Dynamic programming algorithms for the general quay crane double-cycling problem with internal-reshuffles

High utilization of quay cranes is a major objective pursued by seaport terminal managers. Double-cycling technique has been shown to be effective in practice. Complicated with reshuffle operations, the productivity of quay cranes could be further improved, but the problem complexity increases as a side-effect. This paper studies a double-cycling quay crane scheduling problem in which reshuffle containers can be handled internally on the vessel. For this problem, no exact algorithm exists in the literature. We present a dynamic programming approach to optimally solve the problem. Our algorithm runs in polynomial time when the number of container stacks is fixed. We also extend our proposed optimal algorithm to the general case where hatch covers are involved.