Multi-level sequence dependent dynamic lotsizing and scheduling:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Aachen
Shaker
1998
|
| Ausgabe: | Als Ms. gedr. |
| Schriftenreihe: | Berichte aus der Betriebswirtschaft
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: Aachen, Techn. Hochsch., Diss., 1997 |
| Beschreibung: | XIV, 311 S. graph. Darst. |
| ISBN: | 3826556534 |
Internformat
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| 245 | 1 | 0 | |a Multi-level sequence dependent dynamic lotsizing and scheduling |c Tore Grünert |
| 250 | |a Als Ms. gedr. | ||
| 264 | 1 | |a Aachen |b Shaker |c 1998 | |
| 300 | |a XIV, 311 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Berichte aus der Betriebswirtschaft | |
| 500 | |a Zugl.: Aachen, Techn. Hochsch., Diss., 1997 | ||
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Datensatz im Suchindex
| _version_ | 1804126463510708224 |
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| adam_text | Contents iii
Contents
Chapter 1
Introduction 1
Chapter 2
The economical relevance of model based lotsizing
and scheduling decisions 5
2.1 The intervention and modeling process 6
2.2 Planning and control management of production processes
7
2.2.1 Production decision making frameworks 8
2.2.2 The handling of hierarchies 11
2.2.3 Limitations of MRP II 11
2.2.4 Capacity oriented planning 12
2.3 The practice of lotsizing: Production planning and System
integration 14
2.3.1 Implementation 14
2.3.2 Computer integrated manufacturing 16
2.4 The transformation process and target industries 17
2.4.1 The transformation process and the organization of production
18
2.4.2 Target industries 19
2.5 Evaluating lotsizing and scheduling decisions 21
2.5.1 The inventory level dilemma 21
2.5.2 Cost and profit considerations 22
2.6 Applications 23
2.7 Potentials the nine laws of Askin and Standridge 26
2.8 Implications focus of the thesis 28
Chapter 3
Problem definition and model formulation 31
3.1 Problem definition 32
3.2 The Bill of materials and resource oriented product
structures 34
3.3 Time phased production 37
3.3.1 Lead times 38
3.3.2 Earliest production time 39
3.3.3 Planning inputs and Outputs the forecast horizon 40
3.3.4 Latest possible production Start 42
iv Contents
3.3.5 Links to project management 44
3.3.6 Capacity allocation planning extending the forecast horizon44
3.4 The model 47
3.4.1 Model assumptions 47
3.4.2 Formal definition 49
3.4.3 Model size and tractability 57
3.4.4 Setup patterns 57
3.5 Echelon stock, demand, and costs 58
3.5.1 Formal definition 58
3.5.2 Preprocessing using the echelon demand concept 60
Chapter 4
Research on lotsizing and scheduling 61
4.1 Basic research directions 61
4.1.1 A model based classification scheme 62
4.1.2 An algorithm based classification scheme 68
4.1.3 Exploiting algorithmic ideas 77
4.2 Lagrangean relaxation and decomposition 77
4.2.1 Formal definition 78
4.2.2 Mathematical properties 81
4.2.3 Primal partitioning 84
4.2.4 Applications and heuristic considerations 85
4.2.5 Lagrangean algorithms for lotsizing and scheduling 85
4.3 Tabu Search 89
4.3.1 The basic procedure Simple Tabu Search 90
4.3.2 Longer term memory 92
4.3.3 Strategic oscillation 93
4.3.4 Path relinking 94
Chapter 5
Algorithms and lower bounds 97
5.1 A Lagrangean relaxation and decomposition for the MSLS
97
5.1.1 Motivation and formal definition 98
5.1.2 The dynamic lotsizing problem 106
5.1.3 The dynamic Leontief system 107
5.1.4 The mixed binary knapsack problem 108
5.1.5 The elementary shortest path problem HI
5.1.6 The subgradient method and other adjustment techniques .111
5.2 Sequence optimization by local search 114
5.2.1 Formal definition of the LSP I15
5.2.2 Sequence optimization within periods 116
5.2.3 Sequence optimization between periods 118
5.3 Construction of a primally feasible solution 119
Contents v
5.4 Improvement by Lagrangean Tabu Search 123
5.4.1 The setup sequence with insertions and deletions 124
5.4.2 Determination of a neighbor setup pattern 128
5.4.3 The local improvement problem 133
5.4.4 The tabu condition 136
5.4.5 Diversification 137
5.4.6 Intensification by path relinking 139
5.4.7 The Lagrangean Tabu Search algorithm 142
Chapter 6
Specially structured submodels 145
6.1 The dynamic lotsizing problem 145
6.1.1 Algorithms for the DLSP 147
6.1.2 The shortest path formulation of the DLSP 148
6.2 Constrained shortest path problems 149
6.2.1 The generic shortest path model as a relaxation of the MSLS
150
6.2.2 The capacity and path length constrained shortest path problem
152
