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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