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	स्थान-आवंटन मॉडल (Location-Allocation Models)	न्यूनतम-लागत पथ / लागत-दूरी विश्लेषण	रैखिक प्रोग्रामन
क्षेत्र	स्थानिक विश्लेषण	स्थानिक विश्लेषण	अनुकूलन
परिवार	Process / pipeline	Process / pipeline	Process / pipeline
उद्भव वर्ष	1963	1994	1947
प्रवर्तक	Leon Cooper; S. L. Hakimi	Edsger Dijkstra (shortest path); GIS cost-surface adaptation	George B. Dantzig
प्रकार	Spatial facility-location optimization	Raster cost-surface routing	Mathematical programming / continuous optimization
मौलिक स्रोत	Cooper, L. (1963). Location-allocation problems. Operations Research, 11(3), 331–343.	Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269–271.	Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136
उपनाम	facility location, p-median problem, maximal covering location problem, yer-tahsis modelleri	cost-distance analysis, accumulated cost surface, least-cost corridor, en düşük maliyetli yol	LP, linear optimization, Doğrusal Programlama (LP)
संबंधित	4	3	4
सारांश	Location-allocation models decide where to place a set of facilities and simultaneously assign demand points to them so as to optimize an objective such as total travel cost, worst-case distance, or population covered. Rooted in the operations-research work of Cooper (1963) and Hakimi (1964) and central to network GIS, they answer questions like where to site warehouses, hospitals, fire stations, or schools to best serve a spatially distributed population.	Least-cost path analysis finds the route between two locations that minimizes accumulated travel cost across a landscape, rather than minimizing straight-line distance. By encoding terrain, slope, land cover, and other frictions into a cost surface and accumulating cost outward from a source, it identifies optimal corridors for roads, pipelines, trails, power lines, and wildlife movement — a core raster-GIS technique built on Dijkstra's shortest-path logic.	Linear programming (LP), pioneered by George B. Dantzig in 1947, is a mathematical method for finding the best value of a linear objective function — such as minimum cost or maximum profit — subject to a set of linear inequality and equality constraints. It is the foundational technique in operations research and underlies production planning, resource allocation, logistics, diet problems, and countless other decision-making scenarios across engineering, economics, and the natural sciences.