InVestIgatIon of the effeCt of shIp sIZe and marIne transportatIon dIstanCe on the possIBle deCrease of Voyage effICIenCy

Maritime business is highly risky from several points of view. Any planned results even at the operational level is practically not achievable in fact due to a significant effect of climatic conditions, the presence of extensive interconnections of members of the ship and cargo service process and other on transportation process. Therefore, even at the level of a particular voyage, the decision­maker of commercial management of the ship must take into account the possible deviations of various parameters characterizing the marine transportation pro­ cess, and their effect on ship efficiency. This accounting will allow make more informed decisions and improve the efficiency of the ship company as a whole.


Introduction
Maritime business is highly risky from several points of view. Any planned results even at the operational level is practically not achievable in fact due to a significant effect of climatic conditions, the presence of extensive interconnections of members of the ship and cargo service process and other on transportation process. Therefore, even at the level of a particular voyage, the decisionmaker of commercial management of the ship must take into account the possible deviations of various parameters characterizing the marine transportation pro cess, and their effect on ship efficiency. This accounting will allow make more informed decisions and improve the efficiency of the ship company as a whole.

the object of research and its technological audit
The object of this research is the voyage efficiency of ship in terms of its deviation under the influence of risk factors.
As is known, one of the key efficiency parameters of the ship within a particular voyage is «time charter equivalent (TCE)» -parameter that is different from the value of daily profit on standard of fixed costs for the ship. There are following formula for time charter equivalent calculation: where f -the freight rate (marine transportation cost); Q -the number of transported cargo; R var -variable costs for the ship, which consist of expenses for bunker and port charges, fees, costs for passing through the channels; t s -sailing time; t l -laytime; c bunk -the cost of the bunker; c port -rates of port charges and fees, as well as the cost of passing through the channels.
This parameter (1) is used as in the prevoyage review of commercial conditions, and upon its execution.
At the stage of preliminary evaluation of voyage efficiency, the main parameters that can't be reliably determined, because they are the random variables: t s , t l , c bunk . Therefore, mathematical expectation (mean va lues) are used as the projected values of these parameters in (1). The actual values of these parameters cause a deviation of actual achieved efficiency from the planned. It is naturally that increase in these parameters results in a decrease in the voyage efficiency by the value ΔTCE -the difference between the planned and actual efficiency.
In turn, almost all the components of (1) are defined by voyage characteristics (for example, the specificity of the ports of call, transport distance) or ship characteris tics (the main of which is the size of the ship).
The interest for the study is to establish the nature of the effect of ship size and voyage conditions for the pos sible reduction of the TCE parameter, which can be used as a basis for decisionmaking and further research related to commercial and operational management of the ships.

the aim and objectives of research
The aim of this research is to establish the effect of the main characteristics of the ship and the voyage to the possible deviation of the ship efficiency.
Achieving the aim is related to the solution of the following main objectives: 1. Set a fundamental type of income and ship cost elements dependencies on the ship size and marine trans portation distance.
2. Form a parameter for deviation of the ship efficiency, as a function of parameters characterizing the ship size and voyage specifics.
3. Form conclusions on the effect of ship size and marine transportation distance on the voyage efficiency on the basis of functional analysis. Vyshnevska o., Vyshnevsky d.

research of existing solutions of the problem
The problem of the effect of ship size on the various economic and operational parameters of its operation is the subject of various studies.
Many modern publications are devoted to the issues related to the environmental impacts of the ships opera tion and the relationship of this impact (CO emissions) with the ship size (for example, [1]).
Effect of ship size on its cost and efficiency of ship ac quisition project was considered in [3]. Particularly relevant this issue was due to the increase in the size of modern container ship and sufficient instability of container flow. Determination of certain balance «ship size -efficiency» for container ships was considered in [4,5].
Considering the volatility of oil prices and, as a con sequence, the bunker cost, the problem of determining the optimal ship speed during the voyage on the basis of a balance of revenues and expenditures sides in profit forma tion isn't lose its urgency. The series of works are devoted to this subject. One of them [6] is based on the regres sion dependence of the ship speed and fuel consumption.
The problem of risk in an economic context, namely, reducing the ship efficiency in terms of the ship size ef fect or the voyage characteristics wasn't considered. There are a number of publications in which these issues have been addressed, but in the context of the operational pe riod of the ships, rather than a particular voyage. In [7], the ratio of «cash flow -risk» is studied depending on the ship size (deadweight) and VARmethod is used as a measure of risk.
It should be noted that these publications deal with the risk of reducing the financial parameters exclusively by market factors -deviations of the freight rates from planned in the justification of the results of the ship ope ration and evaluate the efficiency of their acquisition projects. But the risk of changes in freight rates, and changes in the ship efficiency under its influence may be considered only in the mediumterm and longterm planning (which was done in [8,9]).
However, even when the particular voyage in accor dance with the signed contract (transportation contractcharter), ship operation is associated with the presence of a plurality of risk factors not related to the volatility of freight rates (as shown above), and, therefore, their influence is also evident in a possible decrease in the efficiency of ship operation.
This problem nowadays is practically not considered, so it is the subject of this research.

