Efficient Algorithm for Generating Order Packing Recommendations (original) (raw)

Decision Support For Packing In Warehouses

Lecture Notes in Computer Science

Packing problems deal with loading of a set of items (ob-jects) into a set of boxes (containers) in order to optimize a performance criterion under various constraints. With the advance of RFID technologies and investments in IT infrastructures companies now have access to the necessary data that can be utilized in cost reduction of packing processes. Therefore bin packing and container loading problems are becoming more popular in recent years. In this research we propose a beam search algorithm to solve a packing problem that we encountered in a real world project. The 3D-MBSBPP (Multiple Bin Sized Bin Packing Problem) that we present and solve has not been analyzed in literature before, to the best of our knowledge. We present the performance of our proposed beam search algorithm in terms of both cost and computational time in comparison to a greedy algorithm and a tree search enumeration algorithm.

3-RECTANGULATIONS: An Algorithm to Generate Box Packings

Environment and Planning B: Planning and Design, 1979

3-rectangulations are spatial representatives of assemblies of boxes into a box. Algorithms to generate various classes of 3-rectangulations are developed. The method is extended to specify the generation of higher-dimensional <2-rectangulations, d > 4.

Heuristics for Offline Rectangular Packing Problems

Packing problems are common in industry and there is a large body of literature on the subject. Two packing problems are considered in this dissertation: the strip packing problem and the bin packing problem. The aim in both problems is to pack a specified set of small items, the dimensions of which are all known prior to packing (hence giving rise to an offline problem), into larger objects, called bins. The strip packing problem requires packing these items into a single bin, one dimension of which is unbounded (the bin is therefore referred to as a strip). In two dimensions the width of the strip is typically specified and the aim is to pack all the items into the strip, without overlapping, so that the resulting packing height is a minimum. The bin packing problem, on the other hand, is the problem of packing the items into a specified set of bins (all of whose dimensions are bounded) so that the wasted space remaining in the bins (which contain items) is a minimum. The bins may all have the same dimensions (in which case the problem is known as the single bin size bin packing problem), or may have different dimensions, in which case the problem is called the multiple bin size bin packing problem (MBSBPP). In two dimensions the wasted space is the sum total of areas of the bins (containing items) not covered by items. Many solution methodologies have been developed for above-mentioned problems, but the scope of the solution methodologies considered in this dissertation is restricted to heuristics. Packing heuristics follow a fixed set of rules to pack items in such a manner as to find good, feasible (but not necessarily optimal) solutions to the strip and bin packing problems within as short a time span as possible. Three types of heuristics are considered in this dissertation: (i) those that pack items into levels (the heights of which are determined by the heights of the tallest items in these levels) in such a manner that all items are packed along the bottom of the level, (ii) those that pack items into levels in such a manner that items may be packed anywhere between the horizontal boundaries that define the levels, and (iii) those heuristics that do not restrict the packing of items to levels. These three classes of heuristics are known as level algorithms, pseudolevel algorithms and plane algorithms, respectively. A computational approach is adopted in this dissertation in order to evaluate the performances of 218 new heuristics for the strip packing problem in relation to 34 known heuristics from the literature with respect to a set of 1170 benchmark problem instances. It is found that the new level-packing heuristics do not yield significantly better solutions than the known heuristics, but several of the newly proposed pseudolevel heuristics do yield significantly better results than the best of the known pseudolevel heuristics in terms of both packing densities achieved and computation times expended. During the evaluation of the plane algorithms two classes of heuristics were identified for packing problems, namely sorting-dependent and sorting-independent algorithms. Two new sorting techniques are proposed for the sorting-independent algorithms and one of them yields the best-performing heuristic overall. A new heuristic approach for the MBSBPP is also proposed, which may be combined with level and pseudolevel algorithms for the strip packing problem in order to find solutions to the problem very rapidly. The best-performing plane-packing heuristic is modified to pack items into the largest bins first, followed by an attempted repacking of the items in those bins into smaller bins with the aim of further minimising wasted space. It is found that the resulting plane-packing algorithm yields the best results in terms of time and packing density, but that the solution differences between pseudolevel algorithms are not as marked for the MBSBPP as for the strip packing problem.

The multiple container packing problem

ACM SIGAPP Applied Computing Review, 1999

This paper presents a genetic algorithm (GA) approach to the problem of choosing C disjoint subsets of n items to be packed into distinct containers, such that the total value of the selected items is ma3rlmi=ed, without exceeding the capacity of each of the containers. This so-called multiple container packing problem (MCPP) has applications in naval as well as financial management. It is a hard combinatorial optimization problem comprising similarities to the knapsack problem and the bin packing problem. A novel technique for encoding MCPP solutions is used within the GA: The genotype is a vector of numerical weights associated with the items of the problem. The corresponding phenotype is obtained by temporarily modifying the original problem according to these weights and applying a greedy decoding heuristic for the MCPP to the new problem. This solution is then evaluated using the original problem data again. Two different techniques for biasing the original problem and four decoding heuristics are discussed. They were tested in a weight-coded steady-state GA on a variety of MCPP instances. One biasing technique and one decoding heuristic turned out to be clearly more effective than the others, and the GA using them found solutions of signiilcantly higher quality than direct-encoded and order-based GAs from a previous work.

