Multi-class pilot dispatching problem with stochastic pilotage duration

In most seaports, pilotage is compulsory for incoming and outgoing vessels to use pilotage services. Maritime pilots play a critical role in providing local knowledge and assistance to ensure the safety of vessels and seafarers. Typically, pilots are classified into multiple classes on the basis of their experiences and qualifications. Moreover, pilotage duration is usually stochastic due to various factors, including harsh weather conditions, visibility, and traffic changes. In this study, we address a multi-class pilot dispatching problem with stochastic pilotage duration. We formulate this problem as a stochastic programming model that considers the expected penalty cost for late arrival at each task's location. To solve this problem, we develop a branch-and-price algorithm that integrates column generation within the branch and bound framework. Additionally, we develop a novel labelling algorithm and several effective acceleration techniques to enhance the efficiency of the proposed algorithm. Extensive numerical experiments demonstrate the effectiveness of the proposed algorithm and show that it can handle realistic-sized instances while outperforming a metaheuristic search method.