Blocks Relocation Problem Research Articles

Integrated optimization of truck appointment quotas and container relocations for multiple blocks considering transshipment containers handling

The container terminal is a crucial transshipment node in the sea and land cargo transport supply chain, and the efficiency of container collection and distribution has always been a research hotspot. In this paper, we consider the impact of transshipment containers resulting from various uncertainties and integrate the operations of external truck pickups with the handling of transshipment containers in the import yard of the container terminal. In light of the varying number of transshipment containers and transit times for different blocks, coupled with the unpredictable arrival order of external trucks leading to the unknown number of relocations, it is proposed to dynamically adjust the upper limit of the appointed quota for each block. We establish a two stage mixed integer programming model for the truck appointment quota and the block relocation problem. The objective functions aim to minimize the number of relocations and minimize the number of yard crane moves under the maximal appointment quota, respectively. This model is utilized for dynamically regulating the upper limit of the appointed quota for each block and determining the time intervals for picking up the appointed and transshipment containers, along with the yard crane scheduling scheme. The problem is solved using CPLEX and the improved variable neighborhood search algorithm (IVNS). The IVNS incorporates the correction strategy, decoding strategy, and scheduling rules designed to align closely with the characteristics of the problem. Through scheme comparison and sensitivity analysis, five management insights are proposed for terminals. Experimental results demonstrate that the approach presented in this paper effectively enhances the utilization efficiency of yard cranes, reduces yard congestion, and yields benefits for both terminals and trucking companies.

A new modeling approach for the unrestricted block relocation problem

We consider the block relocation problem (BRP), a combinatorial optimization problem that may arise in storage systems where items are organized in stacks. The objective is to retrieve all items in a predefined order with a minimal number of relocations. It can be distinguished between a restricted and an unrestricted version of the BRP. While in the restricted BRP (R-BRP) only relocations of items located above the item to be retrieved next are permitted, in the unrestricted BRP (U-BRP) all possible relocations are allowed. Existing exact methods concerning the BRP are frequently search-based methods which appear to be very effective. Nevertheless, recent literature concerning the R-BRP has shown that model-based methods can be competitive and therefore should also be taken into consideration. In this paper, we propose a new model-based approach for the U-BRP. It eliminates the fact that the number of variables is increasing with the number of necessary relocations; a disadvantage most mathematical models for the U-BRP have in common.

The blocks relocation problem with item families minimizing the number of reshuffles

The blocks relocation problem with item families minimizing the number of reshuffles

Valid Inequality and Variable Fixation for Unrestricted Block Relocation Problems

In modern logistics and smart warehouse, a terminal exists as a hub to connect multiple transportation modes and exchange goods. Solving a block relocation problem (BRP) arising from block retrieval processes in a terminal is fundamentally important to enhance the terminal’s overall efficiency and save its energy. In this paper, we improve the state-of-the-art mixed integer programming (MIP) formulation of an unrestricted BRP by extracting valid inequalities from structural properties and proposing a new variable fixation method to solve it. Computational results show that the improved model can be optimally solved much more easily than the original model. Among over five-hundred benchmark instances with height limits, the improved model can solve 12.3% more than the original one. For the instances that can be optimally solved by the latter, the improved model shows six times faster speed than the latter. This work represents a significant advance in this important area.

Machine Learning Guides the Solution of Blocks Relocation Problem in Container Terminals

The blocks relocation problem (BRP) is a well known and important combinatorial optimization problem, in which the initial storage state and retrieval priority of containers are known, and the containers should be picked up in the retrieval order with the goal of minimizing container relocations. This paper studied how machine-learning techniques guide the solution of this Non-deterministic Polynomial problem(NP-hard problem) NP-hard problem. Through our self-developed data generator, we generated initial state stacking matrices and extracted 22 influencing factors for container relocation operations. The supervised learning method and attribution technique were used to verify the relationship between significant container relocated influence features and the number of container relocations using the unrestricted BRP and restricted BRP models. We characterize the potential patterns in the data based on 22 container relocated influence features using four supervised learning models: random forest (RF), extra trees (ET), support vector machine (SVM), and logistic regression (LR). The experimental results demonstrate that RF has a classification accuracy rate of up to 94% on the restricted BRP model. The attribution technique identifies the most sensitive features to the number of container relocations. We organically integrate machine learning into the BRP problem and propose an interactive iterative framework that may provide a novel method for studying the BRP problem.

