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Michał Ćwik1, Jerzy Józefczyk1

  • 1Faculty of Computer Science and Management, Wroclaw University of Science and Technology, Wybrzeze Wyspianskiego 27, 50-370 Wrocław, Poland.

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Summary
This summary is machine-generated.

This study addresses uncertain permutation flow-shop scheduling by using interval processing times. A new constructive heuristic algorithm offers improved performance and computation time for the minmax regret optimization problem.

Keywords:
Computational experimentsFlow-shopHeuristic algorithmsInterval processing timesMinmax regret

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Area of Science:

  • Operations Research
  • Industrial Engineering
  • Computational Optimization

Background:

  • Permutation flow-shop scheduling is complex, especially with uncertain processing times.
  • Evaluating uncertainty using maximum regret and solving minmax regret problems is computationally intensive.

Purpose of the Study:

  • To develop an efficient method for solving the uncertain permutation flow-shop problem with interval processing times.
  • To evaluate uncertainty using the minmax regret criterion.
  • To introduce and assess a novel constructive heuristic algorithm.

Main Methods:

  • The problem is framed as a minmax regret discrete optimization problem.
  • Two relaxations are employed: a greedy procedure for criterion calculation and a lower bound for the deterministic flow-shop.
  • A constructive heuristic algorithm is developed for the relaxed problem.

Main Results:

  • The constructive heuristic algorithm demonstrated superior performance compared to evolutionary and middle interval approaches.
  • The new algorithm achieved better results in terms of both the optimization criterion and computation time.
  • Statistical analysis using the Wilcoxon paired-rank test confirmed the algorithm's advantage.

Conclusions:

  • The proposed constructive heuristic algorithm is effective for uncertain permutation flow-shop scheduling.
  • The relaxations applied significantly simplify the complex optimization procedure.
  • This approach offers a practical and efficient solution for scheduling problems with interval-valued processing times.