Process Operations with Uncertainty and Integration Considerations

......................................................................................................................................................... ii Acknowledgements ........................................................................................................................................iv List of tables ...................................................................................................................................................ix List of illustrations .........................................................................................................................................xi Chapter 1 Introduction ........................................................................................................................ 1 1.1 Planning and scheduling in the process industry .................................................................. 1 1.2 Modeling and optimization for planning and scheduling ..................................................... 3 1.3 Problems and challenges ...................................................................................................... 4 1.3.1 Uncertainty issue ......................................................................................................... 5 1.3.2 Integration issue ........................................................................................................... 6 1.4 Project objectives.................................................................................................................. 7 Chapter 2 Uncertainty Analysis with Parametric Programming ................................................... 10 2.1 Introduction ........................................................................................................................ 10 2.2 Parametric programming algorithm .................................................................................... 12 2.2.1 Problem definition ..................................................................................................... 12 2.2.2 Local parametric solution algorithm .......................................................................... 13 2.2.3 Exploring the parameter space ................................................................................... 16 2.3 Uncertainty analysis for scheduling problem ..................................................................... 21 2.4 Summary ............................................................................................................................ 29 Chapter 3 Robust Preventive Scheduling ......................................................................................... 31 3.1 Introduction ........................................................................................................................ 31 3.2 Robust optimization ............................................................................................................ 34 3.2.1 Soyster’s formulation ................................................................................................. 35 3.2.2 Ben-Tal and Nemirovski’s formulation ..................................................................... 36 3.2.3 Bertsimas and Sim’s formulation............................................................................... 37 3.2.4 Comparison of different formulations ....................................................................... 40 3.3 Robust scheduling .............................................................................................................. 41 vii 3.3.1 Price uncertainty ........................................................................................................ 42 3.3.2 Processing time uncertainty ....................................................................................... 43 3.3.3 Demand uncertainty ................................................................................................... 43 3.4 Examples ............................................................................................................................ 44 3.4.1 Example 1 .................................................................................................................. 44 3.4.2 Example 2 .................................................................................................................. 50 3.5 Summary ............................................................................................................................ 53 Chapter 4 Reactive Scheduling .......................................................................................................... 55 4.1 Introduction ........................................................................................................................ 55 4.2 Reactive scheduling formulation ........................................................................................ 58 4.2.1 General idea ............................................................................................................... 58 4.2.2 Rush order .................................................................................................................. 59 4.2.3 Machine breakdown ................................................................................................... 62 4.3 Examples ............................................................................................................................ 64 4.4 Summary ............................................................................................................................ 76 Chapter 5 Integration of Planning and Scheduling ......................................................................... 77 5.1 Introduction ........................................................................................................................ 77 5.2 Problem structure ............................................................................................................... 80 5.3 Augmented Lagrangian Optimization algorithm ................................................................ 82 5.4 Decomposition strategy ...................................................................................................... 85 5.4.1 Diagonal Quadratic Approximation ........................................................................... 86 5.4.2 Two-Level optimization ............................................................................................ 87 5.5 Examples ............................................................................................................................ 90 5.6 Summaries .......................................................................................................................... 96 Chapter 6 Rolling Horizon Optimization ......................................................................................... 99 6.1 Introduction ........................................................................................................................ 99 6.2 Rolling horizon framework .............................................................................................. 102 6.3 Production capacity model derivation .............................................................................. 108 -