A Multi-objective PSO Approach for Sustainable Production Routing: Balancing Cost, Emissions, and Social Impact - Garside, Annisa Kesy; Setyawan, Novendra; Muhtazaruddin , Mohd Nabil; Ahmad, Robiah; Khoidir , Amelia (Jurnal Teknik Industri, 2025)
The Production Routing Problem (PRP) has been extensively studied in logistics optimization, yet research that explicitly integrates environmental and social sustainability dimensions remains limited. This research proposes a sustainable production routing problem (SU-PRP) as a multi-objective optimization model, minimising the total operating cost, CO₂ emissions cost, and social cost simultaneously. The complex model is addressed using Multi-Objective Particle Swarm Optimization (MOPSO), which has been modified to handle discrete decision variables in a supply chain environment. The algorithm’s performance is benchmarked against NSGA-II using three quality indicators: Spacing Metric (SM), Inverted Generational Distance (IGD), and Hypervolume (HV). Numerical testing was performed using a moderate-sized problem instance comprising two plants, five customers, two products, and a two-period planning horizon, with 663 binary variables and 546 constraints. In the results, it can be observed that MOPSO has reached a larger HV, indicating better coverage of the objective space. Nevertheless, NSGA-II outperforms MOPSO in terms of solution uniformity and convergence, as evidenced by smaller SM and IGD values. The results suggest that MOPSO is more effective in operational planning scenarios where fast computation and solution diversity are crucial, such as real-time production and routing adjustments. In contrast, NSGA-II is more appropriate than MOPSO for strategic planning tasks to obtain more accurate and evenly distributed Pareto solutions.