Enhanced Optimization Strategies for No-Wait Flow Shop Scheduling with Sequence-Dependent Setup Times: A Hybrid NEH-GRASP Approach for Minimizing the Total Weighted Flow Time and Energy Cost

Hafsa Mimouni (), Abdelilah Jalid and Said Aqil
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Hafsa Mimouni: PCMT Laboratory, National Graduate School of Arts and Crafts, Mohamed V University, Rabat 10100, Morocco
Abdelilah Jalid: PCMT Laboratory, National Graduate School of Arts and Crafts, Mohamed V University, Rabat 10100, Morocco
Said Aqil: LISIME Laboratory, National Graduate School of Arts and Crafts, Hassan II University, Casablanca 20360, Morocco

Sustainability, 2025, vol. 17, issue 17, 1-29

Abstract: Efficient production scheduling is a key challenge in industrial operations and continues to attract significant interest within the field of operations research. This paper investigates a range of methodological approaches designed to solve the permutation flow shop scheduling problem (PFSP) with sequence-dependent setup times (SDST). The main objective is to minimize the total weighted flow time (TWFT) while ensuring a no-wait production environment. The proposed solution strategy is based on using algorithms with a mixed integer linear programming (MILP) formulation, heuristics, and their combination. The heuristics utilized in this paper include an advanced greedy randomized adaptive search procedure (GRASP) based on a priority rule and Hybrid-GRASP-NEH (HGRASP), where Nawaz-Enscore-Ham (NEH) takes place to initiate solutions, based on iterative global and local search methods to refine exploration capabilities and improve solution quality. These approaches were validated using a comprehensive set of experiments across diverse instance sizes that proved the efficiency of HGRASP, with the results showing a high-performance level that closely matched that of the exact MILP approach. Statistical analysis via the Friedman test (χ 2 = 46.75, p = 7.04 × 10 −11 ) confirmed significant performance differences among MILP, GRASP, and HGRASP. While MILP guarantees theoretical optimality, its practical effectiveness was limited by imposed computational time constraints, and HGRASP consistently achieved near-optimal solutions with superior computational efficiency, as demonstrated across diverse instance sizes.

Keywords: hybrid-GRASP heuristic; no-wait constraint; energy cost; total weighted flow time; flow shop scheduling (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2025
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