6.2.3 The elementary shortest path problem 154
6.2.4 Solution of the T period problem by dynamic programmingl59
6.3 The mixed binary knapsack problem 161
6.3.1 Problem definition 162
6.3.2 Upper bounds 165
6.3.3 The greedy algorithm 172
6.3.4 Problem reduction by preprocessing 173
6.3.5 A branch and bound algorithm 177
6.4 Linear programming and netform subproblems 181
6.4.1 The dynamic Leontief model 182
6.4.2 The dynamic substitution system with initial inventory and
maximal batchsizes 187
6.4.3 The dynamic substitution system with initial inventory, batchsize,
and capacity constraints 194
Chapter 7
Computational results and practical impacts.... 201
7.1 Testing heuristics 201
7.1.1 Performance measures 203
7.1.2 Performance factors 204
7.2 The mixed binary knapsack problem 205
7.2.1 Computation time as a function of problem size 207
7.2.2 Computation time as a function of problem data 208
7.2.3 Computation time compared to CPLEX 4.0 211
7.2.4 The impact of the preprocessing phase 214
vi Contents
7.3 The elementary shortest path problem 216
7.3.1 Computation time versus number of nodes 219
7.3.2 Computation time versus number of negative arcs 220
7.3 3 The effectiveness of the dynamic programming approach....221
7.4 The generation of test problems 223
7.4.1 The generation of structural data the production system..223
7.4.2 The generation of demand and capacity data the constraints of
the production program 225
7.4.3 The generation of cost data the optimization factors of the
production program 229
7.5 The subgradient algorithms 230
7.5.1 The geometric approach 233
7.5.2 Polyak s approach 235
7.5.3 A comparison of the approaches 237
7.6 The Lagrangean Tabu Search algorithm 239
7.6.1 The number of products 242
7.6.2 The number of periods 245
7.6.3 Time between orders 248
7.6.4 Capacity tightness 249
7.6.5 Demand patterns 250
7.6.6 Demand versus setup times 251
7.6.7 The product structure 252
7.6.8 The influence of intensification 253
7.6.9 The influence of diversification 254
7.6.10 Convergence versus time 255
7.7 Summary, practical impacts, and improvements 259
Chapter 8
Conclusions and further research directions 263
References 267
Contents vii
Appendix 279
A Mathematical statements 279
A.I Equivalence of echelon inventory and physical inventory.... 279
A.2 Proof of dominance criteria for the MBKP 280
A.3 The master problem using Dantzig Wolfe 281
B Subgradients 284
C An algorithm for the calculation of earliest production times
290
D Data and settings of the computational study 290
D.I Problem generation 290
D.2 Data of the computational tests 294
E Netforms 303
F Computational complexity 305
G The correlation coefficient 306
Index 307
List of Figures ix
List of Figures
Figure 2.1: A production decision making framework 10
Figure 2.2: Main elements of the capacity oriented planning framework ... 13
Figure 2.3: Computer integrated manufacturing 16
Figure 3.1: Gozinto graph 34
Figure 3.2: Typical product structures 35
Figure 3.3: The resource graph corresponding to the gozinto graph of figure
3.1 37
Figure 3.4: Gozinto graph with lead times 39
Figure 3.5: Earliest production time 40
Figure 3.6: Relationship between production and demand in a rolling horizon
environment 42
Figure 3.7: Latest possible production start 43
Figure 3.8: Planning intervals 45
Figure 3.9: Forecast horizon and decisions for a single machine 46
Figure 3.10: No setups between periods 48
Figure 3.11: Minimal lead times 49
Figure 3.12: The inventory flow as a generalized netform 54
Figure 3.13: The machine capacity constraints as a discrete netform 55
Figure 3.14: The flow constraints of the embedded shortest path problem.. 56
Figure 4.1: Construction of the TSPTW from the scheduling problem 63
Figure 4.2: A model based classification scheme 67
Figure 4.3: An algorithm based classification scheme 76
Figure 4.4: Oscillation at critical level 94
Figure 4.5: Path relinking 95
Figure 5.1: Constraint matrix of the MSLS 99
Figure 5.2: Constraint matrix of the MSLS after variable aggregation and
copying 101
Figure 5.3: Constraint matrix of the MSLS after Lagrangean relaxation and
decomposition 102
Figure 5.4: Hamiltonian path in the LSP graph 116
Figure 5.5: A TRIA move 117
Figure 5.6: A QUAD move 118
Figure 5.7: A LINK move 119
Figure 5.8: The linking arcs and deletions 125
Figure 5.9: The linking arcs when a setup is involved 125
Figure 5.10: The calculation of insertion setup costs for non linking products
126
Figure 5.11: Blocking deletion and insertion positions for non linking products
127
x List of Figures
