We study a number of retrieval problems that relate to effectively using the throughput of parallel disks. These problems can be formulated as assigning a maximum number of jobs to machines of capacity two, where jobs are of size one or two that must satisfy assignment restrictions. We prove that the LP-relaxation of an integer programming formulation is half-integral, and derive an interesting persistency property. In addition, we derive $ \frac{2} {3} $ \frac{2} {3} -approximation results for two types of retrieval problems.