integrating regulatory compliance into maritime logistics: a constraint-based approach to the tramp ship routing and scheduling problem under cii regulations

The maritime industry is currently navigating a critical transition from purely market-driven operations to a regulated framework governed by stringent decarbonization policies. the implementation of the carbon intensity indicator (cii) by the international maritime organization (imo) represents a paradigm shift in maritime public policy, transforming environmental performance from a voluntary metric into a binding operational condition for market access. this study addresses the intersection of economic law and sustainable development by proposing a mixed-integer linear programming (milp) model for the tramp ship routing and scheduling problem (tsrsp) with multiple cargoes. unlike traditional models that internalize emissions merely as operational costs, which potentially undermines environmental justice by allowing polluters to pay for emissions, this research integrates cii as a non-negotiable constraint. by treating regulatory limits as absolute boundaries, the model forces the alignment of private profit maximization with global marine resource management goals. the proposed framework demonstrates how shipping operators can mathematically guarantee compliance with international statutes while optimizing fleet utilization. this approach provides a quantitative basis for policymakers and stakeholders to evaluate the trade-offs between economic competitiveness and environmental sustainability, ultimately contributing to the balanced development of the maritime economy.