Formulations of the continuous set-covering problem on networks: a comparative study

Abstract

We study the continuous set covering problem on networks and propose several new MILP formulations and valid inequalities. In contrast to state-of-the-art formulations, the new formulations only use edges to index installed points, and the formulation sizes are smaller. The covering conditions can be represented as multivariate piecewise linear concave constraints, which we formulate as disjunctive systems. We propose three MILP formulations based on indicator constraint, big-M, and disjunctive programming techniques for modeling the disjunctive system. Finally, we give a classification of new and old formulations, and conduct experiments to compare them computationally.