The quay crane scheduling problem with time windows

The quay crane scheduling problem consists of scheduling tasks for loading and unloading containers on cranes that are assigned to a vessel for its service. This article introduces a new approach for quay crane scheduling, where the availability of cranes at a vessel is restricted to certain time windows. The problem is of practical relevance, because container terminal operators frequently redeploy cranes among vessels to speed up the service of high-priority vessels while serving low-priority vessels casually. This article provides a mathematical formulation of the problem and a tree-search-based heuristic solution method. A computational investigation on a large set of test instances is used to evaluate the performance of the heuristic and to identify the impact of differently structured crane time windows on the achievable vessel handling time.