Scheduling double-track gantry cranes to minimize the overall loading/unloading time

In this paper, we consider the gantry crane scheduling problem at a single storage block where a total of m gantry cranes are mounted on double tracks so that cranes on different tracks can pass each other while those on the same track cannot. Containers at the storage block are divided into bays and each bay of containers has to be loaded/unloaded together due to the same shipping destination or the same customer. To minimize the overall loading/unloading time of containers, we first formulate the problem to a mixed integer linear programming (MILP) model, and compute the optimal solutions of small instances by the Gurobi solver. Then we design several heuristic algorithms and test their efficiency and performance by a series of large instances. In particular, we present a polynomial time approximation algorithm for the case where all but one gantry crane is mounted on the same track. We show that the algorithm has a worst case ratio of 2 - 2 m, outperforming the partition-based algorithms in the single-track scenario.