On extended formulations for the precedence constrained asymmetric traveling salesman problem

In this article we study the use of formulations with precedence relation variables for the Precedence Constrained Asymmetric Travelling Salesman (PCATS) problem. Contrary to previous articles, the emphasis of this article is on formulations involving exponential sized sets of inequalities and on the development of a cutting plane method together with polynomial routines for separating the new inequalities. Our computational results, taken from a set of benchmark instances, show that our methods improve significantly on most of the best previously known lower bound values. (C) 2006 Wiley Periodicals, Inc.