Solving Real World Linear Ordering Problems Using a Primal Dual Interior Point Cutting Plane Method

Cutting plane methods require the solution of a sequence of linear programs where the solution to one provides a warm start to the next A cutting plane algorithm for solving the linear ordering problem is described This algorithm uses the primal dual interior point method to solve the linear programming relaxations A point which is a good warm start for a simplex based cutting plane algorithm is generally not a good starting point for an interior point method Techniques used to improve the warm start include attempting to identify cutting planes early and storing an old feasible point which is used to help recenter when cutting planes are added Computational results are de scribed for some real world problems the algorithm appears to be competitive with a simplex based cutting plane algorithm Research partially supported by ONR Grant number N J