methods of research
This research is performed in accordance with the logic of the system methodology. The next methods are used taking into account a specifics of the tasks: -regression analysis -to establish a kind of connec tion between the characteristics of the ship (voyage) and elements of the operating costs and income; -apparatus of probability theory (characteristics and properties of the normal distribution law) -to assess possible deviations of voyage time; -functional analysis to investigate the effect of voyage and ship characteristics on possible decrease in the voyage efficiency.
6. research results 6.1. dependence of voyage efficiency deviation on the ship size and transportation distance. It is above noted that the weather and climate conditions, the human fac tor, as well as the dynamics of the market situation may increase in parameters describing the ship voyage process. First of all, we are talking about possible deviations of voyage time as well as increase the cost of the bunker and each port of the call.
Time charter equivalent deviation from the planned values can be expressed as follows: where Δt s , Δt l -an increase of sea time and laytime, respectively; Δc bunk -changes in the bunker cost. The bunker costs are determined by the fuel consump tion values during sea time q s and laytime q l (the fuel consumption in the sea corresponds to economical speed of the ship). In (2) the change in the bunker costs reflects: -by increasing the time parameters at the planned cost of the bunker: -by changing the bunker cost, taking into account changes in voyage time: c c t port port l 1 2 + ( ) -dependence of port costs from time. Earlier in (1) it is assumed that cport is an amount of various types of charges and fees for considered ship. C port decomposition allows to obtain two components: c port 1 -a component of port charges, fees and costs of passage through the channels, which are depend on the ship laytime at the port (for example, ship, lighthouse, etc.); c port 2 -charges that depend on the ship laytime at the port (for example, sanitary at Ukrainian ports).
Taking into account this, a change in the port charges, costs for passing through the channels can be explained as follows: where Δc port 1 -increase of charges and fees are not depen dent on the ship laytime at the port; Δc port 2 -an increase in charges and fees, dependent on the ship laytime.
Planned sea time t s (days) and laytime (days) are de termined based on their desired characteristics of the ship, route and intensity of cargo operations at ports of call.

