Robust vessel traffic scheduling with uncertain Berth Service Times in a Seaport

We consider a planning horizon during which a set of vessels visit a seaport for cargo transshipment. To access the designated berths, vessels should travel from the anchorage ground to the port basin by passing through a navigation channel. As soon as the vessels have completed the cargo transshipment, they need to travel from the port basin back to the anchorage ground through the navigation channel again. Navigation channel traffic is affected by the tidal effect and is bottlenecked by the limited capacity. The incoming vessels may wait for the tide to enter the channel after arriving at the anchorage ground; while the outgoing vessels need to wait for the tide to enter the channel upon completion of cargo transshipment. During these operations, the port operators need to assign tidal windows for vessels to travel into or out of the port, as well as the berthing and unberthing times of vessels, in order to minimize the overall operating cost. We formulate the problem as a two-stage robust optimization model, considering the uncertain vessel service times at berths. By exploiting the problem structure, we develop an adapted column and constraint generation algorithm framework, where the second-stage problem is solved by an enumeration-based method for generating candidate vessel service sequences and a dynamic programming algorithm for allocating the uncertainty budgets to vessels. The computation experiments show that our proposed algorithm generates optimal solutions within acceptable computation times (less than 30 s), and performs better than well established benchmark methods in terms of both worst-case performance and mean performance metrics. Several managerial insights can be derived from our experimental results to guide port operations in terms of the application of the robust models and benefits to the industry.