Business optimisation using mathematical programming:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Basingstoke [u.a.]
Macmillan
1997
|
| Ausgabe: | 1. publ. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007716630&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXII, 423 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0333676238 |
Internformat
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| 100 | 1 | |a Kallrath, Josef |e Verfasser |0 (DE-588)1042215855 |4 aut | |
| 245 | 1 | 0 | |a Business optimisation using mathematical programming |c Josef Kallrath and John M. Wilson |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Basingstoke [u.a.] |b Macmillan |c 1997 | |
| 300 | |a XXII, 423 S. |b graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Wirtschaft | |
| 650 | 4 | |a Business |x Data processing | |
| 650 | 4 | |a Decision support systems | |
| 650 | 4 | |a Programming (Mathematics) | |
| 650 | 0 | 7 | |a Lineare Optimierung |0 (DE-588)4035816-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Wilson, John M. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 902f 2001 A 20091 |
|---|---|
| DE-BY-TUM_katkey | 830872 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020366136 |
| _version_ | 1821931345013637120 |
| adam_text | Contents
List of Figures xvii
Preface xix
1 Optimisation: Using Models, Validating Models, Solutions,
Answers 1
1.1 Introduction: Some Words on Optimisation 1
1.2 The Scope of this Book 6
1.3 The Significance of Models 7
1.4 Mathematical Optimisation 9
1.4.1 A Linear Programming Example 9
1.4.2 A Typical Linear Programming Problem 14
1.5 Using Modelling Systems and Software 15
1.5.1 Implementing a Model 18
1.5.2 Obtaining a Solution 20
1.5.3 Interpreting the Output 23
1.6 Benefiting from and Extending the Simple Model 24
1.7 A Survey of Real World Problems 27
1.8 Summary 30
1.9 Appendix to Chapter 1 30
1.9.1 Notation 30
1.9.2 A Brief History of Optimisation e 31
2 The Scope of Problem Formulation and How to Formulate
the Problem 37
2.1 How to Model and Formulate a Problem 37
2.2 Variables, Indices, Sets and Domains 39
2.2.1 Indices, Sets and Domains 42
2.2.2 Summation 43
2.3 Constraints 45
2.3.1 Types of Constraints 46
2.3.2 Example 49
2.4 Objectives 50
2.5 Building More Sophisticated Models 51
vii
viii Contents
2.5.1 A Simple Production Planning Exercise 52
2.5.1.1 The Model Background 52
2.5.1.2 Developing the Model 52
2.6 Mixed Integer Programming 54
2.6.1 Example: A Farmer Buying Calves and Pigs 56
2.7 Interfaces Spreadsheets and Databases 58
2.7.1 Example: A Blending Problem 60
2.7.2 Developing the Model 61
2.7.3 Re running the Model with New Data 63
2.8 Creating a Production System 64
2.9 Collecting Data 65
2.10 Modelling Logic 66
2.11 Practical Solution of LP Models 67
2.11.1 Problem Size 67
2.11.2 Ease of Solution 68
2.12 Summary 69
2.13 Exercises 70
3 Mathematical Solution Techniques 73
3.1 Introduction 73
3.1.1 Standard Formulation of Linear Programming Problems 73
3.1.2 Slack and Surplus Variables 75
3.1.3 Underdetermined Linear Equations and Optimisation 76
3.2 Linear Programming 77
3.2.1 Simplex Algorithm — A Brief Overview 77
3.2.2 Solving the Boat Problem with the Simplex Algorithm 78
3.2.3 Interior Point Methods — A Brief Overview 84
3.2.4 LP as a Subroutine 85
3.3 Mixed Integer Linear Programming 86
3.3.1 Solving the Farmer s Problem with Branch Bound . 86
3.3.2 Solving Mixed Integer Linear Programming Problems 90
3.3.3 Cutting Planes and Branch Cut 93
3.4 Interpreting the Results 95
3.4.1 LP Solution 95
3.4.2 Outputing Results 96
3.4.3 Dual Value (Shadow Price) 96
3.4.4 Reduced Costs 97
3.4.5 Report Writing 98
3.5 Duality e 98
3.5.1 Constructing the Dual Problem 99
3.5.2 Interpreting the Dual Problem 101
3.5.3 Duality Gap and Complementarity 102
3.6 Summary 104
3.7 Exercises 105
3.8 Appendix to Chapter 39 105
Contents ix
3.8.1 Linear Programming — A Detailed Description .... 105
3.8.2 Computing Initial Feasible LP Solutions 112
