An effective placement method for the single container loading problem

© 2016 Elsevier Ltd. All rights reserved. This study investigates a three-dimensional single container loading problem, which aims to pack a given set of unequal-size rectangular boxes into a single container such that the length of the occupied space in the container is minimized. Motivated by the practical logistics instances in literature, the problem under study is formulated as a zero-one mixed integer linear programming model. Due to the NP-hardness of the studied problem, a simple but effective loading placement heuristic is proposed for solving large-size instances. The experimental results demonstrate that the developed heuristic is capable of solving the instances with more than two hundred boxes and more efficient than the state-of-the-art mixed integer linear program and existing heuristic methods

Sustainable Warehouse Location Selection in Humanitarian Supply Chain: Multi-Criteria Decision-Making Approach

The frequency of catastrophic natural disasters is rising, and much emphasis is being given to the Humanitarian Supply chain (HSC). The main goal of relief efforts is to get enough emergency supplies to the area hit by the disaster as quickly as possible. The decision of where to locate warehouses that will store relief supplies presents a significant obstacle for humanitarian relief organizations as they work to enhance their capacity for providing aid and their rescue plan. A non-optimal location could make the search and rescue efforts harder. More importantly, it has been seen that when these kinds of geographical sites are evaluated, social and environmental issues are not considered. This research paper aims to make humanitarian networks more accountable by determining the ideal warehouse site and considering both traditional and sustainable factors. A framework for selecting warehouses to keep relief goods was devised using the Multi-Criteria Decision Making (MCDM) approach. Best-Worst and TOPSIS (“Technique for Order Performance by Similarity to the Ideal Solution”) methods were used to rank the potential locations based on Cost, Logistics, Environmental, and Social Criteria. A research study has been done in the State of West Bengal (District Arambagh)

Container Loading Problems: A State-of-the-Art Review

Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.In this paper, a review of the state-of-the-art in the field of container loading will be given. We will identify factors which - from a practical point of view - need to be considered when dealing with container loading problems and we will analyze whether and how these factors are represented in methods for the solution of such problems. Modeling approaches, as well as exact and heuristic algorithms will be reviewed. This will allow for assessing the practical relevance of the research which has been carried out in the field. We will also mention several issues which have not been dealt with satisfactorily so far and give an outlook on future research opportunities

High Multiplicity Strip Packing

In the two-dimensional high multiplicity strip packing problem (HMSPP), we are given k distinct rectangle types, where each rectangle type Ti has ni rectangles each with width 0 \u3c wi and height 0 \u3c hi The goal is to pack these rectangles into a strip of width 1, without rotating or overlapping the rectangles, such that the total height of the packing is minimized. Let OPT(I) be the optimal height of HMSPP on input I. In this thesis, we consider HMSPP for the case when k = 3 and present an OPT(I) + 5/3 polynomial time approximation algorithm for it. Additionally, we consider HMSPP for the case when k = 4 and present an OPT(I) + 5/2 polynomial time approximation algorithm for it

Three-Dimensional Capacitated Vehicle Routing Problems with Loading Constraints

City logistics planning involves organizing the movement of goods in urban areas carried out by logistics operators. The loading and routing of goods are critical components of these operations. Efficient utilization of vehicle space and limiting number of empty vehicle movements can strongly impact the nuisances created by goods delivery vehicles in urban areas. We consider an integrated problem of routing and loading known as the three-dimensional loading capacitated vehicle routing problem (3L-CVRP). 3L-CVRP consists of finding feasible routes with the minimum total travel cost while satisfying customers’ demands expressed in terms of cuboid and weighted items. Practical constraints related to connectivity, stability, fragility, and LIFO are considered as parts of the problem. We address the problem in two stages. Firstly, we address the three-dimensional (3D) loading problem followed by 3L-CVRP. The main objective of a 3D loading problem without routing aspect is finding the best way of packing 3D items into vehicles or containers to increase the loading factor with the purpose of minimizing empty vehicle movements. We present the general linear programming model to the pure three-dimensional vehicle loading problem and solve it by CPLEX. To deal with large-sized instances, Column Generation (CG) technique is applied. The designed method in this work outperforms the best existing techniques in the literature.   The 3DVLP with allocation and capacity constraints, called 3DVLP-AC, is also considered. For the 3DVLP-AC, CPLEX could handle moderate-sized instances with up to 40 customers. To deal with large-sized instances, a Tabu Search (TS) heuristic algorithm is developed. There are no solution methods or lower bounds (LBs) for the 3DVLP-AC existent in the literature by which to evaluate the TS results. Therefore, we evaluate our TS with the CPLEX results for small instances. 3L-CVRP is addressed by using CG technique. To generate new columns, the pricing problem that is part of CG is solved by using two approaches: 1-by means of shortest path problem with resource constraints (ESPPRC) and loading problem, and 2-a heuristic pricing method (HP). CG using HP with a simple scheme can attain solutions competitive with the efficient TS algorithms described in the literature

