## 1 Introduction  
The global cargo operations, which had been steadily increasing every year since the global financial crisis in 2008, have been hit hard by COVID-19. Sea transportation regulations such as temporary suspension and cancellation of operations occurred, and 11% of ship operations were canceled for six months since December 2019 when the first case of COVID-19 appeared [1]. For example, 120 out of 126 countries have had restrictions on crew rotation, 92 of these countries have banned crew rotation, and 28 of these countries have allowed crew rotation through the search and approval of the authorities [2]. These restrictions will prevent ships from entering the container terminal until it confirms that the crew has not been infected with the virus (mostly 14 days), impeding the smooth operation of maritime transport. According to the International Association of Ports and Harbors' Port Economic Impact Barometer report [3], major container terminals in Europe and North America need more moves per ship than ever due to the wave of blank sailings. Despite the number of sailings canceled in the past few months, as demand has increased, the utilization of ships has become very high, resulting in sudden peaks of activity at the import container terminals. As a result, ship-to-ship operations and yard activity at the container terminals are at their peak, especially starting to affect land operations on truck arrivals and departures. With several days off duty, the pressure on the workforce in some ports has increased. Increasing levels of congestion at port access roads exacerbates these issues. Therefore, it is necessary to discuss the truck congestion problem that occurs between the gate and the yard of the container terminal (see Figure 1). The truck congestion between the gate and the yard of a container terminal is the main topic of discussion in large-scale import and export container terminals around the world as it causes many trucks to wait and emit more CO\({}_{2}\) than usual [4]. The reasons for congestion of trucks between the gate and the yard vary, and are mainly due to uncertainty in the truck arrivals, an increase in container ship size, an increase in container volume, failure of logistics equipment or IT systems, and changes in work rules. The basic strategy for mitigating the truck congestion between the gate and the yard is to expand yard spaces and gate spaces. However, space expansion requires a lot of time and cost, and we cannot apply a space expansion strategy in a narrow area where it is impossible to secure additional space. Therefore, it is necessary to solve the truck congestion problem not only for the profitability of stakeholders but also for the reduction of CO\({}_{2}\) emissions. If the terminal operator can predict the truck arrivals a few hours in advance, they can adjust the yard volume accordingly. The vehicle booking system is developed and operated in-house at large-scale container terminals. However, the efficiency of the system is low due to frequent truck schedule changes by the transport companies (forwanders). Therefore, it is possible to solve the truck congestion problem by developing a Truck Appointment System (TAS) that allows the transport companies (forwarders) and the terminal operator to cooperate to achieve their goals. The TAS is a practical way for the transport company (forwarder) and the terminal operator to communicate. Some container terminals such as Los Angeles, Long Beach, Hong Kong, Jebel Ali, Antwerp Gateway, and Southampton are applying a TAS [5; 6]. In a traditional TAS, the terminal operator pre-sets the maximum number of trucks that can arrive at the gate for each time window, and the transport company (forwarder) books appropriately so as not to exceed the maximum number of trucks per time window. The terminal operator then rejects reservations for trucks from transport companies (forwarders) that exceed the maximum number of trucks per time window [4].