ESTIMATION OF THE TIME OF THE VESSEL ' S ARRIVAL AT PORT

Dep. «Fleet Operating and Technologies of Sea Carriages», Odesa National Maritime University, Mechnikov St., 34, Odesa, Ukraine, 65029, tel. +38 (067) 557 76 46, e-mail onyshenko@gmail.com, ORCID 0000-0002-9660-1921 Dep. «Fleet Operating and Technologies of Sea Carriages», Odesa National Maritime University, Mechnikov St., 34, Odesa, Ukraine, 65029, tel. +38 (067) 557 76 46, e-mail yuliia.koskina@ukr.net, ORCID 0000-0002-3164-6504


Introduction
The vessel's time en route largely determines the duration of the passage between ports of loading and discharging and both with the voyage charter-party (C/P) terms on laytime (its beginning and duration) it does the total voyage time.This time, in its turn, is a basis for calculation of voyage expenses and that's why it influences the efficiency of the voyage.For the shipowner, who carries the cargo under the voyage C/P, the issues of determining the time of the voyage are therefore of fundamental importance.But the most part of researches dedicated to the voyage planning implies the problem of the time en route indicating the slow steaming as an important factor of the voyage efficiency [6,7,8,10,11,14,15].But the time en route is only the part of the total voyage time and it is no use of searching it just without the time in port as far as time en route (probably the vessel's speed on passage) determines the time of the vessel's arrival to the port for cargo handling.Оn the other hand, the duration of time in port depends on the appropriate terms of the C/P.

Purpose
The purpose of this study is the assessment of the probability of the vessel's arrival at the port at a specified time interval, considering the C/P terms and their wordings, which is quite important both for negotiations before the C/P fixture and for voyage time planning and ensuring the voyage efficiency when performing the voyage.In order to achieve the purpose the following objectives are to be realized: definition of the impact of the appropriate C/P terms and their wordings on the structure and duration of the vessel's time in port; determination the situations, that are of practical importance for assessing the probability of the vessel arriving at a port at a specified time interval, and obtaining the appropriate calculation formulas; conducting statistical studies confirming the validity of using the normal distribution law for the elements of the voyage time in the processes of estimating the probability of a ship arriving at a port at a specified time interval.

Methodology
The definition of the impact of the appropriate C/P terms on the structure and the duration of the vessel's time in port was based on the analysis of the wording of the C/P terms and decomposition of the time in port depending on the possible combinations of the wordings of these terms.The determining of time intervals, for which it is expedient to determine the probability of the vessel's arrival at the ports of cargo handling, was formed on the main principles of the theory of transport processes and systems.The estimates of the probability of a vessel arriving at a port at a specified time interval were carried out taking into account the properties of the normal distribution law for the elements of the voyage time, the validity of which is confirmed by statistical studies.

Findings
General issues regarding the C/P terms which determine the duration of cargo handling and appropriate vessel's time in port are stipulated in [1,2,3,5,7,9,12,13,[16][17][18].These terms are the loading and discharging rates, terms on Notice of Readiness (NOR) tendering/accepting, including or excluding Sundays and Holidays in laytime days, Sunday time duration as itself.The initial point for time in port calculations is NOR terms -is how it's tendering/accepting stipulated in the C/P.There are two main variants: 1) NOR can be tendered whether the vessel in berth or not, whether in free pratique or not, whether in berth or not (www) or 2) NOR can be tendered after the port formalities on arrival, i.e. after the vessel's berthing.Rather important are wordings regarding the time of NOR tendering, i.e. there may be terms in C/P according to which NOR can be tendered only during office hours.That in fact will take some time waiting the office hours if the vessel arrives on day off.Table 1 shows the structure of the vessel's time in port considering the different wordings of C/P terms.As one can see, the C/P terms determining the duration of the elements of the time in port largely depends on the day of the week and time of arrival (before noon of after noon).For instance, when tendering NOR words in C/P as to be given on getting «free pratique», the waiting time w t to tender NOR will be longer if the vessel arrives before noon (b.n.) on day off (w/e) compared with the vessel's arrival early in the morning on the first working day (w.d.).Similarly, the time between tendering/accepting of NOR will be less if the vessel arrives before noon on working day than if she arrives, for instance, the same day but closer to noon.If NOR can be tendered on www terms, the formalities take place during the «grace» period between tendering of NOR and the beginning of cargo handling.The impact of the terms that include/exclude Sundays and holidays as laytime is obvious.But the moment of the vessel's arrival is also important herethe vessel which arrived on Friday evening, for instance, will spend more time in port if the C/P fixed on SHEx terms than on SHInc.
Thus, even under the same C/P terms, which have a varying impact on the duration of time in port, actual duration of the time in port varies and is determined by the time of arrival of the vessel at the port.The decisive factors are: 1) The arrival of the vessel at the port before noon (b.n.) or afternoon (a.n.) which for NOR terms determines the initial point for NOR t ; 2) The vessels staying in port during Sundays and holidays which (under SHEx in the C/P) determines the SHEx t .For estimating with reasonable certainty the possible structure and duration of time in port, the carrier must first assess the probability of the vessel's arrival at the port for cargo handling on a particular day or even within the specified time interval of a particular day.And this, in turn, depends on the duration of the vessel's previous voyage and the duration of the vessel's passage from the last port of call (port of loading) to the port of loading (discharging).
Thus, the estimation of the vessel's time in port is based on a preliminary estimation of the duration of the previous voyage and the vessel's passage to the port of loading/the duration of loading and passage to the port of discharging.Mathematically, these temporal characteristics are continually variable, and it is possible to estimate the probabilities of one or another range of their values given 1) knowledge of the type and parameters of the distribution law of the abovementioned durations of voyage time elements; 2) the availability of reliable information on the present position of the vessel.
A C/P is fixed usually both during the end of cargo handling and the vessel's opening, and much earlier.With significant time intervals between the barging the C/P terms and the planned beginning of the voyage, the assessing with a sufficient degree of certainty of the indicated elements of time is noted to be meaningless (and in this situation one can only rely on average data).So we consider three situations, in which it makes practical sense to assess the probability of a particular duration of the elements of the vessel's time in port (fig.1): 1) reliable information on the vessel's opening is known and it is required to estimate the probability of the vessel's passage to the port of loading t v ; 2) reliable information is known about the arrival of the vessel at the port of discharging in the previous C/P and it is required to estimate the probability of the duration of the vessel's time in   and further evaluation of the probabilities of a certain range of values for the second component.This approach is taken as the basis for this study.
To authors opinion, the following formal descriptions for where L -the passage length (miles), Vthe average speed of the vessel on passage between ports, varies between allowable speeds of the vessel (miles/day).

