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This paper deals with the ring star problem that consists in designing a ring that pass through a central depot, and then assigning each non visited customer to a node of the ring. The objective is to minimize the total routing and assignment costs. A new chain based formulation is proposed. Valid inequalities are proposed to strengthen the linear programming relaxation and are used as cutting planes in a branch-and-cut approach. A large set of instances are tested and show the effectiveness ofdoi:10.1080/02331930903500332 fatcat:lfvggo5ejvdj3pu43bsppcpouq