Stochastic model to estimate the waiting time for container vessel turnaround times

By developing possible solutions for Saudi ports to limit the increase in damage to the marine ecosystem, the random system for estimating the waiting time of ships in Saudi ports has been developed as a model to guide the application of the multiple benefits to the beneficiaries such as ship owners, shipping companies and port authorities so that it is applied to create multiple economic and environmental savings. An imperative optimization model for solving container slot allocation problems for time-sensitive commodities under the dynamics of port congestion pricing. The proposed new pricing mechanism has proven to be effective when compared to a generic slot allocation model that does not take into account shipping time limits and port congestion, with results showing that the proposed pricing scheme can significantly improve ship companies' revenues and improve customer satiation. In terms of reducing carbon emissions from the ship's stay for a longer period at the docks.