A two-stage fuzzy flexible flow shop scheduling problem with no-wait and reentrant constraints using adaptive particle swarm optimization.

To address increasing production and logistical challenges in the fresh livestock processing industry, this study investigates a two-stage multiprocessor flow shop scheduling problem with fuzzy processing times and time window constraints. Ensuring product freshness under urban congestion and limited storage capacity requires precise and flexible scheduling to minimize early and late completion penalties. This study proposes an adaptive particle swarm optimization algorithm that integrates fuzzy processing environments with time-constrained scheduling. The main contributions are threefold: (1) the formulation of a bi-objective mathematical model incorporating fuzzy processing times and time window constraints, (2) the development of an adaptive inertia weight mechanism to enhance the exploration-exploitation balance of particle swarm optimization (PSO), and (3) a comprehensive comparative analysis against benchmark algorithms, including hybrid genetic algorithm, the linearly decreasing inertia weight PSO, and the multi-objective evolutionary algorithm with heuristic decoding. Experimental results demonstrate that the proposed ADPSO significantly outperforms existing methods, achieving an average improvement of 18.10% in total penalty reduction and 19.93% in solution stability, thereby confirming its effectiveness and robustness in solving complex scheduling problems under uncertainty.