Networks of Interacting Machines : Production Organization in Complex Industrial Systems and Biological Cells

Intro -- CONTENTS -- Preface -- 1 Continuum Models for Interacting Machines Dieter Armbruster, Pierre Degond, Christian Ringhofer -- 1.1 Introduction -- 1.2 Heuristic Models -- 1.2.1 Quasistatic Models -- 1.2.2 Advection-Diffusion Equations -- 1.2.3 Policies and Bottlenecks -- 1.2.3.1 Dispatch Rules -- 1.2.3.2 Bottlenecks and Maximal Capacities -- 1.3 First Principle Models -- 1.3.1 Kinetic Models -- 1.3.2 Deterministic Kinetic Models -- Models with capacity constraints: -- The multi - phase model -- An example with bottlenecks: -- 1.3.3 Stochasticity and Diffusion -- Random velocity updates -- Asymptotics for many stage processes: -- A numerical comparison -- 1.4 Conclusions -- Acknowledgements -- References -- 2 Supply and Production Networks: From the Bullwhip Effect to Business Cycles Dirk Helbing, Stefan Lammer -- 2.1 Introduction -- 2.2 Input-Output Model of Supply Networks -- 2.2.1 Adaptation of Production Speeds -- 2.2.2 Modelling Sequential Supply Chains -- 2.2.3 More Detailed Derivation of the Production Dynamics -- 2.2.4 Dynamic Solution and Resonance Effects -- 2.2.5 The Bullwhip Effect -- 2.3 Network Effects -- 2.3.1 General Methods of Solution -- 2.3.2 Examples of Supply Networks -- 2.4 Network-Induced Business Cycles -- 2.4.1 Treating Producers Analogous to Consumers -- 2.5 Reproduction of Some Empirically Observed Features of Business Cycles -- 2.5.1 Dynamic Behaviors and Stability Thresholds -- 2.6 Summary -- 2.7 Future Research Directions -- 2.7.1 Network Engineering -- 2.7.2 Cyclic Dynamics in Biological Systems -- 2.7.3 Heterogeneity in Production Networks -- 2.7.4 Multi-Goal Control -- 2.7.5 Non-Linear Dynamics and Scarcity of Resources -- Acknowledgements -- Appendix A -- 2.8 Boundary between Damped and Growing Oscillations -- 2.9 Boundary between Damped Oscillations and Overdamped Behavior -- References.