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IBM ILOG CPLEX Optimization Studio
OP L Langu age R e fe r ence Manu al
Version12Release4
Copyright notice
Describes general use restrictions and trademarks related to this document and the software described in this
document.
© Copyright IBM Corp. 1987, 2011
US Government Users Restricted Rights - Use, duplication or disclosure restricted by GSA ADP Schedule Contract
with IBM Corp.
Trademarks
IBM, the IBM logo, ibm.com, WebSphere, and ILOG are trademarks or registered trademarks of International
Business Machines Corp., in many jurisdictions worldwide. Other product and service names might be trademarks
of IBM or other companies. A current list of IBM trademarks is available on the Web at Copyright and trademark
information.
Adobe, the Adobe logo, PostScript, and the PostScript logo are either registered trademarks or trademarks of Adobe
Systems Incorporated in the United States, and/or other countries.
Linux is a registered trademark of Linus Torvalds in the United States, other countries, or both.
UNIX is a registered trademark of The Open Group in the United States and other countries.
Microsoft, Windows, Windows NT, and the Windows logo are trademarks of Microsoft Corporation in the United
States, other countries, or both.
Java and all Java-based trademarks and logos are trademarks or registered trademarks of Oracle and/or its
affiliates.
Other company, product, or service names may be trademarks or service marks of others.
© Copyright IBM Corporation 1987, 2011.
US Government Users Restricted Rights – Use, duplication or disclosure restricted by GSA ADP Schedule Contract
with IBM Corp.
Contents
Figures ...............v
Tables ...............vii
Language Reference Manual .....ix
Chapter 1. Why an Optimization
Programming Language? .......1
Chapter 2. OPL, the modeling language 3
Building a model .............3
Data types ...............4
Basic data types ............4
Data structures ............7
Data sources ..............15
Data initialization ...........15
Database initialization ..........24
Spreadsheet Input/Output ........28
Data consistency............32
Preprocessing of data ..........34
Pitfall of lazy initialization of data ......36
Decision types .............37
Decision variables ...........37
Expressions of decision variables ......38
Dynamic collection of elements into arrays . . . 39
Expressions ..............40
Usage of expressions ..........41
Data and decision variable identifiers.....41
Integer and float expressions .......41
Aggregate operators ..........43
Piecewise-linear functions ........43
Set expressions ............48
Boolean expressions ..........50
Constraints ..............51
Introduction .............51
Using constraints ...........51
Constraint labels............53
Types of constraints ..........58
Limitations on constraints ........64
Formal parameters ............65
Basic formal parameters .........65
Tuples of parameters ..........67
Filtering in tuples of parameters ......68
Scheduling ..............69
Introduction .............69
Piecewise linear and stepwise functions ....70
Interval variables ...........71
Unary constraints on interval variables ....75
Precedence constraints between interval variables 75
Constraints on groups of interval variables . . . 76
A logical constraint between interval variables:
presenceOf .............77
Expressions on interval variables ......77
Sequencing of interval variables ......78
Cumulative functions ..........81
State functions ............85
Notation ..............88
Chapter 3. IBM ILOG Script for OPL . . 91
Language structure ............91
Syntax ...............91
Expressions in IBM ILOG Script ......92
Statements..............98
Built-in values and functions ........103
Numbers ..............103
IBM ILOG Script strings .........110
IBM ILOG Script Booleans ........117
IBM ILOG Script arrays .........119
Objects ..............124
Dates ...............126
The null value ............129
The undefined value ..........130
IBM ILOG Script functions ........130
Miscellaneous functions .........131
Index ...............133
© Copyright IBM Corp. 1987, 2011 iii
iv OPL Language Reference Manual
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