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 Faculty of Management, University of Economics in Prague
Keywords: public transportation, line planning, linear programming, criterion, objective function


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.

Author Biographies

Jan Černý, Faculty of Management, University of Economics in Prague
Department of Exact Methods

Štefan Peško, Faculty of Management Science and Informatics, University of Žilina
Department of  Mathematical Methods and Operational Research
Anna Černá, Faculty of Management, University of Economics in Prague

Department of Exact Methods


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How to Cite
Černý J, Peško Štefan, Černá A. Alternate Criteria in LP Solutions of Public Transport Line Planning. PROMET [Internet]. 2019Jun.13 [cited 2019Jun.20];31(3):287-9. Available from: