A stepwise multi-objective framework for strategic trade-offs in inland container transport planning

This paper presents a stepwise penalty function embedded in a multi-objective optimization framework to support strategic planning in inland container transport. The model addresses trade-offs among carbon emissions, container waiting times, and train capacity utilization across a multimodal logistics system linking seaports, dry ports, and inland terminals. The stepwise function captures the nonlinear behavior of underutilized train capacity and enables the framework to guide trade-off solutions toward decision-maker preferences, while maintaining exact solvability through a mixed-integer linear programming (MILP) structure. Unlike traditional models that treat resource usage as a constraint, this approach elevates train utilization to an explicit optimization objective, promoting both operational efficiency and environmental performance. To generate alternative and policy-relevant solutions, the framework combines the augmented ɛ -constraint method with a matheuristic variable-fixing strategy for efficient Pareto front exploration. The resulting trade-offs are evaluated using the Augmented Tchebycheff Method, allowing identification of the most balanced configurations. For sustainability and practical relevance, the model, even generalizable to any medium-size container terminal, is applied to real operational data from the PSA Genova Pra port (Italy) and tested across multiple input scenarios. In an instance involving 1700 container movements, the framework generated compromise solutions in less than 3 s, demonstrating both computational efficiency and scalability. These results offer practical insights for transport managers, port authorities, and policymakers aiming to align sustainability targets with service-level and resource efficiency goals.