The flow shop scheduling problem with sequence-dependent setup times and operator constraints represents a complex and practically relevant production planning challenge, as it simultaneously integrates sequencing, timing, and human resource allocation decisions. Exact solution approaches become computationally intractable for medium- and large-scale instances due to the combinatorial nature of the problem. This study proposes an integrated modeling and solution framework aimed at minimizing total order tardiness while jointly incorporating key operational constraints, including technological precedence, machine non-overlapping, sequence-dependent setup times, and operator capacity limitations. A mixed-integer linear programming (MILP) model is first developed to explicitly capture sequencing, scheduling, and operator assignment decisions within a unified structure. Given the computational complexity of the model, a metaheuristic solution approach based on Particle Swarm Optimization (PSO) is designed. To accommodate the combinatorial structure of the problem, a continuous encoding mechanism combined with a constructive decoder is implemented to enforce feasibility during solution evaluation. The proposed approach is validated through an industrial case study and multiple independent runs with different random seeds. Performance is assessed using the best objective value, mean and standard deviation of results, computational time, and convergence behavior. Results demonstrate that the proposed PSO achieves high-quality and stable solutions with acceptable computational effort. Sensitivity analysis indicates that stronger exploration enhances robustness and solution quality at the cost of longer runtime, whereas exploitative settings accelerate convergence but may reduce solution quality.