Bin Packing Research Articles

A new branch-and-cut approach for integrated planning in additive manufacturing

In recent years, there has been considerable interest in the transformative potential of additive manufacturing (AM) since it allows for producing highly customizable and complex components while reducing lead times and costs. The rise of AM for traditional and new business models enforces the need for efficient planning procedures for AM facilities. In this area, the assignment and sequencing of components to be built by an AM machine, also called a 3D printer, is a complex challenge combining two combinatorial problems: The first decision involves the grouping of parts into production batches, akin to the well-known bin packing problem. Subsequently, the second problem pertains to the scheduling of these batches onto the available machines, which corresponds to a parallel machine scheduling problem. For minimizing makespan, this paper proposes a new branch-and-cut algorithm for integrated planning for unrelated parallel machines. The algorithm is based on combinatorial Benders decomposition: The scheduling problem is considered in the master problem, while the feasibility of an obtained solution with respect to the packing problem is checked in the sub-problem. Current state-of-the-art techniques are extended to solve the orthogonal packing with rotation and used to speed up the solution of the sub-problem. Extensive computational tests on existing and new benchmark instances show the algorithm’s superior performance, improving the makespan by 18.7% on average, with improvements reaching up to 97.6% for large problems compared to an existing integrated mixed-integer programming model.

Algorithms for the bin packing problem with scenarios

Algorithms for the bin packing problem with scenarios

Fast neighborhood search heuristics for the colored bin packing problem

Fast neighborhood search heuristics for the colored bin packing problem

CMSA based on set covering models for packing and routing problems

AbstractMany packing, routing, and knapsack problems can be expressed in terms of integer linear programming models based on set covering. These models have been exploited in a range of successful heuristics and exact techniques for tackling such problems. In this paper, we show that integer linear programming models based on set covering can be very useful for their use within an algorithm called “Construct, Merge, Solve & Adapt”(CMSA), which is a recent hybrid metaheuristic for solving combinatorial optimization problems. This is because most existing applications of CMSA are characterized by the use of an integer programming solver for solving reduced problem instances at each iteration. We present applications of CMSA to the variable-sized bin packing problem and to the electric vehicle routing problem with time windows and simultaneous pickups and deliveries. In both applications, CMSA based on a set covering model strongly outperforms CMSA when using an assignment-type model. Moreover, state-of-the-art results are obtained for both considered optimization problems.

Arc-flow formulation and branch-and-price-and-cut algorithm for the bin-packing problem with fragile objects

This study introduces an arc-flow formulation and the first branch-and-price-and-cut (BPC) algorithm designed to solve the bin-packing problem with fragile objects (BPPFO). This variant of the bin-packing problem originates in the field of telecommunications, particularly in the allocation of cellular calls to frequency channels. The arc-flow formulation is inspired by previous studies and modifies the graph construction method to accommodate fragility constraints. We proved the correctness of this formulation and demonstrated its superiority in instances with small maximum fragility through extensive experiments. The proposed BPC algorithm leverages advanced cutting and packing techniques and incorporates innovative elements such as problem reduction, additional cutting planes, and a label-setting-based exact pricing algorithm. The experimental results demonstrate that the proposed BPC algorithm is highly competitive with the state-of-the-art algorithm for solving the BPPFO and can successfully solve several previously unsolved instances.

Classification and evaluation of the algorithms for vector bin packing

Heuristics for Vector Bin Packing (VBP) play an important role in modern distributed computing systems and other applications aimed at optimizing the usage of multidimensional resources. In this paper we perform a systematic classification of heuristics for VBP, with the focus on construction heuristics. We bring together existing VBP algorithms and their tuning parameters, and propose new algorithms and new tuning parameters. For a less studied class of multi-bin algorithms, we explore their properties analytically, considering monotonic and anomalous behavior and approximation guarantees. For empirical evaluation, all algorithms are implemented as the Vectorpack library and assessed through extensive experiments. Our findings may serve as the basis for the development of more complex, hybrid algorithms, hyperheuristics and machine learning algorithms. The Vectorpack library can also be adjusted for addressing enhanced VBP problems with additional features, which arise in applications, especially those typical for modern distributed computing systems.

