Space planning considering congestion in container terminal yards

This paper proposes a nonlinear mathematical model for solving the problem of allocating storage space to future container arrivals in container terminal yards by considering the waiting times of trucks in the yard, called stochastic space allocation model (SSAM). Three heuristic procedures based on the Frank-Wolfe algorithm and the subgradient optimization method are proposed to efficiently solve the problem. From the numerical experiment, it is found that the proposed al-gorithms for SSAM provide solutions with the gaps between the objective values and the optimal values are no greater than 0.69%. It was also found that the best algorithm among three proposed algorithms (FWMP-S) obtained the average 7.89% improvement in the objective value compared with a previous model with a handling capacity constraint instead of considering waiting time (DSAM). It is found that the SSAM reduces the average system time of transporters for ship operation and that of road trucks by 17.39 and 7.14%, respectively, compared with the DSAM. This study proposes the most appropriate heuristic algorithm depending on the problem char-acteristics of the SSAM.