A survey of optimization methods for Block Relocation and PreMarshalling Problems

Problems of stacking items or goods occur in a plenty of applications, such as container terminals, warehouses, and steel plants. A lot of research has been done in this area in recent years. In this survey, we provide an overview of the Block Relocation Problem (BRP) and the PreMarshalling Problem (PMP) and review optimization methods for these two problems. Due to common properties between these problems, solutions and methods applicable to one problem can often be applied to the other, and vice-versa. We distinguish four categories of optimization methods and propose future directions for each of them.

Solving the Container Relocation Problem by Using a Metaheuristic Genetic Algorithm

Maritime transport is the backbone of international trade of goods. Therefore, seaports are of great importance for maritime transport. Container transport plays an important role in maritime transport and is increasing year by year. Containers transported to a container terminal are stored in container yards side by side and on top of each other, forming blocks. If a container that is not on top of the block has to be retrieved, the containers that are above the required container must be relocated before the required container is retrieved. These additional container relocations, which block the retrieval of the required container, slow down the entire retrieval process. The container relocation problem, also known as the block relocation problem, is an optimization problem that involves finding an optimal sequence of operations for retrieving blocks (containers) from a container yard in a given order, minimizing additional relocations of blocking containers. In this paper, the focus is on the two-dimensional, static, offline and the restricted container relocation problem of real-size yard container bays. A new method for resolving the container relocation problem that uses a genetic algorithm is proposed to minimize the number of relocations within the bay. The method is evaluated on well-known test instances, and the obtained results are compared with the results of various relevant models for resolving the container relocation problem. The results show that the proposed method achieves the best or the second-best result for each test instance within the test set.

An integer programming formulation and iterative scheme algorithm for the block relocation problem

ABSTRACT In this paper, we deal with the unrestricted block relocation problem. We present a new integer programming formulation for solving the problem. The initial formulation is improved by tightening constraints and a pre-processing step to fix several variables. We design a exact iterative scheme algorithm based on a fast heuristic for the integer programming formulation (ISA-FH). Computational results show the effectiveness of the improved formulation and algorithm.

An exact algorithm for the unrestricted container relocation problem with new lower bounds and dominance rules

The container relocation problem, also known as the block(s) relocation problem, is one of the most studied optimization problems in container terminals. The problem aims at minimizing the total number of relocations for retrieving containers from a storage yard according to a specific order. The purpose of this study is to develop an efficient iterative deepening branch-and-bound algorithm for exactly solving one of the most practical variants of the problem, namely the unrestricted container relocation problem with duplicate priorities, which has received less attention in the literature. To improve the search efficiency of the proposed algorithm, we design two new lower bounds that can be computed quickly to incorporate them into the branch-and-bound algorithm. We also present a set of mutually consistent dominance rules to reduce the search space while avoiding over-pruning. The performance of the proposed algorithm is evaluated by extensive computational experiments on three commonly used benchmark datasets. The results show that the proposed algorithm outperforms the state-of-the-art exact algorithm for the unrestricted container relocation problem with distinct priorities, although our algorithm is applicable to a more general variant of the problem. Moreover, it can still provide competitive results for small- and medium-sized instances under a strict time limit of one second in comparison to existing metaheuristic approaches.

On the integration of the parallel stack loading problem with the block relocation problem

The parallel stack loading problem (PSLP) is an NP-hard problem. In this problem, the objective is to optimize assigning a group of arriving items to empty slots of parallel stacks in a storage bay. The PSLP aims to find a bay configuration that minimizes the future retrieval effort of these items. The retrieval effort is generally represented by the number of relocations needed during retrieval. These relocations are obligatory when an item not located at the top of a stack is to be retrieved. The number of relocations for a given bay configuration is minimized by another NP-hard problem, called the block relocation problem (BRP). The simultaneous solution of the PSLP and the BRP is complicated. As an alternative, previous literature studies proposed using a surrogate objective function (SOF) to approximate the number of relocations in the PSLP. This paper proposes two new SOFs which result in bay configurations with a minimized retrieval effort. Also, this paper introduces a new method to represent the retrieval effort. The new method considers the number of empty slots needed for relocations as well as the number of relocations. Extensive computational studies are provided to verify the proposed SOFs, and illustrate that they outperform other SOFs from the literature.

