Solving Pallet loading Problem with Real-World Constraints

Efficient cargo packing and transport unit stacking play a vital role in enhancing logistics efficiency and reducing costs in the field of logistics. This article focuses on the challenging problem of loading transport units onto pallets, which belongs to the class of NP-hard problems. We propose a novel method for solving the pallet loading problem using a branch and bound algorithm, where there is a loading order of transport units. The derived algorithm considers only a heuristically favourable subset of possible positions of the transport units, which has a positive effect on computability. Furthermore, it is ensured that the pallet configuration meets real-world constraints, such as the stability of the position of transport units under the influence of transport inertial forces and gravity.Comment: 8 pages, 1 figure, project report pape

Optimization Approach of the Vehicle Routing Problem with Packing Constraints Using Genetic Algorithm

Vehicle Routing Problem is an issue in item delivery from depot to its customers using several vehicles which have limited capacity with a purpose to minimize transportation cost. The packing constraints exist because the vehicles which are usually used in item delivery have rectangular-box shaped container. Also, the items are commonly in shape of rectangular-box. Therefore, packing or loading method is needed so that containers could load all of the items without causing damage and could ease unloading process. The purpose of this final project is to develop a model and algorithm using metaheuristics method, especially genetics algorithm in order to minimize total delivery distance. A hybrid genetics algorithm and bottom-left fill algorithm also take place to solve the packing process. This algorithm delivered average solution 0.08% worse than ant colony optimization, but had 2.93% better solution than tabu search

A Vehicle Routing Problem with Time Windows Subject to the Constraint of Vehicles and Good’s Dimensions

A vehicle routing problem (VRP) can be defined as a problem of finding the optimal route with the goal to minimize the travel distance, time, and cost used in a distribution process. A vehicle routing problem with time windows also known as a Time Window Priority Model (TWPM) prioritizes time windows in the mathematical modelling so that vehicles would not delay at any point during the distribution process. There exist few literatures discussing a TWPM subject to carrying capacity. They only consider the volume of vehicle container and the volume of items being carried, arbitrary using 90% of the vehicle’s capacity which causes a large unused capacity. The utilization of capacity which is defined as the ratio the actual weight of the items being transported to the maximum weight of the total items with full capacity, is an important factor for an efficient transportation.  We believe that the utilization of the vehicle’s capacity can be increased when taking into account the actual dimensions of goods, such as their lengths, widths, and heights, as well as the dimensions of the vehicle’s containers. In this study, we consider a 3-dimensional loading constraints i.e. the length, width, and height of both items and vehicles. Based on the results of the study, it can be concluded that taking into account the actual dimensions of items and containers in the capacity constraint increases the utilization of vehicles as well as reduces the total travel distance. Moreover, in some cases the total number of routes can be reduced

Online 3D Bin Packing with Constrained Deep Reinforcement Learning

We solve a challenging yet practically useful variant of 3D Bin Packing Problem (3D-BPP). In our problem, the agent has limited information about the items to be packed into the bin, and an item must be packed immediately after its arrival without buffering or readjusting. The item's placement also subjects to the constraints of collision avoidance and physical stability. We formulate this online 3D-BPP as a constrained Markov decision process. To solve the problem, we propose an effective and easy-to-implement constrained deep reinforcement learning (DRL) method under the actor-critic framework. In particular, we introduce a feasibility predictor to predict the feasibility mask for the placement actions and use it to modulate the action probabilities output by the actor during training. Such supervisions and transformations to DRL facilitate the agent to learn feasible policies efficiently. Our method can also be generalized e.g., with the ability to handle lookahead or items with different orientations. We have conducted extensive evaluation showing that the learned policy significantly outperforms the state-of-the-art methods. A user study suggests that our method attains a human-level performance

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

Optimasi Vehicle Routing Problem dengan Packing Constraints Menggunakan Metode Algoritma Genetika

Vehicle Routing Problem adalah suatu permasalahan dalam pengiriman barang dari depot ke beberapa outlet atau pelanggan menggunakan beberapa kendaraan yang memiliki kapasitas terbatas dengan tujuan meminimalkan biaya pengiriman. Adanya packing constraints dikarenakan pada umumnya kendaraan yang digunakan dalam pengiriman barang mempunyai kontainer berbentuk balok. Sehingga diperlukan cara-cara penyusunan agar kendaraan dapat memuat semua barang, tidak merusak barang dan memudahkan dalam mengeluarkan barang Dalam tugas akhir ini akan dikembangkan model dan algoritma untuk menyelesaikan vehicle routing problem with packing contraints dengan metode metaheuristik yaitu algoritma genetika dengan tujuan meminimalkan total jarak tempuh pengiriman. Selain itu gabungan algoritma genetika dan algoritma bottom-left fill digunakan untuk untuk melakukan proses packing agar didapat proses packing yang optimal. Algoritma genetika mengeluarkan hasil 0,08% lebih buruk dari ant colony optimization dan 2,93% lebih baik dari tabu search. Selain itu metode algoritma genetika juga berhasil diterapkan pada suatu perusahaan retail pada jaringan jalan kota Surabaya. ================================================================= Vehicle Routing Problem is a problem in delivering item from depot to all customers using several vehicles whose have limited capacity with purpose minimizing transportation cost. The packing constraints exist because the vehicles usually used in delivering item have a rectangular-box shaped container. The items itself also commonly have a shape of rectangular-box. Therefore, it needs a way to pack or load so that containers could load all of the items, not damage the items and make it easy to unload the items. The aim of this final project is developing a model and method as approach solution of vehicle routing problem with packing constraints using genetic algorithm to minimize the transportation mileage. In addition, a hybrid genetic algorithm and bottom-left fill algorithm also take place to solve the packing proses. This algorithm deliver average solution 0.08% worse than ant colony optimization but has 2.93% better than tabu search

