Single-machine scheduling with machine unavailability periods and resource dependent processing times

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Abstract

We study a single-machine scheduling problem, where each of the job processing times is a bounded linear decreasing function of the amount of resource allocated to its processing operation, and there is a single and fixed machine-unavailability interval that begins at time T. A solution is given by (i) partitioning the jobs into two sets, corresponding to the set of jobs to be processed before and after the unavailability period; and (ii) defining the amount of resource allocated to the processing operation of each of the jobs. A solution is feasible if the total processing time of all jobs assigned to be processed before the unavailability period does not exceed T. Our aim is to find a feasible solution that minimizes the makespan plus the total resource consumption cost. As the problem is known to be NP-hard even for constant processing times, we focus on the design of pseudo-polynomial time and approximation algorithms. Extension to the case of a fixed number of unavailability intervals is also provided.

Original languageEnglish
Pages (from-to)423-439
Number of pages17
JournalEuropean Journal of Operational Research
Volume296
Issue number2
DOIs
StatePublished - 16 Jan 2022

Keywords

  • Approximation algorithms
  • Controllable processing time
  • Machine unavailability period
  • Pseudo polynomial time algorithm
  • Resource allocation
  • Single-machine scheduling

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