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This paper addresses the problem of maximizing lifetime of directional wireless sensor networks, i.e., where sensors can monitor targets in an angular sector only and not all the targets around them. These sectors usually do not overlap, and each sensor can monitor at most one sector at a time. An exact method is proposed using a column generation scheme where a two level strategy, consisting of a genetic algorithm and an integer linear programming approach, is used to solve the auxiliary problem. The role of integer linear programming (ILP) approach is limited to either escaping from local optima or proving the optimality of the current solution. Computational results clearly show the advantage of the proposed approach over a column generation approach based on solving the auxiliary problem through ILP approach alone as the proposed approach is several times faster.