PRINCIPLES
OF MODELLING OF ENTRANCE FEE TO THE BUS TERMINAL
Ing. Martina Lánská, Ph.D.
Faculty of Transportation Sciences – CTU in Prague,
Czech Republic
E-mail: lanska@fd.cvut.cz
Abstract: This Paper deals with the definition of the
general mathematical model for determination of the entrance fee to the bus
terminal (BT) for any bus terminal operator in conditions of Czech Republic.
Presently does not exist model for dermination of the entrance fee for any bus
terminal in Czech Republic, which should be universal and suitable for
determining the entrance fee per any bus terminal.
Keywords: entrance fee, bus terminal, bus terminal operator, bus
terminal owner, moddeling
This Paper deals with the definition of the general mathematical model
for determination of the entrance fee for any bus terminal operator in
conditions of Czech Republic. On the present doesn’t exist model for
determination of the entrance fee for any bus terminal in Czech Republic, which
should be universal and suitable for determining the entrance fee per any bus
terminal. There are three basic types of the bus terminal operators in the
Czech Republic - bus carrier, private subject, which is not bus carrier and
community or city.
One of conditions of the economical stability of bus terminals there
are well set prices of entrance fees to the bus terminal that are on the one
hand acceptable for bus transporters and on the other hand cover costs for the
operating of the bus terminal at least partially.
This model should be universal and suitable for determining the
entrance fee per any BT under the pre-determined conditions that are as
follows: economic information of the BT, operational information of the BT and
information of the interest of carriers in using the services of the BT
(present as well as prospective customers – bus carriers).
The following procedure was chosen for creation of the mathematic
model: the first step was creation of a demand function for entrance to the BT,
the second step was creation of a cost function of BT operator, the third step
was creation of a profit function of the BT operator and the fourth step was
creation of the mathematic tool for determining the entrance fee to the BT,
both for the price for which the operator’s profit is maximum, and the price
when the capacity of the bus terminal will be maximally used.
The demand function of the entrance to the BT is created on the base of
data as acquired from the records of connections using the BT so-called
database of bus connections. The analysis includes connections operated during
the analysis as well as prospective new connections. A prospective connection
means a connection of a bus carrier who was to use services of the BT during
the analysis but who did not perform the business relation by any reason.
Generally is the demand function of specific goods dependent on the
price of a given goods, prices of other goods (substitute or comlementary),
amount of costumer earnings, promotion of a given goods, taste and preference
of costumer, etc. Simplified demand function is function dependent just on the
price of given good. In the case of the BT is demand dependent just on the
price of the entrance fee.
A database of connections presenting a weekly demonstration of traffic
on the BT was generated from all above-mentioned connections. This database of
connections was further supplemented by the following information: from the
list of concrete days when the connection was dispatched one may determine the
number of days when the connection was operating, the connections are divided
into three categories, i.e. international, long-distance and suburban (this
classification is further used for correction of certain features of the
connection), capacity of the connection according to the category (initial
condition), occupancy coefficient according to category (initial condition),
lowest required profit of the bus carrier for the given connection according to
the category (initial condition), length of the route, average costs per one
kilometre (initial condition), price of a basic bus ticket from the point of
departure to the point of destination, the actual entrance fee to the analyzed
BT.
Costs and profits may be calculated from such completed database as
well as the profit per every connection may be calculated from their
difference. This profit is first decisive criterion (economical influence),
which determine if the bus carrier is interested in the entrance of the
connection to the bus terminal (the profit is positive) or is not interested in
the entrance of the connection to the bus terminal (the profit is zero or
negative). On the bus connections, which fulfil the profit condition, is
applied the second decisive criterion so-called willingness of paying
coefficient (uneconomical influence). This coefficient means psychological
aspect of willingness of paying of the entrance fee.
Based on these two decisive criterions we may state the number of
connections and subsequently the number of buses that are interested in the
entrance to the BT for the given entrance fee. By means of a regressive
analysis and from the collected data we may get the demand function describing
the demand of bus carriers for the entrance to the BT. For determining the
amount of the entrance fee with maximally used capacity of the BT it is
necessary to determine first the price from the function at which the BT is
maximally used. Subsequently we may determine the costs, receipts and profit
for the maximally used bus terminal.
Costs associated with the existence and operation of a company are its
basic economic indicator and their cut-down is the main tool for profit
creation at present. Therefore it is not difficult for the BT operator to
create the demand function from his own inter-company economic information.
This function consists of two components: fixed component – costs
independent on production (depreciation, rental, cleaning, lightening, control
signals) and must be thus covered even though the company does not produce, in
case of the BT this is the status when no bus enters the BT and variable
component – costs dependent on the volume of production (for instance material
costs) mostly related to a production unit, in case of the BT there are the
costs related to a single entrance of a single bus to the BT. The decision of
what costs belong to what group is not currently arranged by any regulation and
it is purely the subject of economic arrangement of every company. In the case
of the bus terminal is costs sharing on fixed and variable depend on, if the
bus terminal operator is or is not owner of the bus terminal.
For creation of the profit function of the BT operator it is necessary
to define the function describing the dependency of receipts on the number of
entrances of buses to the BT. The amount of the entrance fee at which the
profit is maximum, may be calculated from the first derivation of the profit
function. This shall be laid equal to the zero and then we can calculate the
corresponding fee for maximal profit. This value may be added to the demand
function, cost function, receipts function and profit function and thus we can
determine the demand, costs and receipts at maximum profit of the BT operator.
For determining the amount of the entrance fee with maximally used
capacity of the BT it is necessary to determine first the price from the demand
function at which the BT is maximally used. Subsequently we may determine the
costs, receipts and profit for the maximally used BT.
There are three basic types of the bus terminal operators in the Czech
Republic - bus carrier, private subject, which is not bus carrier and community
or city. Entrance fee collection by the first and the third type of bus
terminal operator doesn't follow any economical principles, just the second
type of the bus terminal operator – private subject, on which follow all
economical principles (demand and supply, costs, receipts, profit and loss).
Created model of entrance fee (for the price for which the operator’s profit is
maximum and the price when the capacity of the bus terminal will be maximally
used) is not model totally general, which is given for any bus terminal
operator, but is suitable just for private bus terminal operator, which is not
bus carrier and whereupon follow all economical principles (demand and supply,
costs, receipts, profit and loss). The model could be general in case, if of
the unification of bus terminal ownership.
The model of the entrance fee is the model of a hypothesis, which
is a simplified image of the complicated reality. The model is created on basis
available information and qualified rating a given reality. Created model is
suitable just for private bus terminal operator, which is not bus carrier and
whereupon follow all economical principles. The model could be general in case,
if of the unification of bus terminal ownership. Created model helps as a
ground for the objectification of the economical operating of the bus terminal.
The research was supported by the research plan MSM6840770043 of the
Ministry of Education, Youth and Sports of the Czech Republic.
[1] Lánská M.: The Financial Model of the Bus Terminals,
Dissertation thesis, Praha, 2007
[2] Macík, K.: Mikroekonomie, ČVUT, Praha 2007