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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.

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.