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<p>This study considers the single-machine group scheduling problem with convex resource allocations and different due-date assignments. The aim is to determine the optimal group-schedule, an internal job-schedule in each group, due-date of each job, and resource allocations to minimize the linear weighted sum of due-date assignment cost and resource consumption cost, where the weights are position-dependent. For the general problem, we propose a branch-and-bound (<i>BB</i>) algorithm, a tabu search, and a heuristic. Computational experiments are provided to evaluate the performance of these algorithms, which shows that the <i>BB</i> algorithm can solve 120 jobs and 13 groups instances within reasonable time and that tabu search is more accurate than the heuristic.</p>

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Study on Single-Machine Group Scheduling with Convex Resource Allocations and Different Due-Date Assignments

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Li-Han Zhang,
  • Na Yin

摘要

This study considers the single-machine group scheduling problem with convex resource allocations and different due-date assignments. The aim is to determine the optimal group-schedule, an internal job-schedule in each group, due-date of each job, and resource allocations to minimize the linear weighted sum of due-date assignment cost and resource consumption cost, where the weights are position-dependent. For the general problem, we propose a branch-and-bound (BB) algorithm, a tabu search, and a heuristic. Computational experiments are provided to evaluate the performance of these algorithms, which shows that the BB algorithm can solve 120 jobs and 13 groups instances within reasonable time and that tabu search is more accurate than the heuristic.