PROMOTING ACCESS TO AFRICAN RESEARCH

African Journal of Science and Technology

Log in or Register to get access to full text downloads.

Remember me or Register



The linear ordering problem: an algorithm for the optimal solution

A.R Mushi

Abstract


In this paper we describe and implement an algorithm for the exact solution of the Linear Ordering problem. Linear Ordering is the problem of finding a linear order of the nodes of a graph such that the sum of the weights which are consistent with this order is as large as possible. It is an NP - Hard combinatorial optimisation problem with a large number of applications, including triangulation of input - output matrices in Economics, aggregation of individual preferences and ordering of teams in sports. We implement an algorithm for the exact solution using cutting plane and branch and bound procedures. The program developed is then applied to the triangulation
problem for the input - output tables. We have been able to triangulate input - output matrices of size up to 41 x 41.



http://dx.doi.org/10.4314/ajst.v6i1.55167
AJOL African Journals Online