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This study addresses single machine scheduling with past-sequence-dependent setup times and positional effects on job processing. Efficient algorithms were developed for minimizing earliness and tardiness costs, considering different due date assignment methods.

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Area of Science:

  • Operations Research
  • Industrial Engineering
  • Applied Mathematics

Background:

  • Single machine scheduling problems are fundamental in operations research.
  • Past-sequence-dependent (p-s-d) setup times introduce complexity, where setup duration depends on preceding jobs.
  • Positional effects on job processing times further complicate scheduling decisions.

Purpose of the Study:

  • To analyze single machine scheduling problems with p-s-d setup times and job position-dependent processing times.
  • To investigate the impact of two distinct due date assignment methods on scheduling objectives.
  • To develop efficient algorithms for minimizing total earliness, weighted number of tardy jobs, and due date assignment costs.

Main Methods:

  • The study employs a conversion to assignment problems for models with job-dependent position effects.
  • A dynamic programming algorithm is utilized for models with job-independent position effects.
  • Analysis covers objective functions including total earliness, weighted tardiness, and due date assignment costs.

Main Results:

  • For job-dependent position effects, problems are solvable in O(n(4)) time.
  • For job-independent position effects, problems are solvable in O(n(3)) time.
  • The proposed methods provide efficient solutions for complex scheduling scenarios.

Conclusions:

  • The research offers polynomial-time algorithms for sophisticated single machine scheduling problems.
  • Efficient scheduling is achievable even with complex setup times and positional processing effects.
  • The findings contribute to optimizing production and service systems with sequence-dependent and position-dependent factors.