The Bin Packing Problem with Fragile Objects: Models and Solution Methods

The Bin Packing Problem (BPP) is an important optimization problem with many applications. Given a set of items with a certain weight and a set of bins with fixed capacity, the classical BPP seeks to pack the items into the minimum number of bins. In this thesis a variant of the BPP, the Bin Packing Problem with Fragile Objects (BPPFO), is studied. The BPPFO originates in telecommunication systems where cellphone calls are assigned to towers based on the noise level of calls and the tolerance level of each call in the channel.In this case, the calls are represented as objects that are characterized by a weight and a fragility parameter. The fragility parameter corresponds to the noise tolerance level of each call, and the weight corresponds to the noise produced by a call. As calls are assigned, the total noise produced within a channel can not exceed the lowest tolerance level among the calls. The less the tolerance level, the more fragile the line becomes. Hence, the capacity of the bin depends on the smallest fragility of any item packed in it. In this thesis, two new formulations are proposed. The first is based on the classical BPP formulation to which a Lagrangian relaxation is applied. Several heuristics are developed to find upper bounds, including a greedy heuristic. The second is a graph-based formulation that is solved directly. A standard data set is used for testing. It is found that the new formulation based on the classical BPP is more efficient in getting a Lagrangian lower bound and the greedy heuristic outperforms other heuristics in finding good quality upper bounds in very short computational times, especially with very large data instances

Algorithms for the Bin Packing Problem with Scenarios

This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For this problem, we propose an absolute approximation algorithm whose ratio is bounded by the square root of the number of scenarios times the approximation ratio for an algorithm for the vector bin packing problem. We also show how an asymptotic polynomial-time approximation scheme is derived when the number of scenarios is constant. As a practical study of the problem, we present a branch-and-price algorithm to solve an exponential model and a variable neighborhood search heuristic. To speed up the convergence of the exact algorithm, we also consider lower bounds based on dual feasible functions. Results of these algorithms show the competence of the branch-and-price in obtaining optimal solutions for about 59% of the instances considered, while the combined heuristic and branch-and-price optimally solved 62% of the instances considered

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

グリーンロジスティクスのためのコンテナ積載と配車配送経路の最適化に関する研究

京都大学0048新制・課程博士博士(工学)甲第16840号工博第3561号新制||工||1538(附属図書館)29515京都大学大学院工学研究科機械理工学専攻(主査)教授 椹木 哲夫, 教授 西脇 眞二, 教授 松原 厚学位規則第4条第1項該当Doctor of Philosophy (Engineering)Kyoto UniversityDFA

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

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

The three-dimensional single-bin-size bin packing problem: combining metaheuristic and machine learning approaches

The Three-Dimensional Single-Bin-Size Bin Packing Problem is one of the most studied problem in the Cutting & Packing category. From a strictly mathematical point of view, it consists of packing a finite set of strongly heterogeneous “small” boxes, called items, into a finite set of identical “large” rectangles, called bins, minimizing the unused volume and requiring that the items are packed without overlapping. The great interest is mainly due to the number of real-world applications in which it arises, such as pallet and container loading, cutting objects out of a piece of material and packaging design. Depending on these real-world applications, more objective functions and more practical constraints could be needed. After a brief discussion about the real-world applications of the problem and a exhaustive literature review, the design of a two-stage algorithm to solve the aforementioned problem is presented. The algorithm must be able to provide the spatial coordinates of the placed boxes vertices and also the optimal boxes input sequence, while guaranteeing geometric, stability, fragility constraints and a reduced computational time. Due to NP-hard complexity of this type of combinatorial problems, a fusion of metaheuristic and machine learning techniques is adopted. In particular, a hybrid genetic algorithm coupled with a feedforward neural network is used. In the first stage, a rich dataset is created starting from a set of real input instances provided by an industrial company and the feedforward neural network is trained on it. After its training, given a new input instance, the hybrid genetic algorithm is able to run using the neural network output as input parameter vector, providing as output the optimal solution. The effectiveness of the proposed works is confirmed via several experimental tests

This side up!

We consider two- and three-dimensional bin packing problems where 9