Abstract
Machine scheduling is one of the most studied problems due to its technical challenges and prevalence in real life. In the literature, continuous- and discrete-time formulations are the two most known formulations for scheduling problems. However, continuous-time formulations often suffer from weak linear relaxations, while discrete-time formulations struggle with large numbers of variables. In contrast, the bucket-indexed formulation is an alternative that mitigates both issues by working with partial time discretization. We propose a mixed-integer linear programming model based on a bucket-indexed formulation to solve a nonpreemptive scheduling problem of identical parallel machines considering release dates, deadlines, precedence, eligibility, and machine availability constraints. We evaluate the proposed formulation against real-world instances comprising more than 400 jobs and 100 machines, comparing its performance against equivalent continuous- and discrete-time formulations. Remarkably, our formulation can be solved to optimality for all instances, outperforming both continuous- and discrete-time formulations.
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