Our work focuses on automated mobile robot fulfillment systems in distribution centers. From the logistics perspective the main task here is to turn homogeneous item crates into ready-to-ship packages that are send to the customer by using multiple automated transport vehicles. These systems are considered to ensure that these orders are shipped as fast as possible while relieving human order pickers. Our work identifies the main subproblems in such systems as the multi robot path planning, multi agent task allocation, order batching, replenishment batching, item storage assignment and the more uncommon bucket storage assignment problems. In short these decide (in the same order) which paths the robots use, how the tasks are allocated to the different agents, which orders are assigned to which output-station, which incoming items are distributed from which input-station, which new items are put on which bucket and where to park the buckets when bringing them back to the inventory. We present these in the context of the system and draw connections to similar ones in other automated material handling systems. Most of these naturally have to be decided dynamically while they also can be mapped to NP-hard optimization problems. Hence, effective methods have to be evaluated that cooperate best to achieve a globally efficient system. Furthermore, we introduce an extended revision of a previously published framework that allows the integration of different controlling mechanisms in order to compare their performance by simulation. The framework allows a flexible integration of methods capable of solving encapsulated or integrated subproblems. Additionally, we introduce first simple controllers for the identified problem components and discuss them in more detail.