A Tabu Search algorithm for the vehicle routing problem with discrete split deliveries and pickups

•The Vehicle Routing Problem with Discrete Split Deliveries and Pickups (VRPDSPDP) is considered.•Brief and up-to-date reviews of the problems with split loads, problems with discrete demands, as well as Tabu Search and local search algorithms for VRPDPs are presented.•The features and the optimal solution properties of the VRPDSPDP are analyzed.•A Tabu Search algorithm for the VRPDSPDP is proposed.•In proposed TS algorithm, the operations of batch combination and item creation are specially designed.