AMPL: a modeling language for mathematical programming
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Belmont, Calif. [u.a.]
Brooks/Cole
2009
|
| Edition: | 2. ed., [Nachdr.] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXI, 517 S. graph. Darst. |
| ISBN: | 0534388094 9780534388096 |
Staff View
MARC
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| 245 | 1 | 0 | |a AMPL |b a modeling language for mathematical programming |c Robert Fourer ; David M. Gay ; Brian W. Kernighan |
| 250 | |a 2. ed., [Nachdr.] | ||
| 264 | 1 | |a Belmont, Calif. [u.a.] |b Brooks/Cole |c 2009 | |
| 300 | |a XXI, 517 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1821297269534621696 |
|---|---|
| adam_text |
Contents
Introduction
xv
Chapter
1.
Production Models: Maximizing Profits
1
1.1
A two-variable linear program
2
1.2
The two-variable linear program in AMPL
5
1.3
A linear programming model
6
1.4
The linear programming model in AMPL
7
The basic model
8
An improved model
10
Catching errors
12
1.5
Adding lower bounds to the model
13
1.6
Adding resource constraints to the model
15
1.7
AMPL interfaces
18
Chapter
2.
Diet and Other Input Models: Minimizing Costs
27
2.1
A linear program for the diet problem
27
2.2
An AMPL model for the diet problem
30
2.3
Using the AMPL diet model
32
2.4
Generalizations to blending, economics and scheduling
37
Chapters. Transportation and Assignment Models
43
3.1
A linear program for the transportation problem
44
3.2
An AMPL model for the transportation problem
45
3.3
Other interpretations of the transportation model
49
Chapter
4.
Building Larger Models
55
4.1
A multicommodity transportation model
56
4.2
A multiperiod production model
59
4.3
A model of production and transportation
63
Chapters. Simple Sets and Indexing
73
5.1
Unordered sets
73
vii
Viii AMPL:
A MODELING LANGUAGE FOR MATHEMATICAL PROGRAMMING
5.2
Sets of numbers
75
5.3
Set operations
76
5.4
Set membership operations and functions
78
5.5
Indexing expressions
79
5.6
Ordered sets
82
Predefined sets and interval expressions
86
Chapter
6.
Compound Sets and Indexing
91
6.1
Sets of ordered pairs
91
6.2
Subsets and slices of ordered pairs
93
6.3
Sets of longer tuples
96
6.4
Operations on sets of tuples
98
6.5
Indexed collections of sets
100
Chapter
7.
Parameters and Expressions
109
7.1
Parameter declarations
110
7.2
Arithmetic expressions 111
7.3
Logical and conditional expressions
114
7.4
Restrictions on parameters
116
7.5
Computed parameters
118
7.6
Randomly generated parameters
121
7.7
Logical parameters
122
7.8
Symbolic parameters
123
Chapter
8.
Linear Programs: Variables, Objectives and Constraints
129
8.1
Variables
129
8.2
Linear expressions
132
8.3
Objectives
134
8.4
Constraints
137
Chapter
9.
Specifying Data
143
9.1
Formatted data: the data command
143
9.2
Data in lists
145
Lists of one-dimensional sets and parameters
145
Lists of two-dimensional sets and parameters
146
Lists of higher-dimensional sets and parameters
148
Combined lists of sets and parameters
151
9.3
Data in tables
154
Two-dimensional tables
154
Two-dimensional slices of higher-dimensional data
156
Higher-dimensional tables
157
Choice of format
159
9.4
Other features of data statements
160
Default values
160
Indexed collections of sets
161
Initial values for variables
162
AMPL:
A MODELING LANGUAGE FOR MATHEMATICAL PROGRAMMING ¡X
9.5
Reading unformatted data: the read command
163
Chapter
10.
Database Access
169
10.1
Genera) principles of data correspondence
169
10.2
Examples of table-handling statements
174
10.3
Reading data from relational tables
180
Reading parameters only
180
Reading a set and parameters
182
Establishing correspondences
184
Reading other values
185
10.4
Writing data to relational tables
186
Writing rows inferred from the data specifications
186
Writing rows inferred from a key specification
189
10.5
Reading and writing the same table
191
Reading and writing using two table declarations
192
Reading and writing using the same table declaration
193
10.6
Indexed collections of tables and columns
193
Indexed collections of tables
193
Indexed collections of data columns
196
10.7
Standard and built-in table handlers
197
Using the standard ODBC table handler
198
Using the standard ODBC table handler with Access and Excel
200
Built-in table handlers for text and binary files
201
Chapter
11.
