A trapezoidal fuzzy flow shop scheduling framework integrating job block heuristics to reduce waiting time

Document Type : Research Paper

Authors

1 General Shivdev Singh Diwan Gurbachan Singh Khalsa College Patiala

2 Department of Mathematics, Maharishi Markandeshwar (Deemed to be University) Mullana

3 Chandigarh Group of Colleges Jhanjeri, Chandigarh Engineering College, Department of Applied Sciences, Mohali

Abstract

This study addresses a two-machine flow shop scheduling problem with uncertain processing durations represented as trapezoidal fuzzy numbers, which are converted to crisp values using Yager’s ranking index. Job-block formation is introduced to reduce sequencing complexity and suppress waiting on the second machine, and new theorems establish how block aggregation influences waiting-time behavior. A structured heuristic generates the sequence with minimum total waiting time of jobs.
Extensive computational experiments on specially structured instances demonstrate consistent improvements in waiting time. Statistical analysis, including paired t-tests and Wilcoxon signed-rank tests, confirms that the proposed heuristic achieves significant reductions compared to classical rules and recent heuristics across multiple job sizes (p < 0.01), supporting the superiority of the method. The results highlight the practical effectiveness of integrating fuzzy modelling, crisp conversion, and block-based sequencing, providing a theoretically grounded and empirically validated approach for modern production environments with imprecise processing times.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 5
September and October 2026
Pages 185-203

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