  We propose a Boolean Linear Programming model for the preemptive single
machine scheduling problem with equal processing times, arbitrary release dates
and weights(priorities) minimizing the total weighted completion time. Almost
always an optimal solution of the Linear Programming relaxation is integral and
can be straightforwardly converted into an optimal schedule. To deal with the
fractional solutions we present two heuristics. Very often our heuristics find
solutions with objective function values equal to the lower bound found by the
Linear Programming relaxation. For the cases when upper bound returned by our
heuristics differs from the lower bound we embed the bounds into a Branch and
Bound algorithm, which solves the problem to optimality. Exhaustive
computational study showed that the algorithm substantially surpasses
state-of-the-art methods.
