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

Abstract

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.