Dividing a Territory Among Several Vehicles

We consider an uncapacitated stochastic vehicle routing problem in which vehicle depot locations are fixed and client locations in a service region are unknown, but are assumed to be independent and identically distributed samples from a given probability density function. We present an algorithm for partitioning the service region into sub-regions so as to balance the workloads of all vehicles when the service region is simply connected and point-to-point distances follow some “natural” metric, such as any Lp norm. This algorithm can also be applied to load-balancing of other combinatorial structures, such as minimum spanning trees and minimum matchings.