3.8.3 LP Problems with Upper Bounds 114
3.8.4 Dual Simplex Algorithm 118
3.8.5 Interior Point Methods — A Detailed Description . . 118
3.8.5.1 A Primal Dual Interior Point Method .... 121
3.8.5.2 Predictor Corrector Step 124
3.8.5.3 Computing Initial Points 124
3.8.5.4 Updating the Homotopy Parameter 125
3.8.5.5 Termination Criterion 126
3.8.5.6 Basis Identification and Cross Over 126
3.8.5.7 Interior Point versus Simplex Methods . . . 127
3.8.6 Branch Bound with LP Relaxation 128
4 Problems Solvable Using Linear Programming 133
4.1 Trimloss Problem 133
4.1.1 Example: A Trimloss Problem in the Paper Industry . 134
4.1.2 Example: An Integer Trimloss Problem 136
4.1.3 Other Applications 137
4.2 The Food Mix Problem 137
4.2.1 Case Study: Manufacturing Foods 137
4.3 Transportation and Assignment Problems 138
4.3.1 The Transportation Problem 138
4.3.2 The Transshipment Problem 141
4.3.3 The Assignment Problem 142
4.3.4 Transportation and Assignment Problems occurring
as Subproblems 144
4.3.5 Matching Problems 144
4.4 Network Flow Problems 145
4.4.1 Illustrating a Network Flow Problem 146
4.4.2 The Structure and Importance of Network Flow Modelsl48
4.4.3 Case Study: A Telephone Betting Scheduling Problem 148
4.4.4 Other Applications of Network Modelling Technique . 151
4.5 Unimodularity 151
4.5.1 A Unimodular Transportation Matrix 0 151
4.6 Summary 152
4.7 Exercises 152
5 How Optimisation is Used in Practice: Case Studies in
Linear Programming 153
5.1 Optimising the Production of a Chemical Reactor 153
5.2 An Apparently Nonlinear Blending Problem 155
5.2.1 Formulating the Direct Problem 156
5.2.2 Formulating the Inverse Problem 158
5.2.3 Analysing and Reformulating the Model 158
x Contents
5.3 Data Envelopment Analysis (DEA) 161
5.3.1 Example Illustrating DEA 161
5.3.2 Efficiency 163
5.3.3 Inefficiency 164
5.3.4 More than one Input 165
5.3.5 Small Weights 165
5.3.6 Applications of DEA 166
5.3.7 A General Model for DEA 166
5.4 Vector Minimisation and Goal Programming 167
5.4.1 A Case Study Involving Soft Constraints 170
5.5 Limitations of Linear Programming 172
5.5.1 Single Objective 172
5.5.2 Assumption of Linearity 173
5.5.3 Satisfaction of Constraints 173
5.5.4 Structured Situations 174
5.5.5 Consistent and Obtainable Data 174
5.6 Summary 175
5.7 Exercises 175
6 Modelling Structures Using Mixed Integer Programming 177
6.1 Using Binary Variables to Model Logical Conditions 177
6.1.1 General Integer Variables and Logical Conditions . . . 178
6.1.2 Transforming Logical Expressions into Arithmetical
Expressions 179
6.1.3 Logical Expressions with Two Arguments 180
6.1.4 Logical Expressions with More than Two Arguments . 182
6.2 Logical Restrictions on Constraints 184
6.2.1 Bound Implications on Single Variables 185
6.2.2 Bound Implications on Constraints 185
6.2.3 Disjunctive Sets of Implications 187
6.3 Modelling Non Zero Variables 189
6.4 Modelling Sets of All Different Elements 190
6.5 Modelling Absolute Value Terms 0 191
6.6 Modelling Products of Binary Variables 193
6.7 Special Ordered Sets 194
6.7.1 Special Ordered Sets of Type 1 194
6.7.2 Special Ordered Sets of Type 2 197
6.7.3 Linked Ordered Sets 200
6.7.4 Families of Special Ordered Sets 202
6.8 Improving Formulations by Adding Logical Inequalities . . . 203
6.9 Summary 205
6.10 Exercises 205
Contents xj
7 Types of Mixed Integer Linear Programming Problems 209
7.1 Knapsack and Related Problems 209
7.1.1 The Knapsack Problem 209
7.1.2 Case Study: Float Glass Manufacturing 211
7.1.3 The Generalised Assignment Problem 212
7.1.4 The Multiple Binary Knapsack Problem 213
7.2 The Travelling Salesman Problem 213
7.2.1 Postman Problems 217
7.3 Facility Location Problems 218
7.3.1 The Uncapacitated Facility Location Problem 218
7.3.2 The Capacitated Facility Location Problem 219
7.4 Set Covering, Partitioning and Packing 220
7.4.1 The Set Covering Problem 220
7.4.2 The Set Partitioning Problem 222
7.4.3 The Set Packing Problem 223
