Joint scheduling of vessel traffic and pilots in seaport waters

In the busiest seaports, vessel traffic and vessel pilotage management play a crucial role in congestion mitigation. The management of vessel traffic and pilotage involves scheduling the vessels for sailing into and out of a seaport and scheduling the pilots for navigating the vessels in the port waters. In this paper, we study the integrated vessel traffic and pilot scheduling problem of a seaport. We manage the vessel traffic by optimizing the utilization of the navigation channels and the utilization of the anchorage areas in the terminal basin and incorporate the decision of pilot scheduling into the decision of vessel traffic management for congestion mitigation and vessel service enhancement. We formulate the problem on a time–space network with vessel- and pilot-dependent arc costs and develop an integer programming model that minimizes the sum of the berthing and departure tardiness cost of vessels, the cost of unsatisfied vessel service requests, and the pilot dispatching cost. For solving the model, we enumerate feasible vessel paths a priori and develop a Lagrangian relaxation algorithm that decomposes the problem into a vessel and pilot path assignment subproblems. Computational performance of the Lagrangian relaxation algorithm is tested on problem instances generated based on the physical layout and operational data of the Waigaoqiao Port in Shanghai.