Integrated routing for a vehicle-robot pickup and delivery system with time constraints

This paper considers an unmanned vehicle-robot pickup and delivery system, in which a self-driving vehicle carrying multiple unmanned robots in the form of the mother ship travels from a depot to a number of stations distributed in a neighborhood to perform multiple pickup and delivery services. First of all, we present it as a Multi-modal Vehicle Routing Problem (MMVRP) with time constraints, which are typical service requirements for grocery and food delivery in practice. We then formulate it as a Mixed Integer Quadratically Con-strained Program (MIQCP) model to determine the optimal integrated routing plan (vehicle routing and robot routing) to minimize the total weighted tardiness of all services. Finally, a small-size and a medium-size problem instance are solved using the Gurobi solver in Python to demonstrate the validity and the performance of the proposed MIQCP model.