Continuous covering on networks: Improved mixed integer programming formulations

Covering problems are well-studied in the domain of Operations Research, and, more specifically, Location Science. When location space is a network, most frequent assumption to consider candidate facility locations, points be covered, or both, finite sets. In this work, we study set-covering problem when both locations and demand continuous on network. This variant has received little attention, scarce existing approaches have focused particular cases, such as tree networks integer covering radius. Here general present Mixed Integer Linear Programming formulation (MILP) for with edge lengths no greater than The model does not lose generality, any satisfying condition can partitioned into subedges appropriate without changing problem. We propose preprocessing algorithm reduce size MILP, devise tight big-M constants valid inequalities strengthen our formulations. Moreover, second MILP proposed, which admits As opposed formulations (including first proposed herein), number variables constraints depend network’s edges. represents scalable approach that particularly suits real-world networks, whose edges usually Our computational experiments show strengths limitations exact random networks. also tested against an method.