THROUGHPUT OPTIMIZATION IN ROBOTIC CELLS
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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 Travel-Time Metric Number of Part-Types 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 1-Unit Cycles Special Cases General Cases: Constant Travel-Time 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 1-Unit Cycles and Approximation Results Additive Travel-Time Cells Pyramidal Cycles A 1.5-Approximation Algorithm A 10/7-Approximation for Additive Cells Constant Travel-Time Cells A 1.5-Approximation Algorithm Euclidean Travel-Time Cells DUAL-GRIPPER ROBOTS Additional Notation Cells with Two Machines A Cyclic Sequence for m-machine Dual-Gripper Cells Dual-Gripper Cells with Small Gripper Switch Times Comparing Dual-Gripper and Single-Gripper Cells Comparison of Productivity: Computational Results Efficiently Solvable Cases Single-Gripper Cells with Output Buffers at Machines Dual-Gripper Robotic Cells: Constant Travel Time Lower Bounds and Optimal Cycles: m-machine Simple Robotic Cells One-Unit Cycles Multi-Unit Cycles PARALLEL MACHINES Single-Gripper Robots Definitions k-unit Cycles and Blocked Cycles 156
3 Contents xi Structural Results for k-unit Cycles Blocked Cycles LCM Cycles Practical Implications Optimal Cycle for a Common Case Fewest Machines Required to Meet Timelines Dual-Gripper Robots Lower Bound on Per Unit Cycle Time An Optimal Cycle Improvement from Using a Dual-Gripper Robot or Parallel Machines Installing a Dual-Gripper Robot in a Simple Robotic Cell Installing Parallel Machines in a Single-Gripper Robot Cell Installing a Dual-Gripper Robot in a Single-Gripper Robotic Cell with Parallel Machines An Illustration on Data from Implemented Cells MULTIPLE-PART-TYPE PRODUCTION: SINGLE-GRIPPER ROBOTS MPS Cycles and CRM Sequences Scheduling Multiple Part-Types in Two-Machine Cells Scheduling Multiple Part-Types in Three-Machine Cells Cycle Time Derivations Efficiently Solvable Special Cases Steady-State 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 Three-Machine Cells MPS Cycles with the Sequence CRM(π 2 ) MPS Cycles with the Sequence CRM(π 6 ) Complexity of Three-Machine Robotic Cells Scheduling Multiple Part-Types in Large Cells Class U: Schedule Independent Problems Class V 1: Special Cases of the TSP Class V 2: NP-Hard TSP Problems Class W : NP-Hard Non-TSP Problems Overview Heuristics for Three-Machine 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 Three-Machine Problems Heuristics for Large Cells The Cell Design Problem Forming Cells Buffer Design An Example Computational Testing MULTIPLE-PART-TYPE PRODUCTION: DUAL-GRIPPER ROBOTS Two-Machine Cells: Undominated CRM Sequences Two-Machine Cells: Complexity Cycle Time Calculation Strong NP-Completeness Results Polynomially Solvable Problems Analyzing Two-Machine Cells with Small Gripper Switch Times A Heuristic for Specific CRM Sequences A Performance Bound for Heuristic Hard-CRM A Heuristic for Two-Machine Cells Comparison of Productivity: Single-Gripper Vs. Dual- Gripper Cells An Extension to m-machine Robotic Cells MULTIPLE-ROBOT CELLS Physical Description of a Multiple-Robot Cell Cycles in Multiple-Robot Cells Cycle Times Scheduling by a Heuristic Dispatching Rule Computational Results Applying an LCM Cycle to Implemented Cells NO-WAIT AND INTERVAL ROBOTIC CELLS No-Wait Robotic Cells Interval Pick-up 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 Dual-Gripper Robots Flexible Robotic Cells Implementation Issues Using Local Material Handling Devices Revisiting Machines 379 Appendices Appendix A 383 A.1 1-Unit Cycles 383 A Unit Cycles in Classical Notation 384 A Unit Cycles in Activity Notation 385 Appendix B 387 B.1 The Gilmore-Gomory Algorithm for the TSP 387 B.1.1 The Two-Machine No-Wait Flowshop Problem 387 B.1.2 Formulating a TSP 388 B.1.3 The Gilmore-Gomory Algorithm 389 B.2 The Three-Machine No-Wait 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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