Figure 5.12: Blocking positions for linking products 128
Figure 5.13: Current setup sequence 131
Figure 5.14: Neighbor setup sequence I32
Figure 5.15: Setup elimination 133
Figure 5.16: Modification of the setup sequence during diversification 138
Figure 5.17: An improving search 140
Figure 5.18: Calculation of the voting coefficient for intensification 141
Figure 6.1: Netform of the DLSP I48
Figure 6.2: Shortest path graph 151
Figure 6.3: Violation of the tree property of shortest paths 155
Figure 6.4: Example for the operations of the elementary shortest path
algorithm *¦
Figure 6.5: Shortest path graph in a period t 161
Figure 6.6: Solution graph of the knapsack problem 165
Figure 6.7: Decision tree for the computation of upper bounds 170
Figure 6.8: Branch and bound tree for the computation of upper bounds 172
Figure 6.9: Tree generated by the branch and bound algorithm for MBKP
181
Figure 6.10: Block triangular structure of the dynamic Leontief system ... 183
Figure 6.11: Netform model of the substitution system without side constraints
197
Figure 7.1: Flowchart of the optimization algorithm for the MBKP 206
Figure 7.2: Square root of computation time as a function of problem size
208
Figure 7.3: Computation time in seconds for the solution of 20 strongly
correlated problems 210
Figure 7.4: The logarithm of the computation time as a function of the
number of variables 211
Figure 7.5: Computation time of the MBKP algorithm compared to CPLEX
4.0, for uncorrelated problems ^1*
Figure 7.6: Computation times in seconds for 20 strongly correlated problems
for the MBKP algorithm and CPLEX 214
Figure 7.7: Computation times in seconds for the solution of 20 problems
with and without preprocessing ^
Figure 7.8: Flowchart of the elementary shortest path algorithm 217
Figure 7.9: Flowchart of the dynamic programming algorithm 218
Figure 7.10: Computation time as a function of the number of nodes 220
Figure 7.11: Computation time as a function of the relative number of
negative arcs
Figure 7.12: Ratio between computation times and the number of periods 222
Figure 7.13: Capacity calculation and different planning periods 228
Figure 7.14: The structure of the Lagrangean algorithms 232
List of Figures xi
Figure 7.15: Results for different parameter sets of the geometric update
approach 235
Figure 7.16: Results for different parameter sets of the modified Polyak
update approach 237
Figure 7.17: A typical Lagrangean run with different initial values 238
Figure 7.18: A typical Lagrangean run with a variable lamda 239
Figure 7.19: Flowchart of the Lagrangean Tabu Search algorithm 240
Figure 7.20: Performance as a function of the number of products 243
Figure 7.21: Computation time as a function of the number of products... 244
Figure 7.22: Performance as a function of the number of periods 246
Figure 7.23: Computation time as a function of the number of periods 247
Figure 7.24: The influence of TBO on performance 248
Figure 7.25: The influence of capacity tightness on performance 249
Figure 7.26: The performance depending on demand patterns 251
Figure 7.27: Performance as a function of the ratio between demand and
setup times 252
Figure 7.28: The influence of different product structures on the performance
253
Figure 7.29: Performance with and without intensification 254
Figure 7.30: The performance with and without diversification 255
Figure 7.31: Performance of the first and best found solution 256
Figure 7.32: Iteration of the last improvement 257
Figure 7.33: Performance after an increasing number of iterations 258
Figure 7.34: Lower and upper bounds during the iterations 259
Figure E.I: Main elements of a network model 304
List of Tables xiii
List of Tables
Table 2.1: A process oriented classification of production systems 19
Table 2.2: Differences between process and manufacturing industry 20
Table 5.1: Subproblems and variables 112
Table 5.2: Voting coefficients 131
Table 5.3: Setups in the current primal solution 131
Table 6.1: Initial values of the greedy algorithm 173
Table 6.2: EMTR applied to example problem 177
Table 6.3: Single product Leontief problem 191
Table 6.4: Solution of the single product Leontief problem 192
Table 7.1: Computation time in seconds for the solution of 20 instances,
problem size experiment 207
Table 7.2: Computation time in seconds for the solution of 20 instances for
uncorrelated and correlated problems 209
Table 7.3: Computation time in seconds for the solution of 20 uncorrelated
problems with the MBKP algorithm and CPLEX 4.0 212
Table 7.4: Computation time in seconds for the solution of 20 instances for
