A Grasp Algorithm For The Container Loading Problem With Multi-Drop Constraints

This paper examines various container loading issues. In addition to the traditional geometric constraints of packing problems, we add conditions in practical matters called multi-drop constraints. Multi-drop constraints require that all relevant boxes are available at each drop-off point. First, we review the various types of multi-drop limitations functional in literature. Next, we present a GRASP algorithm to solve multi-drop constraints. It also includes realistic constraints like full support for the boxes and load-bearing force. Computational results validate the proposed algorithm. It also outperforms existing methods for multi-drop conditions.

Introduction

One container loading problem (CLP) is one of the most challenging problems in packing and cutting. This is a three-dimensional optimization challenge in which we must pack a collection of rectangular objects (boxes) into a large rectangular container. The packing must meet set criteria while meeting set constraints. This is an essential part of any supply chain as it must be solved daily in many different situations. These include varying types and characteristics of goods, the number of containers or trucks used, and specific loading restrictions for each company. It is essential to load these containers efficiently. This is because it minimizes the amount of space.

Therefore, it is unsurprising that there have been many solutions to this problem in the scientific literature over the past twenty years. However, academic research has primarily focused on the fundamental problem of maximizing volume. This is subject to geometric constraints, which prevent boxes from being too large or overlapping. Bischoff & Ratcliff warned us in 1995 that various essential factors in practical situations did not get enough attention in the OR literature. Twelve applicable conditions must be considered to solve practical problems that require loading plans to be possible. These experimental conditions have been included in the fundamental geometric problem. Nevertheless, there has been extensive research. Bortfeldt & Wascher recently published a comprehensive review of the container loading issue and its practical constraints.

Assigning Realistic Constraints During The Basic Container-Loading Problem

The fundamental Container Loading Problem is the problem of placing boxes in a container within the constraints of geometry. Packages cannot overlap or exceed the container's dimensions. If the boxes are weakly homogeneous, the container loading problem could be classified as either a three-dimensional rectangular single significant item placement problem (3D SLOPP) or a single-knapsack problem (3D SKP) if they are strongly heterogeneous. The CLP can be transformed into the NP-hard, one-dimensional knapsack issue. Unfortunately, there are not many algorithms that can solve this problem. There are, however, many metaheuristic and heuristic methods that pack boxes into containers. These approaches have been classified by Pisinger, Fanslau & Bortfeldt as follows:

Approach To Wall-Building

George & Robinson introduced the wall-building method. It fills the container with a series of vertical layers (walls) that run the length of the container. 

Stack-Building Approach

Gilmore & Gomory's stack-building method packs boxes into stacks placed on the container's floor by solving a 2-dimensional packing problem. Bischoff & Ratcliff use this method in their greedy algorithm. Gehring & Bortfeldt and Gehring & Bortfeldt also use it. Hifi uses the tree-search method.

Approach To Horizontal Layer Building

To cover the maximum area of the container, horizontal layers are applied from the bottom to the top. This is how Bischoff & Ratcliff used their greedy algorithm. 

Block-Building Is An Option

Blocks are placed in the container. They usually consist of boxes of the same kind, but some authors consider using blocks that combine different types of packages. Many authors have used this approach in many different ways. Bortfeldt et al. have used this approach in the Tabu Search algorithm. Eley has used the tree-search. Mack et al. also used the Simulated Annealing/Tabu Search method. Parreno et al. also used the GRASP algorithm. Parreno et al. use the hybrid GRASP/VNS.

Guillotine Cutting Method

This method is based upon a slicing-tree representation of a packing scheme. The branches represent the guillotine division of the container regions into smaller portions. Whereas the leaf nodes correspond with the boxes, the leaf nodes correspond with the containers. This is the basis of Morabito & Arenales' graph-search technique.

Conclusion

However, packing plans must be able to work in real situations. Many authors have added realistic constraints to the problem in recent years. However, more work is needed. We review the significant contributions to the literature following the survey by Bortfeldt & Wascher.