Title: Block-angular linear ratio programmes

Authors: Said El Noshokaty

Addresses: El Esteshary Information Systems (EIS), 637 Horreya Avenue, Genaklis, Alexandria, Egypt

Abstract: The general form of linear ratio programmes has been discussed before. The block-angular form of linear ratio programmes is here discussed for the first time in literature. This form can be solved by modified Dantzig-Wolfe decomposition principle. If the problem has mixed continuous 0-1 variables, modified upper-bound simplex criteria and modified branch-and-bound algorithm are used. Computational experiment proved efficiency of the block-angular form if compared to the general form. Cargo transportation by ship, airplane, truck, or train is a good application candidate of block-angular form of linear ratio programmes. A tramp shipping model is presented to show one possible application in transportation.

Keywords: fractional programming; linear ratio programming; integer programming; branch and bound; decomposition; block angular; cargo transport; tramp shipping model; modelling; freight transport.

DOI: 10.1504/IJOR.2014.059508

International Journal of Operational Research, 2014 Vol.19 No.3, pp.338 - 357

Received: 12 Mar 2012
Accepted: 05 Sep 2012
Published online: 17 Jun 2014 *

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