Scheduling appointments for container truck arrivals considering their effects on congestion

Trucking companies deliver a large number of containers every day to container terminals at hub ports. Truck drivers for the delivery operation can experience long waiting times when they arrive at peak hours. This study proposes a scheduling method for appointments that considers the cost of trucks staying in the terminal, demurrage cost, container delivery cost, number of appointments allowed at each time window and block, and number of trucks available during each time window. Unlike previous studies, this study considers the effects of the appointments on the waiting time at the terminal when the appointment schedule is constructed. This paper introduces a mathematical formulation and a heuristic algorithm based on the Frank-Wolfe algorithm to solve the problem within a reasonable computational time. Numerical experiments are conducted to compare the proposed algorithm with the other heuristic approaches and analyze the effects of the appointments using empirical data. In addition, the impact of appointments by multiple trucking companies is examined.