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We propose a Boolean Linear Programming model for the preemptive singlemachine scheduling problem with equal processing times, arbitrary release datesand weights(priorities) minimizing the total weighted completion time. Almostalways an optimal solution of the Linear Programming relaxation is integral andcan be straightforwardly converted into an optimal schedule. To deal with thefractional solutions we present two heuristics. Very often our heuristics findsolutions with objective function values equal to the lower bound found by theLinear Programming relaxation. For the cases when upper bound returned by ourheuristics differs from the lower bound we embed the bounds into a Branch andBound algorithm, which solves the problem to optimality. Exhaustivecomputational study showed that the algorithm substantially surpassesstate-of-the-art methods.

An efficient model for the preemptive single machine scheduling of equal-length jobs