Computational findings demonstrate an effective integer solution for minimizing job completion times on a single machine, suggesting implications for scheduling efficiency.
The paper considers the following problem of scheduling theory. Jobs are serviced by a single machine. Each job is characterized by a positive weight and a release date. The service durations are the same. Interruptions are allowed in service. Time is assumed to be discrete. It is necessary to find a schedule for servicing jobs that minimizes the weighted sum of moments of completion of processing jobs. The complexity status of the problem is currently unknown. The paper presents a new Boolean linear programming model for this problem that includes some necessary conditions for the optimality of schedules. These conditions are presented as linear inequalities. As a result of the computational experiment, it was noted that the model produces an integer solution even without imposing integer conditions on the variables.
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Simanchev et al. (2025) studied this question.
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