The distribution of relief items during crises is widely recognized as a critical challenge in humanitarian logistics and disaster management. In such contexts, time and operational costs emerge as two pivotal factors determining the success of relief operations. The objective of this research is to optimize the distribution process of essential items through a multi-objective model that concurrently determines optimal depot locations and efficient distribution routes by controlling both cost and time-related performance metrics. The weighted sum method is employed to solve the proposed model. Results indicate that the model effectively identifies the shortest routes, minimizes logistical costs, and enables optimal allocation of vehicles to destinations based on vehicle type. Finally, Pareto-optimal solutions are generated, and a sensitivity analysis is conducted on the time-based connectivity coefficient between routes. Findings demonstrate that the proposed model substantially enhances the efficiency and effectiveness of humanitarian logistics operations. Model validation is performed through a real-world case study, and the results are benchmarked against existing operational plans, revealing superior performance of the proposed approach. Across comparisons of different objective functions, the number of non-dominated solutions ranges from 15 to 86, with evident convergence. The highest number of non-dominated solutions (86) is obtained when comparing the first and fourth objective functions, indicating superior solution quality and convergence relative to other scenarios. Overall, this study provides decision-makers with a scientific, data-driven tool to formulate more effective disaster response strategies through cost reduction and optimal resource utilization.