EXTENDED-CONWIP-KANBAN SYSTEM: CONTROL AND PERFORMANCE ANALYSIS A Dissertation Presented to The Academic Faculty by Karin Boonlertvanich In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Industrial and System Engineering Georgia Institute of Technology April 2005 iii EXTENDED-CONWIP-KANBAN SYSTEM: CONTROL AND PERFORMANCE ANALYSIS Approved by: Dr. Chen Zhou, Advisor Dr. Paul Griffin School of Industrial & Systems School of Industrial & Systems Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Dr. Ronald Billings Dr. Spiridon Reveliotis School of Industrial & Systems School of Industrial & Systems Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Dr. Mark Ferguson School of Management Date Approved: April 6, 2005 Georgia Institute of Technology iv ACKNOWLEDGEMENTS I would like to thank my greatest source of support which is my thesis advisor, Dr. Chen Zhou. His endless intellectual support and encouragement ware a great relief. My views on manufacturing control were greatly influenced by one of my best teacher, Dr. Paul Griffin. The inspiration of this thesis was originated from his manufacturing system course which taught me more about manufacturing control than any other sources. I would like to acknowledge Dr. Mark Ferguson for his suggestion about including a case study for completeness of this thesis and his courtesy of providing reference papers. I would also want to thank Dr. Spiridon Reveliotis for his comments of this dissertation and his kind collaboration when I was his TA for many times. Thanks also go to Dr. Ronald Billings for serving as one of my thesis committee. Finally, I owe a great debt to my girlfriend, Nok, for helping me keep the whole thing in perspective. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS........................................................................................... iii LIST OF TABLES .........................................................................................................ix LIST OF FIGURES........................................................................................................xi NOMENCLATURES....................................................................................................xv SUMMARY ................................................................................................................xvii CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW...................................1 1.1 Introduction..............................................................................................1 1.2 Literature Review.....................................................................................6 CHAPTER 2 PRODUCTION CONTROL POLICIES..................................................10 2.1 Modeling convention..............................................................................10 2.2 CONWIP Control System (CW).............................................................13 2.3 Base Stock Control System (BS) ............................................................15 2.4 Kanban Control System (KB) .................................................................18 2.5 CONWIP Kanban Control System..........................................................21 2.6 Generalized Kanban Control System (GK) .............................................24 2.7 Extended Kanban Control System (EK)..................................................27 CHAPTER 3 EXTENDED-CONWIP-KANBAN CONTROL SYSTEM......................31 3.1 Motivations from Existing Controls........................................................31 3.2 System Characteristics............................................................................36 iv 3.3 Invariants ...............................................................................................39 3.4 Bounds ...................................................................................................45 3.5 Boundary cases.......................................................................................47 3.6 Variation of the Extended CONWIP Kanban Control .............................50 CHAPTER 4 SIMULATION COMPARISIONS ..........................................................53 4.1 Model assumptions.................................................................................53 4.2 Performance Measures............................................................................54 4.3 Simulation models..................................................................................55 4.4 Simulation results...................................................................................57 4.5 Discussion..............................................................................................68 4.6 Discussion..............................................................................................71 4.7 Conclusion .............................................................................................72 CHAPTER 5 PERFORMANCE COMPARISON: STATE SPACE ................................. REPRESENTATION APPROACH.........................................................73 5.1 Elements and notations of a two-stage production system.......................74 5.2 Control objective ....................................................................................75 5.3 Optimum control in the literature............................................................76 5.4 Closed queueing network approximation ................................................82 5.5 Single-stage control policies ...................................................................83 5.5.1 Control function of WIP-controlling policy ............................................84 5.5.2 Control function of finished goods basestock-controlling policy.............91 5.5.3 Control function of single-stage ECK control policy...............................95 5.6 Discussion on single-stage control policies ...........................................101 5.7 Two-stage control policies....................................................................102 5.7.1 Control function of two-stage Base Stock policy...................................103 5.7.2 Control function of two-stage Kanban policy........................................107 5.7.3 Control function of CONWIP-Kanban policy .......................................113 v 5.7.4 Control function of Extended Kanban policy ........................................119 5.7.5 Control function of Generalized Kanban policy ....................................128 5.7.6 Control function of Extended CONWIP Kanban policy ........................136 5.8 Discussion on two-stage control policies ..............................................143 CHAPTER 6 ON THE DESIGN OF ECK CONTROL SYSTEMS.............................147 6.1 Single-stage ECK control system..........................................................148 6.1.1 Single-stage saturated ECK control system...........................................148 6.1.2 Effect of C (or s) in a single-stage unsaturated ECK control system when C = s............................................................................................150 6.1.3 Effect of C and s when C ≠ s ................................................................153 6.2 Effect of ki, si, and C in a multi-stage ECK control system....................154 6.2.1 Effect of ki and C with exponential processing time..............................154 6.2.2 Production capacity of two-stage ECK control system having k1 = k2 = k .............................................................................................158 6.2.3 Effect of si on backorder and cycle time................................................163 6.3 Two-stage ECK control system separated by a bottleneck station .........168 6.3.1 Production capacity of two-stage ECK control system with bottleneck station..........................................................................168 6.3.2 Effect of si in a multi-stage ECK control system with bottleneck station..........................................................................171 6.4 Design procedure for Extended CONWIP Kanban................................174 CHAPTER 7 PARAMETER ADJUSTING MECHANISM FOR SINGLE-STAGE........ ECK POLICY .......................................................................................176 7.1 Prior research .......................................................................................177 7.1.1 Statistical throughput control................................................................177 7.1.2 Control chart-based reactive kanban control .........................................177 7.1.3 Inventory-based adaptive kanban control..............................................178 7.1.4 Summary and design criteria of our control mechanism........................179 7.2 Detecting changes in demand rate.........................................................180 7.3 Inventory level constraint .....................................................................182 7.4 Optimization formulation .....................................................................184 7.4.1 Demand rate changes............................................................................185 7.5 Performance of the purposed control mechanism..................................187 7.6 Conclusion ...........................................................................................192 vi CHAPTER 8 A CASE STUDY OF IRON AND