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A more compact formulation of the symmetric multiple traveling salesman problem with fixed charges

The multiple traveling salesman problem with fixed charges (MTSPF) is an extension of the standard traveling salesman problem (TSP). Previous work by Hong and Padberg showed how to transform to a TSP with n + m + 4 nodes, where m is the number of salesmen. The four extra nodes were included to prevent the transformed problem from escaping part of the fixed costs. This paper shows that two of these nodes can be eliminated without sacrificing the formulation as a TSP. Further, all four extra nodes can be replaced by a pair of simple constraints. All formulations produce equivalent solutions.