Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1987 Modeling and analysis of three-dimensional robotic palletizing systems for mixed carton sizes Du-Ming Tsai Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Industrial Engineering Commons Recommended Citation Tsai, Du-Ming, "Modeling and analysis of three-dimensional robotic palletizing systems for mixed carton sizes " (1987). Retrospective Theses and Dissertations. 9308. https://lib.dr.iastate.edu/rtd/9308 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. 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For the Gradué e College Iowa State University Ames, Iowa 1987 ii TABLE OF CONTENTS Page I. STATEMENT OF PROBLEM 1 II. REVIEW OF RELEVANT LITERATURE 4 A. Introduction 4 B. Robotic Palletization 6 1. Representative palletizing systems for industrial boxes 6 2. Palletizing cell characteristics 7 3. Sorting/stamping applications and multiple outputs 11 A. Palletizing cells with sensory features 14 C. Pallet Loading Problems 15 1. Introduction 15 2. Overview of literature 16 3. Linear and goal programming approaches 18 4. Dynamic programming approaches 22 5. Heuristic approaches 25 6. Integer programming approach 28 7. Combinatoric and network flow approaches 29 8. The tiling aspect 30 9. The loading aspect 32 10. The bin packing aspect 34 III. THREE-DIMENSIONAL PALLET LOADING ALGORITHMS 37 A. Introduction 37 B. The Mixed 0-1 Integer Programming Model 38 1. Constraints of placement location on the pallet 38 2. Formulation of two-dimensional pallet packing 43 3. Formulation of three-dimensional pallet packing problem 54 4. A numerical example 63 5. A branch-and-bound solution procedure 72 ill Page C. The Heuristic Dynamic Programming Approach 79 1. Maximization of pallet space usage (goal 1) 80 2. Restriction on the number of boxes (goal 2) 95 IV. PALLETIZING SYSTEMS AND ROBOT PROGRAMMING 103 A. Introduction 103 B. Two Palletizing Approaches 104 1. Dynamic pallet patterns 104 2. Multi-pallet packing with turntables 106 C. The Robotic Palletizing Cell 111 1. The equipment/hardware 112 2. Software for the Rhino robot 116 D. Palletizing Control Program 133 1. Data input 134 2. Palletizing procedure 143 3. "Match" selection 149 V. THE PALLETIZING SIMULATION 153 A. Introduction 153 B. Condition Setups 154 1. Assumptions 154 2. Box size distributions 155 3. Length of a distribution run 156 4. Box size sequence in a distribution 158 5. Permutation of 20 distributions 161 6. Summary of condition setups 162 7. Collection of robot movement times 164 C. Evaluation Criteria 166 1. Loading statistics 166 2. Queues in storage areas 168 iv Page D. Simulation Results 170 1. Worst-case permutation of distributions 170 2. Multi-pallet packing (known distributions) 174 3. Look-ahead factors (unknown distributions) 180 4. Comparison of known and unknown box distributions 189 5. Summary 200 VI. CONCLUSIONS 202 VII. BIBLIOGRAPHY 204 VIII. ACKNOWLEDGMENTS 212 IX. APPENDIX A. PROGRAM LISTING FOR MIXED 0-1 INTEGER PROGRAMMING 213 X. APPENDIX B. PROGRAM LISTING FOR THE HEURISTIC DYNAMIC PROGRAMMING 222 XI. APPENDIX C. ROBOT CONTROL PROGRAM 230 XII. APPENDIX D. SIMULATION PROGRAM LISTING (KNOWN BOX SIZE DISTRIBUTIONS) 247 XIII. APPENDIX E. SIMULATION PROGRAM LISTING (UNKNOWN BOX SIZE DISTRIBUTIONS) 265 XIV. APPENDIX F. DETERMINATION OF PALLET PATTERNS 283 XV. APPENDIX G. PALLET PATTERNS AND PRECEDENCE DIAGRAMS 291 XVI. APPENDIX H. VARIATION OF BOXES STORED IN THE STORAGE AREA 312 XVII. APPENDIX I. ROBOT MOVEMENT TIMES 316 XVIII. APPENDIX J. RANDOM SEQUENCE OF 20 BOX SIZE DISTRIBUTIONS 324 XIX. APPENDIX K. PALLETIZING STATISTICS OF DISTRIBUTION RUNS 327 1 I. STATEMENT OF PROBLEM Material handling pallets are the most common tool used in warehous­ ing industries. Nearly every warehouse uses them to some extent. Pallets have become an almost universal warehouse operations tool. They provide a convenient, simple way to transport, stack, and store materials. Traditional palletizing methods load only boxes of the same size on one pallet. For retail business such as grocery distribution or manu­ facturers that produce many products of small quantities, a wide product mix of different box sizes must be loaded onto the same pallet. The tra­ ditional palletizing method may not optimize the utilization of the pallet cube. Manual palletizing is an extremely tedious and fatiguing task. Automatic palletization is, therefore, a potentially attractive alterna­ tive. Commercially available palletizers handle only one box size at a time. They cannot meet the requirements of palletizing applications with mixed box sizes. Industrial robots have always been a viable solution to complex loading operations due to their flexibility and programming capa­ bility. Conveyors are the most common device used to transfer boxes to the robotic palletizing station from warehouses or production lines. Since boxes of various sizes can randomly arrive via the conveyor, elaborate consideration must be given for the overall design of the robotic palletiz­ ing system. This enables the system to accommodate variations in the dis­ tributions of box sizes. Off-line storage areas may be required to absorb 2 boxes that cannot be immediately placed onto a pallet. These stored boxes can be picked up later when they can be successfully placed on the pallet. This research is an extension of previous work by Tsai et al. [95, 96,97]. Their early efforts were concentrated on the development of two- dimensional pallet packing algorithm. Tsai's algorithm was static and did not respond to variations in the distributions of box sizes. In this research, three dimensional pallet loading with mixed box sizes has been Investigated. This loading method allows many boxes of various sizes to be placed on the same pallet so as to maximize the pallet volume occupied by the boxes. The developed loading method is dynamically responsive to changes in the size distribution of the boxes in the loading queue. The completion of this research has involved the following tasks: • Development of algorithms that specify an optimal three- dimensional pallet pattern for various mixes of box sizes when such boxes are loaded onto a pallet of fixed dimensions. The two-dimensional algorithm presented by Tsai is not directly extendable to three-dimensional pallet packing model. The developed three-dimensional algorithms are, therefore, new approaches. • Development of a physical simulator of an integrated robotic palletizing system for both warehousing and manufacturing industries. The system design has focused on the problem of variations in box size distributions. • Development of a robot control program for automatic palletization, and completion of a physical simulation of a robotic palletizing station. A Rhino XR-2 robot has been employed for this simulation. Data have been collected and analyzed during the simulation to evaluate the feasibility and performance of the robotic palletiz­ ing system. 3 A variety of literature has been written which addresses both ro­ botic palletizing applications and mathematical algorithms of pallet packing problems.