Efficient algorithm for quay crane scheduling with arbitrary precedence constraint

This paper investigates quay crane scheduling problem at container ports, subject to arbitrary precedence constraint. Differing from traditional machine scheduling problems, non-crossing constraint must be satisfied because parallel quay cranes mount on a same rail to unload or load containers. Precedence relation in an arbitrary form is rarely investigated in the literature, however it may be originated from (i) reefers or dangerous cargo which requires high priority of processing, and (ii) yard stacking plan. We present computational complexity for several problem variations. We show the problem, even without precedence constraint, is strongly NP-hard, which improves the state-of-the-art. A genetic algorithm is proposed to obtain near-optimal solutions. Computational experiments demonstrate the efficiency.