Joint scheduling of vessels and vessel service providers for enhancing the efficiency of the port call process

As ports are experiencing heavier traffic, the pressure to improve port call processes is increasing. Port call optimization (PCO) is one of these improvement initiatives, enabling the arrival of vessels to the port just-in-time when the vessel services, like pilotage, towage, and mooring, are all readily available. Otherwise, vessels that sailed at full speed to arrive at the port may have to wait, idling at anchorage, occupying space, burning fuel, and leading to increased congestion. One of the main challenges in the implementation of PCO is determining the time at which availability of these services can be guaranteed. The paper addresses this challenge by presenting a model that jointly schedules vessels and service providers. It extends the current approaches to allow application to larger and busier ports, where repositioning times for pilots and tugboats is highly variable and vessels experience waiting times between services. The problem is formulated as a mixed-integer linear programming one and is modelled in continuous time. We test alternative scheduling strategies using three different objective functions, based on the current ‘first-come-first-serve’ approach, a minimal level of service, and the best capacity utilization. The model is applied on data made available by the Port of Rotterdam, and it provides a full-service schedule for vessels and service providers.