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

Abstract

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 * Corresponding author: Tel. +33 1 4940 4082.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.

Integer programming models for the pre-marshalling problem

“…This alternative strategy is shown to be much more efficient, in terms of the number of optimal solutions obtained and running times, in an extensive computational study on several datasets from the literature. The computational study also shows that the best of these new models outperforms the previously published models proposed by Lee and Hsu (2007), and the recent model presented by de Melo da Silva et al (2018).…”

“…They illustrate the behaviour of their model on one layout, including several extensions of the basic formulation. More recently, de Melo da Silva et al (2018) propose a unified model for the pre-marshalling and the container relocation problem (CRP). They also discretize time into time segments separated by time points and consider two types of variables: variables describing the state of the bay and variables defining the movements.…”

“…They also discretize time into time segments separated by time points and consider two types of variables: variables describing the state of the bay and variables defining the movements. In this paper, we study the performance and limits of the mathematical formulations for the pre-marshalling problem through an exhaustive computational analysis of the models proposed by Lee and Hsu (2007), by de Melo da Silva et al (2018), and of the several formulations we have developed.…”

“…Moreover, a value obtained by modifying the original instance cannot be considered a valid upper bound. Heuristic algorithms that do not increase the bay size, as that used by de Melo da Silva et al (2018), do not guarantee that a feasible solution will be found in all kind of instances. In de Melo da Silva et al ( 2018), they test their PMP m1 model on the CV dataset from Caserta and Voß (2009).…”

A local-search based heuristic for the unrestricted block relocation problem

“…The pre-marshalling problem concerns the re-ordering of containers stored in stacks such that no reshuffling is necessary during retrieval. New unifying problem formulations of the premarshalling problem, the R-BRP and the U-BRP have recently been developed by de Melo da Silva et al (2018). While the new formulations are more efficient than previous mathematical programming based approaches the authors acknowledge that tailored branch-and-bound algorithms still provide superior performance in terms of run time as well as number of instances solved to optimality.…”