Figure 1.
Each graph corresponds to the transport plan shown below. Directed edges are drawn with arrows. The direction from left to right indicates a ‘same row’ relation between basis entries, right to left shows a ‘same column’ relation. The graph on the left becomes cyclic by adding the pivot element F to the basis (right).
Figure 2.
Visualization of a transportation plan for a very small example with 60 origins (blue) and 60 destinations (red) at the end of phase two (left; initial feasible solution derived from shortlists) and at the end of phase four (right; global optimal solution).
The diameters of the circles correspond to the mass at these origins and destinations. A greater width and darker color of arrows indicates a larger amount of mass being transported.
Figure 3.
Comparison of the Shortlist Method to other methods.
Depicted are total runtimes in seconds (for each method and each number of origins averaged over 100 solved transportation problems) for various initialization methods from the literature combined with one of two pivot strategies: matrix most negative (top) and modified row most negative (bottom). The total runtime encompasses the runtime for finding an initial basis and the runtime for the simplex iterations.
Table 1.
Comparison of the shortlist method with lp_solve [18] and emdist [17]. Runtimes in seconds averaged over 100 solved transportation problems.
Figure 4.
Comparison of the Shortlist Method to two main competitors.
Depicted as circles are the logarithms of total runtimes in seconds (for each method and each number of origins averaged over 10 solved transportation problems) depending on the logarithm of the problem size (circles). The lines have been fitted by least-squares regression.
Table 2.
We assume a relation of between computation time
and problem size
.