Motivated by a real-world application in industrial storage yards, we consider the problem of scheduling predetermined container relocation moves by an automated twin-crane system. In this setting, two gantry cranes operate in parallel on a grid of container stacks but cannot pass each other. The goal is to minimize the total time required to perform all given operations. We show that this problem, which we call Twin-Crane Scheduling, is APX-hard. More precisely, the problem cannot be approximated within a factor smaller than 1.01 unless P = NP. However, we show that the optimal solution can easily be approximated within a factor of 2 through a simple list scheduling algorithm.