7.4.4 Further Applications 224
7.4.5 Case Study: Airline Management at Delta Air Lines . 224
7.5 Satisfiability 226
7.6 Bin Packing 227
7.6.1 The Bin Packing Problem 227
7.6.2 The Capacitated Plant Location Problem 228
7.7 Clustering Problems 229
7.7.1 The Capacitated Clustering Problem 229
7.7.2 The p Median Problem 231
7.8 Scheduling Problems 231
7.8.1 Example A: Scheduling Machine Operations 232
7.8.2 Example B: A Flowshop Problem 234
7.8.3 Example C: Scheduling Involving Job Switching . . . 236
7.8.4 Case Study: Bus Crew Scheduling 237
7.9 Summary 238
7.10 Exercises 239
8 Case Studies and Problem Formulations 243
8.1 A Depot Location Problem 243
8.2 Planning and Scheduling Across Time Periods 245
8.2.1 Indices, Data and Variables 246
8.2.2 Objective Function 247
8.2.3 Constraints 247
8.3 Distribution Planning for a Brewery . . ¦ 249
8.3.1 Dimensions, Indices, Data and Variables 249
8.3.2 Objective Function 251
8.3.3 Constraints 251
8.3.4 Running the Model 253
8.4 Financial Modelling 253
8.4.1 Optimal Purchase 254
xii Contents
8.4.2 A Yield Management Example 258
8.5 Post Optimal Analysis 260
8.5.1 Getting Around Infeasibility 260
8.5.2 Basic Concept of Ranging 262
8.5.3 Parametric Programming 264
8.5.4 Sensitivity Analysis in MILP Problems 266
8.6 Summary 267
9 User Control of the Optimisation Process and Improving
Efficiency 269
9.1 Preprocessing 269
9.1.1 Presolve 270
9.1.1.1 Arithmetic Tests 270
9.1.1.2 Tightening Bounds 272
9.1.2 Disaggregation of Constraints 273
9.1.3 Coefficient Reduction 274
9.1.4 Clique Generation 276
9.1.5 Cover Constraints 277
9.2 Efficient LP Solving 278
9.2.1 Warm Starts 279
9.2.2 Scaling 279
9.3 Good Modelling Practice 280
9.4 Choice of Branch in Integer Programming 283
9.4.1 Control of the Objective Function Cut off 284
9.4.2 Branching Control 284
9.4.2.1 Entity Choice 284
9.4.2.2 Choice of Branch or Node 285
9.4.3 Priorities 286
9.4.4 Branching for Special Ordered Sets 286
9.4.5 Branching on Semi Continuous and Partial Integer
Variables 288
9.5 Summary 289
9.6 Exercises 289
10 How Optimisation is Used in Practice: Case Studies in
Integer Programming 291
10.1 What Can be Learned from Real World Problems? 291
10.2 Three Instructive Solved Real World Problems 292
10.2.1 Contract Allocation 292
10.2.2 Metal Ingot Production 294
10.2.3 Project Planning 295
10.2.4 Conclusions 297
10.3 A Case Study in Production Scheduling 298
10.4 Optimal Worldwide Production Plans 0 303
10.4.1 Brief Description of the Problem 303
Contents x^
10.4.2 Mathematical Formulation of the Model 305
10.4.2.1 General Framework 305
10.4.2.2 Time Discretisation 306
10.4.2.3 Including Several Market Demand Scenarios 306
10.4.2.4 The Variables 306
10.4.2.5 The State of the Production Network .... 307
10.4.2.6 Exploiting Fixed Setup Plans 308
10.4.2.7 Keeping Track of Mode Changes 308
10.4.2.8 Coupling Modes and Production 310
10.4.2.9 Minimum Production Requirements 311
10.4.2.10 Modelling Stock Balances and Inventories . . 311
10.4.2.11 Modelling Transport 312
10.4.2.12 External Purchase 313
10.4.2.13 Modelling Sales and Demands 313
10.4.2.14 Defining the Objective Function 313
10.4.3 Remarks on the Model Formulation 315
10.4.3.1 Including Minimum Utilisation Rates .... 315
10.4.3.2 Exploiting Sparsity 315
10.4.3.3 Avoiding Zero Right Hand Side Equations . 317
10.4.3.4 The Structure of the Objective Function . . 318
10.4.4 Model Performance 319
10.4.5 Reformulations of the Model 319
10.4.5.1 Estimating the Quality of the Solution . . .320
10.4.5.2 Including Mode Dependent Capacities .... 320
10.4.5.3 Modes, Change Overs and Production .... 321
10.4.5.4 Reformulated Capacity Constraints 323
10.4.5.5 Some Remarks on the Reformulation .... 324
10.4.6 What can be Learned from this Case Study? 324
10.5 A Complex Scheduling Problem 0 325
10.5.1 Description of the Problem 325
10.5.2 Structuring the Problem 326
10.5.2.1 Orders, Procedures, Tasks and Jobs 326
10.5.2.2 Labour, Shifts, Workers and their Relations . 327
