The Vehicle Routing Problem (VRP) asks for the minimum-cost set of routes for a fleet of vehicles to serve all customers from a central depot. The capacitated VRP adds vehicle load limits. VRP is NP-hard and subsumes TSP as a special case. Modern solvers use branch-and-price (column generation + branch-and-bound), achieving optimal solutions for ~100 customers. Heuristics like Clarke-Wright savings, 2-opt, and Lin-Kernighan provide fast approximate solutions. VRP models logistics for UPS, Amazon, and emergency dispatch — saving millions of miles annually.