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<p>This paper considers the single-machine scheduling problem with workload-dependent maintenance activities of variable length. The time needed to perform a maintenance activity is a function of the total processing time of the jobs that are processed between the starting time of this activity and the end of the last previous activity. In the case where the function is concave, we study the computational complexity of the three problems with the goal of minimizing the makespan, the total completion time, and the total weighted completion time, respectively. In addition, we propose a 2-approximation algorithm for the first problem and a 2.5-approximation algorithm for the second problem.</p>

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Complexity analysis and approximation algorithms for the single-machine scheduling problem with workload-dependent maintenance activities

  • 期刊论文

  • 发表日期：

    2025年5月26日

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  • Peihai Liu,
  • Manzhan Gu,
  • Xiwen Lu

摘要

This paper considers the single-machine scheduling problem with workload-dependent maintenance activities of variable length. The time needed to perform a maintenance activity is a function of the total processing time of the jobs that are processed between the starting time of this activity and the end of the last previous activity. In the case where the function is concave, we study the computational complexity of the three problems with the goal of minimizing the makespan, the total completion time, and the total weighted completion time, respectively. In addition, we propose a 2-approximation algorithm for the first problem and a 2.5-approximation algorithm for the second problem.