The block relocation problem with appointment scheduling

In many container terminals, containers are piled vertically and horizontally in the terminal yard, limited mainly by the dimensions of the yard crane. Import and export containers are typically stacked separately. An external truck can access the terminal to pick up an import container only after making an appointment reserving a pickup time. To reduce truck waiting time inside the terminal, container pickup appointments are normally scheduled on a time window basis. However, when a truck arrives at the terminal yard at the appointed time, it is common for the target container not to be at the top of its stack, resulting in unproductive relocations to remove all the containers stacked above the target container and thus increasing the truck's waiting time. To minimize the number of relocations, the Block Relocation Problem (BRP) is usually solved independently, without consideration of appointment scheduling. In this paper, we introduce a new optimization problem—the Block Relocation Problem with Appointment Scheduling (BRPAS)—to jointly address the two issues. To solve the problem, two binary IP models are proposed, and examples from the literature are solved to confirm the performance of the two models. The proposed formulations are further extended to cover several operational aspects related to the flexibility of container pickup operations. Results show that the proposed approach can improve container relocation operations at terminal yards by coordinating with appointment scheduling.

An exact approach to the restricted block relocation problem based on a new integer programming formulation

This study addresses the block(s) relocation problem (BRP), also known as the container relocation problem. This problem considers individually retrieving blocks piled up in tiers according to a predetermined order. When the block to be retrieved next is not at the top, we have to relocate the blocks above it because we can access only the topmost blocks. The objective is to retrieve all the blocks with the smallest number of relocations. In this study, a novel exact algorithm is proposed for the restricted BRP, a class of the problem where relocatable blocks are restricted. The proposed algorithm computes lower and upper bounds iteratively by solving the corresponding integer programming problems until the optimality gap is reduced to zero. The novelty of the algorithm lies in the formulations based on complete and truncated relocation sequences of the individual blocks. We examine the effectiveness of the proposed algorithm through computational experiments for benchmark instances from the literature. In particular, we report that, for the first time, all the instances with up to 100 blocks are solved to proven optimality.

Stacking and transporting steel slabs using high-capacity vehicles

Abstract A crucial task of steel plant logistics is the transportation and intermediate storage of semi-finished casting products, so-called steel slabs. We consider a fleet that consists of high-capacity vehicles. The vehicles are used to transport steel slabs within the steel plant, i.e., between facilities and distinct areas of the slab yard, and they can carry out stacking operations autonomously. The slab yard stores a majority of all steel slabs. It is organized in rows that function as a two-dimensional stacking area. Each row consists of multiple stacks built up by steel slabs that are located on top of each other. Retrieving steel slabs from stacks amounts to solving an extended block relocation problem (BRP). We study a combined approach for solving both the routing of steels slabs within the plant and the stacking of steel slabs in storage as part of their retrieval during a vehicle’s pickup operation.

A note on “An exact algorithm for the blocks relocation problem with new lower bounds”

This paper is a note on [Quispe, K. E. Y., Lintzmayer, C. N., & Xavier, E. C. (2018).An exact algorithm for the blocks relocation problem with new lower bounds.Computers &Operations Research, 99, 206–217]. Quispe et al. (2018) presented a new lower bound called LB-LIS for the blocks relocation problem. In this note, we show that the algorithm description of LB-LIS in the referred paper is incomplete. In addition, we propose a faster algorithm for computing this lower bound more efficiently. Computational experiments on a commonly used dataset reveal that the proposed algorithm uses on average 44.48% less time than the original LB-LIS implementation for the instances tested.

A branch-and-cut algorithm for the restricted Block Relocation Problem

We consider the Block Relocation Problem, that has a crucial role in the logistics of containers. It consists of minimizing the number of container relocations within a container bay/yard. Since the number of containers shipped worldwide grew dramatically in the last years, the problem has been widely investigated. Here we propose an exact algorithm for the restricted version of the Block Relocation Problem, based on a new integer linear programming formulation. We compare such new approach with the state-of-art exact methods. The computational results prove its effectiveness and show that it outperforms all the previously proposed procedures, in almost all the considered instances.

