مقایسهٔ روش‌ها

	مسئله مسیریابی وسایل نقلیه (VRP)	برنامه‌ریزی عدد صحیح (IP) و برنامه‌ریزی عدد صحیح مختلط (MIP)	مدل‌های مکان‌یابی-تخصیص
حوزه	بهینه‌سازی	بهینه‌سازی	تحلیل فضایی
خانواده	Process / pipeline	Process / pipeline	Process / pipeline
سال پیدایش	1959	1958	1963
پدیدآور	George Dantzig & John Ramser	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Leon Cooper; S. L. Hakimi
نوع	Combinatorial optimization problem	Mathematical optimisation — exact combinatorial method	Spatial facility-location optimization
منبع بنیادین	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	Cooper, L. (1963). Location-allocation problems. Operations Research, 11(3), 331–343.
نام‌های دیگر	Capacitated Vehicle Routing Problem, Fleet Routing Problem, Multi-Vehicle Routing Problem, Araç Rotalama Problemi	IP, MIP, mixed-integer programming, mixed-integer linear programming	facility location, p-median problem, maximal covering location problem, yer-tahsis modelleri
مرتبط	3	4	4
خلاصه	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.	Location-allocation models decide where to place a set of facilities and simultaneously assign demand points to them so as to optimize an objective such as total travel cost, worst-case distance, or population covered. Rooted in the operations-research work of Cooper (1963) and Hakimi (1964) and central to network GIS, they answer questions like where to site warehouses, hospitals, fire stations, or schools to best serve a spatially distributed population.