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Background: Scheduling the arrival of external trucks in container terminals is a critical operational decision that faces both terminal managers and trucking companies. This issue is crucial for both stakeholders since the random arrival of trucks causes congestion in the terminals and extended delays for the trucks. The objective of scheduling external truck appointments is not only to control the workload inside the terminal and the costs resulting from the excessive waiting times of trucks but also, to reduce the truck turnaround time. Methods: A binary programming model was proposed to minimize the waiting time cost, demurrage cost, and container delivery cost. Moreover, a sensitivity analysis was performed to compare various scenarios in terms of cost and to study to what extent the workload level is affected. The mathematical model was solved using Gurobi© 8.1.0 software. Results: 30 instances found in the literature were solved and evaluated in terms of the objective function value (i.e., cost) and truck turnaround time before and after controlling the workload inside the container terminal using the new proposed constraint. Conclusions: The obtained results showed a better distribution of the terminal workload, as well as a lower truck turnaround time that reduces the total cost.

Background: Random truck arrivals at maritime container terminals are one of the primary reasons for gate congestion. Gate congestion negatively affects the terminal’s and drayage firms’ productivity and the surrounding communities in terms of air pollution and noise. To alleviate gate congestion, more and more terminals in the USA are utilizing a truck appointment system (TAS). Methods: This paper proposes a novel approach to modeling the truck appointment system problem. Unlike previous studies which largely treated this problem as a single-player game, this study explicitly models the interplay between the terminal and drayage firms with regard to appointments. A multi-player bi-level programming model is proposed, where the terminal functions as the leader at the upper-level and the drayage firms function as followers at the lower-level. The objective of the leader (the terminal) is to minimize the gate waiting cost of trucks by spreading out the truck arrivals, and the objective of the followers (drayage firms) is to minimize their own drayage cost. To make the model tractable, the bi-level model is transformed to a single-level problem by replacing the lower-level problem with its equivalent Karush–Kuhn–Tucker (KKT) conditions and the model is solved by finding the Stackelberg equilibrium in one-shot simultaneous-moves among players. For comparison purposes, a single-player version of the TAS model is also developed. Results: Experimental results indicate that the proposed multi-player model yields a lower gate-waiting cost compared to the single-player model, and that it yields higher cost savings for the drayage firms as the number of appointments per truck increases. Moreover, the solution of the multi-player model is not dependent on the objective function coefficients, unlike the single player model. Conclusions: This study demonstrates that a TAS is more effective if it considers how the assigned appointment slot affects a truck’s drayage cost. It is recommended that terminal operators and port authorities initiate conversations with their TAS providers about incorporating this element into their TAS.

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. Ship-to-ship operations and yard activity at the container terminals are at their peak and starting to affect land operations on truck arrivals and departures. In response, a Truck Appointment System (TAS) has been developed to mitigate truck congestion that occurs between the gate and the yard of the container terminal. The vehicle booking system is developed and operated in-house at large-scale container terminals, but efficiency is low due to frequent truck schedule changes by the transport companies (forwarders). In this paper, we propose a new form of TAS in which the transport companies and the terminal operator cooperate. Numerical experiments show that the efficiency of the cooperation model is better by comparing the case where the transport company (forwarder) and the terminal operator make their own decision and the case where they cooperate. The cooperation model shows higher efficiency as there are more competing transport companies (forwarders) and more segmented tasks a truck can reserve.