An integrated quay crane - shuttle vehicle scheduling problem with apron buffer capacity constraints

Abstract

In container terminals equipped with shuttle vehicles, apron buffer zones are necessary for linking up the operations of quay cranes and shuttle vehicles. An integrated quay crane - shuttle vehicle scheduling problem with limited apron buffer capacity is investigated in this paper. This problem is subject to the practical constraints on nonzero traveling time, precedence relationships between container handling jobs, quay crane non-interference, safety margin, blocking, and apron buffer capacity constraint. The objective of this investigation is to minimize the makespan of vessel handling by simultaneous optimization of bay-to-quay crane assignment, the sequences of bays handled by quay cranes, the sequences of jobs handled by quay cranes, job-to-shuttle vehicle assignment and the sequences of jobs handled by shuttle vehicles. To achieve this, a mixed-integer linear programming model is first formulated to solve the scheduling problem. Second, the relationships of decision variables and model constraints are discussed to generate two sub-models: assignment-based and sequence-based. The assignment-based sub-model is developed from the proposed model by pre-determining the assignment of bay-to-quay cranes and job-to-shuttle vehicles, and the other is developed from the proposed model by pre-determining the sequences of jobs handled by each QC and each SV. Third, the hybrid genetic algorithms with the two sub-models are proposed. Fourth, numerical experiments show that the algorithms are competitive, compared to on-the-shelf solvers. Finally, practical implications of this investigation for apron buffer zone design are discussed.