The partner units problem (PUP) is an acknowledged hard benchmark problem for the Logic Programming community with various industrial application fields like surveillance, electrical engineering, computer networks or railway safety systems. However, computational complexity remained widely unclear so far. In this paper we provide all missing complexity results making the PUP better exploitable for benchmark testing. Furthermore, we present QuickPup, a heuristic search algorithm for PUP instances which outperforms all state-of-the-art solving approaches and which is already in use in real world industrial configuration environments.