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| 정수 계획법(IP) 및 혼합 정수 계획법(MIP)× | 최소 비용 경로 / 비용 거리 분석× | |
|---|---|---|
| 분야≠ | 최적화 | 공간분석 |
| 계열 | Process / pipeline | Process / pipeline |
| 기원 연도≠ | 1958 | 1994 |
| 창시자≠ | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) | Edsger Dijkstra (shortest path); GIS cost-surface adaptation |
| 유형≠ | Mathematical optimisation — exact combinatorial method | Raster cost-surface routing |
| 원전≠ | 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. DOI ↗ |
| 별칭≠ | IP, MIP, mixed-integer programming, mixed-integer linear programming | cost-distance analysis, accumulated cost surface, least-cost corridor, en düşük maliyetli yol |
| 관련≠ | 4 | 3 |
| 요약≠ | 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. |
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