Modeling Commands
203
11.1
General principles of commands and options
203
Commands
204
Options
204
11.2
Setting up and solving models and data
206
Entering models and data
206
Solving a model
207
11.3
Modifying data
209
Resetting
209
Resampling
209
The let command
210
11.4
Modifying models
212
Removing or redefining model components
213
Changing the model: fix, unfix; drop, restore
214
Relaxing integrality
215
Chapter
12.
Display Commands
219
12.1
Browsing through results: the display command
219
Displaying sets
220
Displaying parameters and variables
220
Displaying indexed expressions
224
12.2
Formatting options for display
227
AMPL:
A MODELING LANGUAGE FOR MATHEMATICAL PROGRAMMING
Arrangement of lists and tables
227
Control of line width
229
Suppression of zeros
231
12.3
Numeric options for display
232
Appearance of numeric values
233
Rounding of solution values
236
12.4
Other output commands: print and print
f
238
The print command
238
The print
f
command
239
12.5
Related solution values
240
Objective functions
240
Bounds and slacks
241
Dual values and reduced costs
243
12.6
Other display features for models and instances
245
Displaying model components: the show command:
246
Displaying model dependencies: the xref command
247
Displaying model instances: the expand command
247
Generic synonyms for variables, constraints and objectives
249
Resource listings
250
12.7
General facilities for manipulating output
251
Redirection of output
251
Output logs
251
Limits on messages
252
Chapter
13.
Command Scripts
255
13.1
Running scripts: include and commands
255
13.2
Iterating over a set: the
f
or statement
258
13.3
Iterating subject to a condition: the repeat statement
262
13.4
Testing a condition: the if-then-else statement
264
13.5
Terminating a loop: break and continue
266
13.6
Stepping through a script
268
13.7
Manipulating character strings
270
String functions and operators
270
String expressions in AMPL commands
273
Chapter
14.
Interactions with Solvers
275
14.1
Presolve
275
Activities of the presolve phase
276
Controlling the effects of presolve
278
Detecting infeasibility in presolve
279
14.2
Retrieving results from solvers
282
Solve results
282
Solver statuses of objectives and problems
286
Solver statuses of variables
287
Solver statuses of constraints
291
AMPL statuses
293
AMPL:
A MODELING LANGUAGE FOR MATHEMATICAL PROGRAMMING
ХІ
14.3
Exchanging information with solvers via suffixes
295
User-defined suffixes: integer programming directives
296
Solver-defined suffixes: sensitivity analysis
298
Solver-defined suffixes: infeasibility diagnosis
299
Solver-defined suffixes: direction of unboundedness
300
Defining and using suffixes
302
14.4
Alternating between models
304
14.5
Named problems
309
Defining named problems
3
11
Using named problems
3
1
4
Displaying named problems
3 ] 5
Defining and using named environments
316
Chapter
15.
Network Linear Programs 319
15.1
Minimum-cost transshipment models
319
A general transshipment model
320
Specialized transshipment models
323
Variations on transshipment models
326
15.2
Other network models
328
Maximum flow models
328
Shortest path models
329
Transportation and assignment models
330
15.3
Declaring network models by node and arc
333
A general transshipment model
334
A specialized transshipment model
335
Variations on transshipment models
336
Maximum flow models
337
15.4
Rules for node and arc declarations
340
node declarations
340
arc declarations
340
Interaction with objective declarations
341
Interaction with constraint declarations
342
Interaction with variable declarations
342
15.5
Solving network linear programs
343
Chapter
16.
Columnwise Formulations
353
16.1
An input-output model
354
Formulation by constraints
354
A columnwise formulation
355
Refinements of the columnwise formulation
357
16.2
A scheduling model
359
16.3
Rules for columnwise formulations
362
Chapter
17.
