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2017 | Buch

Hard Planning and Scheduling Problems in the Digital Factory Kapitel lesen Erstes Kapitel lesen

Math for the Digital Factory

herausgegeben von: Ph.D. Luca Ghezzi, Prof. Dr. Dietmar Hömberg, Dr. Chantal Landry

Verlag: Springer International Publishing

Buchreihe : Mathematics in Industry

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This volume provides a unique collection of mathematical tools and industrial case studies in digital manufacturing. It addresses various topics, ranging from models of single production technologies, production lines, logistics and workflows to models and optimization strategies for energy consumption in production.

The digital factory represents a network of digital models and simulation and 3D visualization methods for the holistic planning, realization, control and ongoing improvement of all factory processes related to a specific product. In the past ten years, all industrialized countries have launched initiatives to realize this vision, sometimes also referred to as Industry 4.0 (in Europe) or Smart Manufacturing (in the United States). Its main goals are

• reconfigurable, adaptive and evolving factories capable of small-scale production

• high-performance production, combining flexibility, productivity, precision and zero defects

• energy and resource efficiency in manufacturing

None of these goals can be achieved without a thorough modeling of all aspects of manufacturing together with a multi-scale simulation and optimization of process chains; in other words, without mathematics.

To foster collaboration between mathematics and industry in this area the European Consortium for Mathematics in Industry (ECMI) founded a special interest group on Math for the Digital Factory (M4DiFa). This book compiles a selection of review papers from the M4DiFa kick-off meeting held at the Weierstrass Institute for Applied Analysis and Stochastics in Berlin, Germany, in May 2014. The workshop aimed at bringing together mathematicians working on modeling, simulation and optimization with researchers and practitioners from the manufacturing industry to develop a holistic mathematical view on digital manufacturing.

This book is of interest to practitioners from industry who want to learn about important mathematical concepts, as well as to scientists who want to find out about an exciting new area of application that is of vital importance for today’s highly industrialized and high-wage countries.

