# Ferry Scheduling Optimization Considering Arrival Time Uncertainty and In-Place Time Differences
## 1 Introduction
[24] described the original uncertainty problem with many deterministic scenarios through multi-scenarios for the flight taxi scheduling problem. The biggest difficulty of this method is the probability of each deterministic scenario. Unlike the multi-scenario approach, the sample average approximation (SAA) method assumes equal probability for each sample. Since the SAA method does not need to depend on the probability of each scenario, it is easy to implement and is increasingly recognized by researchers. Due to its equal probability nature, the sample size is a very important parameter. With too small a sample size, the results are highly episodic, and with too large a sample size, the impact of the problem size on the computational efficiency increases exponentially. Both [19; 20] used chance constraints to describe stochastic problems while designing some efficient heuristics. This paper focuses on the ferry scheduling problem considering the in-place time requirement under the uncertainty of flight arrival and departure times. The ferry is an important means of transportation for passengers to transfer between the remote parking stand and the terminal. As each flight carries a different number of passengers, the number of ferry demands is also different. The object of the ferry service is passengers, and safety and timeliness are important indicators of the airport's original airfield security services. Therefore, most airports require ferries to arrive at the designated position a certain time in advance to wait when the flight ferry service time arrives. According to Civil Aviation Authority (CAA) regulations, when multiple ferries are required for a flight, the first ferry needs to be in place a certain amount of time in advance. The subsequent ferries need to be in place within a certain amount of time of the departure of the previous ferry with passengers. Therefore, the problem of scheduling multiple ferries on the same flight is essentially a dynamic programming problem. In this paper, according to the characteristics of the ferry scheduling problem, the dynamic programming model is constructed, and the minimum number of ferry cars is used as the optimization objective. Considering the uncertainty of flight arrival and departure time, the uncertainty is described by opportunity constraints, the model is transformed into a stochastic model, and a genetic algorithm (GA) is designed to solve the probabilistic model. The remaining contents of this paper are organized as follows. In Section 2, the ferry scheduling problem is analyzed in detail, and the dynamic programming scheduling model of the ferry is constructed in the static case considering the in-place time requirement. In Section 3, the impact of flight arrival and departure time on ferry scheduling is considered, and the chance constraints are used to describe the uncertainty of the problem, which transforms the original model into a stochastic dynamic programming model. To solve the stochastic dynamic programming model, the stochastic model is transformed into a deterministic model, and a genetic algorithm is designed to solve it. In Section 4, the data from an international airport in South China is used as the experimental case of this paper. The summary section is presented in Section 5.