Gate appointment design in a container terminal: A robust optimization approach

Gate congestion is a main challenge faced by container terminals worldwide. In the scenario of gate congestion, the long waiting line of container trucks can block the traffic into the terminal, leading to disrupted terminal operations and unsatisfactory operating efficiency. In this paper, we study a gate appointment design problem that aims to manage the number of trucks allowed to a container terminal over time, so as to minimize the length of the truck waiting line and alleviate gate congestion. To optimize the gate appointment strategy, the truck service plans need also be devised, which involve the decisions for assigning trucks to yard blocks for container transhipment. We develop a two-stage robust optimization model for the problem by taking into account the uncertain service capacities of the yard blocks. Our model considers two decision stages, where the first-stage decision allocates slot capacities for the appointment slots, whereas the second-stage decision designs truck service plans with observed yard service capacity. We solve the two-stage robust model using an adapted column-and-row generation algorithm. In each iteration of the adapted column-and-row generation algorithm, the second-stage decision is generated by means of a pseudo-polynomial-time dynamic programming algorithm, while the first-stage decision is generated by a tailored scenario decomposition method. We test the computational performance of the proposed solution method on instances generated from real terminal operation data, and reveal managerial insights that would inspire terminal operators in the management of truck appointment for gate congestion mitigation.