Probabilistic Set Covering with Correlations

Probabilistic Set Covering with Correlations

We consider a probabilistic set covering problem where there is uncertainty regarding whether a selected set can cover an item, and the objective is to determine a minimum-cost combination of sets so that each item is covered with a pre-specified probability. To date, literature on this problem has focused on the special case in which uncertainties are independent. In this paper, we formulate c...

MIP reformulations of the probabilistic set covering problem

In this paper, we address the following probabilistic version (PSC) of the set covering problem:min{cx |P(Ax ≥ ξ) ≥ p, x ∈ {0, 1}N }where A is a 0-1matrix, ξ is a random 0-1 vector and p ∈ (0, 1] is the threshold probability level. We introduce the concepts of p-inefficiency and polarity cuts. While the former is aimed at deriving an equivalentMIP reformulation of (PSC), the latter is used as a...

A Short Note on the Probabilistic Set Covering Problem

In this paper we address the following probabilistic version (PSC) of the set covering problem: min{cx | P(Ax ≥ ξ) ≥ p, xj ∈ {0, 1} j ∈ N} where A is a 0-1 matrix, ξ is a random 0-1 vector and p ∈ (0, 1] is the threshold probability level. In a recent development Saxena, Goyal and Lejeune proposed a MIP reformulation of (PSC) and reported extensive computational results with small and medium si...

Probabilistic covering problems

Diagnostic Reasoning with Multilevel Set-Covering Models

We consider multilevel set-covering models for diagnostic reasoning: though a lot of work has been done in this field, knowledge acquisition efforts have been investigated only insufficiently. We will show how set-covering models can be build incrementally and how they can be refined by knowledge enhancements or representational extensions. All these extensions have a primary characteristic: th...