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 field of geospatial analytics and modeling has a long history coinciding with the physical and cultural evolution of humans. This history is analyzed relative to the four scientific paradigms: (1) empirical analysis through description, (2) theoretical explorations using models and generalizations, (3) simulating complex phenomena and (4) data exploration. Correlations among developments in general science and those of the geospatial sciences are explored. Trends identify areas ripe for growth and improvement in the fourth and current paradigm that has been spawned by the big data explosion, such as exposing the ‘black box’ of GeoAI training and generating big geospatial training datasets. Future research should focus on integrating both theory- and data-driven knowledge discovery.
Local multivariate statistical models are increasingly encountered in geographical research to estimate spatially varying relationships between a response variable and its associated predictor variables. In geography and many other disciplines, such models have been largely embedded within the framework of regression and can reveal significantly more information about the determinants of observed spatial distribution of the dependent variable than their global regression model counterparts. This section introduces one type of local statistical modeling framework: Geographically Weighted Regression (GWR). Models within this framework estimate location-specific parameter estimates for each covariate, local diagnostic statistics, and bandwidth parameters as indicators of the spatial scales at which the modeled processes operate. These models provide an effective means to estimate how the same factors may evoke different responses across locations and by so doing, bring to the fore the role of geographical context on human preferences and behavior.
Define the following terms pertaining to a network: Loops, multiple edges, the degree of a vertex, walk, trail, path, cycle, fundamental cycle
List definitions of networks that apply to specific applications or industries
Create an adjacency table from a sample network
Explain how a graph can be written as an adjacency matrix and how this can be used to calculate topological shortest paths in the graph
Create an incidence matrix from a sample network
Explain how a graph (network) may be directed or undirected
Demonstrate how attributes of networks can be used to represent cost, time, distance, or many other measures
Demonstrate how the star (or forward star) data structure, which is often employed when digitally storing network information, violates relational normal form, but allows for much faster search and retrieval in network databases
Discuss some of the difficulties of applying the standard process-pattern concept to lines and networks
Demonstrate how a network is a connected set of edges and vertices