The motivation for this study was the observation of a practical scenario that involves scheduling of two parallel machines attended by a single setup crew so as to minimize the makespan. This problem is known in scheduling literature as the parallel machine scheduling problem with a single server, P2S1/ / C max. In order to gain insight on this problem, we analyzed a constrained version of it. In this constrained case, jobs are dedicated to each machine, and the processing sequence on each machine is given and fixed. The problem is thus referred to as the parallel, dedicated machine scheduling problem with a single server and full precedence, PD2S1/full prec./ C max. We explore the combinatoric structure of the problem, and develop a branch and bound procedure and five heuristic algorithms.