<p>While in warehouses serving classical store-based retailers, each product (or stock keeping unit, SKU) is stored in only one storage position, many online retailers utilize a mixed-shelves or scattered storage assignment strategy, where the units of incoming SKUs are distributed across multiple open storage positions within the warehouse. This ensures that an item of each SKU lies in vicinity of each other SKU such that this storage assignment strategy accommodates the typical heterogeneous and unpredictable order structure in the e-commerce business. A common approach to facilitate an efficient order picking process in those warehouses is to minimize the unproductive walking times of the picker collecting the demanded SKUs from the warehouse shelves. This task, known as the single picker routing problem in scattered storage warehouses (SPRP-SS), consists of two interdependent layers, namely selecting a subset of storage positions to visit so that a sufficient number of items per SKU is picked, and finding the shortest route between the selected positions, which increases the complexity of the problem compared to the classical warehousing case. Although picker routing in scattered storage warehouses has received much attention in literature recently, most solution approaches presented are based on crucial assumptions, like, e.g., a distinct (often rectangular) warehouse layout or unit-demand (where all orders contain only one unit per SKU at most). This emphasizes the need for a flexible exact solution approach that is able to solve the single picker routing problem in scattered storage warehouses in its general form, i.e., with an arbitrary warehouse layout as well as the varying-demand case, where several pieces of the same SKU can appear together in the same order. Employing a branch-and-cut methodology, this paper introduces valid inequalities as well as related separation algorithms, either by exploiting relationships to associated routing problems or by developing new, customized procedures for SPRP-SS. Furthermore, the approach is extended to a warehouse setting with multiple depots. A thorough computational study is conducted by assessing the effectiveness of the branch-and-cut algorithm against off-the-shelf solver Gurobi using both an established benchmark set of rectangular instances from literature and a newly created benchmark set that includes a non-rectangular aisle layout and multiple depots.</p>