Piecewise-Linear Programs
365
17.1
Cost terms
366
Fixed numbers of pieces
366
Xii
AMPL:
A MODELING LANGUAGE FOR MATHEMATICAL PROGRAMMING
Varying numbers of pieces
368
17.2
Common two-piece and three-piece terms
369
Penalty terms for "soft" constraints
369
Dealing with infeasibility
373
Reversible activities
377
17.3
Other piecewise-linear functions
379
17.4
Guidelines for piecewise-linear optimization
382
Forms for piecewise-linear expressions
382
Suggestions for piecewise-linear models
383
Chapter
18.
Nonlinear Programs
391
18.1
Sources of nonlinearity
392
Dropping a linearity assumption
393
Achieving a nonlinear effect
396
Modeling an inherently nonlinear process
397
18.2
Nonlinear variables
397
Initial values of variables
398
Automatic substitution of variables
399
18.3
Nonlinear expressions
400
18.4
Pitfalls of nonlinear programming
403
Function range violations
403
Multiple local optima
407
Other pitfalls
410
Chapter
19.
Complementarity Problems
419
19.1
Sources of complementarity
419
A complementarity model of production economics
420
Complementarity for bounded variables
423
Complementarity for price-dependent demands
425
Other complementarity models and applications
426
19.2
Forms of complementarity constraints
427
19.3
Working with complementarity constraints
428
Related solution values
428
Presolve
429
Generic synonyms
431
Chapter
20.
Integer Linear Programs
437
20.1
Integer variables
438
20.2
Zero-one variables and logical conditions
439
Fixed costs
440
Zero-or-minimum restrictions
444
Cardinality restrictions
445
20.3
Practical considerations in integer programming
448
AMPL:
A MODELING LANGUAGE FOR MATHEMATICAL PROGRAMMING
ХІІІ
Appendix A. AMPL Reference Manual
453
A.
1
Lexical rules
453
A.2 Set members
454
A.3 Indexing expressions and subscripts
455
A.4 Expressions
455
A.4.1 Built-in functions
45g
A.4.2 Strings and regular expressions
459
A.4.3 Piecewise-linear terms
460
A.5 Declarations of model entities
461
A.6 Set declarations
461
A.6.
1
Cardinality and
arity
functions
462
A.6.2 Ordered sets
463
A.6.3 Intervals and other infinite sets
463
A.
7
Parameter declarations
465
A.7.1 Check statements
465
A.7.2 Infinity
466
A.8 Variable declarations
466
A.8.1 Defined variables
467
A.9 Constraint declarations
468
A.9.1 Complementarity constraints
469
A.
10
Objective declarations
470
A.ll Suffix notation for auxiliary values
470
A.
11.1
Suffix declarations
471
A.
11.2
Statuses
473
A.
12
Standard data format
473
A.12.1 Set data
473
A.
12.2
Parameter data
475
A.
13
Database access and tables
477
A.
14
Command language overview
479
A.
14.1
Options and environment variables
481
A.
15
Redirection of input and output
481
A.
16
Printing and display commands
482
A.
17
Reading data
484
A.
18
Modeling commands
485
A.
18.1
The solve command
485
A.18.2 The solution command
487
A.18.3 The write command
487
A.
18.4
Auxiliary files
487
A.18.5 Changing a model: delete, purge, redeclare
488
A.18.6 The drop, restore and objective commands
489
A.18.7 The fix and unfix commands
489
A.
18.8
Named problems and environments
489
A.
18.9
Modifying data: reset, update, let
490
A.
19
Examining models
491
A.
19.1
The show command
491
Xiv
AMPL:
A MODELING LANGUAGE FOR MATHEMATICAL PROGRAMMING
A.19.2 The xref command
492
A.19.3 The expand command
492
A.
19.4
Generic names
492
A.
19.5
The check command
492
A.20 Scripts and control flow statements
492
A.20.1 The for, repeat and if-then-else statements
493
A.20.2 Stepping through commands
495
A.21 Computational environment
495
A.2
1.1
The shell command
495
A.21.2 The
cd
command
495
A.21.
3
The quit, exit and end commands
496
A.21
.4
Built-in timing parameters
496
A.2
1.5
Logging
496
A.22 Imported functions
497
A.23 AMPL invocation
499
Index
501
Al
VI
r L
is a language for large-scale optimization and mathematical
programming problems in production, distribution, blending, scheduling,
and many other applications. Combining familiar algebraic notation
and a powerful interactive command environment, AMPL makes it easy
to create models, use a wide variety of solvers,
ond
examine solutions.
