Introduction to Computational Optimization Models for Production Planning in a Supply Chain

Table of Contents......Page 8
1.1 Supply Chains and Production Planning......Page 12
1.2 Optimization......Page 13
1.3 Components of Supply Chain Management......Page 15
1.4 Scope of this Book......Page 16
2.1 Abstraction......Page 18
2.2.1 Variables, Data, Subscripts, and Math......Page 20
2.2.3 Objective Functions and Constraints......Page 22
2.3 Finding Solutions......Page 25
2.3.2 A Few Words About Uncertainty......Page 26
2.3.3 Solvers and Model Structure......Page 27
2.4 Implementing the Models in this Book......Page 28
3.1 An Example......Page 30
3.2 mrp Mechanics......Page 31
3.3 mrp Data......Page 33
3.4 mrp Optimization Formulation......Page 35
3.5 Discussion of mrp......Page 37
3.5.1 Troubles......Page 38
3.5.2 Virtues......Page 40
4.1 MRP II Mechanics......Page 41
4.2 MRP II Data and Constraints......Page 44
4.3 Discussion of MRP II......Page 46
4.4.1 A Straightforward Modification......Page 48
4.4.2 Production that Spans Time Buckets......Page 49
4.4.3 Parallel Machines......Page 50
4.4.4 Sequence Dependent Changeovers......Page 51
4.4.5 A Few Remarks About Changeovers......Page 52
5.1.1 Costs......Page 54
5.1.2 Objective Function......Page 56
5.2.1 A Simple Model......Page 58
5.2.2 Complications......Page 59
5.3 Allowing Tardiness......Page 60
5.3.1 A Simple Model......Page 61
5.3.2 Complications......Page 62
5.4 Objective Function Issues......Page 63
5.5 The Model......Page 64
6.1 Substitutes, Multiple Routings and Subcontractors......Page 67
6.2 Penalizing Changes to the Plan......Page 70
6.3 End-of-horizon Effects and Minimum Inventories......Page 72
6.4 Modeling Product Movement and Transport......Page 74
6.4.3 Fixed Costs and Consolidations......Page 75
6.4.4 Transportation Discounts......Page 77
6.5 Summarizing the Model......Page 78
6.6 Aggregation and Consolidation......Page 79
6.6.1 Consolidating Resources......Page 81
6.6.2 Aggregating Parts......Page 82
6.6.3 Discussion of Disaggregation......Page 87
7. Implementation Examples......Page 88
7.1 AMPL......Page 91
7.1.1 mrp Model......Page 93
7.1.2 mrp Data......Page 94
7.1.3 Results of Running mrp......Page 95
7.1.4 MRPII Model......Page 96
7.1.5 Data for MRPII......Page 97
7.1.6 SCPc Model......Page 98
7.1.7 Data for SCPc......Page 101
7.2 GAMS......Page 103
7.2.1 mrp and MRPII Models......Page 105
7.2.2 SCPc Model......Page 108
7.3 Maximal MPL......Page 113
7.3.1 mrp Model......Page 114
7.3.2 MRPII......Page 116
7.3.3 SCPc......Page 117
7.4 OPL......Page 121
7.4.1 mrp......Page 122
7.4.3 SCPc......Page 125
7.5 Xpress-Mosel......Page 130
7.5.1 mrp Model......Page 132
7.5.2 mrp Data......Page 135
7.5.4 MRPII Model......Page 136
7.5.5 SCPc Model......Page 137
8.1 MIPs and Relaxations......Page 141
8.2 Branch and Bound......Page 144
8.3.1 Semi-continuous Variables......Page 147
8.3.2 General Integer Variables......Page 148
8.3.3 Special Ordered Sets......Page 149
8.4 Heuristic Search Methods......Page 151
8.4.1 A Brief Primer on Heuristics......Page 152
8.4.2 Abstract Formulation and Solution Representation......Page 153
8.4.3 Example of an Embedded Problem......Page 155
8.4.4 Neighborhoods and Evaluation Functions......Page 156
8.4.5 Simulated Annealing......Page 160
8.4.6 Tabu Search......Page 162
8.4.7 Genetic and Evolutionary Algorithms......Page 163
8.5 Constraint Programming......Page 166
9. Some Stochastic Extensions......Page 168
9.1 Lead Times and Congestion......Page 169
9.1.1 The Issues......Page 170
9.1.2 Load Dependent Lead Times......Page 172
9.1.3 Solver Issues......Page 175
9.1.4 Example......Page 177
9.1.5 Complications and Discussion......Page 178
9.2 Scenarios......Page 179
9.2.1 The Issues......Page 180
9.2.2 A Multi-stage Probabilistic Model With Recourse......Page 183
9.2.3 Progressive Hedging......Page 185
9.2.4 A PH based Heuristic for SCPc......Page 189
10.1 Supply Chain Management......Page 191
10.1.1 The Evolution of Logistics......Page 192
10.1.3 The Importance of Information Technology......Page 195
10.1.4 Supply Contracts......Page 202
10.2.1 The Early Steps......Page 204
10.2.2 Supply Chain Planning......Page 205
10.3.1 Lot Sizing Models......Page 206
10.3.2 Planning and Inventory Control......Page 212
10.3.3 Machine Scheduling......Page 215
10.3.4 Aggregation and Part Families......Page 216
10.3.5 Load Dependent Lead Times......Page 218
10.4 Transportation......Page 223
10.5 Optimization......Page 227
10.5.2 Heuristic Search Methods......Page 229
10.5.3 Progressive Hedging......Page 233
10.5.4 Simulation......Page 234
10.6 Modeling......Page 235
Bibliography......Page 237
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L......Page 258
P......Page 259
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Y......Page 261