After you have written a description of the problem, you can use classes of ILOG Concert Technology for .NET users with ILOG CPLEX to build a model.

Open the file yourCPLEXhome\examples\src\tutorials\LPex1lesson.cs in your integrated development environment, such as Microsoft Visual Studio.

That statement creates an empty instance of the class Cplex. In the next steps, you will add methods that make it possible for your application populate the model with data, either by rows, by columns, or by nonzeros.

Again, those lines populate the model with data specific to this problem. From them you can see how to use the interface IMPModeler to add columns to an empty model.

While for many examples population by rows may seem most straightforward and natural, there are some models where population by columns is a more natural or more efficient approach to implement. For example, problems with network structure typically lend themselves well to modeling by column. Readers familiar with matrix algebra may view the method populateByColumn as the transpose of populateByRow.

In this approach, range objects are created for modeling by column with only their lower and upper bound. No expressions over variables are given because building them at this point would be impossible since the variables have not been created yet. Similarly, the objective function is created only with its intended optimization sense, and without any expression.

Next the variables are created and installed in the existing ranges and objective. These newly created variables are introduced into the ranges and the objective by means of column objects, which are implemented in the class IColumn. Objects of this class are created with the methods Cplex.Column, and can be linked together with the method IColumn.And to form aggregate IColumn objects.

An IColumn object created with the method ICplex.Column contains information about how to use this column to introduce a new variable into an existing modeling object. For example if obj is an IObjective object, cplex.Column(obj, 2.0) creates an IColumn object containing the information to install a new variable in the expression of the IObjective object obj with a linear coefficient of 2.0. Similarly, for an IRange constraint rng, the method call cplex.Column(rng, -1.0) creates an IColumn object containing the information to install a new variable into the expression of rng, as a linear term with coefficient -1.0.

In short, when you use a modeling-by-column approach, new columns are created and installed as variables in all existing modeling objects where they are needed. To do this with ILOG Concert Technology, you create an IColumn object for every modeling object in which you want to install a new variable, and link them together with the method IColumn.And.

In those lines, you can see how to populate an empty model with data indicating the nonzeros of the constraint matrix. Those lines first create objects for the objective and the ranges without expressions. They also create variables without columns; that is, variables with only their bounds. Then those lines create expressions over the objective, ranges, and variables and add the expressions to the model.