This example demonstrates:

Here is the problem example ilolpex3 solves:

Minimize	c^Tx
subject to	Hx = d   Ax = b   l x u
where	H =	( -1 0 1 0 1 0 0 0 )	d =	( -3 )
		( 1 -1 0 1 0 0 0 0 )		( 1 )
		( 0 1 -1 0 0 1 -1 0 )		( 4 )
		( 0 0 0 -1 0 -1 0 1 )		( 3 )
		( 0 0 0 0 -1 0 1 -1 )		( -5 )
	A =	( 2 1 -2 -1 2 -1 -2 -3 )	b =	( 4 )
		( 1 -3 2 3 -1 2 1 1 )		( -2 )
	c =	(-9 1 4 2 -8 2 8 12 )
	l =	( 0 0 0 0 0 0 0 0 )
	u =	(50 50 50 50 50 50 50 50 )

The constraints Hx=d represent the flow conservation of a pure network flow. The example solves this problem in two steps:

Notice that the 0 values in the data are omitted in the example program. ILOG CPLEX makes extensive use of sparse matrix methods and, although ILOG CPLEX correctly handles any explicit zero coefficients given to it, most programs solving models of more than modest size benefit (in terms of both storage space and speed) if the natural sparsity of the model is exploited from the very start.