Manual order picking, the process of retrieving stock keeping units from their storage location to fulfil customer orders, is one of the most labour-intensive and costly activity in modern supply chains. To improve the outcome of order picking systems, automated and robotized components are increasingly introduced creating hybrid order picking systems where humans and machines jointly work together. This study focuses on the application of a hybrid picker-to-parts order picking system, in which human operators collaborate with Automated Mobile Robots (AMRs). In this paper a warehouse with a two-blocks layout is investigated. The main contributions are new mathematical models for the optimization of picking operations and synchronizations. Two alternative implementations for an AMR system are considered. In the first one handover locations, where pickers load AMRs) are shared between pairs of opposite sub-aisles, while in the second they are not. It is shown that solving the mathematical models proposed by the meaning of black-box solvers provides a viable algorithmic optimization approach that can be used in practice to derive efficient operational plannings. The experimental study presented, based on a real warehouse and real orders, finally allows to evaluate and strategically compare the two alternative implementations considered for the AMR system.