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<p>We study scheduling problems on <i>parallel dedicated</i> machines and assume that a specific job can only be processed on one specific machine. We concentrate on solving scheduling problems involving <i>convex resource allocation</i> and address three of the most fundamental measures in scheduling theory, i.e., makespan, total load, and total weighted completion time. Firstly, we focus on <i>position-independent workloads,</i> and then we study the setting of <i>general position-dependent workloads</i>, i.e., the workloads are not restricted to be either monotone functions of the job positions or any specific functions. In all problems, we assume a common <i>continuous</i> and <i>non-renewable</i> (limited) resource and adapt known results from scheduling theory to solve the considered problems.</p>

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Scheduling problems on parallel dedicated machines with non-renewable resource

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月6日

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  • Baruch Mor,
  • Joanna Berlińska

摘要

We study scheduling problems on parallel dedicated machines and assume that a specific job can only be processed on one specific machine. We concentrate on solving scheduling problems involving convex resource allocation and address three of the most fundamental measures in scheduling theory, i.e., makespan, total load, and total weighted completion time. Firstly, we focus on position-independent workloads, and then we study the setting of general position-dependent workloads, i.e., the workloads are not restricted to be either monotone functions of the job positions or any specific functions. In all problems, we assume a common continuous and non-renewable (limited) resource and adapt known results from scheduling theory to solve the considered problems.