Authors:
Rajvinder Kaur,Deepak Gupta,Sonia Goel,DOI NO:
https://doi.org/10.26782/jmcms.2026.05.00011Keywords:
Interval-Valued Intuitionistic Fuzzy Sets,Hybrid Flow Shop Scheduling,Score Function,Makespan,Abstract
Scheduling problems represent a core challenge in the efficient management of industrial and service operations. Due to their structural complexity and significant practical relevance in both manufacturing and service sectors, Hybrid Flow Shop Scheduling Problems (HFSSPs) are widely recognized as NP-hard. Scheduling in contemporary manufacturing and production systems sometimes entails ambiguous and uncertain information, rendering classical deterministic methods less efficacious. This work presents a novel comparative analysis of the exact method Branch and Bound (BB) and heuristic algorithm Nawaz, Enscore, and Ham (NEH) for addressing the hybrid flow shop scheduling problem (HFSSP), where processing times are articulated via Interval-Valued Intuitionistic Fuzzy Sets (IVIFS). A ranking and scoring algorithm is utilised to convert IVIFS data into computationally manageable values, facilitating integration with BB and NEH methodologies. The results offer valuable insights for scheduling in uncertain and imprecise production environments, demonstrating how hybrid decision-making strategies that combine exact and heuristic methods can lead to more effective solutions.Refference:
I. Atanassov, Krassimir T. "Intuitionistic Fuzzy Sets." Fuzzy Sets and Systems, vol. 20, no. 1, 1986, pp. 87–96. 10.1016/S0165-0114(86)80034-3.
II. Atanassov, Krassimir, and George Gargov. "Interval Valued Intuitionistic Fuzzy Sets." Fuzzy Sets and Systems, vol. 31, no. 3, 1989, pp. 343-49. 10.1016/0165-0114(89)90205-4.
III. Dessouky, Maged M., et al. "Flowshop Scheduling with Identical Jobs and Uniform Parallel Machines." European Journal of Operational Research, vol. 109, no. 3, 1998, pp. 620-31. 10.1016/S0377-2217(97)00111-2.
IV. Dubois, Didier, and Henri Prade. "Systems of Linear Fuzzy Constraints." Fuzzy Sets and Systems, vol. 3, no. 1, 1980, pp. 37-48. 10.1016/0165-0114(80)90004-4.
V. Gholami-Zanjani, Seyed Mohammad, et al. "Robust and Fuzzy Optimisation Models for a Flow Shop Scheduling Problem with Sequence Dependent Setup Times: A Real Case Study on a PCB Assembly Company." International Journal of Computer Integrated Manufacturing, vol. 30, no. 6, 2017, pp. 552-63. 10.1080/0951192X.2016.1187293.
VI. Gupta, Deepak, and Sonia Goel. "Branch and Bound Technique for Two Stage Flow Shop Scheduling Model with Equipotential Machines at Every Stage." International Journal of Operational Research, vol. 44, no. 4, 2022, pp. 462-72. 10.1504/IJOR.2022.126588.
VII. Johnson, Selmer Martin. "Optimal Two- and Three-Stage Production Schedules with Setup Times Included." Naval Research Logistics Quarterly, vol. 1, no. 1, 1954, pp. 61–68. 10.1002/nav.3800010110.
VIII. Kurniawan, Latief Anggar, and F. Farizal. "Development of Flow Shop Scheduling Method to Minimize Makespan Based on Nawaz Enscore Ham (NEH) and Campbell Dudek and Smith (CDS) Method." Proceedings of the 3rd African International Conference on Industrial Engineering and Operations Management, 2022, pp. 1224-31. 10.46254/AF03.20220230.
IX. Lee, Gyu-Chang, and Yeong-Dae Kim. "A Branch-and-Bound Algorithm for a Two-Stage Hybrid Flowshop Scheduling Problem Minimizing Total Tardiness." International Journal of Production Research, vol. 42, no. 22, 2004, pp. 4731-43. 10.1080/00207540412331285841.
X. Linn, Richard, and Wei Zhang. "Hybrid Flow Shop Scheduling: A Survey." Computers & Industrial Engineering, vol. 37, no. 1-2, 1999, pp. 57-61. 10.1016/S0360-8352(99)00024-X.
XI. Malhotra, Khushboo, et al. "Bi-Objective Flow Shop Scheduling with Equipotential Parallel Machines." Malaysian Journal of Mathematical Sciences, vol. 16, no. 3, 2022, pp. 451-70. 10.47836/mjms.16.3.04.
XII. Nawaz, Muhammad, et al. "A Heuristic Algorithm for the M-Machine, N-Job Flow-Shop Sequencing Problem." Omega, vol. 11, no. 1, 1983, pp. 91-95. 10.1016/0305-0483(83)90088-9.
XIII. Ruiz, Rubén, et al. "Solving the Flowshop Scheduling Problem with Sequence Dependent Setup Times Using Advanced Metaheuristics." European Journal of Operational Research, vol. 165, no. 1, 2005, pp. 34-54. 10.1016/j.ejor.2004.01.041.
XIV. Ruiz, Rubén, and José Antonio Vázquez-Rodríguez. "The Hybrid Flow Shop Scheduling Problem." European Journal of Operational Research, vol. 205, no. 1, 2010, pp. 1-18. 10.1016/j.ejor.2009.09.024.
XV. Senapati, Tapan, et al. "Analysis of Interval-Valued Intuitionistic Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making." Axioms, vol. 11, no. 6, 2022, pp. 258. 10.3390/axioms11060258.
XVI. Xu, Ze Shui. "Methods for Aggregating Interval-Valued Intuitionistic Fuzzy Information and Their Application to Decision Making." Control and Decision, vol. 22, no. 2, 2007, pp. 215-19. https://www.researchgate.net/publication/271843255_Methods_for_aggregating_intervalvalued_intuitionistic_fuzzy_information_and_their_application_to_decision_making