## 1 Introduction
The traditional TAS allows the terminal operator to control the truck congestion between the gate and the yard by limiting the maximum number of truck arrivals. However, transport companies  
Figure 1: Truck congestion at the container terminal. (forwarders) have difficulty meeting the different situations and the transport requirements of individual containers. In this paper, we propose a new TAS that helps improve the profitability of stakeholders by considering the positions of the transport companies (forwarders) and the terminal operator, respectively, and comparing them with cooperation cases. To this end, we develop a mathematical model from the perspective of (1) the transport company (forwarder), (2) the terminal operator, and (3) cooperation between the transport companies (forwarders) and the terminal operator. The new TAS reflects each stakeholder's penalties as the objective function of the mathematical model. We define these penalties in terms of collectively expressing the time, number, and capacity that should be optimized to reduce truck congestion. In a mathematical model for the transport company (forwarder), the penalties are the waiting time for the truck and the number of rehandling for carry-out containers. In a mathematical model for the terminal operator, the penalties are the unassigned and unreserved slot capacity (the tasks a truck can reserve). Figure 2 shows a framework of the new truck appointment system. From the perspective of the transport company (forwarder), it is necessary to reduce the truck turnaround time. The turnaround time consists of a fixed service time, a variable waiting time, and a variable rehandling time. Therefore, the transport companies (forwarders) aim to reduce the truck waiting time and the container rehandling time. From the perspective of the terminal operator, it is necessary to balance the workload of the yard crane. The more tasks that can be reserved and booked, the better the productivity of the container terminal. Therefore, the terminal operator aims to increase the number of slots that can be reserved. From the perspective of cooperation between the transport companies (forwarders) and the terminal operator, it is necessary to consider the purpose of the transport company (forwarder) and the terminal operator at the same time. We multiply each objective function by its weight and add them. Weight refers to the position of the stakeholders in cooperation. In this study, the transport company (forwarder) and the terminal operator have the same weight (transport company's weight = terminal operator's weight = 1). By comparing the results of numerical experiments for cases where transport companies (forwarders) and terminal operator make their own decisions and cooperate, we propose a model that is beneficial to all stakeholders. The rest of this paper consists of the following topics. Section 2 discusses the literature related to this paper. Section 3 defines the TAS problem and proposes a mathematical model for the perspective of the transport company (forwarder), the terminal operator, and cooperation between the transport companies (forwarders) and the terminal operator. Section 4 shows the results of numerical experiments on the mathematical model in three cases. Section 5 provides conclusions and implications for all stakeholders. Figure 2: A framework of the new Truck Appointment System (TAS).