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 +...+ c_nx_n
subject to	a₁₁x₁ + a₁₂x₂ +...+ a_1nx_n ~ b₁ a₂₁x₁ + a₂₂x₂ +...+ a_2nx_n ~ b₂ ... a_m1x₁ + a_m2x₂ +...+ a_mnx_n ~ b_m
with these bounds	l₁ x₁ u₁ ... l_n x_n u_n

where ~ can be , , or =, and the upper bounds u_i and lower bounds l_i 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, ... , c_n
Constraint coefficients	a₁₁, a₂₁, ... , a_n1 ... a_m1, a_m2, ..., a_mn
Right-hand sides	b₁, b₂, ... , b_m
Upper and lower bounds	u₁, u₂, ... , u_n and l₁, l₂, ... , l_n

The optimal solution that ILOG CPLEX computes and returns is:

ILOG CPLEX also can solve several extensions to LP: