Alternate Criteria in LP Solutions of Public Transport Line Planning

Jan Černý
Faculty of Management, University of Economics in Prague

Štefan Peško
Faculty of Management Science and Informatics, University of Žilina

Anna Černá

Abstract

In the paper, the public transportation line planning means planning of routes and frequencies of vehicles on them. In the world literature, different criteria are used in this context; mainly the variable costs of lines, the fixed costs of lines, the fixed plus variable costs of lines, the number of direct travellers, the total or average riding time and the total or average travelling time. The current paper adds two more: the total number of used vehicles (to be minimized when all passengers are transported) and relative excess of supply over demand (to be maximized without exceeding the number of available vehicles). Basic mathematical models for both cases are presented and the motivation of such approach is described including a brief excursion into the history of the Czech and Slovak research of line planning where the use of these objectives has arisen. Further, the basic models were modified for the cases of fourteen special practical requirements, e.g. heterogeneous vehicle fleet (= rolling stock), limitation of transfers, elastic demand, limited total number of lines, etc. The brief outline of the experience with practical use is added as well.