. The UPS Problem consists of the following: given a vertex set V , vertex probabilities (pv )v2V , and distances l : V 2 ! R + that satisfy the triangle inequality, nd a Hamilton cycle such that the expected length of the shortcut that skips each vertex v with probability 1 pv (independently of the others) is minimum. This problem appears in the following context. Drivers of delivery companies visit customers daily to deliver packages. For the company, the shorter the distance traversed, the better. For a driver, routes that change dramatically from one day to the other are inconvenient; it is better if one only has to shortcut a xed route. The UPS problem, whose objective captures these two points of view, is at least as hard to approximate as the Metric TSP. Given that one of the vertices has probability one, we show that the performance ratio of a TSP tour for the UPS problem is 1=pmin , where pmin := minv2V pv . We also show that this is tight. Consequently, Chr..
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