Pickup and delivery problems with autonomous vehicles on rings

In this paper we introduce a new class of Pickup and Delivery problems on circles (or rings). These arise in the field public transportation systems where autonomous (i.e. driverless) vehicles travel circular networks. We consider set stations arranged circle requests. Each request asks for certain quantity from pickup station to delivery station. A fleet capacitated is available at depot. first part propose classification scheme these problems. second part, address variants which are allowed move single direction (either clockwise or counterclockwise) objective minimize number tours ring while serving all provide complexity analysis develop polynomial time algorithms that polynomially solvable proofs NP-hardness NP-hard. addition, latter, mathematical formulations perform computational tests show effectiveness formulations. Finally, compare optimal solutions with those obtained using straightforward greedy algorithm.