Bi-objective Dynamic Tugboat Scheduling with Speed Optimization under Stochastic and Time-Varying Service Demands

With the growing emphasis on green shipping to reduce the environmental impact of maritime transportation, optimizing fuel consumption with maintaining high service quality has become critical in port operations. Ports are essential nodes in global supply chains, where tugboats play a pivotal role in the safe and efficient maneuvering of ships within constrained environments. However, existing literature lacks approaches that address tugboat scheduling under realistic operational conditions. To fill the research gap, this is the first work to propose the bi-objective dynamic tugboat scheduling problem that optimizes speed under stochastic and time-varying demands, aiming to minimize fuel consumption and manage service punctuality across a heterogeneous fleet. For the first time, we develop an extended Markov decision process framework that integrates both reactive task assignments and proactive waiting decisions, considering the dual objectives. Subsequently, an initial schedule for known requests is established using a mixed-integer linear programming model, and an anticipatory approximate dynamic programming method dynamically incorporates emerging demands through task assignments and waiting plans. This approach is further enhanced by an improved rollout algorithm to anticipate future scenarios and make decisions efficiently. Applied to the Singapore port, our methodology achieves a 12.8% reduction in the total sail cost compared to the tugboat company’s scheduling practices, resulting in significant daily savings. The results with benchmarking against three methods demonstrate improvements in cost efficiency and service punctuality, meanwhile, extensive sensitivity analysis provides managerial insights for operational practice.