In the Berth Allocation Problem (BAP) the aim is to optimally schedule and assign ships to berthing areas along a quay. The objective is the minimization of the total (weighted) service time for all ships, defined as the time elapsed between the arrival in the harbor and the completion of handling. Two versions of the BAP are considered: the discrete case and the continuous case. The discrete case works with a finite set of berthing points. In the continuous case ships can berth anywhere along the quay. Two formulations and a tabu search heuristic are presented for the discrete case. Only small instances can be solved optimally. For these sizes the heuristic always yields an optimal solution. For larger sizes it is always better than a truncated branch-and-bound applied to an exact formulation. A heuristic is also developed for the continuous case. Computational comparisons are performed with the first heuristic and with a simple constructive procedure.
In this paper we integrate at the tactical level two decision problems arising in container terminals: the berth allocation problem, which consists of assigning and scheduling incoming ships to berthing positions, and the quay crane assignment problem, which assigns to incoming ships a certain QC profile (i.e. number of quay cranes per working shift). We present two formulations: a mixed integer quadratic program and a linearization which reduces to a mixed integer linear program. The objective function aims, on the one hand, to maximize the total value of chosen QC profiles and, on the other hand, to minimize the housekeeping costs generated by transshipment flows between ships. To solve the problem we developed a heuristic algorithm which combines tabu search methods and mathematical programming techniques. Computational results on instances based on real data are presented and compared to those obtained through a commercial solver.2
Abstract:The quay crane scheduling problem consists of determining a sequence of unloading and loading movements for cranes assigned to a vessel in order to minimize the vessel completion time as well as the crane idle times. Idle times originate from interferences between cranes since these roll on the same rails and a minimum safety distance must be maintained between them. The productivity of container terminals is often measured in terms of the time necessary to load and unload vessels by quay cranes, which are the most important and expensive equipment used in ports. We formulate the quay crane scheduling problem as a vehicle routing problem with side constraints, including precedence relationships between vertices. For small size instances our formulation can be solved by CPLEX. For larger ones we have developed a branch-and-cut algorithm incorporating several families of valid inequalities, which exploit the precedence constraints between vertices.
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