Container Pre-Marshaling Problem with Uncertain Intra-Group Retrievals

Abstract

In real-world terminals, containers are divided into multiple groups according to the reservation time. The container retrieval order between different groups is known, while the retrieval order within the same group is unknown. Previous research studies prioritize between groups but seldom prioritize within the same group, especially uncertain intra-group priorities. This paper studies the container pre-marshaling problem with uncertain intra-group retrievals (CPMP-UIR). Since the retrieval order of intra-group containers is uncertain, after the pre-marshaling, containers still need to be relocated during retrieval. CPMP-UIR conducts pre-marshaling, ensuring no relocations between groups and a minimum expected number of overstows during retrieval. In this paper, we first give the formula for calculating the expected number of overstows in a layout. The value obtained by the formula is a lower bound for the expected number of relocations. Second, we develop an algorithm called the Expected Overstow-based Heuristic (EOH) for solving CPMP-UIR. In addition, a hard-enough dataset is generated to evaluate the performance of EOH. Finally, our numerical experiments show that the expected number of overstows during the retrieval phase is reduced dramatically after the pre-marshaling.