Summary: This paper presents the theoretical foundations for controlling pile-up systems. A pile-up system consists of one or more stacker cranes picking up bins from a conveyor and placing them onto pallets with respect to costumer orders. The bins usually arrive at a conveyor from an orderpicking system. We give a mathematical definition of the pile-up problem, define a data structure for control algorithms, introduce polynomial time algorithms for deciding whether a system can be blocked by making bad decisions, and show that the pile-up problem is in general NP-complete. For pile-up systems with a restricted storage capacity or with a fixed number of pile-up places the pile-up problem is proved to be solvable very efficiently.