A reliability-oriented conflict robust optimization model for berth allocation under operational disturbances

The berth allocation problem concerns assigning service times and quay spaces to vessels at container terminals. Ensuring reliable and safe port operations under uncertain disturbances has become increasingly critical. This study addresses the berth allocation problem considering unpredictable vessel arrivals. Possible scenarios are represented by uncertainty sets rather than probability distributions, which are often unavailable before decision making. A conflict-based reliability measure is introduced to quantify schedule robustness and recoverability. A two-stage conflict robust optimization model is proposed, where the first stage determines baseline berthing times and positions, and the second stage minimizes conflicts that represent potential operational failures. Two model extensions, namely the expanded variant and the risk-constrained variant, explicitly incorporate reliability trade-offs between conservatism, cost, and safety. An exact iterative algorithm is developed to solve the models efficiently. Computational experiments show that the proposed algorithm outperforms several benchmark methods. The results indicate that a small increase in operational cost can substantially enhance schedule reliability and system resilience, while the expanded and risk-constrained models provide flexible options for balancing cost, reliability, and worst-case performance.