A Study on the Block Relocation Problem: Lower Bound Derivations and Strong Formulations

The block relocation problem (BRP) is a fundamental operational issue in modern warehouse and yard management, which, however, is very challenging to solve. In this paper, to advance our understanding on this problem and to provide a substantial assistance to practice, we (i) introduce a classification scheme and present a rather comprehensive review on all 16 BRP variants; (ii) develop a general framework to derive lower bounds on the number of necessary relocations and demonstrate its connection to existing lower bounds of the unrestricted BRP variants; (iii) propose and employ a couple of new critical substructures concepts to analyze the BRP and obtain a lower bound that dominates all existing ones; (iv) build a new and strong mixed integer programming (MIP) formulation that is adaptable to compute 8 BRP variants, and design a novel MIP-formulation-based iterative procedure to compute exact BRP solutions; (v) extend the MIP formulation to address four typical industrial considerations. Computational results on standard test instances show that the new lower bound is significantly stronger, and our new MIP computational methods have superior performances over a state-of-the-art formulation.

Optimizing the Stowage Planning and Block Relocation Problem in Inland Container Shipping

The stowage planning and block relocation problem (SPBRP) consider the relations between stowage planning and block relocation comprehensively, in which the retrieval sequence of containers in yard and the stowage plan of a ship are concerned. In this paper, an integer programming formulation called SPBRP-I is presented for the proposed problem in inland container liner shipping to minimize the total number of relocations in yard and re-handles in ship. To deal with the utilization preference in inland shipping, the minimization of ship stack occupancy number is introduced into SPBRP-I to develop a new model called SPBRP-II. In view of the complexity of problem-solving, a heuristic algorithm (HA) based on priority sorting, retrieval and local search strategies is proposed to achieve the efficient optimization. The algorithm consists of three parts including the yard container retrieving, yard container relocation and ship stowage planning. Finally, the container liner shipping on the Yangtze River is chosen with some typical ships for the case study. Numerical results show that SPBRP-II performs better than the original SPBRP-I, and it's more suitable for solving the small-sized cases. Compared with the models, the algorithm with retrieval strategy RS1 (HA_RS1) can achieve the efficient problem solving with high-quantity solutions and very short computational time.

An Integer Programming Model and Variable Fixation for The Block Relocation Problem

In this paper we deal with the unrestricted Block Relocation Problem. We present a new integer integer programming model for solving the problem. The initial model formulation is improved by tightening constraints and a pre-processing step to fix several variables. Computational results show the efficiency of the improved model for small and medium sized instances.

Minimizing the operating cost of block retrieval operations in stacking facilities

This paper addresses the Blocks Relocation Problem with Operating Costs, whose main objective is to retrieve a set of blocks from a stacking facility while minimizing the operating cost. An integer programming model and a deterministic algorithm are developed to solve the problem from an exact standpoint. Both approaches are able to solve the problem optimally only for small size problem scenarios, requiring large amount of computational time and memory in medium and large size problem instances. On the other hand, a heuristic algorithm based on A∗ is also proposed with the goal of reducing considerably the computational resources, allowing to solve large problem instances. The computational results disclose this algorithm generates high-quality solutions in reasonable computational times.

An exact algorithm for the block relocation problem with a stowage plan

In this paper we address an exact algorithm for the block relocation problem with a stowage plan. This problem is an extension of the container (block) relocation problem that aims at minimizing the total number of relocations required for retrieving containers piled up in a container yard. The difference is that a stowage plan in a vessel is given in advance and it is taken into consideration when retrieving containers. More specifically, the retrieval order of containers should be feasible with respect to a given stowage plan. We construct a branch-and-bound algorithm with iterative deepening for unrestricted and restricted variants of this problem. To this end, we propose three lower bounds on the total number of relocations. We also extend dominance rules for the container relocation problem, in order to restrict the search space and improve the search efficiency. The effectiveness of the proposed algorithm is examined by numerical experiments for benchmark instances from the literature.