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<p>In recent years, production scheduling problems have increasingly incorporated real-world constraints. Within this domain, green scheduling has garnered significant attention among operational research practitioners. This class of problems typically involves various resource constraints, often pertaining to energy consumption or carbon emissions. This study addresses single-machine scheduling problems with controllable processing times and limited resource consumption. It considers distinct operation modes within the machine and non-renewable resources associated with job processing. We evaluate two performance measures: the minimization of the makespan and total tardiness, both belong to the NP-hard class of combinatorial optimization problems. Due to the complexity of the studied variants, this study develops two mixed-integer linear programming (MILP) models and three constraint programming (CP) models for the problems under study. Two performance indicators are considered: the Average Relative Percentage Deviation (ARPD) and the Average Relative Deviation Index (ARDI). Concerning the performance indicators, the third CP formulation achieved an ARPD of 10.63% for makespan minimization. In comparison, the second CP formulation achieved an ARDI of 2.51% for total tardiness minimization, highlighting the superiority of these solution approaches for each respective objective function.</p>

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A comparative computational study for single-machine problems with controllable processing times and limited resource consumption

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Levi R. Abreu,
  • Bruno A. Prata

摘要

In recent years, production scheduling problems have increasingly incorporated real-world constraints. Within this domain, green scheduling has garnered significant attention among operational research practitioners. This class of problems typically involves various resource constraints, often pertaining to energy consumption or carbon emissions. This study addresses single-machine scheduling problems with controllable processing times and limited resource consumption. It considers distinct operation modes within the machine and non-renewable resources associated with job processing. We evaluate two performance measures: the minimization of the makespan and total tardiness, both belong to the NP-hard class of combinatorial optimization problems. Due to the complexity of the studied variants, this study develops two mixed-integer linear programming (MILP) models and three constraint programming (CP) models for the problems under study. Two performance indicators are considered: the Average Relative Percentage Deviation (ARPD) and the Average Relative Deviation Index (ARDI). Concerning the performance indicators, the third CP formulation achieved an ARPD of 10.63% for makespan minimization. In comparison, the second CP formulation achieved an ARDI of 2.51% for total tardiness minimization, highlighting the superiority of these solution approaches for each respective objective function.