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The main characteristic of the ship, affecting the laytime is a load Q (tons). For dry bulk ships and the majority of the bulk cargo, it is determined by the cargo capa city D c (tons). Therefore, in such cases, without loss of meaning, it can be taken as: where K -coefficient, which takes into account the share of the cargo capacity used on the voyage reserves (pri marily fuel). Also, if we assume that the laytime at port equals to time for cargo operations and averaged intensity of execu tion of cargo loading and unloading works (tons/days) are identical to simplify further formalization, then: This assumption is not contrary to the essence of the problem, since in terms of the solved problem deviation of time parameters Δt s and Δt l are interesting as against the time parameters.
Sea time t s depends on the ship speed (taking as an average for the ballast voyage and the load voyage) and the transportation distance L. In view of the made above comments about the assumptions, for this problem we can be neglected passage of areas with limited speed, so sea time is defined as: Freight rate (USD/tons) at the relevant point in time (for a given market situation) is depend on voyage charac teristics (primarily, transportation distance) and cargo capacity D c , so: Bunkering costs are determined by daily fuel consump tion values q s , q l (tons/days), depending on the ship speed and performance of ship propulsion plants, which, in turn, are in regression dependence on the ship size.
According to the characteristics of dry bulk ships of 10000-22000 tones, presented in [10], regression depen dence «ship displacement -normative voyage fuel con sumption» is built (Fig. 1). Several ships are excluded from the considered statisti cal base because they have a certain structural specificity, which is not inherent to the basic set. As can be seen, for the ship with considered displacement, dependences have a distinct linear character.
For power determination of main propulsion plant of the ships in a wide range of displacement, various two component formulas [11] are used. They establish the dependence of the power main propulsion plant (kW) on displacement D (tons) and the ship speed (knots). In particular, Davydov formula has the following form: where C -coefficient, which changes in the range of 103-119.
Taking into account the fact that displacement D and cargo capacity D c are in direct dependency (e. g., Fig. 2 shows a similar dependence for bulk carriers with a dis placement of 10000-22000 tons), the above considerations lead to the conclusion on the validity of the submission of fuel consumption values in the form of dependencies: considering that q s (D c ) is considered for received speed level. Port charges and fees in the various ports of the world are taken either with net and gross register tonnage (NRT, BRT), or with a deadweight or with conditional module of the ship (the product of the length, width and height). In view of a dependence between these characteristics and their regression relationship with the cargo capa city (Fig. 2), can be taken: According to the practice of ships for the cargo trans portation, within the time frame of a particular voyage, it is almost certain that:   In [12] to estimate the possible deviations of efficiency parameters of ships it is proposed to use a method based on the parameters of a normal distribution law. The pre sented results of statistical studies have proved a validity of this approach. Generalization of this approach allows to estimate the time and bunker cost deviations as follows: R add may be taken on the basis of statistical data or expert way. Given the lack of appropriate information base, in this study to draw conclusions about the na ture of R add behavior is not possible. It should be noted that in assessing a possible decrease in the efficiency of a particular voyage in R add are recorded various unforeseen costs associated with the call at the ports and doesn't take into account possible costs due to unforeseen breakdowns and related repairs.
These factors are taken into account in the annual planning of the results of the shipping company's ships in general.
Thus, taking into account time variance estimations and increase of the bunker cost, (11) can be transformed as follows: 6.2. effect of ship cargo capacity and transportation distance on ship efficiency deviation. On the basis of (17) it is possible to investigate an effect of ship size and marine transportation distance on time charter equivalent deviation, and possible reduction in voyage efficiency.
Let's carry out some researches for ships with cargo capacity of 5000-30000 tons, which are the most charac teristic for the domestic cargo base and Ukrainian ports.
To perform these studies the following types of depen dencies of individual cost elements on the ship and voyage characteristics have been taken in accordance with the results of statistical researches of specialists in marine transport.
Conducted statistical studies allow to take the depen dence of freight rates on the cargo capacity and trans portation distance in the form of a linear relationship: Despite the fact that most of the researches proved that the freight rate has a nonlinearly dependence on the ship size, however, a linear relationship also ensures sufficient confidence level (Fig. 3).
The following regression model is obtained by regres sion data analysis on freight rates transportation of bulk cargo in the Black SeaMediterranean region, which is accepted as a basis below: The costs of port charges and fees can be represented as linear relations taking into account common practice of determining the rate of port charges for the unit of In most of the world ports there is a practice of charg ing that implies consideration, as a rule, the two slots for port charges, which depend on the time (such as moorage charge -up to 10 days and more than 10 days). Given the relatively small size of the ships that are considered in this research, we assume that laytime of the ships, even taking into account their possible delays at the port, fits in the first determined time range. Therefore, based on the results obtained by the analysis of port charges at the ports of Ukraine, Turkey, Romania, we accept: Fuel consumption values can be taken as a linear func tion on cargo capacity: In further experimental calculations let's assume the following dependencies of fuel consumption (Fig 4, 5 For experimental researches let's note: ship speed -V = 12 knots = 288 miles/day, K = 0,95, cargo operation norms -M n = 3000 (which is average norms of cargo opera tions for bulk cargo), bunker cost -C bunk = = 300 dollars/ton. The standard deviation of the bunker cost -σ cbunk = 10 dollars ton. σ ts , σ tl may depend and aren't depend on the trans portation distance and the ship size, although it would be logical to assume a link between the time deviation and transportation distance. Given the lack of an ade quate information base for the formulation of such con clusions (it could be the object of separate researches), the standard deviations of sea time and laytime (days) will take 5-8 % of the average (which corresponds to the results of statistical analysis). Next, we denote their equivalent value in a percentage as σ, considering that an increase in laytime isn't required for cargo operations and isn't a responsibility of the cargo owner.
Unforeseen expenditures in the test studies can't be taken into consideration, taking into account the speci fics of the problem.
After all the above expression for elements of incomes and expenses, assumptions and transformations, we get the following: The graphs of time charter equivalent change for different values σ (5 %, 7 %, 8 %) are made for given k(α) = 1,65 for ships of various deadweight and for voyages of diffe rent duration in Fig. 6 in accordance with (24).
As can be seen, possible reduction in the time charter equivalent with an increase in voyage duration is less signifi cant than at shorter distances. Naturally, possible decrease in time charter equivalent for larger ships is more significant. It should be noted that σ -standard deviation of voyage time has a significant effect on ΔTCE(L, D c , α) behavior. Fig. 7 is a graphic illustration of (24) for two levels of freight rates, the difference between which is 10 %.
As we can see, this influence is also quite essential, along with a standard deviation of voyage time.

