An exact algorithm for the preemptive single machine scheduling of equal-length jobs

Abstract

Many real-world production and service environments can be modeled using the preemptive single machine scheduling problem with equal processing times, arbitrary release dates and weights (priorities) minimizing the total weighted completion time. For this problem we propose a Boolean Linear Programming model, two heuristics based on the model’s relaxation, and an exact Branch and Bound algorithm incorporating the model and heuristics. Our computational study involved more than one million problem instances with up to 350 jobs. Each generated instance has been solved to optimality within 31 min. That improves state-of-the art (at most 20 jobs in 60 min) by more than an order of magnitude. Our benchmark instances and optimal schedules are publicly available at https://data.mendeley.com/datasets/nrkx7467tf/1.