Models and Solution Methods for the Pallet Loading Problem

The three-dimensional bin packing problem (3DBPP) seeks to find the minimum number of bins to pack a finite number of rectangular boxes. It has a wide array of applications, ranging from airline cargo transportation to warehousing. Its practical extension, the distributor's pallet loading problem (DPLP), requires the pallets to be stable, packable, and adhering to several industry requirements such as packing sequences and weight limits. Despite being studied extensively in the optimization literature, the 3DBPP is still one of the most difficult problems to solve. Currently, medium to large size instances are only solved heuristically and remain out of reach of exact methods. This also applies to the DPLP, as the addition of practical constraints further complicates the proposed models. A recent survey identified the scarcity of exact solution methods that are capable of handling practical versions of the problem and the lack of a realistic benchmark data set as major research gaps. In this thesis, firstly, we propose a novel formulation and an exact solution approach based on column generation for the 3DBPP, where the pricing subproblem is a two-dimensional layer generation problem. Layers are highly desirable in practical packings as they are easily packable and can accommodate important practical constraints such as item support, family groupings, isle friendliness, and load bearing. Being key to the success of the column generation approach, the pricing subproblem is solved optimally as well as heuristically, and is enhanced using item grouping, item replacement, layer reorganization, and layer spacing. We also embed the column generation approach within a branch-and-price framework. We conduct extensive computational experiments and compare against existing approaches. The proposed approach outperforms the best performing algorithm in the literature \boldred{in most instances} and succeeds to solve practical size instances in very reasonable computational times. Secondly, we extend the column generation scheme to incorporate practical constraints set by the warehousing industry. We introduce a nonlinear layer spacing model to improve the stability of the planned pallets, which we then reformulate as an SOCP. In order to calculate the weight distribution within pallets, we introduce a new graph representation for placed items. Finally, we propose construction and improvement heuristics to tackle each practical constraint, such as vertical support, different item shapes, planogram sequencing, load bearing, and weight limits. We conduct extensive computational experiments to demonstrate the good performance of the proposed methodology, and provide results for future benchmarking. To the best of our knowledge, this is the first approach to fully solve the DPLP. Computational experiments show that the proposed approach succeeds in solving industry size instances in record computational times and achieves high quality solutions that account for all practical constraints. Finally, we propose realistic benchmark instances by designing and training an instance generator using industry data. We apply clustering and curve fitting techniques to 342 industry instances with 166,406 items to obtain the distributions for item volumes, dimensions, and frequencies. We separate the instances into several classes and categories using $k$-clustering and generate multiple instances with different sizes. We, then, extend the generator to incorporate practical features such as weight, load capacity, shape, planogram sequencing, and reduced edge support

Üç boyutlu palet yükleme probleminin karışık tam sayılı programlama (MILP) ve hibrit genetik algoritma ile çözümü

