Berth allocation in container terminals under fuzzy uncertain conditions

The arrival and handling times of vessels are subject to significant uncertainty. Triangular fuzzy numbers,characterized by upper and lower bounds and a most likely value,provide an effective means of representing such imprecise information. In this context,this paper first establishes a fuzzy integer programming model for berth allocation at container terminals,aiming to minimize the total departure delay time of vessels. An improved Multi-Verse Optimizer（ MVO）algorithm is then proposed to solve the model,incorporating solution repair and breakout strategies. Comparative analysis shows that,in contrast to deterministic berth allocation schemes,the proposed fuzzy berth allocation approach demonstrates notable advantages in reducing total departure delay time and exhibits greater effectiveness in handling uncertainty.Moreover,the improved MVO algorithm achieves solution speed improvements of 59. 9%,44%,and 26. 1% in small,medium,and large scale experiments,respectively,compared to the standard multi-verse optimizer. These results indicate that the proposed algorithm can efficiently solve the fuzzy integer programming model for berth allocation and offers valuable decision-making support for addressing berth allocation problems under fuzzy uncertainty.