مقایسهٔ روش‌ها

	برنامه‌ریزی عدد صحیح (IP) و برنامه‌ریزی عدد صحیح مختلط (MIP)	تحلیل مسیر کم‌هزینه / تحلیل هزینه-فاصله	برنامه‌ریزی خطی
حوزه	بهینه‌سازی	تحلیل فضایی	بهینه‌سازی
خانواده	Process / pipeline	Process / pipeline	Process / pipeline
سال پیدایش	1958	1994	1947
پدیدآور	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Edsger Dijkstra (shortest path); GIS cost-surface adaptation	George B. Dantzig
نوع	Mathematical optimisation — exact combinatorial method	Raster cost-surface routing	Mathematical programming / continuous optimization
منبع بنیادین	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.	Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136
نام‌های دیگر	IP, MIP, mixed-integer programming, mixed-integer linear programming	cost-distance analysis, accumulated cost surface, least-cost corridor, en düşük maliyetli yol	LP, linear optimization, Doğrusal Programlama (LP)
مرتبط	4	3	4
خلاصه	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.	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.