What Is ILOG CPLEX?

ILOG CPLEX is a tool for solving linear optimization problems, commonly referred to as Linear Programming (LP) problems, of the form:

Maximize (or Minimize) 
c1x1 + c2x2 +...+ cnxn
subject to 
a11x1 + a12x2 +...+ a1nxn ~ b1
a21x1 + a22x2 +...+ a2nxn ~ b2
...
am1x1 + am2x2 +...+ amnxn ~ bm
with these bounds 
l1 x1 u1
...
ln xn un

where ~ can be , , or =, and the upper bounds ui and lower bounds li may be positive infinity, negative infinity, or any real number.

The elements of data you provide as input for this LP are:

Objective function coefficients 
c1, c2, ... , cn
Constraint coefficients 
a11, a21, ... , an1
...
am1, am2, ..., amn
Right-hand sides 
b1, b2, ... , bm
Upper and lower bounds 
u1, u2, ... , un and l1, l2, ... , ln

The optimal solution that CPLEX computes and returns is:

Variables 
x1, x2, ... , xn

CPLEX also can solve several extensions to LP:

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