Erlander Principle in Managerial Decision Making on Czech and Slovak Urban Transport Routes

In the beginning of the paper, the position of routing problems in the historical development of public transport is outlined. It is explained why the boom of research papers on this issue came in the seventies of the last century. It is described, how the contacts of Czechoslovak and Swedish researchers, at the same time, motivated the first ones to use the Erlander principle, i.e. starting with a set of “candidate” routes and afterwards choosing some of them by variables which are equal to the number of assigned buses. Afterwards it is shown that the original Erlander approach used the total passenger time losses as objective function. It led to a non-linear model since the unknown variable expressing the number of vehicles enters into the denominator of the objective function. Another complication of the model was in the necessity to avoid zeroes in the denominators. Czechoslovak researchers did not possess any computer enabling to solve non-linear optimization problems of the dimensions met in practice, Therefore, they decided to replace the indicator of total passenger time losses by another one which would not contain the decision variable in the denominator, but in the numerator. They took the numerical ratio of number of places in vehicles to the number of passengers. Further, the paper embodies the results achieved in the Czech and Slovak Republic into the context of world literature. The optimization methodology PRIVOL is then described in details, together with a brief outline of its application. Finally, the further development of research is predicted. E.g. the incorporation of demand elasticity with respect to the transport supply into the constraints in the model.