In this paper we consider the Split Delivery Vehicle Routing Problem (SDVRP
), a relaxation of the known Capacitated Vehicle Routing Problem (CVRP) in
which the demand of any client can be serviced by more than one vehicle. We
define a feasible solution of this problem, and we show that the convex hu
ll of the associated incidence vectors is a polyhedron (P-SDVRP), whose dim
ension depends on whether a vehicle visiting a client must service, or not
at least one unit of the client demand. From a partial and linear descripti
on of PSDVRP and a new family of Valid inequalities, we develop a lower bou
nd whose quality is exhibited in the computational results provided, which
include the optimal resolution of some known instances-one of them with 50
clients. This instance is, as far as we know, the biggest one solved so far
.