Inhaltsverzeichnis

Frontmatter

Planning and Scheduling of Production Systems

Frontmatter
Hard Planning and Scheduling Problems in the Digital Factory
Abstract
Production planning and scheduling with the aid of software tools in today’s manufacturing industries have become a common practice which is indispensable for providing high level customer service, and at the same time to utilize the production resources, like workforce, machine tools, raw materials, energy, etc., efficiently. To meet the new requirements, problem modeling tools, optimization techniques, and visualization of data and results have become part of the software packages. In this chapter some recent developments in problem modeling and optimization techniques applied to important and challenging industrial planning and scheduling problems are presented. We will focus on new problem areas which are still at the edge of current theoretical research, but they are motivated by practical needs. On the one hand, we will discuss project based production planning, and on the other hand, we will tackle a resource leveling problems in a machine environment. We will present the problems, some modeling and solution approaches, and various extensions and applications.
Tamás Kis, Márton Drótos
Modeling of Material Flow Problems
Abstract
In this article we discuss the description of modern manufacturing or production problems using continuous models. Instead of a detailed description of the production process, a mathematical formulation is used based on transport equations. The challenge is to derive novel and nonstandard approaches that allow to incorporate detailed nonlinear dynamic behavior, which is currently not possible with the widely applied linear or mixed integer linear approaches. Starting from discrete event simulations as a basic description we explore the relation between the product density and the flow of parts (also known as clearing function). Data-fitting procedures help to identify the underlying parameters. We show the relationships between discrete event simulations, queuing models and transport model-based methods, and present several applications.
Simone Göttlich, Michael Herty, Melanie Luckert
Max-Plus-Linear Systems for Modeling and Control of Manufacturing Problems
Abstract
In this chapter, the dynamics of manufacturing systems is characterized through the occurrence of events such as parts entering or leaving machines. Furthermore, we assume that the relations between events are expressed by synchronizations (i.e., conditions of the form: for all k ≥ l, occurrence k of event e 2 is at least τ units of time after occurrence k − l of event e 1). Note that this assumption often holds when the considered manufacturing system is functioning under a predefined schedule. First, we discuss the modeling of such systems by linear state-space models in the \(\left (\max,+\right )\)-algebra (due to this property, such systems are often called \(\left (\max,+\right )\)-linear systems). Second, standard open-loop and closed-loop control structures for \(\left (\max,+\right )\)-linear systems are recalled. These control structures lead to a trade-off between the rapidity of systems and their internal buffer sizes. Some techniques to influence this trade-off are presented.
Xavier David-Henriet, Laurent Hardouin, Jörg Raisch
Stochastic Optimal Sizing of a Warehouse
Abstract
The problem is considered of determining how many pieces to stock in a warehouse, for a multitude of stockable goods and accounting for random market demand and supply lead time. Classical reorder point theory is revisited, the underlying model is no longer linearized and the involved stochastic variables need not be normally distributed but, rather, are empirically deduced from historical data. Uncertainty propagation is carried out either by Monte Carlo method or by a Polynomial Chaos Expansion. A Quadratic Programming procedure is proposed to regularize data by filtering rare events out. Performance vs. cost curves are obtained and the global problem of choosing optimal points over them, subject to a global cost budget constraint, is set as a combinatorial, constrained optimization. The solution of a simplified version is attained by Linear Programming, while the full problem is addressed by Mixed Integer Linear Programming.
Luca Ghezzi
Challenges of Mechatronical Engineering of Production Systems: An Automation System Engineering View
Abstract
The importance of quality and efficiency of engineering process for production system is continuously increasing. Engineering sciences are encouraged to improve its tool and method sets to face this challenge. But in several cases engineers are not the real specialists for improving the toolbox of engineering. Here mathematical science can assist engineering sciences.
Within this paper open research issues for mathematical sciences are derived from the current state of the art in mechatronical engineering of production system intending to encourage joined research activities of mathematical and engineering science.
Arndt Lüder, Nicole Schmidt

