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DM-16 - Linear Referencing

Linear referencing is a term that encompasses a family of concepts and techniques for associating features with a spatial location along a network, rather than referencing those locations to a traditional spherical or planar coordinate system. Linear referencing is used when the location on the network, and the relationships to other locations on the network, are more significant than the location in 2D or 3D space. Linear referencing is commonly used in transportation applications, including roads, railways, and pipelines, although any network structure can be used as the basis for linearly referenced features. Several data models for storing linearly referenced data are available, and well-defined sets of procedures can be used to implement linear referencing for a particular application. As network analysis and network based statistical analysis become more prevalent across disciplines, linear referencing is likely to remain an important component of the data used for such analyses.

DA-04 - GIS&T and Civil Engineering

Civil Engineering, which includes sub-disciplines such as environmental, geotechnical, structural, and water resource engineering, is increasingly dependent on the GIS&T for the planning, design, operation and management of civil engineering infrastructure systems.  Typical tasks include the management of spatially referenced data sets, analytic modeling for making design decisions and estimating likely system behavior and impacts, and the visualization of systems for the decision-making process and garnering stakeholder support.

PD-01 - Linear Programming and GIS

Linear programming is a set of methods for finding optimal solutions to mathematical models composed of a set of linear functions. Many spatial location problems can be structured as linear programs. However, even modest-sized problem instances can be very difficult to solve due to the combinatorial complexity of the problems and the associated computational expense that they incur. Geographic Information Systems software does not typically incorporate formal linear programming functionality, and instead commonly uses heuristic solution procedures to generate near-optimal solutions quickly. There is growing interest in integrating the spatial analytic tools incorporated in Geographic Information Systems with the solution power of linear programming software to generate guaranteed optimal solutions to spatial location problems.

AM-42 - The Classic Transportation Problem

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.

FC-19 - Networks Defined

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.