Robust optimization for the integrated berth allocation and quay crane assignment problem

This paper studies the berth allocation and quay crane assignment problem (denoted by BACAP) under uncertainty. We assume that the ships' arrival and operation time is uncertain in this problem. We merge the proactive and reactive strategies to address the two-stage robust optimization (denoted by RO) model for the BACAP to obtain a complete schedule with robustness. We obtain the berth allocation and quay crane assignment with a proactive strategy in the first stage. In the second stage, we formulate a rescheduling model with a reactive strategy considering the sensitivity towards the change in the complete schedule. The second stage model is based on the prospect theory, a quantitative way to describe the stakeholders' perception, including the port managers and shipowners, of the deviation from the baseline plan. The two stages are iterated until a favorable schedule with high robustness is found. To illustrate the superiority of the two-stage robust optimization model with the prospect theory for the complete schedule, we give an intuitive example to compare the performance among the related models. The two-stage RO model with the prospect theory for the complete schedule can generate a lower cost and higher robustness schedule. As for the solution methods, the column and constraint generation (denoted by C&CG) algorithm is applied to obtain the exact solution for the two-stage RO model. Moreover, we propose the scenario-constrained C&CG (denoted by SC) algorithm, which can reduce constraints and variables for the master problem to accelerate the solving process of the two-stage RO model. In addition, the optimality of the SC algorithm is verified by analyzing the pattern of the occurrence of the worst-case scenarios. Besides, to tackle the large-scale instances, we propose the schedule-fixed (denoted by SF) algorithm, in which the results of the previous iterations are treated as fixed. The SF algorithm can increase computing efficiency with a small gap compared to the optimal solution value. Furthermore, extensive numerical experiments are conducted on both real-life instances and randomly generated instances to verify the superiority and generality of our model and algorithms.