قارن الطرق

	تحليل المسار الأقل تكلفة / تحليل المسافة والتكلفة	نموذج CA-Markov لتغير استخدام الأراضي	نماذج التخصيص والمواقع
المجال	التحليل المكاني	التحليل المكاني	التحليل المكاني
العائلة	Process / pipeline	Process / pipeline	Process / pipeline
سنة النشأة	1994	1997	1963
صاحب الطريقة	Edsger Dijkstra (shortest path); GIS cost-surface adaptation	Cellular automata (Clarke) + Markov chain (Muller & Middleton)	Leon Cooper; S. L. Hakimi
النوع	Raster cost-surface routing	Spatio-temporal land-use change simulation	Spatial facility-location optimization
المصدر التأسيسي	Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269–271.	Clarke, K. C., Hoppen, S., & Gaydos, L. (1997). A self-modifying cellular automaton model of historical urbanization in the San Francisco Bay area. Environment and Planning B, 24(2), 247–261.	Cooper, L. (1963). Location-allocation problems. Operations Research, 11(3), 331–343.
الأسماء البديلة	cost-distance analysis, accumulated cost surface, least-cost corridor, en düşük maliyetli yol	CA-Markov model, cellular automata Markov, land-use change simulation, CA-Markov arazi kullanımı modeli	facility location, p-median problem, maximal covering location problem, yer-tahsis modelleri
ذات صلة	3	3	4
الملخص	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.	CA-Markov is a hybrid spatio-temporal model that projects land-use and land-cover change by combining a Markov chain — which predicts how much of each class will change — with cellular automata, which decide where that change happens. Widely used for urban-growth and land-cover forecasting, it answers both the quantity and the location of change, something neither component does well alone.	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.