Abstract
The probabilistic traveling salesman problem (PTSP) is a variant of the classical traveling salesman problem in which only a subset of customers (nodes) may be present in any given instance of the problem. We derive a lower bounding procedure for the PTSP using an extended concept of valid inequalities that play a central role in polyhedral approach to combinatorial optimization problems. We also present a variant of the branch-and-bound method, which we call the fathoming procedure for a generalization of the facility location problem, the probabilistic traveling salesman facility location problem.
