LOP {ConcordanceTest}  R Documentation 
Linear Ordering Problem (LOP)
Description
This function computes the solution of the Linear Ordering Problem.
Usage
LOP(mat_LOP)
Arguments
mat_LOP 
Preference matrix defining the Linear Ordering Problem. A numeric square matrix for which we want to obtain the permutation of rows/columns that maximizes the sum of the elements above the main diagonal. 
Value
The function returns a list with the following elements:

obj_val
: Optimal value of the solution of the Linear Ordering Problem, i.e., the sum of the elements above the main diagonal under the permutation rows/cols solution. 
permutation
: Solution of the Linear Ordering Problem, i.e., the rows/cols permutation. 
permutation_matrix
: Optimal permutation matrix of the Linear Ordering Problem.
References
MartÃ, R. and Reinelt, G. The Linear Ordering Problem: Exact and Heuristic Methods in Combinatorial Optimization. Springer, first edition 2011.
Examples
## Square matrix
##
##  1 2 2 
##  2 3 3 
##  3 2 2 
##
## The optimal permutation of rows/cols is (2,3,1),
## and the solution of the Linear Ordering Problem is 8.
## Te permutation matrix of the solution is
##  0 0 0 
##  1 0 1 
##  1 0 0 
mat_LOP < matrix(c(1,2,3,2,3,2,2,3,2), nrow=3)
LOP(mat_LOP)