Mixed-integer programming approaches for the time-constrained maximal covering routing problem

Abstract In this paper, we study the recently introduced time-constrained maximal covering routing problem. problem, are given a central depot, set of facilities, and customers. Each customer is associated with subset facilities which can cover it. A feasible solution consists k Hamiltonian cycles on subsets depot. cycle must contain depot respect distance limit. The goal to maximize number customers covered by contained in cycles. We develop two exact algorithms for problem based new mixed-integer programming models. One algorithm compact model, while other model contains an exponential constraints, separated on-the-fly, i.e., use branch-and-cut. also describe preprocessing techniques, valid inequalities primal heuristics both evaluate our approaches instances from literature able find provably optimal 267 out 270 instances, including 123 was not known before. Moreover, most only take few seconds, thus up five magnitudes faster than previous approaches. Finally, discuss some issues present instances.