In this paper, we extend the classical multiple traveling salesman problem (mTSP) by imposing a minimal number of nodes that a traveler must visit as a side condition. We consider single and multidepot cases and propose integer linear programming formulations for both, with new bounding and subtour elimination constraints. We show that several variations of the multiple salesman problem can be modeled in a similar manner. Computational analysis shows that the solution of the multidepot mTSP with the proposed formulation is significantly superior to previous approaches. © 2005 Elsevier B.V. All rights reserved.
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