## Mathematics of Stochastic Manufacturing Systems: AMS-SIAM Summer Seminar in Applied Mathematics, June 17-22, 1996, Williamsburg, VirginiaThis volume presents the proceedings of the 26th AMS-SIAM Summer Seminar in Applied Mathematics, "The Mathematics of Stochastic Manufacturing Systems", held in June 1996 at the College of William and Mary (Williamsburg, VA, USA). Manufacturing is facing rapidly growing challenges in the global marketplace. As an ever growing discipline, its research involves a wide spectrum of techniques that go far beyond traditional applied mathematics. Manufacturing research cuts across the disciplines of operations research, management science, industrial engineering, systems theory, and applied mathematics. At the forefront of this interdisciplinary area, research in mathematical and computational sciences has become indispensable in the development of existing techniques and management practices. In this volume, leading experts in mathematical manufacturing research and related fields review and update recent advances in mathematics of stochastic manufacturing systems and attempt to bridge the gap between theory and applications. The topics covered include scheduling and production planning, modeling of manufacturing systems, hierarchical control for large and complex systems, Markov chains, queueing networks, numerical methods for system approximations, singular perturbed systems, risk-sensitive control, stochastic optimization methods, discrete event systems, and statistical quality control. This book presents research problems, techniques for dealing with problems, and future directions. The interdisciplinary nature is of great advantage to the applied mathematics and manufacturing research community. |

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### Contents

1 | |

Robust Control of Semiconductor Manufacturing Processes | 37 |

Maintenance and Production Control of Manufacturing Systems with Setups | 55 |

Optimal sS Production Policies with Delivery Time Guarantees | 71 |

Identification and Control of a Stochastic Manufacturing System with Noisy Demand | 83 |

Stochastic Optimization via Grid Search Katherine Bennett Ensor and Peter W Glynn | 89 |

Optimal Ergodic Control of Singularly Perturbed Hybrid Stochastic Systems | 101 |

Bounding | 127 |

Stochastic Adaptive Control and Manufacturing Systems | 201 |

Coupling Ergodicity and Sensitivity of Markov Processes | 219 |

Optimal Feedback Controls in Dynamic Stochastic Jobshops | 235 |

Using Renyi entropies to measure uncertainty in search problems | 253 |

The Role of Information in Scheduling Machines to Supply a Production Line | 269 |

Some Insights into NearOptimal Plans for Stochastic Manufacturing Systems | 287 |

On Stochastic Optimization and Its Applications to Manufacturing | 317 |

Stochastic Scheduling via Polymatroid Optimization David D Yao and Li Zhang | 333 |

bounds for closed queueing networks a primal approach | 139 |

Risk Sensitive Optimal Control of Wear Processes | 163 |

Stability and optimization of queueing networks and their fluid models | 175 |

Maximum Principle for Control of Piecewise Deterministic Markov Processes | 365 |

Autocorrelation Analysis of Some Linear Transfer Function Models and Its Applications in the Dynamic Process Systems | 385 |

### Common terms and phrases

adaptive control admissible controls algorithm apply approach approximation assume assumption asymptotically optimal autocorrelation average bound buffer capacity computational condition conservation laws consider constant constraints convergence convex corresponding cost functional defined definition denote deterministic differential discrete distribution dynamic programming entropy ergodic estimate example feasible feedback control finite fluid limit model fluid model given hierarchical HJB equation implies inequality initial input inventory jobshop Lemma linear program Lipschitz continuous Markov chain Markov process Mathematics Subject Classification maximum principle minimize minivan minivan bodies obtained optimal control optimal control problem optimal feedback optimal policy Ordinal Optimization parameter performance perturbation polymatroid polytope pr(T priority proof queueing networks random variables Renyi entropies satisfies scheduling sequence Sethi setup simulation solution solve space stationary stochastic manufacturing systems supermodularity switch curve Theorem trajectory value function vector Zhang