Robust periodic berth planning of container vessels

We consider a container operator, who serves a number of shipping lines by discharging and loading their periodically arriving container vessels. Disruptions on vessels’ travel times lead to stochastic arrivals in the port. To cope with these disturbances, the operator and each vessel line agree on two types of arrivals: arrivals i) within, and ii) out of a so-called arrival window. If a vessel arrives within its window, the operator guarantees a maximal process time. If not, the operator is not bound to any guaranteed process time. The problem is to construct a periodic window-based i) arrival, ii) departure and iii) time-variant crane capacity plan to minimize the maximal crane capacity reservation. In this paper, we propose a mixed integer linear program (MILP) that minimizes the maximal crane capacity reservation while window agreements are satisfied for all scenarios in which vessels arrive within their windows. Results of a case study suggest that with slight modifications to an existing plan, significant reductions in the maximal crane capacity reservation can be achieved. As a particular case, the MILP determines the conventional optimal window-ignoring plan. Results suggest that although the windowignoring plan on itself requires less crane capacity than the window-based plan, it is much more sensitive to the arrival window agreements.