A new binary formulation of the restricted Container Relocation Problem based on a binary encoding of configurations

Galle, Virgile; Barnhart, Cynthia; Jaillet, Patrick

doi:10.1016/j.ejor.2017.11.053

Cited by 50 publications

(25 citation statements)

References 22 publications

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“…They also considered a lexicographic bi-objective problem whose secondary objective is the expected number of relocations of the forthcoming retrieval. Galle et al [28] proposed another ILP formulation of the restricted BRP with distinct priorities based on binary encoding of bay configurations [7]. Their formulation currently yields the best IP approach for this class of problem.…”

Section: Literature Reviewmentioning

confidence: 99%

An exact algorithm for the unrestricted block relocation problem

Tanaka

Mizuno

2018

Computers & Operations Research

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The purpose of this study is to propose an exact algorithm for the unrestricted block relocation problem with distinct priorities. In this problem, a storage area is considered where blocks of the same size are stacked vertically in tiers. Because we can access only topmost blocks, relocations of blocks are required when other blocks are retrieved. The objective is to minimize the total number of such relocations necessary for retrieving all the blocks one by one according to a specified order. In the restricted version of this problem, only the topmost block above the target block is relocatable. On the other hand, no such restriction is imposed on the unrestricted problem, which is considered in this study. We also assume that each block is assigned a distinct retrieval priority and the retrieval order of blocks is unique. To improve the efficiency of a branch-and-bound algorithm for this problem, we propose several dominance properties to eliminate unnecessary nodes in the search tree. Furthermore, we propose a new lower bound of the total number of relocations. The effectiveness of the proposed exact algorithm is verified by numerical experiments for benchmark instances in the literature.

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Section: Literature Reviewmentioning

confidence: 99%

An exact algorithm for the unrestricted block relocation problem

Tanaka

Mizuno

2018

Computers & Operations Research

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“…All the methods proposed by Lee & Hsu (2007), Tierney et al (2016) and Tanaka & Tierney (2018) (2015) and Zehendner et al (2015) proposed corrections and improvements for the r-brp model presented by Caserta et al (2012). Galle et al (2018) recently put forward a new MIP formulation for the r-brp which explores a binary representation that was initially described on the work of .…”

Section: Related Workmentioning

confidence: 99%

“…As for the brp, the quality of these bounds decreases as the height of the stacks increases. When compared to the literature, the best linear programming based formulation for the r-brp was proposed by Galle et al (2018), and is followed by Zehendner et al (2015), which is an improved version of the r-brp model of Caserta et al (2012). In both works, their implementation employs preprocessing mechanisms for eliminating variables.…”

Section: Block Relocation Problemsmentioning

confidence: 99%

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

Silva

Toulouse

Calvo

2018

European Journal of Operational Research

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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.

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“…Eskandari and Azari (2015) propose corrections and improvements to one of the formulations proposed in Caserta et al (2012) and present improved results for the R-BRP and Ku and Arthanari (2016b) develop an exact method which relies on clever ways to reduce the search space as well as on a bi-directional search scheme. Very recently, Galle et al (2018) have propose a new mathematical formulation relying on a binary encoding of different configurations.…”

Section: Introductionmentioning

confidence: 99%

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

Feillet

Parragh

Tricoire

2019

Computers & Operations Research

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The unrestricted block relocation problem is an important optimization problem encountered at terminals, where containers are stored in stacks. It consists in determining the minimum number of container moves so as to empty the considered bay following a certain retrieval sequence. A container move can be either the retrieval of a container or the relocation of a certain container on top of a stack to another stack. The latter types of moves are necessary so as to provide access to containers which are currently not on top of a stack. They might also be useful to prepare future removals. In this paper, we propose the first local search type improvement heuristic for the block relocation problem. It relies on a clever definition of the state space which is explored by means of a dynamic programming algorithm so as to identify the locally optimal sequence of moves of a given container. Our results on large benchmark instances reveal unexpectedly high improvement potentials (up to 50%) compared to results obtained by state-of-the-art constructive heuristics.

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A new binary formulation of the restricted Container Relocation Problem based on a binary encoding of configurations

Cited by 50 publications

References 22 publications

An exact algorithm for the unrestricted block relocation problem

An exact algorithm for the unrestricted block relocation problem

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

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

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