This research paper presents a novel bi-objective mixed-integer nonlinear programming (MINLP) model designed to optimize truck scheduling operations within a cross-docking warehouse system. A key innovation of this study is its incorporation of the position-based learning effect of human resources, acknowledging that the time required to perform operations decreases with repetition due to increasing worker proficiency. This model simultaneously addresses two critical objectives: the minimization of makespan (the total completion time for all trucks) and the reduction of carbon emissions generated by warehouse activities. To accurately capture the environmental impact, an expanded objective function is introduced to calculate the carbon emissions resulting from the internal movement of goods, forklift operations, and truck idling times. Furthermore, recognizing the inherent uncertainties present in real-world logistics, such as variable processing and loading/unloading times, the model parameters are treated using triangular fuzzy numbers. This approach transforms the deterministic model into a robust bi-objective possibilistic programming framework, effectively handling epistemic uncertainty.



This fuzzy model is then solved using an enhanced goal programming method, which efficiently navigates the trade-offs between the two conflicting objectives. The effectiveness and practical applicability of the proposed model and its solution methodology were rigorously validated through an extensive numerical analysis and an applied case study. The computational results demonstrate the model's significant potential, showing that integrating human learning effects can lead to a substantial 15.2% reduction in makespan. Concurrently, the strategic optimization guided by the emission-minimization function achieved a remarkable 75% decrease in carbon emissions from warehouse operations. This study underscores the profound benefits of integrating human factors and environmental sustainability considerations into logistics optimization. The proposed fuzzy-goal programming approach proves highly capable of managing real-world uncertainties while delivering dramatic improvements in both operational efficiency and ecological performance. These findings offer valuable, actionable insights for warehouse and logistics managers aiming to enhance productivity while minimizing their environmental impact. For future research directions, investigating dynamic learning models and exploring advanced multi-objective solution techniques for larger, more complex supply chain networks is recommended.