Robust concave utility maximization over chance constraints

This paper first studies an expected utility problem with chance constraints and incomplete information on a decision maker’s utility function. The model maximizes the worst-case expected utility of random outcome over a set of concave functions within a novel ambiguity set, while the underlying probability distribution is known with the assumption of a discretization of possible realizations for the uncertainty parameter. To obtain computationally tractable formulations, we employ a discretization approach to derive a max–min chance-constrained approximation of this problem. This approximation is further reformulated as a mixed-integer program. We show that the discrete approximation converges to the true counterpart under mild assumptions. We also present a row generation algorithm for optimizing the max–min program. A computational study for a bin-packing problem and a multi-item newsvendor problem is conducted to demonstrate the benefit of the proposed framework and the computational efficiency of our algorithm. We find that the row generation algorithm can significantly reduce the computational time, and our robust policy could achieve a better out-of-sample performance when compared with the non-robust policy and the one without the chance constraints.

Deep Study on the Application of Machine Learning in Bin Packing Problems

Deep Study on the Application of Machine Learning in Bin Packing Problems

Good Prophets Know When the End Is Near

We consider a class of online decision-making problems with exchangeable actions, where in each period a controller is presented an input type drawn from some stochastic arrival process. The controller must choose an action, and the final objective depends only on the aggregate type-action counts. Such a framework encapsulates many online stochastic variants of common optimization problems with knapsack, bin packing, and generalized assignment as canonical examples. In such settings, we study a natural model-predictive control algorithm. We introduce general conditions under which this algorithm obtains uniform additive loss (independent of the horizon) compared with an optimal solution with full knowledge of arrivals. Our condition builds on the recently introduced compensated coupling technique, providing a unified view of how uniform additive loss arises as a consequence of the geometry of the underlying decision-making problem. Our characterization allows us to derive uniform loss algorithms for several new settings, including the first such algorithm for online stochastic bin packing. It also lets us study the effect of other modeling assumptions, including choice of horizon, batched decisions, and limited computation. In particular, we show that our condition is fulfilled by the above-mentioned problems when the end of the time horizon is known sufficiently long before the end. In contrast, if at a late stage, there is still uncertainty about the end of the time horizon we show that such uniform loss guarantees are impossible to achieve. We use real and synthetic data to illustrate our findings. This paper was accepted by J. George Shanthikumar, data science. Funding: This work was supported by the Division of Mathematical Sciences [Grant 1839346]; the Division of Electrical, Communications and Cyber Systems [Grant 1847393]; and the Army Research Laboratory [Grant W911NF-17-1-0094]. The authors also gratefully acknowledge support from the NSF [Grants ECCS-1847393, CNS-195599, and DMS-1839346], AFOSR [Grant FA9550-23-1-0068], an ARL award [Grant W911NF-17-1-0094], and ARO MURI [Grant W911NF-19-1-0217]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.04307 .

Task scheduling for control system based on deep reinforcement learning

We investigate the control system’s computational task scheduling problem within limited time and with limited CPU cores in the cloud server. We employ a neural network model to estimate the runtime consumption of linear quadratic regulators (LQR) under varying numbers of CPU cores. Building upon this, we model the task scheduling problem as a two-dimensional bin packing problem (2D BPP) and formulate the BPP as a Markov Decision Process (MDP). By studying the characteristics of the MDP, we simplify the action space, design an efficient reward function, and propose a Double DQN-based algorithm with a simplified action space. Experimental results demonstrate that the proposed approach has improved training efficiency and learning performance compared to other packing algorithms, effectively addressing the challenges of task scheduling in the context of the control system.

Capacity planning in logistics corridors: Deep reinforcement learning for the dynamic stochastic temporal bin packing problem

