An integrated multi-ship crane allocation in Beirut Port container terminal

This paper investigates the integration between the quay and yard sides for multiple berthing ships with transshipment containers. This paper is motivated by the experience of an operator at Beirut Port. An integer linear programming model is formulated to minimize the total number of cranes used in both quay and yard sides for all berthing ships with transshipment containers unloading during a finite and discretized time horizon. The number of containers to be unloaded is determined in each time period, by each quay crane, at each ship bay location, along with the designated storage location at the yard side. The number of yard cranes needed at each storage yard block is also determined over the time horizon. Major capacity, time, and spatial constraints related to transshipment operations are taken into consideration. One insight from our numerical results is that restricting resources at the yard side will lead to an increase in required cranes at the quay side, and vice versa, which confirm results in earlier literature on single ship. However, we argue, via several counter examples, that single-ship solutions are not easily adaptable to multi-ship situations, which justifies the purpose of integrated formulations such as ours.