In this case
L V is a deterministic value; Δt v is a random component of the time interval t v .The sense Δt vthe additional time, which is formed under the impact of a variety of factors of different nature (in particular, these issues were considered in [4]), for example: 1) weather conditions that lead to the need to reduce the average speed at the transition or increase the length of the passage (changes in the route); 2) the need to wait in queue when passing channels, straits (in particular, the Bosporus).It should be noted that the expectation of the passage of the Bosporus by vessels is an important problem, especially in winter due to weather conditions.Thus, the assessment of the probability of the vessel's arrival at the port for the three situations and the time points of the A, B, C assessment comes to (4)-( 6):

Authors express t
    where  

,
tt -the set time interval.
Considering the presence in the structure of t v , t v  , t v  deterministic and random components (4)-( 6) are equivalent, respectively, to the following expressions: ** * 12 In turn the problem of defining ( 7)-( 9) is reduced to the problem of determining where t and t are formed after the transformation of the constraints in ( 7)-( 9) considering the deterministic components in the structure of Thus, to calculate (10)-( 12), it is necessary to know the type and parameters of the distribution laws of random components in the constraint structure of the elements of the voyage time.
In studies of the probabilistic nature of the voyage time and its elements (for instance, [4]) the authors substantiate the validity of using the normal distribution law for the mathematical description of their behavior, in particular, the time en route and time in port.The authors [4] studied statistical data on the operation of bulk-carriers of up to 25000 tons of deadweight in the Black Sea-Mediterranean region.At the same time, the study was not connected with the total duration of the time en route or time in port, but with the study of their individual components (the time required to complete the formalities in the ports, the waiting time for the vessels starting the lay time), which essentially determine the probabilistic nature of the consolidated elements of the voyage time.
This conclusion is valid considering the fact that the speed of the vessel V and the cargo handling rates M DR , for example, are not random values, but are formed as a result of the «purposeful» actions of the Master and the stevedoring company, respectively.In this case, due to, for example, weather conditions, the Master may be forced to slow steaming for a certain period of time, which is just a part of the Δt v or * Δt v random component of the time en route.
In particular, as a result of statistical studies of the time of port formalities (that is, in essence Δt v  ), the hypothesis about the normal distribution law of this quantity was confirmed with a sufficient degree of reliability.Fig. 2 shows the result of testing the hypothesis of the normal distribution law of waiting time for the beginning of the laytime.Also, as a result of studies of the vessel's time waiting for the beginning of the counting of the lay time, the validity of using the normal distribution law for * Δt v was verified (fig.3).According to the obtained results, the p-value significantly exceeds 0.05 (usually the accepted level for testing hypotheses), therefore, the analyzed data do not contradict the normal distribution law.The following quantile-quantile graphs (Fig. 4) also provide visual confirmation that the data under consideration do not contradict the normal distribution law.The homogeneity of the initial information is noted to be important for the «purity» of statistical studies.Therefore, to obtain reliable information on the distribution law parameters, it is necessary to systemize the source data (for example, by navigation regions, by season of work (summer, winter, autumn-spring), by countries of ports of Thus, the legitimacy of using the properties of the normal distribution law for the numerical estimate ( 10)-( 12) is substantiated.Knowing the parameters of the laws of the distribution of random variables Δt  10)-( 12) expressions ( 16)-( 18) where   is a Laplas function.
If estimated at time points A, B, or C (Fig. 1) the probability of a vessel arriving at a port at a specified time interval is less than a specified value * 0 p 1  , that is, it does not hold, respectively so next, the time in port of loading under the C/P in question should be estimated, taking into account arrivals after the set time interval, and this becomes the basis for the ship-owner to insist on certain C/P terms regarding the time in port or freight rate in order to ensure the required level of the voyage efficiency.
As noted above, the time of arrival of the vessel at the port of loading under the C/P in question affects the structure and duration of the vessels time in port, which naturally has a further effect on the time of arrival of the vessel at the port of discharging, which in turn affects the structure and duration of the time in the port of discharging (Fig. 5).
Thus, after conclusions on the basis of ( 19)-(21) on the time of arrival of the vessel at the port of loading, conclusions can be made regarding the vessel's time in port under loading L t , as well as the probability of the vessel's arrival at the port of discharging at different time intervals (Fig. 5), which also provides information on the probability of the time under discharging D t , considering the time of the vessel's passage N v t .The basis of these conclusions is the reasoning and formulas similar to those presented above, regarding the time of arrival of the vessel at the port of loading., random components can be distinguished and, using the information on the parameters of their distribution laws, for a given probability, the calculated values of the elements of the voyage time for the C/P in question are obtained.In particular, in [4], an approach to estimating a possible increase in time en route and time in port using the VAR method is presented and one can take into account the influence of random components in the structure  At the same time, this assessment will largely correspond to the practice of the shipping business, since in (18) the elements of the vessel's time in port consider the specific structure and duration depending on a) the C/P terms and their wordings; b) the probability estimations of the vessel's arrival at the port of loading.