This paper addresses the challenge of managing uncertainty in the daily capacity planning of a terminal in a corridor-based logistics system. Corridor-based logistics systems facilitate the exchange of freight between two distinct regions, usually involving industrial and logistics clusters. In this context, we introduce the dynamic stochastic temporal bin packing problem. It models the assignment of individual containers to carriers’ trucks over discrete time units in real-time. We formulate it as a Markov decision process (MDP). Two distinguishing characteristics of our problem are the stochastic nature of the time-dependent availability of containers, i.e., container delays, and the continuous-time, or dynamic, aspect of the planning, where a container announcement may occur at any time moment during the planning horizon. We introduce an innovative real-time planning algorithm based on Proximal Policy Optimization (PPO), a Deep Reinforcement Learning (DRL) method, to allocate individual containers to eligible carriers in real-time. In addition, we propose some practical heuristics and two novel rolling-horizon batch-planning methods based on (stochastic) mixed-integer programming (MIP), which can be interpreted as computational information relaxation bounds because they delay decision making. The results show that our proposed DRL method outperforms the practical heuristics and effectively scales to larger-sized problems as opposed to the stochastic MIP-based approach, making our DRL method a practically appealing solution.

Causal Analysis to Explain the Performance of Algorithms: A Case Study for the Bin Packing Problem

This work presents a knowledge discovery approach through Causal Bayesian Networks for understanding the conditions under which the performance of an optimization algorithm can be affected by the characteristics of the instances of a combinatorial optimization problem (COP). We introduce a case study for the causal analysis of the performance of two state-of-the-art algorithms for the one-dimensional Bin Packing Problem (BPP). We meticulously selected the set of features associated with the parameters that define the instances of the problem. Subsequently, we evaluated the algorithmic performance on instances with distinct features. Our analysis scrutinizes both instance features and algorithm performance, aiming to identify causes influencing the performance of the algorithms. The proposed study successfully identifies specific values affecting algorithmic effectiveness and efficiency, revealing shared causes within some value ranges across both algorithms. The knowledge generated establishes a robust foundation for future research, enabling predictions of algorithmic performance, as well as the selection and design of heuristic strategies for improving the performance in the most difficult instances. The causal analysis employed in this study did not require specific configurations, making it an invaluable tool for analyzing the performance of different algorithms in other COPs.

A Plant Propagation Algorithm for the Bin Packing Problem

A Plant Propagation Algorithm for the Bin Packing Problem

Rapid prediction for the transient dispersion of leaked airborne pollutant in urban environment based on graph neural networks

Rapidly predicting airborne pollutant dispersion in urban is vital for ventilation design and evacuation planning. Computational fluid dynamics (CFD) simulations are commonly used to provide accurate predictions, but the computational cost is too high. Although graph neural networks (GNNs) provide fast predictions of flow fields by manipulating unstructured mesh on GPU, they suffer from high memory usage and accuracy decreases when applied to large-scale urban scenes. Moreover, it is difficult for GNNs to learn the coupled relationship between wind field and pollutant concentration field. We propose a multi-objective GNN model as CFD surrogate to rapidly predict the transient dispersion of airborne pollutant under the influence of complex wind field patterns in urban environment. Based on random urban layouts generated by a 2D bin packing algorithm, we employ a validated CFD model to construct a sample dataset of wind fields and concentration fields. We leverage graph pooling and multi-scale feature fusion to improve prediction accuracy, and subgraph partitioning of both wind field and concentration field to reduce GPU memory usage. The results show that our GNN model at its best runs 1–2 orders of magnitude faster than CFD simulation with accuracy evaluation metrics R2=0.92, and achieves 70 % GPU memory reduction.

Trolley Optimisation for Loading Printed Circuit Board Components

A trolley is a container for loading printed circuit board (PCB) components, and a trolley optimisation problem (TOP) is an assignment of PCB components to trolleys for use in the production of a set of PCBs in an assembly line. In this paper, we introduce the TOP, a novel operation research application. To formulate the TOP, we derive a novel extension of the bin packing problem. We exploit the problem structure to decompose the TOP into two smaller, identical, and independent problems. Further, we develop a mixed integer linear programming model to solve the TOP and prove that the TOP is an NP-complete problem. A case study of an aerospace manufacturing company is used to illustrate the TOP which successfully automated the manual process in the company and resulted in significant cost reductions and flexibility in the building process.

