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.
Highlights
The current paper deals with the public transport line design, i.e. the design of routes and frequencies of vehicles on them
The main purpose of this paper is to explain to the readers its essence and to demonstrate its ability to work with Mixed Integer Linear Programming (MILP) models to address many specific transport situations
Comfort is expressed by the relative excess of passenger places supply over demand
Summary
The current paper deals with the public transport line design, i.e. the design of routes and frequencies of vehicles on them This issue belongs to the general theory of public transport planning presented in books like [1], extensive book sections as [2] or large survey-type papers such as [3] or [4]. The structure of this planning process and the line planning position in it are described in more detail later . PRIVOL is a linear modification, avoiding the passenger time loss criterion (used by Erlander), which is non-linearly linked to the number of vehicles deployed, as presented later
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