THROUGHPUT OPTIMIZATION IN ROBOTIC CELLS


 Amie Young
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1 Contents Preface xv 1. ROBOTIC CELLS IN PRACTICE Cellular Manufacturing Robotic Cell Flowshops Throughput Optimization Historical Overview Applications A CLASSIFICATION SCHEME FOR ROBOTIC CELLS AND NOTATION Machine Environment Number of Machines Number of Robots Types of Robots Cell Layout Processing Characteristics Pickup Criterion TravelTime Metric Number of PartTypes Objective Function An α β γ Classification for Robotic Cells Cell Data Processing Times Loading and Unloading Times Notations for Cell States and Robot Actions CYCLIC PRODUCTION Operating Policies and Dominance of Cyclic Solutions 29 ix
2 x THROUGHPUT OPTIMIZATION IN ROBOTIC CELLS 3.2 Cycle Times Waiting Times Computation of Cycle Times Lower Bounds on Cycle Times Optimal 1Unit Cycles Special Cases General Cases: Constant TravelTime Cells Optimization over Basic Cycles General Cases: Time Cells Additive and Euclidean Travel Calculation of Makespan of a Lot A Graphical Approach Algebraic Approaches Quality of 1Unit Cycles and Approximation Results Additive TravelTime Cells Pyramidal Cycles A 1.5Approximation Algorithm A 10/7Approximation for Additive Cells Constant TravelTime Cells A 1.5Approximation Algorithm Euclidean TravelTime Cells DUALGRIPPER ROBOTS Additional Notation Cells with Two Machines A Cyclic Sequence for mmachine DualGripper Cells DualGripper Cells with Small Gripper Switch Times Comparing DualGripper and SingleGripper Cells Comparison of Productivity: Computational Results Efficiently Solvable Cases SingleGripper Cells with Output Buffers at Machines DualGripper Robotic Cells: Constant Travel Time Lower Bounds and Optimal Cycles: mmachine Simple Robotic Cells OneUnit Cycles MultiUnit Cycles PARALLEL MACHINES SingleGripper Robots Definitions kunit Cycles and Blocked Cycles 156
3 Contents xi Structural Results for kunit Cycles Blocked Cycles LCM Cycles Practical Implications Optimal Cycle for a Common Case Fewest Machines Required to Meet Timelines DualGripper Robots Lower Bound on Per Unit Cycle Time An Optimal Cycle Improvement from Using a DualGripper Robot or Parallel Machines Installing a DualGripper Robot in a Simple Robotic Cell Installing Parallel Machines in a SingleGripper Robot Cell Installing a DualGripper Robot in a SingleGripper Robotic Cell with Parallel Machines An Illustration on Data from Implemented Cells MULTIPLEPARTTYPE PRODUCTION: SINGLEGRIPPER ROBOTS MPS Cycles and CRM Sequences Scheduling Multiple PartTypes in TwoMachine Cells Scheduling Multiple PartTypes in ThreeMachine Cells Cycle Time Derivations Efficiently Solvable Special Cases SteadyState Analyses Reaching Steady State for the Sequence CRM(π 2 ) Reaching Steady State for the Sequence CRM(π 6 ) A Practical Guide to Initializing Robotic Cells Intractable Cycles for ThreeMachine Cells MPS Cycles with the Sequence CRM(π 2 ) MPS Cycles with the Sequence CRM(π 6 ) Complexity of ThreeMachine Robotic Cells Scheduling Multiple PartTypes in Large Cells Class U: Schedule Independent Problems Class V 1: Special Cases of the TSP Class V 2: NPHard TSP Problems Class W : NPHard NonTSP Problems Overview Heuristics for ThreeMachine Problems A Heuristic Under the Sequence CRM(π 2 ) 270
4 xii THROUGHPUT OPTIMIZATION IN ROBOTIC CELLS A Heuristic Under the Sequence CRM(π 6 ) Computational Testing Heuristics for General ThreeMachine Problems Heuristics for Large Cells The Cell Design Problem Forming Cells Buffer Design An Example Computational Testing MULTIPLEPARTTYPE PRODUCTION: DUALGRIPPER ROBOTS TwoMachine Cells: Undominated CRM Sequences TwoMachine Cells: Complexity Cycle Time Calculation Strong NPCompleteness Results Polynomially Solvable Problems Analyzing TwoMachine Cells with Small Gripper Switch Times A Heuristic for Specific CRM Sequences A Performance Bound for Heuristic HardCRM A Heuristic for TwoMachine Cells Comparison of Productivity: SingleGripper Vs. Dual Gripper Cells An Extension to mmachine Robotic Cells MULTIPLEROBOT CELLS Physical Description of a MultipleRobot Cell Cycles in MultipleRobot Cells Cycle Times Scheduling by a Heuristic Dispatching Rule Computational Results Applying an LCM Cycle to Implemented Cells NOWAIT AND INTERVAL ROBOTIC CELLS NoWait Robotic Cells Interval Pickup Robotic Cells OPEN PROBLEMS Simple Robotic Cells Simple Robotic Cells with Multiple Part Types 376
5 Contents xiii 10.3 Robotic Cells with Parallel Machines Stochastic Data DualGripper Robots Flexible Robotic Cells Implementation Issues Using Local Material Handling Devices Revisiting Machines 379 Appendices Appendix A 383 A.1 1Unit Cycles 383 A Unit Cycles in Classical Notation 384 A Unit Cycles in Activity Notation 385 Appendix B 387 B.1 The GilmoreGomory Algorithm for the TSP 387 B.1.1 The TwoMachine NoWait Flowshop Problem 387 B.1.2 Formulating a TSP 388 B.1.3 The GilmoreGomory Algorithm 389 B.2 The ThreeMachine NoWait Flowshop Problem as a TSP 394 Copyright Permissions 409 Index 413
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vii TABLE OF CONTENTS CHAPTER TITLE PAGE DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK
vii TABLE OF CONTENTS CHAPTER TITLE PAGE DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF ABBREVIATIONS LIST OF SYMBOLS LIST OF APPENDICES
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