방법 비교

	차량 경로 문제 (VRP)	정수 계획법(IP) 및 혼합 정수 계획법(MIP)	서비스 영역 분석
분야	최적화	최적화	공간분석
계열	Process / pipeline	Process / pipeline	Process / pipeline
기원 연도	1959	1958	2001
창시자	George Dantzig & John Ramser	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Harvey Miller & Shih-Lung Shaw
유형	Combinatorial optimization problem	Mathematical optimisation — exact combinatorial method	Network GIS pipeline
원전	Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80–91.	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	Miller, H. J., & Shaw, S.-L. (2001). Geographic Information Systems for Transportation: Principles and Applications. Oxford University Press. ISBN: 978-0-19-512394-4
별칭	Capacitated Vehicle Routing Problem, Fleet Routing Problem, Multi-Vehicle Routing Problem, Araç Rotalama Problemi	IP, MIP, mixed-integer programming, mixed-integer linear programming	Isochrone Analysis, Network Catchment Area Analysis, Travel-Time Polygon Analysis, Hizmet Alanı Analizi
관련	3	4	3
요약	The Vehicle Routing Problem (VRP) seeks the minimum-cost set of routes for a fleet of vehicles to serve a collection of geographically dispersed customers, each with a known demand, departing from and returning to a central depot. Originally formulated as the Truck Dispatching Problem by Dantzig and Ramser in 1959, VRP is a foundational model in logistics, supply chain management, and operations research, applicable whenever goods or services must be delivered efficiently across multiple stops.	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.	Service Area Analysis delineates the geographic region reachable from one or more origin facilities within a specified travel cost — typically time, distance, or generalized impedance — by traversing a real road or transit network. It is widely used by urban planners, public health officials, logistics managers, and emergency response coordinators who need to understand actual accessibility rather than simple straight-line buffers.