Solving the two-dimensional bin packing problem

Das ”two-dimensional bin packing” Problem mit orientierten Elementen und freiem Schneiden (2BP|O|F) wurde in dieser Arbeit diskutiert. Für dieses Problem müssen ein Set kleiner, rechteckiger Elemente in ein unbegrenztes Set von einheitlichen großen Objekten gepackt werden. Orientiert heißt, dass die Elemente nicht gedreht werden dürfen und freies Schneiden heißt, dass die Elemente überall im großen Objekt platziert werden können, solange sie innerhalb von diesem platziert werden und sich dabei nicht überlappen. Es gibt eine große Anzahl an Variationen für das Problem, wie zum Beispiel eine unterschiedliche Dimensionalität, unterschiedlich große Objekte, unregelmäßig geformte Elemente, rotierbare Elemente oder dass nur Guillotineschnitte vorgenommen werden können. Für diese Arbeit wurde ein neues ILP Modell entwickelt. Weiters wurde eine bereits existierende Heuristik (LGFi) verbessert, indem ein auf Wahrscheinlichkeiten basierender Ansatz verwendet wurde. Die Heuristik besteht aus einem Vorverarbeitungsschritt und einem zweiten Schritt in dem die Elemente gepackt werden. Das Ziel des Vorverarbeitungsschrittes ist es die Elemente zu sortieren und das Ziel des zweiten Schrittes ist es die sortierten Elemente zu packen. Was verändert wurde ist, dass die Elemente nicht mehr auf eine deterministische Weise sortiert werden sondern basierend auf Wahrscheinlichkeiten. Diese verbesserte Heuristik wurde mit Hilfe von drei verschiedenen Ansätzen auf 500 Instanzen, die von der Literatur zur Verfügung gestellt wurden, angewendet. Diese drei sind ein multi-start Ansatz, Beam Search und Variable Neighborhood Search. Alle drei übertreffen die bisher dagewesenen Ansätze, wobei Beam Search die schlechteste ist und der multi-start Ansatz und Variable Neighborhood Search am besten und etwa gleich gut sind. Außerdem wurden drei neue beste Lösungen für die 500 Instanzen gefunden

A memory-integrated artificial bee algorithm for heuristic optimisation

A thesis submitted to the University of Bedfordshire in partial fulfilment of the requirements for the degree of Master of Science by ResearchAccording to studies about bee swarms, they use special techniques for foraging and they are always able to find notified food sources with exact coordinates. In order to succeed in food source exploration, the information about food sources is transferred between employed bees and onlooker bees via waggle dance. In this study, bee colony behaviours are imitated for further search in one of the common real world problems. Traditional solution techniques from literature may not obtain sufficient results; therefore other techniques have become essential for food source exploration. In this study, artificial bee colony (ABC) algorithm is used as a base to fulfil this purpose. When employed and onlooker bees are searching for better food sources, they just memorize the current sources and if they find better one, they erase the all information about the previous best food source. In this case, worker bees may visit same food source repeatedly and this circumstance causes a hill climbing in search. The purpose of this study is exploring how to embed a memory system in ABC algorithm to avoid mentioned repetition. In order to fulfil this intention, a structure of Tabu Search method -Tabu List- is applied to develop a memory system. In this study, we expect that a memory system embedded ABC algorithm provides a further search in feasible area to obtain global optimum or obtain better results in comparison with classic ABC algorithm. Results show that, memory idea needs to be improved to fulfil the purpose of this study. On the other hand, proposed memory idea can be integrated other algorithms or problem types to observe difference

Um modelo matemático para o problema de carregamento de múltiplos contêineres

Orientador : Prof. Dr. Cassius Tadeu ScarpinDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 27/02/2015Inclui referências : f.73-81Resumo: Este trabalho apresenta um modelo de Programação Linear Inteira que visa carregar, de modo ortogonal e sem sobreposição, um subconjunto de caixas retangulares no interior de contêineres, de modo a minimizar o espaço não utilizado dos contêineres selecionados. Com base em propostas realizadas anteriormente na literatura, a formulação matemática descrita neste trabalho considera as restrições de limitação de peso do contêiner, orientação das caixas e estabilidade vertical da carga, além de utilizar uma técnica heurística para realizar o pré-processamento dos dados. Tanto conjuntos de teste gerados aleatoriamente quanto da literatura foram utilizados para avaliar o desempenho computacional da formulação matemática proposta, e um software de otimização foi empregado para a resolução dos modelos gerados. A análise dos resultados obtidos permite concluir que a proposta gera resultados satisfatórios, com padrões de carregamento que atendem as restrições abordadas neste trabalho, dentro de um limite de tempo estabelecido para a execução dos testes. Palavras-chave: Matemática Discreta e Combinatória. Programação Linear Inteira. Modelagem Matemática. Problemas de Corte e Empacotamento. Carregamento de Contêineres.Abstract: This work presents an Integer Linear Programming model that aims loading, orthogonally and without overlap, a subset of rectangular boxes inside containers, in order to minimize the idle space of the selected containers. Based on proposals previously made in the literature, the mathematical formulation described in this work regards the restrictions of weight limit of the container, box orientation and vertical stability of the load, and also uses a heuristic technique to preprocess the data. Both randomly generated sets of trials and ones from literature were used to evaluate the computational performance of the proposed mathematical formulation, and an optimization software was employed for the resolution of the generated models. The analysis of the obtained results allow the conclusion that the proposition generates satisfactory results, with loading patterns that meet the restrictions addressed in this work within a time limit set for the tests. Keywords: Discrete and Combinatorial Mathematics. Integer Linear Programming. Mathematical Modeling. Cutting and Packing Problems. Container Loading