In this paper we present a Boolean Linear Programming Model (BLPM) as well as exact and heuristic algorithms for solving the preemptive single-machine scheduling problem with a finite set of jobs, arbitrary release and due dates, priorities of one job in favor of another job (weights) and equal-length processing times minimizing either the Total Weighted Completion Time (TWCT) or Total Weighted Tardiness (TWT). Our computational study involves more than one million problem instances with up to 350 jobs and shows that 2 heuristics based on the linear programming relaxation of the BLPM return optimal schedules for TWCT and TWT in more than \(99\%\) of generated instances. Each generated instance has been solved to optimality within 31 min on a standard PC. That improved the current state of the art with at most 20 jobs and at least 60 min by more than an order of magnitude. We show the flexibility of BLPM to be generalized for other objective functions including Total Weighted Earliness-Tardiness with respect to the recommended (not penalized) starting and completion time intervals (TWET), Total Weighted Number of Tardy Jobs (TWNTJ), and their variations.