Modified Evans' algorithms for solving the combined trip distribution and assignment problem

Horowitz (1989) proposed a modification of Evans' algorithm for solving the combined trip distribution and assignment model with a reduction in computational time and memory, but without proof of convergence. It is shown here that his modified algorithm does not always converge to the optimal solution; in fact, it may fail in two of the total of seven possible cases. In these two cases either the iterative scheme falls into a deadlock or the new feasible solution is worse than the old one. On this basis another modified algorithm which first identifies the cases and then solves them by Horowitz's modification or Evans' original approach is presented. This new algorithm always converges to the correct solution and needs less computational time than Evans' method, but slightly more than Horowitz's modification. Computational results of the three algorithms on test networks are reported and their effectiveness compared.