Bi-objective optimization model for biomass supply chains towards net-zero goals: integrating queuing systems and solar panel technologies

Growing environmental pressures and energy-related expenses in biomass supply chains (BSCs) call for operational strategies that simultaneously reduce emissions and total system costs. Despite extensive research on sustainable logistics, the environmental burden caused by transportation delays and queue-induced idling has been largely neglected. This study introduces the first bi-objective optimization model that integrates a G/M/S//M queuing system (QS) into BSC transportation operations while deploying solar panels (SPs) to power agricultural facilities with clean energy. The model explicitly minimizes both pollution and cost by reducing idle emissions during waiting times (WTs) and replacing grid-supplied electricity with renewable energy. Small-scale instances are solved using an exact analytical approach, while large-scale scenarios are optimized through the Grasshopper Optimization Algorithm (GOA). Sensitivity analyses confirm that increasing truck capacity without enlarging fleet size significantly decreases queue lengths, leading to lower emissions and reduced fuel-related costs. Furthermore, solar energy usage consistently outperforms grid electricity in economic performance, especially under higher-capacity SP installations. The proposed solution framework offers practical guidance for decision-makers seeking cleaner and more cost-efficient biomass logistics operations.