A general outline of various types of vehicle routing problems in the field of reverse logistics was given.The vehicle routing problems were divided into two classes,i.e.the problem of single demand and double demands,according to the demand characteristic of the customer node.The vehicle routing problem with simultaneous delivery and pickup (VRPSDP) and the vehicle routing problem with split deliveries and pickups (SVRPPD) were called as the vehicle routing problem with nodes of double demands (VRPNDD).Their definitions and mathematic models were given.Then as the preliminary work for designing the heuristics,some constitutive properties of the solution for the VRPNDD were investigated.The difference in properties of optimal solutions between SVRPPD and SDVRP (the vehicle routing problem with split delivery) was illustrated,and a theorem was proved to show the significance of the heuristics’ improving on cost saving analysis of SVRPPD relative to VRPSDP.