In this paper we deal with the problem of assigning a set of n jobs, with release dates and tails, to either one of two unrelated parallel machines and scheduling each machine so that the makespan is minimized. This problem will be denoted by R2|ri,qi|Cmax. The model generalizes the problem on one machine 1|ri,qi|Cmax, for which a very efficient algorithm exists. In this paper we describe a Branch and Bound procedure for solving the two machine problem which is partly based on Carlier's algorithm for the 1|ri,qi|Cmax. An O(n log n) heuristic procedure for generating feasible solutions is given. Computational results are reported.
