In this paper we study the use of formulations with precedence relation variables for the Precedence Constrained Asymmetric Travelling Salesman (PCATS) problem. Contrary to previous papers, the emphasis of this paper 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.