A new effective unified model for solving the Pre-marshalling and Block Relocation Problems

Container terminals are exchange hubs that interconnect many transportation modes and facilitate the flow of containers. Among other elements, terminals include a yard which serves as temporary storage space. In the yard, containers are piled up by cranes to form blocks of stacks. During the shipment process, containers are carried from the stacks to ships following a given sequence. Hence, if a high priority container is placed below low priority ones, such obstructing containers have to be moved (relocated) to other stacks. Given a set of stacks and a retrieval sequence, the aim in the Pre-marshalling Problem (PMP) is to sort the initial configuration according to the retrieval sequence using a minimum number of relocations, so that no new relocations are needed during the shipment. The objective in the Block Relocation Problem (BRP) is to retrieve all the containers according to the retrieval sequence by using a minimum number of relocations. This paper presents a new unified integer programming model for solving the PMP, the BRP, and the Restricted BRP (R-BRP) variant. The new formulations are compared with existing mathematical models for these problems, as well as with other exact methods that combines combinatorial lower bounds and the branch-and-bound (B&B) framework, by using a large set of instances available in the literature. The numerical experiments show that the proposed models are able to outperform the approaches based on mathematical programming. Nevertheless, the B&B algorithms achieve the best results both in terms of computation time and number of instances solved to optimality

Minimizing crane times in pre-marshalling problems

[EN] The pre-marshalling problem has been extensively studied in recent years with the aim of minimizing the number of movements needed to rearrange a bay of containers. Time is a more realistic objective for measuring process efficiency, and we show that it does not correlate with the number of movements. As a result, we study the problem of minimizing crane times and develop two exact approaches to solve it: an integer linear model, and a branch and bound algorithm, with new upper and lower bounds, dominance criteria, and a heuristic procedure, to provide optimal solutions for problems of practical sizeThis work has been partially supported by the Spanish Ministry of Science, Innovation, and Universities, FPU Grant A-2015-12849 and under the project "OPTEP-Port Terminal Operations Optimization" (No. RTI2018-094940-B-I00) financed with FEDER funds.Parreño-Torres, C.; Álvarez-Valdés, R.; Ruiz García, R.; Tierney, K. (2020). Minimizing crane times in pre-marshalling problems. 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