Solution of the Linear Ordering Problem (NP=P)

j=1 cijxij s. t. 0 6 xij 6 1, xij + xji = 1, 0 6 xij + xjk − xik 6 1, i 6= j, i 6= k, j 6= k, i, j, k = 1, ..., n. We denote the corresponding polytope by Bn. The polytope Bn has integer vertices corresponding to feasible solutions of the linear ordering problem as well as non-integer vertices. We denote the polytope of integer vertices as Pn. Let us give an example of non-integer vertex in Bn and describe an exact facet cut. In what follows we will interested only in generating exact facet cuts. Fig. 1 shows a graph interpretation of a non-integer vertex [1], i1