Block-angular linear ratio programmes

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.