  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.