Optimization of Production Lines

Frontmatter
Physics-Based Simulation for Energy Consumption Optimization of Automated Assembly Systems in the Automotive Industry
Abstract
In this chapter a simulation based approach for optimizing energy consumption of automated assembly systems in the automotive industry from a production planning perspective is presented. Employing innovative simulation capabilities, originating from the computer gaming industry, automated assembly system’s energy consumption is prognosticated and visualized in virtual validation procedures, based on its corresponding digital models. Potential energy efficiency improvement measures (EEIMs) gathered from different fields of application are identified and exemplarily tailored to specific automated assembly system’s requirements. Considerations for suitable EEIM implementation to create energy-efficient system designs are proposed. Ultimately, a case study for improving energy-efficiency of automated assembly systems including preliminary results is presented.
Felix Damrath, Anton Strahilov, Thomas Bär, Michael Vielhaber
Optimisation of Power Consumption for Robotic Lines in Automotive Industry
Abstract
A novel mathematical formulation of the energy optimisation problem for robotic lines is presented, which allows minimising the energy consumption in a robotic cell while keeping the required production cycle time. Different energy saving modes of the robots are utilised as well as the fact that the robot energy consumption during its movement depends on the movement duration. This dependency is modelled with a so-called energy function, which can be obtained by measurements, physical modelling of the robots or simulation. Each of these areas is covered by the presented work. The achieved results show there is a good potential to achieve energy savings at existing robotic cells and their series, and an even bigger potential if the presented approach is used during the design phase of new robotic cells.
Pavel Burget, Libor Bukata, Přemysl Šůcha, Martin Ron, Zdeněk Hanzálek
Production Line Optimization with Model Based Methods
Abstract
In this paper we deal with different models of production lines of factories and consider the makespan optimization problem based on these models. We consider state-of-the-art and novel mathematical optimizers including exact and heuristic methods. We apply these optimizers to both standard academic and industrial data sets. We see that in a large rate of the considered cases the novel exact optimizers converged to the optimum fast which is surprising being the problems NP-hard and the problem sizes big. This shows the importance of exploiting the structure present in the industrial data using standardized industrial data sets for testing mathematical algorithms devoted to solve industrial problems and that some provided exact mathematical optimizers are fast and perform accurately on the considered industrial problems.
T. Hajba, Z. Horváth, C. Kiss-Tóth, J. Jósvai
Automatic Reconfiguration of Robotic Welding Cells
Abstract
Robotic welding cells are at the core of many complex production systems, especially in automotive industry. In these cells, a certain number of robots perform spot welding tasks on a workpiece. The configuration of the cells can have a huge impact on the production rate. The smaller the cycle time is, the higher the production is. In this paper, we present a complete algorithm that automatically configures the welding cell such that the given cycle time of the production process is kept. This algorithm assigns tasks to the different robots, decides in which order the tasks are executed and computes the fastest collision-free trajectory of the robots between two consecutive tasks.
Dietmar Hömberg, Chantal Landry, Martin Skutella, Wolfgang A. Welz
Numerical Approaches Towards Bilevel Optimal Control Problems with Scheduling Tasks
Abstract
In this paper, we consider the problem of scheduling N robots interacting with a moving target. Both, the sequence of the robots and their trajectories are unknown and subject to optimization. Such type of problems appear in highly automated production plants and in the simulation of virtual factories. The purpose of the paper is to provide a mathematical model and to suggest a numerical solution approach. Our approach is based on the formulation of the problem as a bilevel optimization problem, where the lower level problem is an optimal control problem, while the upper level problem is a finite dimensional mixed-integer optimization problem. We approach the problem by exploitation of necessary optimality conditions for the lower level problem and by application of a Branch & Bound method for the resulting single level optimization problem. Two settings are taken into account. Firstly, no state constraints are assumed on the lower level problem, thus the local minimum principle applies directly. Secondly, the problem setting is augmented by pure state constraints, which are being handled by virtual controls in order to regularize the problem.
Konstantin D. Palagachev, Matthias Gerdts

