A Proactive-Reactive-Based Approach for Continuous Berth Allocation and Quay Crane Assignment Problems with Hybrid Uncertainty

Abstract

Port operations have been suffering from hybrid uncertainty, leading to various disruptions in efficiency and tenacity. However, these essential uncertain factors are often considered separately in literature during berth and quay crane assignments, leading to defective, even infeasible schedules. This paper addressed the integrated berth allocation and quay crane assignment problem (BACAP) with stochastic vessel delays under different conditions. A novel approach that combines both proactive and reactive strategies is proposed. First, a mixed-integer programming model is formulated for BACAP with quay crane maintenance activities under the ideal state of no delay. Then, for minor delays, buffer time is added to absorb the uncertainty of the arrival time of vessels. Thus, a robust optimization model for minimizing the total service time of vessels and maximizing the buffer time is developed. Considering that the schedule is infeasible when a vessel is seriously delayed, a reactive model is built to minimize adjustment costs. According to the characteristics of the problem, this article combined local search with the genetic algorithm and proposed an improved genetic algorithm (IGA). Numerical experiments validate the efficiency of the proposed algorithm with CPLEX and Squeaky Wheel Optimization (SWO) in different delay conditions and problem scales. An in-depth analysis presents some management insights on the coefficient setting, uncertainty, and buffer time.