Enhanced Milp Approach for Long-Term Multi-Vessel Maritime Inventory Routing with Application to Antarctic Logistics

The maritime inventory routing problem (MIRP) integrates vessel routing and inventory management over a planning horizon to optimize logistical operations in marine environments. While existing models predominantly address short-term planning with single vessels, this research advances the field by presenting a tightened mixed-integer linear programming (MILP) model designed for long-term planning with multiple vessels. The proposed model leverages an improved mathematical formulation and state-of-the-art optimization solvers to enhance computational performance. To demonstrate its applicability, the model was evaluated using benchmark instances from the literature and new instances derived from the logistics of Chilean scientific bases in Antarctica, a challenging and underexplored maritime environment. The results show computational time reductions of up to 98% for small to medium-sized instances, achieved through the incorporation of valid inequalities into the model and the use of advanced hardware and solvers. For larger instances, optimal or near-optimal solutions were achieved within one hour for a planning horizon of 60 time units, with optimality gaps below 24.7% for a 120-time-unit horizon. These findings highlight the potential of the model to support decision-making in complex maritime logistics scenarios, extending its application to long-term, multi-vessel operations in remote and environmentally sensitive regions. The proposed framework provides a valuable tool for enhancing the sustainability and efficiency of maritime logistics systems. © 2025 by the authors.