Selected Production Technologies

Frontmatter
Math-Based Algorithms and Software for Virtual Product Realization Implemented in Automotive Paint Shops
Abstract
We present a simulation framework that makes it possible to accurately simulate spray painting of e.g. a truck cab in only a few hours on a standard computer. This is an extreme improvement compared to earlier approaches that require weeks of simulation time. Unique algorithms for coupled simulations of air flows, electrostatic fields and charged paint particles make this possible. In addition, we demonstrate that the same framework can be used to efficiently simulate the laydown of sealing or adhesive material. In the virtual paint factory the production preparation process can be performed in the computer, which allows the engineers to replace physical prototypes with virtual ones to shorten the lead time in product development, and avoid future unforeseen technological and environmental problems that can be extremely costly if they are discovered at the end of the production line, or even worse by the costumer.
Fredrik Edelvik, Andreas Mark, Niklas Karlsson, Tomas Johnson, Johan S. Carlson
Hot Blade Cuttings for the Building Industries
Abstract
The constructions of advanced architectural designs are presently very labour intensive, time consuming, and expensive. They are therefore only applied to a few prestige projects, and it is a major challenge for the building industry to bring the costs down and thereby offer the architects more variability in the (economically allowed) designs—i.e., to allow them to think out of the box. To address this challenge The Danish National Advanced Technology Foundation (now Innovation Fund Denmark) is currently supporting the BladeRunner project that involves several Danish companies and public institutions. The project aims to reduce the amount of manual labour as well as production time by applying robots to cut expanded polystyrene (EPS) moulds for the concrete to form doubly curved surfaces. The scheme is based upon the so-called Hot Wire or Hot Blade technology where the surfaces are essentially swept out by driving an Euler elastica through a block of EPS. This paper will be centered around the mathematical challenges encountered in the implementation of this idea. Since the elastica themselves are well known and described in the works of Euler et al. already in eighteenth century, these new challenges are mainly concerned with the rationalization of the architects’ CAD drawings into surfaces that can be created via this particular sweeping and cutting technology.
David Brander, Andreas Bærentzen, Anton Evgrafov, Jens Gravesen, Steen Markvorsen, Toke Bjerge Nørbjerg, Peter Nørtoft, Kasper Steenstrup
Model-Based Design of Self-Correcting Forming Processes
Abstract
In this paper, a self-correcting strategy for a metal forming process is presented. This strategy entails continuously observing the properties of the product and ensuring that these properties stay in the required tolerances. This reduces the scrap rate and the need to adapt the configuration of the machine manually, both aspects leading to an increase of the productivity and efficiency of the process. For the development of the strategy, a structured design method for mechatronic systems is adapted. During the whole development process, it uses intensively mathematical models of system dynamics to ensure a high quality of the results. There are two commonly used model types to describe the behavior of a forming process: finite-element models and multibody system models. For the development of such a mathematical model, the process has to be examined. It is analyzed regarding its disturbances, influences and possibilities to take action. In this paper, the bending-process is modeled as a multibody system. It describes the most significant influences and is fundamental to develop the self-correcting closed-loop control. The presented model includes a good compromise between computation time and accuracy. After introducing the structured developed closed-loop control, the implementation and the results are presented.
M. Krüger, M. Borzykh, U. Damerow, M. Gräler, A. Trächtler
Discrete Cosserat Rod Models Based on the Difference Geometry of Framed Curves for Interactive Simulation of Flexible Cables
Abstract
For software tools currently used in industry for computer aided design (CAD), digital mock-up and virtual assembly there is an increasing demand to handle not only rigid geometries, but to provide also capabilities for realistic simulations of large deformations of slender flexible structures in real time (i.e.: at interactive rates). The theory of Cosserat rods provides a framework to perform physically correct simulations of arbitrarily large spatial deformations of such structures by stretching, bending and twisting. The kinematics of Cosserat rods is described by the differential geometry of framed curves, with the differential invariants of rod configurations corresponding to the strain measures of the mechanical theory. We utilize ideas from the discrete differential geometry of framed curves in combination with the variational framework of Lagrangian mechanics to construct discrete Cosserat rod models that behave qualitatively correct for rather coarse discretizations, provide a fast computational performance at moderate accuracy, and thus are suitable for interactive simulations. This geometry based discretization approach for flexible 1D structures has industrial applications in design and digital validation. We illustrate this with some application examples from automotive industry.
Joachim Linn, Klaus Dreßler
The Production of Filaments and Non-woven Materials: The Design of the Polymer Distributor
Abstract
We present results from the joint research project ProFil (Stochastic Processes for the Production of Filaments and Non-wovens), which were derived for the optimal design of the polymer distributor. In particular, one is interested in designs which prevent the cooling and degeneration of the polymer due to long occupation times. Since this is directly related to the wall shear stress distribution the questions arise, which wall shear stresses are attainable and how the corresponding design can be computed numerically. Employing the concept of approximate controllability we can answer the first one and characterize the set of attainable wall shear stresses. Further, we present a new numerical approach based on conformal mappings which allows for an optimization in the supremum norm and for an additional incorporation of state constraints. Finally, we show how the real industrial problem is solved by a least-squares optimization using shape gradients.
Christian Leithäuser, René Pinnau
Backmatter
Metadaten
Titel
Math for the Digital Factory
herausgegeben von
Ph.D. Luca Ghezzi
Prof. Dr. Dietmar Hömberg
Dr. Chantal Landry
Copyright-Jahr
2017
Electronic ISBN
978-3-319-63957-4
Print ISBN
978-3-319-63955-0
DOI
https://doi.org/10.1007/978-3-319-63957-4

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