Currently, there is only a fraction of papers focusing on the management problems regarding the ferry servicing. Among these works, the ferry network design problem (FNDP), which optimizes the ferry servicing network and passenger flow, is extensively studied. The FNDP was first proposed by [3]. They focused on a multiple origin–destination network flow problem with ferry capacity constraint. In [4], they extended [3] by introducing different ferry servicing types and passenger preferences with arrival time windows. Later, Ref. [5] studied a stochastic FNDP under uncertain demand and formulated a two-stage stochastic model. As an extension of the earlier works, Ref. [6] involved user equilibrium flows and hard capacity constraints. In [7], they proposed two robust optimization models for their FNDP. Recently, Ref. [8] utilized the maximum passenger utility spanning tree approach to optimize the connection between all pairs of ferry stations and the locations of hubs. In [9], they considered FNDP by introducing autonomous ferries. A two-step optimization approach was proposed to identify the optimal autonomous ferry servicing schedules. In their later study, Ref. [10], they focused on planning the ferry servicing schedule, which combined the dial-a-ride on-demand servicing and fixed schedule servicings simultaneously.

Although there has been some ferry-servicing-related research, the ferry visit planning problem that determines the berthing time, berthing location, and servicing time has rarely been studied. Our ferry visit planning problem relates closely to the berth allocation problem (BAP), which allocates the berthing time and locations to the arriving vessels. In the past two decades, many researchers and practitioners have made great efforts to solve the BAP arising in the container port terminal. An early study was proposed by [11], and they focused on the objective of minimizing the overall staying time of vessels and dissatisfaction with vessel berthing order in the BAP. Later, some researchers studied the deterministic BAP by incorporating practical characteristics. For example, Ref. [12] investigated the integration of BAP, quay crane assignment problem, and yard allocation problem. In [13], they also studied an integrated problem that combined BAP with the quay crane allocation and scheduling problems. In practice, it is generally impossible for all the parameters to be fixed and known in advance. Uncertainties often arise in practical operations due to weather conditions and mechanical failures. A comprehensive review of the BAP under uncertainties was given by [14]. According to the review, uncertain factors regarding the arrival time [15,16,17,18], handling time [19,20,21,22], quay crane breakdown [23,24,25], and unscheduled vessel calling [26,27] were commonly considered in BAP problems. Arrival time and handling time are the most common uncertain parameters to be considered in the BAP. For the uncertain arrival time, Ref. [28] introduced a time buffer to handle the uncertain arrival time in the robust BAP. In [29], they proposed a robust model to optimize the berth allocation and quay crane assignment considering arrival time uncertainty. In [30], they addressed a berth allocation and assignment problem under uncertain vessel arrival time and port servicing time, where the cooperation among the liner carriers and that between port operator and liner shipping carriers were involved. For the uncertain handling time, Refs. [31,32] used the robust optimization method and distributionally robust optimization method to solve BAP, respectively. There are also many scholars who considered the uncertainties of arrival time and handling time simultaneously. In [22], they focused on the weekly berth and quay crane planning, where the berth position, berthing time, and quay crane assignment were optimized. In [33], they integrated BAP with yard space allocation, where the uncertain handling time was incurred by the uncertain number of loading and unloading containers. In [34], they optimized the berth allocation, assignment of tugboats, and the vessel sequence at the seaport.

To sum up, most of the existing literature has focused on either FNDP regarding the ferry servicing or BAP targeting the vessels transferring cargoes in the container port terminal. There is no paper studying the ferry visit planning problem that considers the deviation between the redesigned ferry visit plan and the current one, uncertain servicing time, and time-dependent revenue simultaneously. Firstly, the ferry passengers typically prefer the current ferry visit plan. If the redesigned ferry visit plan deviates from the current one, passengers’ travel plans will be affected. Hence, the deviation between the redesigned ferry visit plan and the current one should be considered. Secondly, the passenger demand is uncertain, resulting in an uncertain servicing time. Considering the servicing time uncertainty will make the ferry visit plan more applicable in practical operations. Thirdly, the passenger demand varies throughout the day, which introduces time-dependent revenue.