Though flexible and convenient for rapid prototyping and development
of models, AMPL also offers the speed and generality needed for
repeated large-scale production runs.
This book, by the creators of AMPL, is a complete guide for modelers
at all levels of experience. It begins with a tutorial on widely used linear
programming models and presents all of AMPL's features for linear
programming with extensive examples. Additional chapters cover
network, nonlinear, piecewise-linear, and integer programming;
database and spreadsheet interactions; and command scripts. Most
chapters include exercises.
Download free versions of AMPL and several solvers from www.ampl.com
for experiment, evaluation, and education. The Web site also lists vendors
of the commercial version of AMPL and a variety of solvers. |
| any_adam_object | 1 |
| author | Fourer, Robert Gay, David M. Kernighan, Brian W. 1942- |
| author_GND | (DE-588)138445281 (DE-588)138447284 |
| author_facet | Fourer, Robert Gay, David M. Kernighan, Brian W. 1942- |
| author_role | aut aut aut |
| author_sort | Fourer, Robert |
| author_variant | r f rf d m g dm dmg b w k bw bwk |
| building | Verbundindex |
| bvnumber | BV035796535 |
| classification_rvk | ST 601 |
| classification_tum | MAT 910 DAT 356f |
| ctrlnum | (OCoLC)634692286 (DE-599)BVBBV035796535 |
| discipline | Informatik Mathematik |
| edition | 2. ed., [Nachdr.] |
| format | Book |
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| id | DE-604.BV035796535 |
| illustrated | Illustrated |
| indexdate | 2025-01-15T07:00:28Z |
| institution | BVB |
| isbn | 0534388094 9780534388096 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018655755 |
| oclc_num | 634692286 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-523 DE-634 DE-20 DE-29T DE-706 |
| owner_facet | DE-91G DE-BY-TUM DE-523 DE-634 DE-20 DE-29T DE-706 |
| physical | XXI, 517 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Brooks/Cole |
| record_format | marc |
| spelling | Fourer, Robert Verfasser aut AMPL a modeling language for mathematical programming Robert Fourer ; David M. Gay ; Brian W. Kernighan 2. ed., [Nachdr.] Belmont, Calif. [u.a.] Brooks/Cole 2009 XXI, 517 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier AMPL (DE-588)4407769-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Programmiersprache (DE-588)4047409-4 gnd rswk-swf AMPL (DE-588)4407769-5 s DE-604 Optimierung (DE-588)4043664-0 s Programmiersprache (DE-588)4047409-4 s Gay, David M. Verfasser (DE-588)138445281 aut Kernighan, Brian W. 1942- Verfasser (DE-588)138447284 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018655755&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018655755&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Fourer, Robert Gay, David M. Kernighan, Brian W. 1942- AMPL a modeling language for mathematical programming AMPL (DE-588)4407769-5 gnd Optimierung (DE-588)4043664-0 gnd Programmiersprache (DE-588)4047409-4 gnd |
| subject_GND | (DE-588)4407769-5 (DE-588)4043664-0 (DE-588)4047409-4 |
| title | AMPL a modeling language for mathematical programming |
| title_auth | AMPL a modeling language for mathematical programming |
| title_exact_search | AMPL a modeling language for mathematical programming |
| title_full | AMPL a modeling language for mathematical programming Robert Fourer ; David M. Gay ; Brian W. Kernighan |
| title_fullStr | AMPL a modeling language for mathematical programming Robert Fourer ; David M. Gay ; Brian W. Kernighan |
| title_full_unstemmed | AMPL a modeling language for mathematical programming Robert Fourer ; David M. Gay ; Brian W. Kernighan |
| title_short | AMPL |
| title_sort | ampl a modeling language for mathematical programming |
| title_sub | a modeling language for mathematical programming |
| topic | AMPL (DE-588)4407769-5 gnd Optimierung (DE-588)4043664-0 gnd Programmiersprache (DE-588)4047409-4 gnd |
| topic_facet | AMPL Optimierung Programmiersprache |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018655755&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018655755&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT fourerrobert amplamodelinglanguageformathematicalprogramming AT gaydavidm amplamodelinglanguageformathematicalprogramming AT kernighanbrianw amplamodelinglanguageformathematicalprogramming |