Scheduling quay cranes and shuttle vehicles simultaneously with limited apron buffer capacity

Abstract

How to schedule quay cranes (QCs) and shuttle vehicles (SVs) simultaneously or model them in an integrated scheduling problem is one of the most important problems in operations and management of a container terminal. This paper investigates an integrated QC and SV scheduling problem constrained by apron buffer capacity. In this problem, the decisions to make include the bay-to-QC assignment, the QC-bay sequence, the QC-job sequence, the job-to-SV assignment and the SV-job sequence. First, a mixed-integer linear programming model is formulated for this problem to minimize the makespan. Second, the relationships and interactive variables among the four segments of constraints of the proposed model (i.e., scheduling QCs for vessel bays, sequencing jobs handled by a QC in each bay, scheduling SVs for jobs, apron buffer capacity constraints for each vessel bay) are analyzed to present three rules: vessel block rule, near-to-far rule and full-buffer rule. Finally, a sequential insertion algorithm, a greedy insertion algorithm and an improved genetic algorithm are proposed to solve mid- and large-sized cases for the problem. Numerical experiments show that the algorithms perform well, compared to the off-the-shelf solver. Based on these experiments, managerial implications are discussed for container terminal operations and management.