Contents
Figures ...............v
Tables ...............vii
Language User’s Manual .......ix
Chapter 1. Introduction to OPL .....1
Language overview ............1
Modeling languages ...........1
Mathematical programming ........2
Constraint programming .........3
Constraint programming versus mathematical
programming .............5
Scripting...............9
A short tour of OPL ............9
Linear programming: a production planning
example ...............9
Integer programming: the knapsack problem . . 19
Mixed integer-linear programming: a blending
problem ..............21
Constraint programming: an inventory matching
problem ..............24
Modeling tips .............27
Efficient models ............27
Sparsity ..............27
About arrays .............31
Other modeling tips ..........32
Chapter 2. The application areas . . . 33
Some examples .............33
Linear programming: a product mix problem . . 33
Integer programming: a warehouse location
problem ..............35
Applications of linear and integer programming . . 37
Linear programming ..........37
Integer programming ..........47
Mixed integer-linear programming .....55
Piecewise linear programming .......57
Applications of constraint programming.....62
What is constraint programming? ......62
The vellino example (column generation) . . . 62
The car sequencing example ........67
The time tabling example.........70
Modeling and solving a simple problem: house
building ..............76
Quadratic programming ..........81
Tutorial: Using CPLEX logical constraints ....82
What are logical constraints? .......82
Description of the problem ........82
Representing the data ..........83
Using logical constraints .........85
Chapter 3. IBM ILOG Script for OPL . . 87
Introduction to scripting ..........87
What is IBM ILOG Script? ........87
Preprocessing and postprocessing ......88
A few tips ..............95
Common pitfalls............97
Tutorial: Flow control and multiple searches . . . 98
The production planning problem ......98
Procedure summary ..........98
Detailed steps ............99
Doing more with mulprod_main ......103
Basic flow control script .........105
Tutorial: Flow control and column generation . . 106
What is model decomposition? ......106
The cutting stock problem ........106
Procedure summary ..........107
Detailed steps ............108
Doing more with cutstock_main ......111
Tutorial: Changing default
behaviors in flow control .........112
What you are going to do ........112
Setting an initial solution for the CPLEX engine 112
Setting preferences on the search for conflicts
and relaxations ............114
Searching for relaxation and conflicts .....116
Using IBM ILOG Script in constraint programming 116
Setting CP parameters .........116
Defining search phases .........118
Accessing solutions in postprocessing ....122
Chapter 4. Advanced features ....125
Tutorial: External functions.........125
Context of external functions .......125
Using an external knapsack algorithm ....126
Using data from other sources.......131
Debugging custom Java code using Eclipse . . 132
Chapter 5. Performance and memory
usage...............137
Performance tips ............137
Memory usage .............138
If your system runs out of memory .....138
Building data structures differently .....138
Terminating data objects.........139
Changing engine parameters .......139
Using oplrun ............140
Changing to a 64-bit platform .......140
Using 4GT tuning ...........141
Scaling down the size of the model .....141
Multi-threading ............141
A typical problem to solve ........141
From the mathematical model to the OPL code 145
Index ...............147
© Copyright IBM Corp. 1987, 2011 iii
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