Theoretical research and practical applications in the ?eld of vehicle routing started in 1959 with the truck dispatching problem posed by Dantzig and Ramser [ 1]: ?nd the . . . optimum routing of a ?eet of gasoline delivery trucks between a bulk terminal and a large number of service stations supplied by the terminal. Using a method based on a linear programming formulation, their hand calculations produced a near-optimal solution with four routes to aproblemwithtwelve service stations. The authorsproclaimed:Nopractical applications of the method have been made as yet. In the nearly 50 years since the Dantzig and Ramser paper appeared, work in the ?eld has exploded dramatically. Today, a Google Scholar search of the words vehicle routing problem (VRP) yields more than 21,700 entries. The June 2006 issue of OR/MS Today provided a survey of 17 vendors of commercial routing software whose packages are currently capable of solving average-size problems with 1,000 stops, 50 routes, and two-hour hard-time windows in two to ten minutes [ 2]. In practice, vehicle routing may be the single biggest success story in operations research. For example, each day 103,500 drivers at UPS follow computer-generated routes. The drivers visit 7. 9 million customers and handle an average of 15. 6 million packages [ 3].
