A data-driven semi-relaxed MIP model for decision-making in maritime transportation

Abstract

Maritime transportation companies operate in highly volatile environments, where data-driven decision-making is critical to navigating fluctuating freight revenue, fuel and transit costs, and dynamic trade-related policies. This study addresses the liner service network design and container flow management problem, with the objective of maximizing weekly profit, calculated as total freight revenue minus comprehensive operational costs associated with fuel, berthing, transit, and policy-driven extra fees. We formulate a mixed-integer programming (MIP) model for the problem and demonstrate that the constraint matrix associated with vessel leasing is totally unimodular. This property permits the reformulation of the original MIP model into a semi-relaxed MIP model, which maintains optimality while improving computational efficiency. Using shipping data in a realistic liner service network, the proposed model demonstrates its practical applicability in balancing complex trade-offs to optimize profitability. Sensitivity analyses provide actionable insights for data-driven decision-making, including when to expand service networks, discontinue unprofitable routes, and strategically deploy vessel leasing to mitigate rising operational costs and regulatory penalties. This study provides a practical, computationally efficient, and data-driven framework to support liner shipping companies in making robust tactical decisions amid economic and regulatory dynamics.