3-D Container Packing Heuristics

Applied Intelligence, 2005

In this paper, we study the 3-D container packing problem. The problem is divided into box selection, space selection, box orientation and new space generation sub-problems. As a first step, a basic heuristic is devised. From results using this heuristic, problems are categorized as homogeneous and heterogeneous. Two augmenting heuristics are then formulated to deal with these categories. They are complementary in their capabilities in dealing with a range of practical problems, and in terms of their computational consumption. Results using our algorithms exceed the benchmark by 4.5% on average.

Guidance and Visualization of Optimized Packing Solutions

Journal of Information Processing

Packing optimization is a challenging and time-consuming task for a number of industry and logistics applications. Efficient packing can reduce the cost of storage and shipping and also guarantee that damage will not occur during shipping. To help address this problem, we propose a spatial augmented reality-based support system for assisting workers with packing optimization. Our packing support system first uses an RGB-D camera to acquire color and depth information of the items to be packed and the destination container. Then, object segmentation and dimension estimation are simultaneously carried out, and the position and orientation of packing items inside the container are calculated using a bin-packing algorithm. Finally, the optimized packing instructions are projected onto the user's work area. We then developed and tested two user interfaces (UI) for visualizing instructions called Rotation and Object Movement. Experimental results showed that both methods help reduce packing time up to 57.89% in Rotation and 55.63% in Object Movement, compared to a non-UI method.

TS2PACK: A two-level tabu search for the three-dimensional bin packing problem

European Journal of Operational Research, 2009

Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins. We present a two-level tabu search for this problem. The first-level aims to reduce the number of bins. The second optimizes the packing of the bins. This latter procedure is based on the Interval Graph representation of the packing, proposed by Fekete and Schepers, which reduces the size of the search space. We also introduce a general method to increase the size of the associated neighborhoods, and thus the quality of the search, without increasing the overall complexity of the algorithm. Extensive computational results on benchmark problem instances show the effectiveness of the proposed approach, obtaining better results compared to the existing ones.

An efficient metaheuristic for multi-dimensional multi-container packing

2011

In this paper, we introduce GASP-Greedy Adaptive Search Procedure, a metaheuristic able to efficiently address two and three-dimensional multiple container packing problems. GASP combines the simplicity of greedy algorithms with learning mechanisms aimed to guide the overall method towards good solutions. Extensive experiments indicate that GASP attains near-optimal solutions in very short computational times, and improves state-of-the-art results in comparable computational times. Keywords. Three-dimensional packing, two-dimensional packing, greedy adaptive search procedure. Acknowledgements. Funding for this project has been provided by the Italian Ministry of University and Research, under the 2007 PRIN Project "Optimization of Distribution Logistics" and by the Natural Sciences and Engineering Research Council of Canada (NSERC), through its Industrial Research Chair and Discovery Grants programs. Results and views expressed in this publication are the sole responsibility of the authors and do not necessarily reflect those of CIRRELT. Les résultats et opinions contenus dans cette publication ne reflètent pas nécessairement la position du CIRRELT et n'engagent pas sa responsabilité.

Effective methods for a container packing operation

Mathematical and Computer Modelling, 1997

China started its economic reform, many Hong Kong companies have moved to China. While reducing labor costs, the move has also increased transportation costs. In some cases, transportation cost can reach 30% of total product cost. This work is based on the cargo loading operation of a Hong Kong manufacturer that uses standard containers to ship its products from China, and then onto its customers abroad. Its cargo loading problem is complicated by certain operational constraints. We present several heuristics to solve the problem. Computational tests on the company's actual data indicate an annual saving of over HK$3,000,000, which corresponds to 10.58% of the transportation cost. More importantly, our methods can change the management of the loading operation from the current experience-based system into a systematic, accurate, reliable, and efficient system.

Search Strategies for Rectangle Packing

Lecture Notes in Computer Science

Rectangle (square) packing problems involve packing all squares with sizes 1 × 1 to n × n into the minimum area enclosing rectangle (respectively, square). Rectangle packing is a variant of an important problem in a variety of real-world settings. For example, in electronic design automation, the packing of blocks into a circuit layout is essentially a rectangle packing problem. Rectangle packing problems are also motivated by applications in scheduling. In this paper we demonstrate that an "off-the-shelf" constraint programming system, SICStus Prolog, outperforms recently developed ad-hoc approaches by over three orders of magnitude. We adopt the standard CP model for these problems, and study a variety of search strategies and improvements to solve large rectangle packing problems. As well as being over three orders of magnitude faster than the current state-of-the-art, we close eight open problems: two rectangle packing problems and six square packing problems. Our approach has other advantages over the state-of-the-art, such as being trivially modifiable to exploit multi-core computing platforms to parallelise search, although we use only a single-core in our experiments. We argue that rectangle packing is a domain where constraint programming significantly outperforms hand-crafted ad-hoc systems developed for this problem. This provides the CP community with a convincing success story.