So sánh phương pháp

	Bài toán Định tuyến Phương tiện (VRP)	Lập trình nguyên (Integer Programming
Lĩnh vực	Tối ưu hóa	Tối ưu hóa
Họ	Process / pipeline	Process / pipeline
Năm ra đời	1959	1958
Người khởi xướng	George Dantzig & John Ramser	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
Loại	Combinatorial optimization problem	Mathematical optimisation — exact combinatorial method
Công trình gốc	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
Tên gọi khác	Capacitated Vehicle Routing Problem, Fleet Routing Problem, Multi-Vehicle Routing Problem, Araç Rotalama Problemi	IP, MIP, mixed-integer programming, mixed-integer linear programming
Liên quan	3	4
Tóm tắt	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.