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Abstract <p> The paper considers the following problem of scheduling theory. Jobs are serviced bya single machine. Each job is characterized by a positive weight and a release date. The servicedurations are the same. Interruptions are allowed in service. Time is assumed to be discrete. It isnecessary to find a schedule for servicing jobs that minimizes the weighted sum of moments ofcompletion of processing jobs. The complexity status of the problem is currently unknown. Thepaper presents a new Boolean linear programming model for this problem that includes somenecessary conditions for the optimality of schedules. These conditions are presented as linearinequalities. As a result of the computational experiment, it was noted that the model producesan integer solution even without imposing integer conditions on the variables.</p>

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An Integer Model with Optimality Conditions for the Total Weighted Minimizing Problem on a Single Machine

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • R. Yu. Simanchev,
  • I. V. Urazova

摘要

Abstract

The paper considers the following problem of scheduling theory. Jobs are serviced bya single machine. Each job is characterized by a positive weight and a release date. The servicedurations are the same. Interruptions are allowed in service. Time is assumed to be discrete. It isnecessary to find a schedule for servicing jobs that minimizes the weighted sum of moments ofcompletion of processing jobs. The complexity status of the problem is currently unknown. Thepaper presents a new Boolean linear programming model for this problem that includes somenecessary conditions for the optimality of schedules. These conditions are presented as linearinequalities. As a result of the computational experiment, it was noted that the model producesan integer solution even without imposing integer conditions on the variables.