قارن الطرق

	البرمجة الصحيحة	تحليل المسار الأقل تكلفة / تحليل المسافة والتكلفة
المجال	التحسين	التحليل المكاني
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1958	1994
صاحب الطريقة	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Edsger Dijkstra (shortest path); GIS cost-surface adaptation
النوع	Mathematical optimisation — exact combinatorial method	Raster cost-surface routing
المصدر التأسيسي	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269–271.
الأسماء البديلة	IP, MIP, mixed-integer programming, mixed-integer linear programming	cost-distance analysis, accumulated cost surface, least-cost corridor, en düşük maliyetli yol
ذات صلة	4	3
الملخص	Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems.	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.