Linganisha mbinu

	Uchanganuzi wa Maamuzi wa Vigezo-Nyingi unaotumia GIS (GIS-MCDA)	Utekelezaji wa Namba Kamili	Uchanganuzi wa Njia ya Gharama Chini / Umbali wa Gharama	Usanifu wa Mipango
Nyanja	Uchanganuzi wa Kimaeneo	Uboreshaji	Uchanganuzi wa Kimaeneo	Uboreshaji
Familia	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
Mwaka wa asili	2006	1958	1994	1947
Mwanzilishi	Jacek Malczewski (GIS-MCDA synthesis)	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Edsger Dijkstra (shortest path); GIS cost-surface adaptation	George B. Dantzig
Aina	Spatial multi-criteria suitability/decision analysis	Mathematical optimisation — exact combinatorial method	Raster cost-surface routing	Mathematical programming / continuous optimization
Chanzo asilia	Malczewski, J. (2006). GIS-based multicriteria decision analysis: a survey of the literature. International Journal of Geographical Information Science, 20(7), 703–726.	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
Majina mbadala	GIS-MCDM, spatial multi-criteria analysis, GIS-AHP, weighted overlay suitability	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)
Zinazohusiana	4	4	3	4
Muhtasari	GIS-MCDA combines the map layers of a geographic information system with multi-criteria decision analysis to produce suitability or priority maps — ranking locations by how well they satisfy several weighted criteria at once. It is the standard framework for spatial decisions such as siting hospitals, solar farms, landfills, or evacuation areas, integrating methods like AHP, TOPSIS, and weighted overlay with spatial data.	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.