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This paper treats an automated warehousing system, known as the KIVA system, where mobile robots lift complete racks and autonomously move them to stationary pickers. This innovative parts-to-picker system relieves the pickers from unproductive walking times without requiring high investment costs into inflexible hardware such as conveyors, storage and retrieval machines, or lifts. In this context, we treat the decision problem where to park the racks during order processing when they are consistently moved between the picking stations and the storage area. We formalize the resulting rack assignment problem as a special interval scheduling problem and introduce a new matheuristic dubbed adaptive programming. In a comprehensive computational study, we compare the results of our optimization approach with simple rule-based assignment policies. Our results reveal that the well-established rules widely applied in traditional picker-to-parts warehouses, for example, random and dedicated storage, lead to considerable optimality gaps. Adapted rules, however, which consider the peculiarities of KIVA warehouses, lead to very good results. The e-companion is available at https://doi.org/10.1287/trsc.2018.0826 .