Vehicle routing problem

The vehicle routing problem is the optimization problem of designing routes for a fleet to serve specified locations while minimizing cost or distance under operational constraints.

Traveling salesman problem: The optimization problem of finding a shortest tour that visits each specified location once and returns to its start. A single-vehicle routing problem reduces to this tour problem when capacity and other constraints are absent.
Combinatorial optimization: Optimization over a finite set of discrete choices, often with constraints linking those choices. Choosing route assignments and visit orders makes vehicle routing a combinatorial optimization problem.
Last-mile delivery: The movement of goods from a distribution point to their final recipients. Urban delivery fleets use routing to schedule customer visits while controlling distance and cost.
Vehicle scheduling: The assignment of vehicles to trips or tasks over time while satisfying operational requirements. Scheduling allocates vehicles across trips; routing determines the sequences of locations within trips.
Vehicle routing problem with time windows: A vehicle routing problem in which each location must be served within a specified time interval. Time-window constraints make route feasibility depend on arrival times as well as distance.
Graph theory: The mathematical study of vertices and edges and the structures formed by their connections. Locations and travel links form the graph on which routes are planned.
Dial-a-ride problem: A transport problem that plans vehicle trips for passengers who request individual pickups and drop-offs. Passenger requests turn routing into a service problem with paired origins and destinations.
Shortest path problem: The problem of finding a minimum-cost path between specified vertices in a network. A shortest-path problem connects a given pair, while routing coordinates visits to many locations.
Vehicle capacity constraint: A limit on the total load a vehicle may carry during a route. Capacity restricts which customer sets can be combined on one route.
Integer programming: Optimization in which some or all decision variables are restricted to integer values. Binary decisions can represent whether a vehicle travels between two locations.

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