An optimization problem is represented by a set of interconnected modeling objects in an IloCplex object. Modeling objects in Concert Technology are objects of type IloNumVar and its extensions, or IloAddable and its extensions. Since these are Java interfaces and not classes, objects of these types cannot be created explicitly. Rather, modeling objects are created using methods of an IloModeler or one of its extensions, such as IloMPModeler or IloCPModeler.

For this discussion we will concentrate on IloModeler and IloMPModeler because the class IloCplex implements these interfaces. To create a new modeling object, you must first create the IloModeler which will be used to create the modeling object. For the discussion here, the model will be an instance of IloCplex, and it will be created as follows:

IloCplex cplex = new IloCplex();

Since class IloCplex implements IloMPModeler (and thus its parent interface IloModeler) all methods from IloMPModeler and IloModeler can be used for building a model. IloModeler defines the methods to:

• create modeling variables of type integer, float, or Boolean;
• construct simple expressions using modeling variables;
• create objective functions; and
• create ranged constraints, that is, constraints of the form lb expression ub.

Models that consist only of such constructs can be built and solved with any ILOG optimizer implementing the IloModeler interface, including IloCplex which implements the IloMPModeler extension.

The IloMPModeler interface extends IloModeler by adding functionality specific to mathematical programming applications. This functionality includes these additional modeling object types:

• semi-continuous variables;
• special ordered sets; and
• piecewise linear functions.

It also includes these modeling features to support specific needs:

• change of type for previously declared variables;
• modeling by column; and
• general manipulations of model entities.