| Preface | 5 |
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| Contents | 7 |
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| Introduction | 15 |
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| Processes | 22 |
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| Predictive Planning and Systematic Action-On the Control of Technical Processes | 23 |
| Executive Summary | 23 |
| A Long Success Story | 24 |
| The Stability Criterion of Hurwitz | 24 |
| Pontryagin's Maximum Principle | 26 |
| Conclusion | 27 |
| State-of-the-Art and Current Developments: The Example | 27 |
| State-of-the-Art and Current Developments: The Example | 27 |
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| 28 | 27 |
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| A Short Introduction to Control Engineering | 28 |
| The Principle of Model Predictive Control | 31 |
| Stability of MPC | 33 |
| Application Fields | 34 |
| Direct Optimal Control Methods | 36 |
| Challenges | 41 |
| Modeling | 41 |
| Parameter Estimation | 43 |
| Optimum Experimental Design | 43 |
| Robustness of Solutions, Uncertainties | 44 |
| Further Challenges | 45 |
| Visions and Recommendations | 46 |
| Theory and Praxis | 47 |
| Interdisciplinary in Education | 48 |
| References | 48 |
| Data Compression, Process Optimization, Aerodynamics: A Tour Through the Scales | 52 |
| Executive Summary | 52 |
| Some Guiding Ideas | 53 |
| Mathematics as an Interface Between Real and Virtual Worlds | 53 |
| A Universe of Scales | 54 |
| Success Stories | 55 |
| Information Retrieval from Huge Datasets | 55 |
| Information Retrieval from Huge Datasets | 55 |
| Adaptively Optimized | 56 |
| Aerodynamics under a Mathematical Microscope | 60 |
| Fluid-Structure-Interaction | 60 |
| Wake Turbulence | 61 |
| Status Quo | 63 |
| Multiscale-Decomposition: Wavelets | 63 |
| Images are Just Functions | 64 |
| Functions are Just Sequences | 66 |
| Multiscale Methods for Process Data Analysis | 69 |
| Solving Optimal Control Problems with Adaptive Wavelet Discretization | 72 |
| Elimination | 74 |
| Refinement | 74 |
| Example | 74 |
| Adaptive Methods for Partial Differential Equations in Fluid Mechanics | 75 |
| Model | 76 |
| Discretization | 77 |
| A New Concept for Adaptivity-How far Does the Analogy to Signal Compression Carry? | 79 |
| An Adaptive Grid Generator | 81 |
| Analysis of Strengths and Weaknesses | 82 |
| Visions and Recommended Course of Action | 83 |
| References | 83 |
| Active Flow Control-A Mathematical Challenge | 86 |
| Executive Summary | 86 |
| Success Stories | 87 |
| Active Flow Control, Status Quo | 88 |
| Modelling | 90 |
| Analysis of Strengths and Weaknesses, Challenges | 92 |
| Visions and Recommendations | 92 |
| References | 93 |
| Data Mining for the Category Management in the Retail Market | 94 |
| Executive Summary | 94 |
| Category Management in the Retail Market: Overview and Status Quo | 95 |
| Optimization of Campaigns | 96 |
| Success Story: Optimization of Mailings | 97 |
| Cross- and Up-Selling | 98 |
| Success Story: Product Recommendations | 100 |
| Outlook | 102 |
| Visions and Suggested Actions | 104 |
| References | 104 |
| Networks | 106 |
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| Planning Problems in Public Transit | 107 |
| Executive Summary | 107 |
| Success Stories | 108 |
| Electronic Trip Planners | 108 |
| Revenue Management | 109 |
| Vehicle and Crew Scheduling | 110 |
| PT Planning Problems: Survey and Status Quo | 111 |
| Scheduling | 112 |
| Vehicle Scheduling | 113 |
| Crew Scheduling | 115 |
| Control | 115 |
| Stochastic and Robust Optimization | 117 |
| Online Optimization | 117 |
| Service Design | 118 |
| Infrastructure Construction | 118 |
| Vehicle Procurement | 119 |
| Line, Timetable, and Fare Planning | 119 |
| Regulation | 120 |
| Strengths, Weaknesses, and Challenges | 120 |
| General Conditions for the Use of Mathematics | 121 |
| Centralized Forms of Organization | 121 |
| Availability of Data and Information Technology | 121 |
| Complexity | 121 |
| Standardization | 123 |
| Regulation and Deregulation | 123 |
| Mathematical Models and Algorithms | 124 |
| Standard Models and Techniques | 125 |
| Data for Academic Research | 125 |
| Theory and Algorithms | 125 |
| Transfer and Education | 127 |
| Communication and Education | 127 |
| Business Environment | 127 |
| Conclusion | 128 |
| Visions and Recommendations | 129 |
| Discrete Optimal Control: Real-Time Re-Planning of Traffic Systems in Case of Disruptions | 129 |
| Model Integration: Service Design in Bus and Rail Traffic | 131 |
| References | 131 |
| Towards More Intelligence in Logistics with Mathematics | 134 |
| Executive Summary | 134 |
| Examples of Success | 136 |
| Logistics Chains | 136 |
| Shipping | 137 |
| Production Logistics | 138 |
| Controlling Logistical Networks | 140 |
| Logistics and Mathematics: the Status Quo | 143 |
| On the Development of Logistics | 143 |
| Mathematics in Logistics | 144 |
| Future Challenges | 144 |
| Visions and Recommendations for Action | 146 |
| References | 147 |
| Optimization of Communication Networks | 149 |
| Executive Summary | 149 |
| Mathematics as the Foundation of Every Network | 150 |
| Routing in the Internet | 150 |
| Quality Control in Phone Networks and the Internet | 151 |
| Cost Optimization of Network Investments | 152 |
| Networks, Planning and Methods | 153 |
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