Simulation-based optimization for discharge/loading operations at a maritime container terminal

The discharge/loading process of a single container ship by multiple quay cranes and shuttle vehicles moving back and forth from the quay to the yard and vice versa is focused in this paper. The core problem of this major operational issue reduces to finding the optimal assignment and optimal sequencing (schedule) of bays (jobs) processed by a fixed number of available cranes (machines). Under the classical assumption that machines have no release time and that their processing occurs with continuity, at a constant rate, in literature it has been tackled as a deterministic machine scheduling problem and formulated by integer programming as the quay crane scheduling problem (QCSP). Here, instead, the QCSP is viewed as a decisional step within an uncertain and dynamic logistic process where the quay cranes are the resources to be managed at the best, i.e., by minimizing the time spent waiting for each other due to conflicts, as well as the time wasted for blocking and starvation phenomena due to congestion occurring along the path from the quay area and to the stacking yard and vice versa. We present a simulation-based optimization (SO) model for this wider modeling problem with the objective of finding the schedule which optimizes a classical objective function. The search process for the optimal schedule is accomplished by a simulated annealing (SA) algorithm, while performance estimation of the overall container discharge/loading process is provided by the simulation framework as a whole. Numerical experiments on a real instance are presented for tuning purposes of the SA procedure implemented within the simulator.