Multi-Objective Queuing Optimization for Oil Depots Balancing Cost, Carbon Emissions and Customer Satisfaction

Refined oil depots are critical nodes in energy supply chains. Tank truck queuing increases costs and idling carbon emissions while reducing customer satisfaction. This research proposes a modified finite capacity Markovian queuing system (M/M/c/N) with random service interruptions and establishes a multi-objective model covering expected cost, carbon emissions and customer satisfaction. We derive core metrics and formulate corresponding unit time objective functions. The Bayesian optimization-based NSGA-II (BO-NSGA-II) hybrid algorithm is adopted to solve the proposed model. Comparisons against four algorithms are conducted using four multi-objective evaluation metrics: hypervolume (HV), Inverted Generational Distance (IGD), generational distance (GD) and spacing, which confirm that BO-NSGA-II achieves a balanced overall performance. Its HV reaches 0.657, while IGD (0.0066), GD (0.0009) and spacing (0.0069) remain low, demonstrating broad Pareto front coverage, high convergence accuracy and uniform solution distribution. Trade-off analysis indicates that the algorithm entails a marginal expected cost increase of merely 1.15% compared with the minimum expected cost solution obtained by MOEA/D. Meanwhile, carbon emissions drop to 11.25 kgCO2/h and customer satisfaction rises to 0.9769, achieving coordinated economic, environmental and service benefits. Sensitivity analysis further identifies the optimal loading bay configuration range of 2 to 4. Insufficient allocation leads to congestion, while excessive allocation causes equipment idling and higher emissions. Blind expansion also raises the expected cost. This study provides methodological references for the collaborative optimization of oil depot resource allocation, low-carbon scheduling and service performance.