A Faster Branch-and-Bound Algorithm for the Block Relocation Problem

Abstract

The block relocation problem, which is also known as the container relocation problem, is an optimization problem to find an optimal sequence of operations for retrieving blocks (containers) from a container yard in a given order. The objective function to be minimized is the number of necessary relocations. In this study, we propose an efficient exact algorithm for two variants of the block relocation problem, those with distinct and duplicate retrieval priorities. In the former problem, the retrieval order of blocks is uniquely provided, whereas in the latter problem, it is given only among groups of blocks. The primary contribution of this study is a tighter lower bound of the number of relocations than existing ones. This enables us to construct a faster branch-and-bound algorithm. Its effectiveness is demonstrated by extensive numerical experiments. Note to Practitioners-A container terminal plays an important role in logistics chains by offering a temporary storage location for containers. Containers transported to a container terminal by vessels, trucks, or trains are stored in container yards. They are piled up vertically to form several stacks. A gantry crane is commonly used to move containers in a container yard, which can access only the topmost containers.When the container that we want to retrieve next from the yard is not on the top of a stack, those stacked above it should be relocated to other stacks. The reduction of such undesirable relocation operations is crucial in container operational decisions because the throughput of cranes is one of the key factors that affect the overall efficiency of container terminals. The algorithm proposed in this paper enables us to obtain an optimal relocation plan that minimizes the number of required relocations in a shorter computation time. When the number of stacks is not large, we can solve the problem to optimality without resorting to heuristic or metaheuristic approaches that only search for near-optimal solutions. Index Terms-Block relocation problem, branch-and-bound algorithm, container terminal, lower bound.Manuscript

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

“…All these features provide a strong basis for future research using this approach. Finally, our formulation outperforms in terms of computation time all previous mathematical formulation and most other exact methods, except the B&B approach from Tanaka and Takii (2016).…”

“…Future research could include the use of combinatorial lower bounds (from Zhu et al (2012) or Tanaka and Takii (2016)) to increase the efficiency of this formulation. Another direction could be the application of other typical techniques such as branch-and-cut or branch-and-price to this formulation.…”

“…This paper focuses on finding optimal solutions for the CRP so we restrict the rest of the review to exact approaches. There are several exact methods worth mentioning such as algorithms based on A * (Zhu et al (2012), Borjian et al (2015), Tanaka and Takii (2016)), branch-and-bound (B&B) approaches ( Ünlüyurt and Aydın (2012), Expósito-Izquierdo et al (2015)) and the abstraction method (Ku and Arthanari (2016a)).…”

“…López-Plata et al (2017) propose a binary IP to minimize waiting times. Priorities could also be given among groups of blocks, and Zhu et al (2012) and Tanaka and Takii (2016) consider B&B approaches for this case. Ku and Arthanari (2016b) and Galle et al (2017) study the stochastic version of the CRP, while de Melo da Silva et al ( 2017) introduces another variant of the CRP called the Block Retrieval problem.…”

Neurofuzzy c-Means Network-Based SCARA Robot for Head Gimbal Assembly (HGA) Circuit Inspection

“…In [22], branch and bound (BNB) was used for cyclic scheduling of timed Petri nets (TPN) based on the manufacturing systems. The speed of solving the block relocation problem [23] was improved by using the branch and bound algorithm. The concept is to minimize the number of necessary relocations; however, it still requires the future work to support the relaxed constraint.…”