# Ferry Scheduling Optimization Considering Arrival Time Uncertainty and In-Place Time Differences
## 1 Introduction
Due to the airport support manual, the process of passenger loading and unloading is not performed at the same time as refueling. [PERSON] et al. [12] proposed a multi-agent-based decision support model to minimize the vehicle allocation cost in the multi-resource cooperative scheduling problem of water trucks, cleaning trucks and tractors. Common single-type resource scheduling problems include tractor [13; 14], ferry, de-icing vehicle and taxiway scheduling. [PERSON] et al. [13] constructed a mixed-integer programming model based on the vehicle routing problem (VRP) as the core with the minimum operation cost as the optimization objective. Then, they proposed a column generation heuristic solution method. In terms of the optimization objective, [PERSON] et al. [14] comprehensively considered the cost impacts of various aspects such as tractor configuration cost, maintenance cost and secondary sales. They aimed to obtain a fleet composition with the lowest cost. The fleet composition had a large impact on the operating cost. [PERSON] et al. [15] considered the impact of electric equipment on the previous fuel-only fleet composition model. They synthesized the time cost, energy cost and scheduling cost to provide a reference for the introduction of electric equipment in airports. The airport special vehicle traveling road network is a complex multi-loop structure with multiple paths between any two points. [PERSON] et al. [16] emphasized that the basis of the rationality of ferry scheduling lies in the transfer between nodes. For this reason, the transfer time between nodes was mined through graph theory. The Floyd algorithm was used to obtain the shortest paths and times of all origin-destination (OD) points. In the process of transferring, in addition to the distance and time, other optimization components need to be considered. In [17], an active path framework was proposed for the resource movement problem, which can support the selection of multi-objective paths. In the static problem, an enumeration-based algorithm was designed to provide optimal or suboptimal solutions quickly. [PERSON] et al. [18] constructed a quadratic planning model with VRPTW as the core to obtain a scheduling scheme for the minimum number of ferry usage. Uncertainty is inherent in the ground support resource scheduling problem [19]. A flight is defined as on-time if its actual arrival and departure time deviates less than 15 min from the estimated arrival and departure time. This deviation time cannot be ignored in the problem of actual ground support resources. Research for uncertainty problems can be classified into the following methods: delayed decision making [5; 20], robust optimization [21; 22; 23] and stochastic planning [19; 24; 25; 26]. The basic principle of delayed decision making is to make the original fuzzy uncertainty certain by postponing the decision as much as possible. In [20], considering the impact of uncertainty in flight arrival and departure times on tractor scheduling, accessing the A-CDM system was proposed, which can obtain basic data with higher reliability. The A-CDM data reliability was reflected in the dynamic prediction, which made the support resource scheduling not only dependent on the scene feedback or flight schedule. In terms of robustness optimization, a more robust scheduling scheme was generated based on existing resources. [PERSON] et al. [22] increased the stability of task sequences for each guaranteed resource execution by maximizing the buffer time between support resource execution services. This method could improve the robustness of the overall scheduling scheme. However, it often did not intuitively show the degree of resource surpluses and deficits. It was necessary to react to the reasonableness of the current resource allocation through simulation or actual execution results. Like robust optimization, stochastic planning makes decisions under the inevitable presence of uncertainty. Multi-scenario is a common approach. [PERSON] et al.