sWot analysis of research results
These results allow to estimate the possible deviations of voyage efficiency under the influence of risk factors. ΔTCE(α) value can serve as an additional criterion for decision about ship charter, along with parameters of the daily incomes and time charter equivalent, being a kind of risk assessment of voyage efficiency reduction.
Results are based on the regression relationships of the individual elements of the ship costs on its size and marine transportation distance. However, information about bulk ships up to 30,000 tons and transportation distance of 1,300 miles are used as statistical base. So it would be inte resting to conduct similar studies in larger statistical material.
In addition, the weakness of this research is the lack of practical information, which would allow to make a con clusion about the specifics of the standard deviations of voyage time for different traffic directions and ships of various sizes -this parameter is considered as independent of these characteristics. It largely determines the possible deviation of the efficiency parameter It should be noted that the main external factors that have a negative effect on the efficiency of ship voyage and its possible deviation are the specificity of Ukrainian ports of call, which results in increase of costs for call at the port. And, as a consequence, the formation of a significant level of R add value.

Conclusions
1. Principal types of dependen cies of income and cost elements for ship (freight rate, fuel consumption, port charges) in voyage on cargo capacity and transportation distance are established on the basis of regression analysis, as well as the mathematical relationships between the individual characteristics of the ship and the voyage.
2. These patterns allow to formu late expression of efficiency parameter deviation of the voyage ship as a func tion of voyage and ship characteristics. Time charter equivalent deviation -the quantity characterizing the daily profit of the ship, excluding standard fixed costs, is considered as this parameter. This equation describes the nonlinear dependence of this parameter on the ship size (cargo capacity) and voyage characteristics (transportation distance).

Introduction
Modern transport systems need to make informed de cisions about their development, change and adaptation to the operational environment of these systems. Opera tional environment of the transport system is manmade, artificially created to meet the needs of humanity with the carriage of passengers or goods. To achieve the state in which transport system has the ability to satisfy the needs of transportation, we must carefully decide on the change of the elements of transport system.
All elements of the transport systems are required to be revised and adapted to modern conditions. It should be noted that the transport systems have the elements, which production is costly time, financial and human resources. Place of passenger transport systems in the development of society can't be overemphasized. Therefore, the deci sions to reform elements of the transport system have taken relying on calculations made in terms of modernity.
Passenger is the basis for all calculations in orga nization of passenger transportation. It is wellknown that schedule, the number and type of vehicles, vehicle traffic scheme are depend on the volume and characteris tics of passenger transportation. Traffic volumes cause cash flow of the company. The importance of estab lishing traffic volumes for passenger transport system is significant.

the object of research and its technological audit
The object of research is the modern intercity passenger transport system in Ukraine. Intercity passenger transport correspondence, which is formed in the current system, is considered in this research.
One of the problem areas is to study actual sustainable intercity correspondence, which is in obtaining still not defined corrective coefficients for calculation of potential intercity correspondence. The knowledge provides an op portunity in the use of this method of correspondence calculations between cities towards the passenger trans portation market in Ukraine.