10.5.2.3 Machines 328
10.5.2.4 Services 328
10.5.2.5 Objectives 329
10.5.3 Mathematical Formulation of the Problem 329
10.5.3.1 General Framework 329
10.5.3.2 Time Discretisation 330
10.5.3.3 Indices 330
10.5.3.4 Data 330
10.5.3.5 Main Decision Variables 330
10.5.3.6 Other Variables 331
10.5.3.7 Auxiliary Sets 331
10.5.4 Time Indexed Formulations 331
xiv Contents
10.5.4.1 The 6 Formulation 332
10.5.4.2 The a Formulation 333
10.5.5 Numerical Experiments 334
10.5.5.1 Description of Small Scenarios 334
10.5.5.2 A Client s Prototype 336
10.5.6 What can be Learned from this Case Study? 342
10.6 Telecommunication Service Network 0 343
10.6.1 Description of the Model 344
10.6.1.1 Technical Aspects of Private Lines 344
10.6.1.2 Tariff Structure of Private Line Services . . .344
10.6.1.3 Demands on Private Line Services 346
10.6.1.4 Private Line Network Optimisation 346
10.6.2 Mathematical Model Formulation 346
10.6.2.1 General Foundations 347
10.6.2.2 Flow Conservation Constraints 350
10.6.2.3 Edge Capacity Constraints 351
10.6.2.4 Additional Constraints 352
10.6.2.5 Objective Function of the Model 354
10.6.2.6 Estimation of Problem Size 354
10.6.2.7 Computational Needs 355
10.6.3 Analysis and Reformulations of the Models 356
10.6.3.1 Basic Structure of the Model 356
10.6.3.2 Some Valid Inequalities: Edge Capacity Cuts 356
10.6.3.3 Some Improvements to the Model Formulation358
10.6.3.4 A Surrogate Problem with a Simplified Cost
Function 359
10.6.3.5 More Valid Inequalities: Node Flow Cuts . . 360
10.6.3.6 Some Remarks on Performance 361
10.7 Summary 361
10.8 Exercises 361
11 Other Types of Optimisation Problems 0 365
11.1 Recursion or Successive Linear Programming 365
11.1.1 An Example 366
11.1.2 The Pooling Problem 368
11.2 Stochastic Programming 372
11.3 Quadratic Programming 372
11.4 Mixed Integer Nonlinear Programming 376
11.4.1 Definition of an MINLP Problem 376
11.4.2 Some General Comments on MINLP 377
11.4.3 Deterministic Methods for Solving MINLP Problems . 379
11.4.4 The Program DICOPT 380
11.5 Summary 380
Contents xv
12 Conclusion: The Impact and Implication of Optimisation 381
12.1 What the Users Can Get Out of the Case Studies 381
12.2 Benefits of Mathematical Programming to Users 382
12.3 Implementing and Validating Solutions 383
12.4 Communicating with Management 383
12.5 Keeping a Model Alive 384
12.6 Mathematical Optimisation in Small and Medium Size Business385
12.7 On Line Optimisation by Exploiting Parallelism? 386
12.7.1 Algorithmic Components Suitable for Parallelisation . 386
12.7.2 Non determinism in Parallel Optimisation 387
12.7.3 Platforms for Parallel Optimisation Software 388
12.7.4 Design Decisions 388
12.7.5 Implementation 390
12.7.6 Performance 390
12.7.7 Acceptability 391
12.8 Future Developments and Conclusions 391
12.9 Summary 396
A Software Related Issues 397
A.I Accessing Data from Harddisk 397
A.I.I The DISKDATA statement 397
A.1.2 Connecting to Spreadsheets 397
A.2 List of Case Studies and Model Files 398
B Glossary 399
Bibliography 405
Index 417
List of Figures
1.1 Transforming a real world problem 4
1.2 Graphical solution of an LP problem in two variables 13
1.3 Initial screen 19
1.4 New problem 20
1.5 Boats model 21
1.6 Changing minimise to maximise 22
1.7 Saving the file 23
1.8 Results from model 24
1.9 Erroneous model 25
1.10 Extended model 27
1.11 Results from extended model 28
2.1 Integer model 57
2.2 Progress to integer solution 58
2.3 Simple spreadsheet 59
3.1 Illustration of interior point methods 84
3.2 LP relaxation and the first two subproblems of a B B tree . 88
3.3 LP relaxation, convex hull, and a B B tree 92
3.4 Illustrating the idea of Branch Cut 94
3.5 Feasible region of an LP problem 106
3.6 The revised simplex algorithm 109
3.7 Logarithmic penalty term 119
3.8 The Branch Bound algorithm 129
3.9 Two Branch k Bound trees 131
4.1 Trimloss problem 134
4.2 Routes on transportation and transshipment networks .... 143
