We consider a manufacturer's dual distributions channels consisting on the one hand of a virtual (online) channel operated directly by a manufacturer and on the other hand of a real (offline) channel operated by an intermediate retailer. Customers are assumed heterogeneous in their virtual...

This paper introduces an extension of the vehicle routing problem by including several distributors in competition. Each customer is characterized by demand and a wholesale price. Under this scenario a solution may have unserviced customers and elementary routes with no customer visits. The...