A note on scheduling container storage operations of two non‐passing stacking cranes

Abstract

We study a scheduling problem for a container block, in which there are incoming containers only. Container placement is served by two non‐passing stacking cranes based at the opposite sides of the container block. The same time is required for any crane to move between two adjacent bays of the container block and the same different time is required for any crane to perform any down‐and‐up operation related to container lifting at the pick‐up point or container lowering at the storage point. Containers are assigned to the cranes according to one of the following policies: (1) two fixed sequences policy where a container processing sequence is given for each crane, (2) dedicated crane policy where containers are preassigned to the cranes, (3) one fixed, one arbitrary sequence policy where a container processing sequence is given for one crane and it can be arbitrary for the other crane, (4) flexible policy where any container can be assigned to any crane at any time, and (5) global fixed sequence policy where the container sequence is given and the relative processing order of containers in this sequence must be preserved by any crane. The objective is to minimize the completion time of the latest operation. We show that the problem is polynomially solvable for policy 1 and, if the number of containers to be placed in the same bay is no more than a half of all containers, for policy 4. It is NP‐hard in the strong sense for policies 2 and 3. Approximation algorithms with guaranteed absolute and relative deviations from the optimum are devised for policies 4 and 5. The results translate for the case of outgoing containers only.

Twin-crane scheduling during seaside workload peaks with a dedicated handshake area

“…Crane scheduling approaches for this setting are provided for instance by Gharehgozli et al (2014b) and Boysen and Stephan (2016). But twin cranes (without handshake area or any-bay handover) where one crane is fixedly assigned to all seaside-related container moves and the other to all landside-related moves, so that crane scheduling has to avoid interference whenever both cranes meet (e.g., see Boysen et al, 2015;Briskorn & Angeloudis, 2016;Gharehgozli et al, 2014a;Kovalyov et al, 2018), also do not cooperate in the strict sense we presuppose in this paper. Cooperation between cranes requires that there is (at least some) flexibility in the assignment of container moves to cranes, so that by varying these assignments the division of labor between cranes can be altered.…”

Routing two stacking cranes with predetermined container sequences

“…Jaehn and Kress (2018) and Kress et al (2019) extend the setting to handovers on both sides. Kovalyov et al (2018) examine the computational complexity of scheduling twin cranes under various protocols for assigning tasks to cranes.…”

Container depot location problem in the frame of the Polish part of the New Silk Road

“…Reshuffling causes cost and energy consumption and should be avoided as much as possible. Methods for optimally stacking and retrieving containers to/from storage yard blocks have been described in Kovalyov et al [13] and Nossack et al [14].…”