AMPL : a modeling language for mathematical programming / Robert Fourer, David M. Gay, Brian W. Kernighan.

Format:

Book

Author/Creator:

Fourer, Robert.

Contributor:

Gay, David M.

Kernighan, Brian W.

Language:

English

Subjects (All):

Programming (Mathematics).

Linear programming.

Physical Description:

xxi, 517 pages : illustrations ; 25 cm

Edition:

Second edition.

Place of Publication:

Pacific Grove, CA : Thomson/Brooks/Cole, [2003]

Contents:

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

Chapter 3. 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

Chapter 5. Simple Sets and Indexing 73

5.1 Unordered sets 73

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

8.4 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

9.5 Reading unformatted data: the read command 163

Chapter 10. Database Access 169

10.1 General 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

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 printf 238

The print command 238

The printf 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 for 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

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 311

Using named problems 314

Displaying named problems 315

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

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

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 458

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.11 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

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.21.1 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.21.5 Logging 496

A.22 Imported functions 497

A.23 AMPL invocation 499.

ISBN:

0534388094

OCLC:

51638824