Systems & Control

I. Introduction and Models of Manufacturing Systems.- 1. Concepts of hierarchical decision making.- 1.1 Introduction.- 1.2 A brief review of the literature.- 1.3 Our approach to hierarchical decision making.- 1.4 Plan of the book.- 2. Models of manufacturing systems.- 2.1 Introduction.- 2.2 A parallel-machine, single product model.- 2.3 A parallel-machine, multi-product model.- 2.4 A single product dynamic flowshop.- 2.5 A dynamic jobshop.- 2.6 Setup costs and setup times.- 2.7 Interaction with other functional areas.- II. Optimal Control of Manufacturing Systems: Existence and Characterization.- 3. Optimal control of parallel machine systems.- 3.1 Introduction.- 3.2 Problem formulation.- 3.3 Properties of the value function.- 3.4 Turnpike sets with constant demand.- 3.5 Turnpike sets with reliable machines.- 3.6 Miscellaneous results.- 3.7 Notes.- 4. Optimal control of dynamic flowshops.- 4.1 Introduction.- 4.2 Problem formulation.- 4.3 Properties of the value function.- 4.4 An equivalent deterministic problem.- 4.5 HJBDD equations and boundary conditions.- 4.6 Extension of results to dynamic jobshops.- 4.7 Notes.- III: Asymptotic Optimal Controls.- 5. Hierarchical controls in systems with parallel machines.- 5.1 Introduction.- 5.2 Formulation of the single product case.- 5.3 Properties of the value function.- 5.4 The limiting control problem.- 5.5 Convergence of the value function.- 5.6 Asymptotic optimal feedback controls.- 5.7 A simple example.- 5.8 Capacity dependent on production rate.- 5.9 Machine states with weak and strong interactions.- 5.10 The multi-product case.- 5.11 Concluding remarks.- 5.12 Notes.- 6. Hierarchical controls in dynamic flowshops.- 6.1 Introduction.- 6.2 Formulation of the m-machine flowshop.- 6.3 A special case: The two-machine flowshop.- 6.4 Construction of candidate open-loop controls.- 6.5 Preliminary results.- 6.6 Proof of asymptotic optimality.- 6.7 Concluding remarks.- 6.8 Notes.- 7. Hierarchical controls in dynamic jobshops.- 7.1 Introduction.- 7.2 A graph-theoretic framework.- 7.3 The optimization problem.- 7.4 Lipschitz continuity.- 7.5 Asymptotic optimal open-loop controls.- 7.6 Concluding remarks.- 7.7 Notes.- 8. Hierarchical production and setup scheduling in a single machine system.- 8.1 Introduction.- 8.2 Problem formulation.- 8.3 HJB equations.- 8.4 The limiting decision problem.- 8.5 Asymptotic optimal open-loop decisions.- 8.6 Asymptotic optimal feedback decisions.- 8.7 A simple example.- 8.8 Concluding remarks.- 8.9 Notes.- 9. Hierarchical feedback controls in two-machine flowshops.- 9.1 Introduction.- 9.2 Original and limiting problems.- 9.3 An explicit solution of the limiting problem.- 9.4 An asymptotic optimal feedback control.- 9.5 Relationship to the Kanban control.- 9.6 Concluding remarks.- 9.7 Notes.- IV: Multilevel Hierarchical Decisions.- 10. A production and capacity expansion model.- 10.1 Introduction.- 10.2 Problem formulation.- 10.3 Viscosity solutions of HJB equations.- 10.4 The limiting control problem.- 10.5 Verification theorems.- 10.6 Asymptotic optimal feedback decisions.- 10.7 Concluding remarks.- 10.8 Notes.- 11. Production-marketing systems.- 11.1 Introduction.- 11.2 Problem formulation and possible hierarchies.- 11.3 Analysis of the value functions.- 11.4 Asymptotic optimal feedback controls.- 11.5 Concluding remarks.- 11.6 Notes.- V: Computations and Conclusions.- 12. Computations and evaluation of hierarchical controls.- 12.1 Introduction.- 12.2 Problems and policies under consideration.- 12.3 Computational issues.- 12.4 Comparison of HC with other policies.- 12.5 Concluding remarks.- 12.6 Notes.- 13. Further extensions and open research problems.- 13.1 Introduction.- 13.2 Asymptotic optimal feedback controls.- 13.3 Error bounds for feedback controls.- 13.4 Average costs and robust controls.- 13.5 General systems.- 13.6 Final thoughts.- VI: Appendices.- A. Finite state Markov chains.- B. Martingale problems, tightness, and Skorohod representation.- C. Rate of convergence of Markov chains.- D. Control-dependent Markov chains.- E. Convergence of Markov chains with two parameters.- F. Convex functions.- G. Viscosity solutions of HJB equations.- H. Value functions and optimal controls.- I. A review of relevant graph theory.- J. Miscellany.- Author index.- Copyright permissions.