The Determination of the Optimal Variant of Public Bus Line Transport Vehicles in the Daily Circulation

KLJUČNE RIJEČI optimalna varijanta javna autobusna linija vozila dnevni protok modeli Rudolf Kampf Department of Transport and Logistics Institute of Technology and Business in České Budějovice, Czech Republic e-mail: kampf@mail.vstecb.cz Karel Zeman Director of the M-Line, a.s. company České Budějovice,Czech Republic e-mail: karel.zeman@m-line.cz Pavel Beneš B&C Dopravní systémy s.r.o. Czech Republic e-mail: benes@bcds.cz


INTRODUCTION
The implementation and operation of public line bus transport is the daily task of the selected transportation company.It is a process, which is implemented by the time conditioned deployment of the necessary transport technology (transport capacity) and space arrangement of the individual source and destination stops.Both the conditions are defined by a timetable, which is elaborated as the requirement reflecting the transport needs of the inhabitants.
The beginnings of transfer relations are called the sources and the ends and they are also called destinations.Then transport relations are the result of the difference between the transfer relations in total and the walks.Transport relations are established by the conversion of transfer relations to the necessary number of vehicles in a process called the distribution of transport performance.Transport relations quantify the basic indicators both in the preparation itself and in the environment where the transport is implemented.

THE IMPORTANT REGULATORY FUNCTIONS, ORGANIZATION AND MANAGEMENT OF THE TRANSPORT PROCESS
The process of the provision of the daily transport task can be described and quantified.It is based on its feasibility.Each process is loaded by regular quantifiers which may be determined and the coincidental quantifiers that enter randomly into the process.
The following may be included among the basic regulatory functions [1]: a) the regularity of the transport task: both time and spatial, b) the feasibility of a transport task with the optimum number of vehicles and drivers, c) the cost that is necessary for the provision of the required transport system function.This article does not deal with the complete solution of the transport performance distribution.It assesses transport relations within a selected transport company at the level of the division of transport systems and the existing structure of the centres from which the transport task is solved [1], [2].

DAILY CIRCULATION AS AN IMPORTANT OPERATIONAL PARAMETER OF THE PROCESS
Daily vehicle circulation (the turn, the introductory order etc.) is the basic output from the daily dispatcher activity.The daily circulation represents the basic sum of the necessary economically substantiated costs to be spent on fulfillment of the transport task.
The base for its evaluation is [3], [4]: a) a feasibility assessment, -organizational, -in terms of safety at work, b) an assessment of the total necessary cost.
The company then evaluates all of the daily circulations and the solution quality is usually expressed by the [3]: a) total quantity of necessary transport technology, b) total number of necessary drivers, c) number of kilometres done in one turn (one vehicle), d) total number of necessary unproductive kilometres, e) total waiting hours of the transport technology, f ) complexity of the weekly and fortnightly circulations, their differences and repeatability possibilities.

THE BASIC EVALUATION METHODS
The implementation process of the daily circulations is a quantifiable one.The basic quantifiers are also the descriptive characteristics that may be compared and evaluated.We usually talk about direct quantities, which are expressed by the basic descriptive values of distance, time, number etc. and on the derived quantities, which are related to a performance element, activity or the performance itself [3] - [5].
The quantitative indicators serve as the expression and description of the qualitative process indicators.The nonmeasurable quantities need to be expressed through the measurable ones for the whole process evaluation [5].

THE QUANTITATIVE INDICATORS
The whole transport activity can be described as the performed transport performance in the transport task implementation.The following quantitative indicators are used to describe and evaluate the performed transport performance [2], [5]: a) descriptive, which characterize the transport task size and the size of vehicles solving the task b) performance, describing necessary time deployment and use of vehicles for the daily transport task c) derived, formed by the combination of the descriptive and performance indicators For the needs of the study the structure of indicators is as follows (Table 1):

THE QUALITATIVE INDICATORS
The qualitative indicators usually evaluate a set of several quantifiable indicators that improve quality and effectiveness of the incurred costs, time etc. [2], [4].
More quantifiers (the total operation time, the total drive time, the number of daily circulations, and the number of drivers) can be used for the evaluation of daily circulations.

THE OPERATIONAL ANALYSIS AND THE OPERATIONAL RESEARCH METHODS
Numerous methods are used in solving the optimized number of daily circulations.However, these methods are based on thelong-term experience of experts.Empiric methods are also applied in some situations.However, it is quite complicated to find a real criterion for the evaluation of the optimum number of daily circulations [6] - [8].
The application of graph theory methods is the base of the solution of the daily circulations in our approach.A large number of applicable operation research methods exist, such as the solution of the graph algorithm problems [7], [9].
The maximum number of realized links at a time point (the so called "Critical Cut") is the basic criterion for the comparison of the effectiveness of the achieved result of the number of necessary daily circulations [6], [7].
The applied method evaluates not only the current links, but in the case of the composition of the circulations (the so called "Raw circulations") also shows how many the means of transport are at the maximum cut passing between the previous destination stop and the next source stop [7], [9].
The "Shortest Path Method" calculated from the existing routes of the valid timetables is applied to the passages because of the ensuring the passing ability of the transport technology.The speed of the passages is defined by the distance where determination of passage speed is based on the consideration that the shortest passages are in the city districts and the longest distances are in passing the long lines at the highest speed (see figure 1).The value of the passage speed setting is assigned in the calculation solution [9], [10].

