A Variable Neighborhood Search Algorithm for the Integrated Berth Allocation and Quay Crane Assignment Problem

To improve the utilization of port resources and reduce the consumption of resources due to vessel waiting and delays, this paper investigates the Berth Allocation and Quay Crane Assignment Problem (BACAP) in container ports, focusing on the Quay Crane (QC) profile. The objective is to assign berths, berthing times, and QC profiles to vessels arriving at the port within a given planning horizon, thereby extending the traditional BACAP framework. To minimize the sum of idle time costs caused by vessel waiting and delay time costs due to late vessel departures, a mixed-integer linear programming (MILP) model is proposed. Additionally, a variable neighborhood search (VNS) algorithm is designed to solve the model, tailored to the specific characteristics of the problem. The proposed MILP model and VNS algorithm are evaluated using two sets of BACAP instances. The numerical results demonstrate the effectiveness of both the model and the algorithm, showing that VNS efficiently and reliably solves instances of various sizes. Furthermore, each neighborhood structure contributes uniquely to the iterative process. This study also analyzes the impact of different idle and delay costs on BACAP, providing valuable managerial insights. The proposed framework contributes to enhancing operational efficiency and supports sustainable port management.