Multiobjective Γ-Robust Port Service-Capacity Planning Under Demand Uncertainty: Evidence from Chilean Vessel Movements

Port authorities must commit service capacity before monthly vessel demand is known. This study develops a multiobjective linear programming model based on Bertsimas–Sim Γ-robustness that jointly determines lower-cost regular capacity and higher-cost surge capacity. Monthly vessel-call uncertainty is represented by a budgeted uncertainty set, while an independent full-stress constraint imposes a minimum service level when all modeled upward deviations occur. A lexicographic ε-constraint procedure generates Pareto-optimal cost–shortage policies, and a balanced policy is selected by distance to the ideal point. The model is evaluated using 2020 data from 28 Chilean maritime authorities and validated with 2018–2022 data. At Γ = 0.10, the balanced policy allocates 647.0 regular and 207.5 surge units and achieves 98.41% full-stress service, with CostIdx 21% above the minimum-cost policy. The 15% deviation matches the historical year-ahead bound, and Γ = 0.10 is the smallest tested budget meeting the 95% out-of-sample target in three of four transitions. Full-stress reliability is the main CostIdx driver, whereas the base-capacity quantile mainly determines the capacity mix. Among alternatives meeting the same full-stress standard, the proposed model has the lowest CostIdx without requiring an assumed demand distribution.