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Bu tez çalışmasında, konteyner yükleme problemlerinin (KYP) bir çeşidi olan üç boyutlu palet yükleme problemi (3B-PYP), problemin doğası gereği göz önüne alınması gereken kısıtların yanı sıra, kontrollü döndürme kısıtı, kırılganlık kısıtı, yüke dayanım kısıtı ve bağlantılı nesnelerin bir arada olması kısıtı gibi ek yükleme kısıtları altında ele alınmıştır. Ele alınan 3B-PYP'nin optimum çözümü için bir karışık tam sayılı doğrusal programlama (MILP) modeli geliştirilmiştir. Geliştirilen model, küçük ölçekli 3B-PYP'yi optimize etmek için kullanılabilmekte fakat müşteri sayısı, nesne sayısı ve palet yükleme oranı gibi problem parametrelerindeki artışlara bağlı olarak büyük ölçekli gerçek hayat problemlerinin optimizasyonu için kabul edilebilir bir sürede cevap verememektedir. Bu sebeple büyük ölçekli problemlerin çözümü için biri yığın oluşturma tabanlı, diğeri yatay katman oluşturma tabanlı olmak üzere iki farklı sezgisel yaklaşım ile hibritlenmiş bir hibrit genetik algoritma (HGA) geliştirilmiştir. Önerilen HGA'daki yığın oluşturma tabanlı sezgisel yaklaşım, yüklenecek olan nesnelerden en az iki boyutu birbirine eşit olanları genetik algoritma (GA) arama yapısını kullanarak belirler ve bu nesneleri birbiriyle birleştirerek, iki nesneyi de kapsayan yeni bir nesne olarak tanımlar. Bu şekilde yerleştirilecek nesne sayısının azaltılması sağlanmış olur. Birleştirme işlemleri yapılırken GA'daki kromozom uzunlukları bozulabilir. Bu sebepten dolayı literatürdeki mevcut çaprazlama operatörleri kullanılamamaktadır ve akıllı dinamik çaprazlama operatörü (A-DÇO) adı verilen bir çaprazlama operatörü geliştirilmiştir. Önerilen HGA'daki bir diğer sezgisel algoritma da literatürde var olan en dip alt sol doldurma (DASD) algoritmasıdır. Bu algoritmanın adımları sayesinde tüm nesnelerin paletlere nihai yüklemesi yapılır ve tüm nesnelerin paletler üzerindeki koordinatları belirlenir. Önerilen HGA'nın klasik DASD ile test problemleri üzerinde karşılaştırılması yapılmış ve daha iyi çözümler verdiği istatistiksel olarak gösterilmiştir. Ayrıca önerilen HGA, literatürde var olan bir parçacık sürü eniyileme algoritması (PSO) ve HGA-L adı verilen bir başka HGA ile de test problemleri üzerinde karşılaştırılmıştır. Önerilen HGA'nın bu algoritmalardan da daha iyi sonuçlar verdiği istatistiksel olarak gösterilmiştir. Sonuç olarak, ele alınan 3B-PYP için önerilen HGA, daha iyi sonuçlar vermekte ve özellikle gerçek hayatta robot kolları vasıtası yapılan otomatik paletleme operasyonları için kullanılması önerilmektedir.In this thesis, the three-dimensional pallet loading problem (3D-PLP), which is a kind of container loading problems (CLP), was studied under the constraints as rotation, fragility, load-bearing strength, relative positioning as well as the constraints that should be considered due to the nature of the problem. A mixed integer linear programming (MILP) model was developed for the optimal solution of the studied 3D-PLP. The developed model can be used to optimize small-scale 3D-PLP. However, due to increase in some problem parameters as the number of customers, the number of objects and the pallet loading rate, it cannot be solved in an acceptable time for large-scale real-life problems. For this reason, a new hybrid genetic algorithm (HGA) was developed for solving large-scale problems. It was hybridized with two different heuristic approaches, one of them is based on a stack-building approach and the other one is based on a layer building approach. The stack-building approach determines the objects which have at least two equal dimensions by searching structure of genetic algorithm (GA). This operation reduces the number of objects to be placed. The chromosome lengths in the GA may change because of the combining operation. For this reason, existing crossover operators in the literature cannot be employed. And a crossover operator called the intelligent dynamic crossover operator (I-DCO) was developed. Another heuristic approach in the proposed HGA is deepest bottom left fill (DBLF) approach which is available in the literature. Under favor of the steps of DBLF, all objects can be loaded to the pallets and the coordinates of all objects on the pallets are determined. The proposed HGA was compared with classical DBLF on test problems and it was shown that the proposed HGA produced better solutions statistically. In addition, the proposed HGA was compared with two existing meta-heuristic algorithms on test problems. It was shown that the proposed HGA achieved better results than these algorithms. As a result, the proposed HGA for the 3D-PLP yielded much better results

Algorithms and data structures for three-dimensional packing

Cutting and packing problems are increasingly prevalent in industry. A well utilised freight vehicle will save a business money when delivering goods, as well as reducing the environmental impact, when compared to sending out two lesser-utilised freight vehicles. A cutting machine that generates less wasted material will have a similar effect. Industry reliance on automating these processes and improving productivity is increasing year-on-year. This thesis presents a number of methods for generating high quality solutions for these cutting and packing challenges. It does so in a number of ways. A fast, efficient framework for heuristically generating solutions to large problems is presented, and a method of incrementally improving these solutions over time is implemented and shown to produce even higher packing utilisations. The results from these findings provide the best known results for 28 out of 35 problems from the literature. This framework is analysed and its effectiveness shown over a number of datasets, along with a discussion of its theoretical suitability for higher-dimensional packing problems. A way of automatically generating new heuristics for this framework that can be problem specific, and therefore highly tuned to a given dataset, is then demonstrated and shown to perform well when compared to the expert-designed packing heuristics. Finally some mathematical models which can guarantee the optimality of packings for small datasets are given, and the (in)effectiveness of these techniques discussed. The models are then strengthened and a novel model presented which can handle much larger problems under certain conditions. The thesis finishes with a discussion about the applicability of the different approaches taken to the real-world problems that motivate them