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.
A network is a widely used term with different definitions and methodologies depending on the applications. In GIS, a network refers to an arrangement of elements (i.e., nodes, links) and information on their connections and interactions. There are two types of networks: physical and logical. While a physical network has tangible objects (e.g., road segments), a logical network represents logical connections among nodes and links. A network can be represented with a mathematical notion called graph theory. Different network components are utilized to describe characteristics of a network including loops, walks, paths, circuits, and parallel edges. Network data are commonly organized in a vector format with network topology, specifically connectivity among nodes and links, whereas raster data can be also utilized for a least-cost problem over continuous space. Network data is utilized in a wide range of network analyses, including the classic shortest path problem.
In this article, return on investment (ROI) calculations are applied to analyzing the current costs and financial benefits of geographic information systems (GIS) as a GIS management tool. How to develop GIS ROI methodologies to document the current financial value of GIS operations, as well as an outline of a ROI research design without and without GIS, are also included. Before the development and widespread use of GIS by government agencies and private enterprises, maps provided benefits and value to society. Early attempts to catalog the societal and financial benefits from mapping include examples related to geological mapping. An ROI analysis calculates the financial values of all the inputs into a system and all the outputs from the system, and then calculates the differences in value of the inputs and outputs. A key challenge to the growth of the emerging geospatial technology industry was to convince agencies and companies that GIS provided both societal and financial benefits. Companies and agencies often used benefit-cost analysis as a decision support tool when deciding to invest in GIS. But usually there was no effort or requirement by agencies to prove the ROI achieved after a project was completed and put into operation.