Institute of Transportation Studies at UC Berkeley

Loading ships as they are unloaded (double-cycling) can improve the efficiency of a quay crane and thus container port. This paper describes the double-cycling problem, and presents two solution algorithms and simple formulae to estimate reductions in the number of operations, and operating time. The problem is formulated as a scheduling problem. Small problems can be solved to optimality with a standard numerical solver, but problems of typical size are computationally burdensome and terminated after 10 hours with optimality gaps larger than 50%. A formula for an improved lower bound to the optimal solution is developed and shows the optimality gaps are actually below 2.5% in all cases. The paper presents a greedy algorithm that can obtain solutions in seconds. A formula for an upper bound to the greedy algorithm's performance can be used to accurately predict crane performance. The problem is extended to include an analysis of double-cycling when ships have deck hatches. Results are presented for many simulated vessels, and compared to empirical data from a real-world trial. The paper demonstrates that analytical methods can be used in addition to numerical methods to provide greater insight. More importantly, the paper demonstrates that double-cycling can create significant efficiency gains.