Integrated packing and routing: A model and its solutions

This paper introduces the two-level vehicle routing and loading problem (2L-VRLP), an innovative model integrating the two-level bin packing and vehicle routing problems to address real-world logistics challenges that require simultaneous packing and transportation decisions. By capturing the essence of dual-level packing (boxes onto pallets, pallets onto vehicles) and optimising vehicle routing, the 2L-VRLP offers an integrated framework that outperforms traditional separated models, demonstrating superior solutions that align closely with practical logistics operations. We propose a set of heuristic algorithms tailored for the 2L-VRLP’s unique requirements and explore automated algorithm selection using an artificial neural network (ANN), marking a step towards incorporating machine learning in logistics optimisation. This work not only showcases the 2L-VRLP model’s potential to enhance logistics management but also sets the groundwork for future research and applications in this domain.

Models for two-dimensional bin packing problems with customer order spread

Models for two-dimensional bin packing problems with customer order spread

Combining vehicle routing and bin packing problem for vehicle routing planning: A case study of a chemical factory

In the logistics distribution process, effective transportation management is required to ensure quality and timely delivery. In addition, transportation must be more economical and faster. The case study company is a chemical plant, an industrial company that produces products for hygiene and cleaning. The delivery manager plans the transportation routes based only on her experience because no decision-making aids are available. In addition, the manager considers the shipping order from first to last when arranging the products on the transportation vehicles. The goods for the final delivery location are placed at the back and bottom of the delivery truck. This cannot guarantee that the transportation routes set by the manager are suitable. Therefore, this study aims to plan delivery routes, arrange items in trucks, and reduce transportation costs for a case study of a chemical factory by using vehicle route problems and container filling problems. Then, the program is developed in Python using the Saving Algorithm, the 3D First Fit Decreasing Algorithm, and the 3D Best Fit Algorithm. The results show that the program method can reduce the use of transportation vehicles from 19 to 14, which is 26.32%; reduce the total distance from 5,499.8 kilometers to 3,406.92 kilometers, which is 38.05%; reduce the wages of transportation vehicles from 36,666 to 24,993 baht, which is 31.84%; can increase the average total weight per vehicle from 961.22 to 1,319.71 kilograms, which is 37.30%; and increase the average space utilization per vehicle from 37.93% to 51.47%, which is 13.54%. This method can reduce costs and increase efficiency for the company. Finally, the developed program also supports inexperienced operations managers in making decisions when planning transportation routes and loading goods, Thereby saving working time.

Optimization research on multi-trip distribution of reverse logistics terminal for automobile scrap parts under the background of sustainable development strategy

To effectively solve the reverse logistics distribution problem caused by the increasing number of scrapped parts in the automotive market, this study constructs a multi-trip green vehicle routing problem model with time windows by comprehensively considering the coordination between carbon dioxide emissions and cost efficiency. A hybrid adaptive genetic algorithm is proposed to solve this problem, featuring innovative improvements in the nearest neighbor rule based on minimum cost, adaptive strategies, bin packing algorithm based on the transfer-of-state equation, and large-scale neighborhood search. Additionally, to efficiently obtain location data for supplier factory sites in the distribution network, a coordinate extraction method based on image recognition technology is proposed. Finally, the scientific validity of this study is verified based on the actual case data, and the robust optimization ability of the algorithm is verified by numerical calculations of different examples. This research not only enriches the study of green vehicle routing problems but also provides valuable insights for the industry to achieve cost reduction, efficiency enhancement, and sustainable development in reverse logistics.

An online dynamic dual bin packing with lookahead approach for server-to-cell assignment in computer server industry

Efficient production scheduling in computer server industry remains a critical challenge. This challenge becomes particularly acute during the testing phase, where servers are assigned for testing in a modular environment consisting of test banks. Unique characteristics such as online arrival of servers known only over a short time window, skewed arrival pattern, power and cooling compatibility constraints, and dynamic assignment complicate decision making, a situation we observed at our industry partner’s site, which often leads to missing due dates and loss of customer trust. Motivated by this challenge, we introduce an Online Dynamic Dual Bin Packing with Lookahead problem and propose an integer linear programming model that maximizes the number of assigned servers. To efficiently solve this model, we decompose the problem into a set of subproblems for a given lookahead length. A ‘2-phase’ computational framework is proposed that seamlessly integrates mathematical programming with genetic algorithm. Based on realistic data available from a server manufacturer, our findings suggest that solutions are sensitive to (i) the length of the lookahead window, (ii) testing capacity and server arrival pattern, (iii) test processing time requirement, and (iv) physical allocation of servers.