correlated problems with CPLEX and the MBKP algorithm. 213
Table 7.5: Computation times in seconds for preprocessing experiment with
20 variables 215
Table 7.6: Computation times in seconds for the solution of 20 problems as
a function of the number of nodes 219
Table 7.7: Computation time in seconds as a function of the relative number
of negative arcs 220
Table 7.8: Computation time in seconds as a function of the number of
periods 222
Table 7.9: Parameter sets for the geometric update approach 234
Table 7.10: Parameter sets for the modified Polyak approach 236
Table D.I: Data for generation of basic test problems 291
Table D.2: Problem numbers and number of products 291
Table D.3: Problem numbers and number of periods 292
Table D.4: Problem numbers and time between orders 292
Table D.5: Problem numbers and capacity 292
Table D.6: Problem numbers and demand patterns 293
Table D.7: Problem numbers and ratio between demand and setup times293
Table D.8: Problem numbers and product structures 293
Table D.9: Test of different subgradient algorithms, part 1 295
Table D.10: Test of different subgradient algorithms, part 2 296
Table D.ll: Performance as a function of the number of products, part 1 297
Table D.12: Performance as a function of the number of products, part 2 297
xiv List of Tables
Table D.13: Computation time as a function of the number of products .. 297
Table D.14: Performance as a function of the number of periods 298
Table D.15: Performance as a function of time between orders 298
Table D.16: Performance as a function of time between orders 298
Table D.17: Performance depending on the capacity tightness 299
Table D.18: Performance depending on the demand distribution 299
Table D.19: Performance as a function of the ratio between demand and
setup times 300
Table D.20: Performance depending on the product structure 300
Table D.21: Initial and best performance 301
Table D.22: The last improving iteration 301
Table D.23: The influence of intensification of performance 302
Table D.24: The influence of diversification and an increased number of
iterations on the performance 303
|
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV011875861 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:17:51Z |
| institution | BVB |
| isbn | 3826556534 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008024324 |
| oclc_num | 75914460 |
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| owner_facet | DE-19 DE-BY-UBM DE-384 DE-945 DE-83 DE-11 |
| physical | XIV, 311 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Shaker |
| record_format | marc |
| series2 | Berichte aus der Betriebswirtschaft |
| spelling | Grünert, Tore Verfasser aut Multi-level sequence dependent dynamic lotsizing and scheduling Tore Grünert Als Ms. gedr. Aachen Shaker 1998 XIV, 311 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Berichte aus der Betriebswirtschaft Zugl.: Aachen, Techn. Hochsch., Diss., 1997 Losgrößenmodell (DE-588)4261231-7 gnd rswk-swf Reihenfolgeproblem (DE-588)4242167-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Losgrößenmodell (DE-588)4261231-7 s Reihenfolgeproblem (DE-588)4242167-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008024324&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grünert, Tore Multi-level sequence dependent dynamic lotsizing and scheduling Losgrößenmodell (DE-588)4261231-7 gnd Reihenfolgeproblem (DE-588)4242167-6 gnd |
| subject_GND | (DE-588)4261231-7 (DE-588)4242167-6 (DE-588)4113937-9 |
| title | Multi-level sequence dependent dynamic lotsizing and scheduling |
| title_auth | Multi-level sequence dependent dynamic lotsizing and scheduling |
| title_exact_search | Multi-level sequence dependent dynamic lotsizing and scheduling |
| title_full | Multi-level sequence dependent dynamic lotsizing and scheduling Tore Grünert |
| title_fullStr | Multi-level sequence dependent dynamic lotsizing and scheduling Tore Grünert |
| title_full_unstemmed | Multi-level sequence dependent dynamic lotsizing and scheduling Tore Grünert |
| title_short | Multi-level sequence dependent dynamic lotsizing and scheduling |
| title_sort | multi level sequence dependent dynamic lotsizing and scheduling |
| topic | Losgrößenmodell (DE-588)4261231-7 gnd Reihenfolgeproblem (DE-588)4242167-6 gnd |
| topic_facet | Losgrößenmodell Reihenfolgeproblem Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008024324&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT grunerttore multilevelsequencedependentdynamiclotsizingandscheduling |