Integrated quay crane - shuttle vehicle scheduling problem capacitated by apron buffer

This paper investigates an integrated quay crane (QC) - shuttle vehicle (SV) scheduling problem (SP) with capacitated apron buffer, which is subject to practical constraints on non-zero travelling time, precedence relationships between container-handling jobs, QC non-interference, safety margin, blocking and apron buffer capacity. The objective is to minimise the makespan of vessel handling by simultaneous optimisation of bay-to-QC assignment, the sequences of bays handled by QCs, the sequences of jobs handled by QCs, job-to-SV assignment and the sequences of jobs handled by SVs. To achieve this, a mixed-integer linear programming model is first formulated to solve the SP. The relationships of decision variables and model constraints are then analysed to generate two sub-models: assignment based and sequence based. The former sub-model is developed from the proposed model by pre-determining the assignment of bay-to-QC and job-to-SV, and the latter is developed from the proposed model by pre-determining the sequences of jobs handled by each QC and each SV. Hybrid genetic algorithms with the two sub-models are proposed for numerical experiments. Practical implications of this investigation for apron buffer zone design are discussed.