Originality and practical value
The authors have formed the structure of the vessel's time in port, based on the terms of the C/P and their possible wordings, and established their influence on the duration of the vessel's time in the ports under cargo handling.The estimation of the probability of the vessel's arrival at the ports of loading and discharging at certain time intervals has been completed considering the laytime terms stipulated in the C/P, based on the current position of the vessel.The obtained results can be used in the practice of shipping companies in order to plan the work of vessels on the carriage of goods, as well as to ensure the effectiveness of the voyage both at the negotiation on fixing and during the voyage on the already fixed C/P.

Conclusions
To ensure the effective organization and operation of the fleet for the carriage of goods, it is important to estimate the time required to carry out voyages.The results presented in this paper allow us to solve tasks related to the operation of a vessel on the terms of the voyage C/P, according to the estimation of duration of the vessels time in port under cargo handling, based on the terms and wordings in the С/Р.
Ключевые слова: рейс судна; стояночное время; рейсовая чартер-партия; планирование рейса Наука та прогрес транспорту.Вісник Дніпропетровського національного університету залізничного транспорту, 2019, № 1 (79) ЕКСПЛУАТАЦІЯ ТА РЕМОНТ ЗАСОБІВ ТРАНСПОРТУ Creative Commons Attribution 4.0 International doi: 10.15802/stp2019/158478 © S. P. Onyshchenko, Y. A. Koskina, 2019 port of discharging in the previous voyage and the vessel's passage to the port of loading t v  ; 3) reliable information about the position of the vessel on the passage to the port of discharging in the previous C/P is known and it is required to estimate the probability of the duration of the vessel's passage to the port of discharging, the vessel's time in the port of discharging in the previous voyage and the vessel's passage to the port of loading t v  .The identified above practical situations determine three versions of the problem of estimating the probability of the vessel arriving at the port of loading in the time interval   12 , tt The assessment takes place at points A, B, C.

Fig. 1 .
Fig. 1.Three situations, which are of practical sense to assess the probability of a duration the voyage time elements It seems appropriate, the solution to this problem is associated with the determination of deterministic and probabilistic components in the structure of t v , t vvthe time en route to the port of discharging in the previous voyage (days); * Lvoyage distance (miles), * Δt va random component of the time en route (days), takes place being influenced by factors similar to Δt v

Fig. 2 .Fig. 3 .
Fig. 2. The results of testing the hypothesis of the normal distribution law of waiting time for the beginning of the counting of the laytime

-Fig. 4 .
Fig. 4. Quantile-quantile graphs for normal distribution law and searched statistical sample and the properties of the composition of normal values authors obtain equivalent to (

Lt
and get their total values.So it becomes possible to estimate the duration of the voyage under the C/P in question: becomes the basis for evaluating the time-charter equivalent, as an indicator of the efficiency of a voyage.

Fig. 5 .
Fig. 5.The impact of the time of arrival of the vessel at the port of loading at the time of arrival at the port of discharging in terms of «probabilities»