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The optimal assignment of berth slots and cranes to shipping services is the central logistics problem at modern marine container terminals and should be formulated to specifically account for its stochastic nature. We use a computational grid to solve a major seaport logistic problem by a simulation optimization approach centred around a queuing network model of the logistic process of interest. We emphasize the power of grid computing for the simulation optimization studies and we design and implement an algorithm for distributing the computational load to parallel processors. Performance of the algorithm is demonstrated numerically using real-sized problem instances.