Tugboat scheduling under ship arrival and tugging process time uncertainty

This study addresses an interesting tugboat scheduling problem considering uncertainty in both container ship arrival and tugging process times for large container ports. The uncertain ship arrival and tugging process times are formulated as a finite set of discrete scenarios that can be generated from historical port traffic data. We deal with the uncertainty by integrating proactive and reactive scheduling strategies such that this study is distinct from most existing studies in the literature. The proactive scheduling strategy considers the expected degree of variability and uncertainty during the execution of a tugboat fleet schedule while the reactive scheduling strategy properly adjusts the initial schedule to cope with unexpected scenarios with minimum recovery cost. A mixed-integer linear programming model for the proposed tugboat scheduling problem is established. For a large-scale problem, an ad-hoc algorithm is designed to generate tugging chains such that the large-scale problem can be tackled effectively. The extensive numerical experiments are finally carried out to demonstrate the practical significances of the models and algorithms developed by this study.