We introduce the time-constrained maximal covering routing problem -TCMCRP-, as a generalization of the covering salesman problem. In this problem, we are given a central depot, a set of facilities and several customers which are located within a pre-determined coverage distance of available facilities. Each facility can supply the demand of some customers which are within its coverage radius. Starting from the depot, the goal is to maximize the total number of covered customers, by constructing a set of p length constraint Hamiltonian cycles. We have proposed a mixed integer linear programming model and three heuristic algorithms, namely iterated local search -ILS-, tabu search -TS- and variable neighborhood search -VNS-, to solve the problem. Extensive computational tests on this problem and some of its variants clearly indicate the effectiveness of the developed solution methods.

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