An asymptotic simplex method for singularly perturbed linear programs

We study singularly perturbed linear programs. These are linear programs whose constraints and objective coefficients depend on a small perturbation parameter, and furthermore the constraints become linearly dependent when the perturbation parameter goes to zero. Problems like that were studied by Jeroslow in 1970s. He proposed 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 simple updating formulae for the perturbed solution.