Dynamic tugboat deployment and scheduling with stochastic and time-varying service demands

Container ports serve as crucial logistics hubs in global supply chains, but navigating ships within such ports is complex due to restricted waterways. Tugboats play a critical role in ensuring safety and efficiency by escorting and towing ships under these conditions. However, the tugboat deployment and scheduling problem has received little attention. To fill the research gap, we propose a new research problem - the dynamic tugboat deployment and scheduling problem, in which not all requests are confirmed initially but dynamically confirmed over time and future tugging demands need to be anticipated when managing the utilization of tugboats. To formulate the problem, we propose an extended Markov decision process (MDP) that incorporates both reactive task assignment decisions and proactive tugboat waiting decisions, creating a reactive and proactive MDP. To solve the advanced MDP model efficiently for real-time decisions, we develop an anticipatory approximate dynamic programming method that incorporates appropriate task assignment and waiting strategies for deploying and scheduling a heterogeneous tugboat fleet and embed the method into an improved rollout algorithm to anticipate future scenarios. The effectiveness, efficiency, and performance sensitivity of the developed modeling and solution methods are demonstrated via extensive numerical experiments for the Singapore container port.