Chance-Constrained Set Covering with Wasserstein Ambiguity

TL;DR

This paper introduces a novel distributionally robust chance-constrained set covering model with Wasserstein ambiguity, providing new reformulations, valid inequalities, and demonstrating improved reliability and computational effectiveness.

Contribution

It formulates a new Wasserstein-based distributionally robust set covering problem with binary decisions and develops decomposition algorithms and valid inequalities for it.

Findings

The DRC model is NP-hard.

Reformulation as a two-stage stochastic program facilitates solution.

Proposed inequalities improve computational performance.

Abstract

We study a generalized distributionally robust chance-constrained set covering problem (DRC) with a Wasserstein ambiguity set, where both decisions and uncertainty are binary-valued. We establish the NP-hardness of DRC and recast it as a two-stage stochastic program, which facilitates decomposition algorithms. Furthermore, we derive two families of valid inequalities. The first family targets the hypograph of a "shifted" submodular function, which is associated with each scenario of the two-stage reformulation. We show that the valid inequalities give a complete description of the convex hull of the hypograph. The second family mixes inequalities across multiple scenarios and gains further strength via lifting. Our numerical experiments demonstrate the reliability of the DRC model and the effectiveness of our proposed reformulation and valid inequalities.