4.3 Flows between nodes of a network 147
4.4 Partial network [from Wilson and Willis (1983)] 150
6.1 Using Si sets to select capacity size 195
6.2 Using S2 sets to model a nonlinear curve 198
7.1 Travelling salesman problem with four cities 216
xvii
xviii List of Figures
7.2 A set covering problem 220
7.3 Gantt chart showing the schedule 234
8.1 Cost as a function of number of items 255
8.2 Sensitivity analysis: objective versus optimal value 263
8.3 Sensitivity analysis: optimal value versus unit profit 264
8.4 Sensitivity analysis: slope of objective function 265
10.1 Production network with three sites 304
10.2 Illustration of a set up change 309
10.3 Production plan 316
10.4 Precedence relations between jobs 339
10.5 Gantt chart and personnel occupation diagram 340
10.6 Cost of bandwidth for POP to POP private lines 345
10.7 A possible routing via hub sites for a demand Dij 349
11.1 The pooling problem and a process unit fed by a pool .... 370
11.2 Convex and non convex sets and functions 378
12.1 Speed up achieved with eight slaves 387
|
| any_adam_object | 1 |
| author | Kallrath, Josef Wilson, John M. |
| author_GND | (DE-588)1042215855 |
| author_facet | Kallrath, Josef Wilson, John M. |
| author_role | aut aut |
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| callnumber-subject | HD - Industries, Land Use, Labor |
| classification_rvk | QH 421 SK 870 |
| classification_tum | WIR 527f MAT 902f |
| ctrlnum | (OCoLC)53388483 (DE-599)BVBBV011469708 |
| dewey-full | 658.4033 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 658 - General management |
| dewey-raw | 658.4033 |
| dewey-search | 658.4033 |
| dewey-sort | 3658.4033 |
| dewey-tens | 650 - Management and auxiliary services |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV011469708 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:13:06Z |
| institution | BVB |
| isbn | 0333676238 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007716630 |
| oclc_num | 53388483 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 DE-384 DE-945 DE-706 DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-384 DE-945 DE-706 DE-83 DE-188 |
| physical | XXII, 423 S. graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Macmillan |
| record_format | marc |
| spellingShingle | Kallrath, Josef Wilson, John M. Business optimisation using mathematical programming Datenverarbeitung Wirtschaft Business Data processing Decision support systems Programming (Mathematics) Lineare Optimierung (DE-588)4035816-1 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4035816-1 (DE-588)4043664-0 |
| title | Business optimisation using mathematical programming |
| title_auth | Business optimisation using mathematical programming |
| title_exact_search | Business optimisation using mathematical programming |
| title_full | Business optimisation using mathematical programming Josef Kallrath and John M. Wilson |
| title_fullStr | Business optimisation using mathematical programming Josef Kallrath and John M. Wilson |
| title_full_unstemmed | Business optimisation using mathematical programming Josef Kallrath and John M. Wilson |
| title_short | Business optimisation using mathematical programming |
| title_sort | business optimisation using mathematical programming |
| topic | Datenverarbeitung Wirtschaft Business Data processing Decision support systems Programming (Mathematics) Lineare Optimierung (DE-588)4035816-1 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Datenverarbeitung Wirtschaft Business Data processing Decision support systems Programming (Mathematics) Lineare Optimierung Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007716630&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kallrathjosef businessoptimisationusingmathematicalprogramming AT wilsonjohnm businessoptimisationusingmathematicalprogramming |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 902f 2001 A 20091
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |