highly relevant in transportation studies while defining traffic volume and traffic routing through the city. In such a case each street intersection becomes a single node within the network and the streets themselves are the edges. A network-based understanding of the city’s pulse is essential to model the behavior of human mobility, network accessibility and understanding of safety and emergency needs during times of extreme events. The most important aspect of network analyses till date has been routing and allocation modeling. In a complex network the problem of finding the shortest optimal route from an origin to a destination can be a np hard problem depending upon the number of parameters needed to reach the optimal solution. There are several mechanisms to resolve the complexity of the routing problem one of the common methods being multicriteria decision analyses which I will elaborate in detail in the following sections.