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| Introduction | |
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| Production Models: Maximizing Profits | |
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| A two-variable linear program | |
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| The two-variable linear program in AMPL | |
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| A linear programming model | |
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| The linear programming model in AMPL | |
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| The basic model | |
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| An improved model | |
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| Catching errors | |
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| Adding lower bounds to the model | |
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| Adding resource constraints to the model | |
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| AMPL interfaces | |
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| Diet and Other Input Models: Minimizing Costs | |
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| A linear program for the diet problem | |
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| An AMPL model for the diet problem | |
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| Using the AMPL diet model | |
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| Generalizations to blending, economics and scheduling | |
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| Transportation and Assignment Models | |
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| A linear program for the transportation problem | |
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| An AMPL model for the transportation problem | |
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| Other interpretations of the transportation model | |
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| Building Larger Models | |
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| A multicommodity transportation model | |
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| A multiperiod production model | |
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| A model of production and transportation | |
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| Simple Sets and Indexing | |
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| Unordered sets | |
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| Sets of numbers | |
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| Set operations | |
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| Set membership operations and functions | |
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| Indexing expressions | |
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| Ordered sets | |
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| Predefined sets and interval expressions | |
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| Compound Sets and Indexing | |
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| Sets of ordered pairs | |
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| Subsets and slices of ordered pairs | |
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| Sets of longer tuples | |
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| Operations on sets of tuples | |
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| Indexed collections of sets | |
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| Parameters and Expressions | |
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| Parameter declarations | |
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| Arithmetic expressions | |
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| Logical and conditional expressions | |
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| Restrictions on parameters | |
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| Computed parameters | |
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| Randomly generated parameters | |
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| Logical parameters | |
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| Symbolic parameters | |
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| Linear Programs: Variables, Objectives and Constraints | |
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| Variables | |
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| Linear expressions | |
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| Objectives | |
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| Constraints | |
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| Specifying Data | |
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| Formatted data: the data command | |
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| Data in lists | |
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| Lists of one-dimensional sets and parameters | |
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| Lists of two-dimensional sets and parameters | |
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| Lists of higher-dimensional sets and parameters | |
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| Combined lists of sets and parameters | |
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| Data in tables | |
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| Two-dimensional tables | |
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| Two-dimensional slices of higher-dimensional data | |
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| Higher-dimensional tables | |
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| Choice of format | |
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| Other features of data statements | |
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| Default values | |
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| Indexed collections of sets | |
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| Initial values for variables | |
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| Reading unformatted data: the read command | |
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| Database Access | |
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| General principles of data correspondence | |
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| Examples of table-handling statements | |
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| Reading data from relational tables | |
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| Reading parameters only | |
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| Reading a set and parameters | |
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| Establishing correspondences | |
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| Reading other values | |
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| Writing data to relational tables | |
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| Writing rows inferred from the data specifications | |
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| Writing rows inferred from a key specification | |
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| Reading and writing the same table | |
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| Reading and writing using two table declarations | |
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| Reading and writing using the same table declaration | |
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| Indexed collections of tables and columns | |
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| Indexed collections of tables | |
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| Indexed collections of data columns | |
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| Standard and built-in table handlers | |
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| Using the standard ODBC table handler | |
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| Using the standard ODBC table handler with Access and Excel | |
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| Built-in table handlers for text and binary files | |
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| Modeling Commands | |
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| General principles of commands and options | |
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| Commands | |
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| Options | |
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| Setting up and solving models and data | |
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| Entering models and data | |
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| Solving a model | |
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| Modifying data | |
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| Resetting | |
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| Resampling | |
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| The let command | |
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| Modifying models | |
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| Removing or redefining model components | |
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| Changing the model: fix, unfix; drop, restore | |
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| Relaxing integrality | |
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| Display Commands | |
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| Browsing through results: the display command | |
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| Displaying sets | |
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| Displaying parameters and variables | |
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| Displaying indexed expressions | |
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| Formatting options for display | |
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| Arrangement of lists and tables | |
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| Control of line width | |
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| Suppression of zeros | |
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| Numeric options for display | |
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| Appearance of numeric values | |
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| Rounding of solution values | |
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| Other output commands: print and printf | |
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| The print command | |
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| The printf command | |
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| Related solution values | |
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| Objective functions | |
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| Bounds and slacks | |
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| Dual values and reduced costs | |
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| Other display features for models and instances | |
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| Displaying model components: the show command | |
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| Displaying model dependencies: the xref command | |
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| Displaying model instances: the expand command | |
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| Generic synonyms for variables, constraints and objectives | |
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| Resource listings | |
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| General facilities for manipulating output | |
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| Redirection of output | |
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| Output logs | |
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| Limits on messages | |
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| Command Scripts | |
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| Running scripts: include and commands | |
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| Iterating over a set: the for statement | |
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| Iterating subject to a condition: the repeat statement | |
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| Testing a condition: the if-then-else statement | |
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| Terminating a loop: break and continue | |
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| Stepping through a script | |
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| Manipulating character strings | |
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| String functions and operators | |
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| String expressions in AMPL commands | |
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| Interactions with Solvers | |
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| Presolve | |
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| Activities of the presolve phase | |
