Robust continuous linear programs

Abstract

Continuous linear programs (CLPs) arise in applications such as production/economic planning, continuous-time network flow problems, fluid relaxations of multiclass queueing networks, and control. To the best of the author’s knowledge, this paper proposes the first robust optimization framework for CLPs. The main result of the paper is that the robust counterpart of a CLP is also a CLP. Thus, any computational method for the original problem can be applied to the robust problem. For instance, a recent polynomial-time approximation algorithm applies. Further, if the original problem possesses a so-called separable structure, then the robust problem is also separable. Then existing Simplex-type and other discretization-based solution methods can be applied to the robust problem. The paper also provides a bound on the probability that an optimal solution to the robust counterpart violates a constraint in the original problem. Qualitative properties of this bound are discussed and compared with similar bounds for robust finite-dimensional linear programs.