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.
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.