An asymptotic simplex method for parametric linear programming

We study singularly perturbed linear programs. These are parametric linear programs whose constraints become linearly dependent when the perturbation parameter goes to zero. Similar problems were studied by Jeroslow (1973). He proposed a simplex-like method, which works over the field of rational functions. Here we develop an alternative asymptotic simplex method based on Laurent series expansions. This approach appears to be more computationally efficient. In addition, we point out several possible generalizations of our method and provide new simple updating formulae for the perturbed solution