THE PREPARATION OF A MODEL OF ORGANIZATION AND MANAGEMENT OF PUBLIC BUS TRANSPORT A MODEL OF THE DAILY CIRCULATIONS OF THE COMPANY AS A WHOLE WITHOUT THE DIVISION OF OPERATIONS AND TRANSPORT TECHNOLOGY TYPES
This model is the basic one in preparation of transport task solution models [9].Its importance is in initial quantification of the individual transport and operation indicators.The proportional indicators showing the basic parameters of the expected solution have to be expressed in the assignment (table 2).
The presented values are as follows as the: a) average speed of a link is constant unless timetables are generally modified b) average drive time of a link also represents a constant value c) average waiting time is a value that can be influenced within the performed model d) average link length is also constant; a change would involve a change of timetables.

The Model Variant Evaluation (table 3):
The model reflects the lowest value of the daily circulations; the time values are higher than in timetables.This is caused by the higher number of kilometres that arise from the drives between the destination stop of the previous link and the source stop of the next link [5], [9].
The variant may also be generally expressed by means of the value of the funds, if we introduce the values for vehicle use, the cost of waiting, the cost of km of passage and the cost of the second shift of drivers.

A MODEL OF THE DAILY CIRCULATIONS OF THE COMPANY AS A WHOLE WITH THE DIVISIONACCORDING TO THE TRANSPORT SYSTEMS (HIGH CAPACITY TRANSPORT, MPT, OTHER TRANSPORT)
The model enables the separation of the defined links according to the required vehicle type.It is based on a file of input data, which determine the final solution (table 4).

It is obvious from the above table of individual model parts:
The variant of separation of the set of high capacity links increases the number of daily circulations to 104, The variant of separation of the set of the municipality Source: authors transport links and the integration of the set of high capacity links to the other links particularly increases the number of daily circulations in the others group, namely from 88 circulations to 95 circulations, This is caused by low number of high capacity vehicles and time incompatibility of long distance and suburban transport The variant with separated set of high capacity links and other links without separation to others and municipal as one operation is interesting in terms of economy as it represents 104 daily circulations (vehicles).Total price is CZK 795,033 per day.
The variant of separation of the set of municipal links and leaving the set of high capacity links in the set of others represents CZK 813,043 per day.

THE MODEL OF THE DAILY CIRCULATIONS ACCORDING TO THE OPERATIONS
This article now focuses on the evaluation of the possibility to retain the existing organizational structure for the transport task fulfilment.The company is now divided into two operations and the transport task is fulfilled by the mutual coexistence of the links according to the operations.
The basic classification for the evaluation is as follows: a) each operation operates all transport systems (suburban, long-distance, municipal transport), b) the removal of the set of long distance links with necessity of a high capacity means of transport, The above variants show that the variants of the separate operations and the separation of the MPT representthecost value of CZK 791,960 per day.This variant requires more overhead kilometres and less transport technology.The number of drivers can be derived from the number of daily circulations and the number of turns to be modified, i.e. 139 drivers per day.
The variants of separation of the set of high capacity vehicles, the MPT and other suburban transport links represent the cost value of CZK 814,551 per day.
Variants A and C prove to be suitable for the solution.Variant C is infeasible if the requirement for the limited number of vehicles for the set of high capacity links is to be adhered to.
Thus Variant A is a variant requiring 104 vehicles and the lowest number of overhead kilometres and the slightly increased indicator of the other times (waiting).The total value of the variant implementation as the solution of the transport task is CZK 795,835 per day.

CONCLUSION
This article has shown the possible solutions of the daily circulations in terms of ensuring the daily performance of vehicles and staffing.An analysis of the transport solution has shown to be the first step in the determination of a successful and optimum solution of the transport performance volume.However, the transport solution should also be subject to the economic solution.
The requirement for the type structure of the service on the defined links and the real number of vehicles of the required type and their transport capacity is another important indicator for the determination of optimum solution.Diversification of a unified type increase costs both in the process of ensuring the transport performance and in the company investments [1], [10]- [13].
The organization and management process is permanently conditioned by the changes of the economic and legislative conditions for the transport task implementation.It is always necessary to set the basic priorities of the solution and the subsequent interpretation which substantially influences the whole solution of given optimizing task.
The whole process of planning, management and control is then conditioned by the duration of processing the task into a feasible form.Introduction and permanent monitoring of the important indicators then brings final effect: cost saving both in the form of the solution found and in the form of investments into renewal of transport technology.

Table 1
The summary of the input and output indicators

Table 2
Basic parameters of the expected model solution

Table 3
The evaluation of the model variants

Table 4
The values of the individual parts of the model

Table 5
The values of the individual parts of the model removal of the set of municipal links and the set of links with a high capacity means of transport.The values of the individual parts of the models can be seen in table5.