Linear programming, in its general form, involves optimizing a deterministic objective function over a deterministic feasible set, i.e a convex set, the simplex algorithm provides a systematic way to go from one extreme point in this convex set to the next with iteratively reducing the cost function, in that sense, it is a deterministic mathematical framework for deterministic linear optimization problem.
The Simplex algorithm is a mathematical tool primarily. Some statistical fitting problems can be cast as a linear program, but I consider this incidental.