4.3 Operator-Machine Interactions......Page 7
6.5 Processing Step Modeling Paradigm......Page 9
9.3 Example of a Kanban Serial System......Page 13
Cover......Page 1
9.2 Modeling the Two-Node Subsystem......Page 4
Contents......Page 10
1.5 Multivariate Distributions......Page 24
Appendix......Page 32
Problems......Page 33
9.4.2 Cycle Time Restriction......Page 35
9.4.3 Serial Factory Results......Page 36
Problems......Page 37
References......Page 44
9.1 The Decomposition Approach Used for Kanban Systems......Page 2
Index......Page 5
9.2.4 Connecting the Subsystems......Page 11
Symbols......Page 14
8.2 Closed Queueing Networks with Multiple Products......Page 15
8.2.1 Mean Value Analysis for Multiple Products......Page 16
1.1 Basic Definitions......Page 18
1.2 Random Variables and Distribution Functions......Page 21
3.7.1 General Service Distributions......Page 23
Preface......Page 8
7.4.1 A Serial System Topology......Page 17
6.6 Group Technology and Cellular Manufacturing......Page 19
8.2.3 General Service Time Approximation for Multiple Products......Page 22
3.7.2 Approximations for G/G/1 Systems......Page 25
1.3 Mean and Variance......Page 27
8.3.2 Push Strategy Model......Page 29
References......Page 39
A.2 Event-Driven Simulations......Page 3
7.5.1 Batch Network Example 1......Page 26
9.3.4 Convergence and Factory Performance Measures......Page 28
7.1.3 Batch Move Processing Time Delays......Page 6
8.1.2 Analysis with General Processing Times......Page 12
References......Page 38
1.4 Important Distributions......Page 30
Problems......Page 34
9.3.2 The Backward Pass......Page 20
9.4.1 Allocating a Fixed Number of Buffer Units......Page 31
References......Page 40
1.5 Multivariate Distributions......Page 41
1.6.1 Fixed Sum of Random Variables......Page 49
1.6.2 Random Sum of Random Variables......Page 50
1.6.3 Mixtures of Random Variables......Page 52
Appendix......Page 53
Problems......Page 54
References......Page 61
2.1 The Basics......Page 62
2.1.1 Notation, Definitions and Diagrams......Page 63
2.1.2 Measured Data and System Parameters......Page 66
2.2 Introduction to Factory Performance......Page 71
2.2.1 The Modeling Method......Page 72
2.2.2 Model Usage......Page 75
2.2.3 Model Conclusions......Page 76
2.3 Deterministic vs Stochastic Models......Page 77
Appendix......Page 79
Problems......Page 82
References......Page 84
3.1 First Model......Page 85
3.2 Diagram Method for Developing the Balance Equations......Page 89
3.3 Model Shorthand Notation......Page 92
3.4 An Infinite Capacity Model (M/M/1)......Page 93
3.5 Multiple Server Systems with Non-identical Service Rates......Page 97
3.6.1 Erlang Processing Times......Page 101
3.6.2 Erlang Inter-Arrival Times......Page 103
3.6.3 Phased Inter-arrival and Processing Times......Page 105
3.7 Single Server Model Approximations......Page 106
3.7.1 General Service Distributions......Page 107
3.7.2 Approximations for G/G/1 Systems......Page 109
3.7.3 Approximations for G/G/c Systems......Page 111
Appendix......Page 113
Problems......Page 116
References......Page 123
4 Processing Time Variability......Page 125
4.1 Natural Processing Time Variability......Page 127
4.2 Random Breakdowns and Repairs During Processing......Page 129
4.3 Operator-Machine Interactions......Page 131
Problems......Page 137
References......Page 139
5.1 Approximating the Departure Process from a Workstation......Page 140
5.2 Serial Systems Decomposition......Page 143
5.3.1 Merging Inflow Streams......Page 148
5.3.2 Random Splitting of the Departure Stream......Page 150
5.4 The General Network Approximation Model......Page 153
5.4.1 Computing Workstation Mean Arrival Rates......Page 154
5.4.2 Computing Squared Coefficients of Variation for Arrivals......Page 156
Appendix......Page 165
Problems......Page 167
References......Page 172
6 Multiple Product Factory Models......Page 173
6.1 Product Flow Rates......Page 174
6.2 Workstation Workloads......Page 176
6.3 Service Time Characteristics......Page 177
6.4 Workstation Performance Measures......Page 178
6.5 Processing Step Modeling Paradigm......Page 181
6.5.1 Service Time Characteristics......Page 184
6.5.2 Performance Measures......Page 186
6.5.3 Alternate Approaches......Page 188
6.6 Group Technology and Cellular Manufacturing......Page 191
Problems......Page 198
References......Page 210
7 Models of Various Forms of Batching......Page 211
7.1 Batch Moves......Page 212
7.1.1 Batch Forming Time......Page 213
7.1.2 Batch Queue Cycle Time......Page 215
7.1.3 Batch Move Processing Time Delays......Page 216
7.1.4 Inter-departure Time SCV with Batch Move Arrivals......Page 218
7.2 Batching for Setup Reduction......Page 220
7.2.1 Inter-departure Time SCV with Batch Setups......Page 223
7.3.1 Cycle Time for Batch Service......Page 224
7.3.2 Departure Process for Batch Service......Page 225
7.4.1 A Serial System Topology......Page 227
7.4.2 Branching Following a Batch Server......Page 228
7.5.1 Batch Network Example 1......Page 236
7.5.2 Batch Network Example 2......Page 240
Problems......Page 244
References......Page 254
8 WIP Limiting Control Strategies......Page 255
8.1 Closed Queueing Networks for Single Products......Page 256
8.1.1 Analysis with Exponential Processing Times......Page 259
8.1.2 Analysis with General Processing Times......Page 266
8.2 Closed Queueing Networks with Multiple Products......Page 269
8.2.1 Mean Value Analysis for Multiple Products......Page 270
8.2.2 Mean Value Analysis Approximation for Multiple Products......Page 274
8.2.3 General Service Time Approximation for Multiple Products......Page 276
8.3 Production and Sequencing Strategies......Page 281
8.3.1 Problem Statement......Page 282
8.3.2 Push Strategy Model......Page 283
8.3.3 CONWIP Strategy Model......Page 285
Appendix......Page 286
Problems......Page 287
References......Page 293
9 Serial Limited Buffer Models......Page 295
9.1 The Decomposition Approach Used for Kanban Systems......Page 296
9.2 Modeling the Two-Node Subsystem......Page 298
9.2.1 Modeling the Service Distribution......Page 299
9.2.2 Structure of the State-Space......Page 302
9.2.3 Generator Matrix Relating System Probabilities......Page 304
9.2.4 Connecting the Subsystems......Page 305
9.3 Example of a Kanban Serial System......Page 307
9.3.1 The First Forward Pass......Page 308
9.3.2 The Backward Pass......Page 314
9.3.3 The Remaining Iterations......Page 321
9.3.4 Convergence and Factory Performance Measures......Page 322
9.3.5 Generalizations......Page 324
9.4.1 Allocating a Fixed Number of Buffer Units......Page 325
9.4.2 Cycle Time Restriction......Page 329
9.4.3 Serial Factory Results......Page 330
Problems......Page 331
References......Page 334
A.1 Random Variates......Page 335
A.2 Event-Driven Simulations......Page 337
References......Page 344
Glossary......Page 345
Index......Page 349