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| Controlling the effects of presolve | |
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| Detecting infeasibility in presolve | |
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| Retrieving results from solvers | |
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| Solve results | |
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| Solver statuses of objectives and problems | |
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| Solver statuses of variables | |
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| Solver statuses of constraints | |
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| AMPL statuses | |
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| Exchanging information with solvers via suffixes | |
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| User-defined suffixes: integer programming directives | |
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| Solver-defined suffixes: sensitivity analysis | |
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| Solver-defined suffixes: infeasibility diagnosis | |
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| Solver-defined suffixes: direction of unboundedness | |
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| Defining and using suffixes | |
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| Alternating between models | |
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| Named problems | |
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| Defining named problems | |
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| Using named problems | |
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| Displaying named problems | |
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| Defining and using named environments | |
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| Network Linear Programs | |
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| Minimum-cost transshipment models | |
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| A general transshipment model | |
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| Specialized transshipment models | |
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| Variations on transshipment models | |
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| Other network models | |
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| Maximum flow models | |
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| Shortest path models | |
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| Transportation and assignment models | |
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| Declaring network models by node and arc | |
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| A general transshipment model | |
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| A specialized transshipment model | |
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| Variations on transshipment models | |
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| Maximum flow models | |
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| Rules for node and arc declarations | |
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| node declarations | |
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| arc declarations | |
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| Interaction with objective declarations | |
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| Interaction with constraint declarations | |
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| Interaction with variable declarations | |
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| Solving network linear programs | |
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| Columnwise Formulations | |
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| An input-output model | |
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| Formulation by constraints | |
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| A columnwise formulation | |
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| Refinements of the columnwise formulation | |
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| A scheduling model | |
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| Rules for columnwise formulations | |
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| Piecewise-Linear Programs | |
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| Cost terms | |
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| Fixed numbers of pieces | |
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| Varying numbers of pieces | |
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| Common two-piece and three-piece terms | |
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| Penalty terms for "soft" constraints | |
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| Dealing with infeasibility | |
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| Reversible activities | |
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| Other piecewise-linear functions | |
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| Guidelines for piecewise-linear optimization | |
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| Forms for piecewise-linear expressions | |
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| Suggestions for piecewise-linear models | |
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| Nonlinear Programs | |
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| Sources of nonlinearity | |
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| Dropping a linearity assumption | |
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| Achieving a nonlinear effect | |
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| Modeling an inherently nonlinear process | |
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| Nonlinear variables | |
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| Initial values of variables | |
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| Automatic substitution of variables | |
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| Nonlinear expressions | |
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| Pitfalls of nonlinear programming | |
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| Function range violations | |
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| Multiple local optima | |
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| Other pitfalls | |
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| Complementarity Problems | |
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| Sources of complementarity | |
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| A complementarity model of production economics | |
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| Complementarity for bounded variables | |
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| Complementarity for price-dependent demands | |
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| Other complementarity models and applications | |
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| Forms of complementarity constraints | |
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| Working with complementarity constraints | |
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| Related solution values | |
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| Presolve | |
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| Generic synonyms | |
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| Integer Linear Programs | |
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| Integer variables | |
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| Zero-one variables and logical conditions | |
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| Fixed costs | |
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| Zero-or-minimum restrictions | |
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| Cardinality restrictions | |
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| Practical considerations in integer programming | |
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| AMPL Reference Manual | |
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| Lexical rules | |
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| Set members | |
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| Indexing expressions and subscripts | |
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| Expressions | |
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| Built-in functions | |
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| Strings and regular expressions | |
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| Piecewise-linear terms | |
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| Declarations of model entities | |
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| Set declarations | |
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| Cardinality and arity functions | |
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| Ordered sets | |
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| Intervals and other infinite sets | |
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| Parameter declarations | |
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| Check statements | |
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| Infinity | |
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| Variable declarations | |
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| Defined variables | |
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| Constraint declarations | |
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| Complementarity constraints | |
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| Objective declarations | |
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| Suffix notation for auxiliary values | |
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| Suffix declarations | |
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| Statuses | |
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| Standard data format | |
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| Set data | |
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| Parameter data | |
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| Database access and tables | |
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| Command language overview | |
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| Options and environment variables | |
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| Redirection of input and output | |
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| Printing and display commands | |
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| Reading data | |
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| Modeling commands | |
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| The solve command | |
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| The solution command | |
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| The write command | |
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| Auxiliary files | |
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| Changing a model: delete, purge, redeclare | |
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| The drop, restore and objective commands | |
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| The fix and unfix commands | |
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| Named problems and environments | |
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| Modifying data: reset, update, let | |
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| Examining models | |
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| The show command | |
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| The xref command | |
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| The expand command | |
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| Generic names | |
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| The check command | |
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| Scripts and control flow statements | |
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| The for, repeat and if-then-else statements | |
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| Stepping through commands | |
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| Computational environment | |
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| The shell command | |
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| The cd command | |
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| The quit, exit and end commands | |
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| Built-in timing parameters | |
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| Logging | |
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| Imported functions | |
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| AMPL invocation | |
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| Index | |