เปรียบเทียบวิธี

	ปัญหาการจัดเส้นทางการขนส่ง (Vehicle Routing Problem - VRP)	การโปรแกรมจำนวนเต็ม (Integer Programming
สาขาวิชา	การหาค่าเหมาะที่สุด	การหาค่าเหมาะที่สุด
ตระกูล	Process / pipeline	Process / pipeline
ปีกำเนิด	1959	1958
ผู้ริเริ่ม	George Dantzig & John Ramser	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
ประเภท	Combinatorial optimization problem	Mathematical optimisation — exact combinatorial method
แหล่งต้นตำรับ	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
ชื่อเรียกอื่น	Capacitated Vehicle Routing Problem, Fleet Routing Problem, Multi-Vehicle Routing Problem, Araç Rotalama Problemi	IP, MIP, mixed-integer programming, mixed-integer linear programming
ที่เกี่ยวข้อง	3	4
สรุป	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.