Probability Modelling and Optimal Location of a Travelling Salesman

The ‘random part’ of an operations research model may be less satisfactory than the ‘deterministic part’, and it may thus be desirable to design algorithms that require few probability assumptions and make few calls to a suitable ‘probability oracle’. We consider here the problem of locating a service facility on a tree network so as to minimize the expected length of a travelling salesman tour through a random set of demand nodes.