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Intellectual Technologies on Transport. 2015. №2
Forecasting the Size of the Grant Facilities for the Transportation of Passengers by Rail
Gerasimenko P.V.
Petersburg State Transport University Saint Petersburg, Russia pv39@mail.ru
Abstract. This study proposes an algorithm for forecasting the volume of subsidies for passenger transportation. The basis of the algorithm put construction on the basis of statistical data of North-West branch of the mathematical model and the validation of production-economic activity of the branch of JSC "Federal passenger company". Justification is made for assessing the quality of three types of regression models: linear, type of Cobb-Douglas and Allen. For the proposed model produced prediction and estimation error. Set the level of losses in the revenue of the branch by increasing the volume of passenger traffic and forecast subsidies.
Keywords: passenger transport; repair and maintenance; revenue; regression model; coefficient of determination; Fisher's criterion.
Rail transport is the most important sector of the country, providing economic and cultural ties, the development of many areas of the state [1,2]. The role of transport increases significantly in conditions of market economy, as it affects the acceleration or deceleration of delivery of passengers and cargo, the speed of turnover of capital, management of goods flows, the development of the social sphere of society, etc. In turn, the level of the economy puts demands on transport [3,4].
The reform of the Railways has led to the division freight and passenger companies. This transformation has excluded the possibility to compensate for the loss in passenger revenues freight. These losses are now pinned on the state. A feature of recent years has been the slowdown in economic growth and the reduction of social benefits for the population in Russia, resulting in a reduction of the needs of the population in transport services. The share of rail transport in domestic and international traffic decreased by 4.3% in 2014.
Today, one of the important problems to be solved by the specialists of railway transport is the development of the methodological apparatus for estimating and forecasting the economic and enterprise performance, providing timely and quality transport of passengers.
In Saint-Petersburg Transport University, based on the curriculum of masters in "System analysis and management", the study of theoretical principles of the discipline "Fundamentals of strategic management" is done by the masters themselves. A teacher in specialized classrooms equipped with computers conducts practical classes. The main purpose of training is to develop management decisions based on mathematical models.
The report gives examples of the method of making a strategic decision on the size of subsidies to affiliates of the joint stock company Federal passenger company (FPC). JSC "FPC" carries more than 110 million passengers a year. The company
Stasishina A.
Petersburg State Transport University Saint Petersburg, Russia stasishinanastya@gmail.com
has 16 branch offices, extensive network of depots and car divisions and personnel in support of all business processes.
Business architecture of the Company is JSC "FPC" as an integrated business system, which operation should be aimed at meeting the needs for the transportation of passengers and baggage trains. An additional objective of the Branch is receiving scheduled JSC "FPC" financial result from passenger transport long-distance and related works and services.
Starting in 2013, for the first time since the formation of the Company was forced to work in conditions of reduction of volumes of transportations of passengers. Passenger traffic for 2014 was 107,0 billion pass.-km, down 6.1% compared to 2013, the Main contribution to the reduction of passenger traffic of the Company in 2014 has made a significant growth of tariffs for passenger transportation in the regulated sector (over 30% in some months of the year) in the Wake of increased competition from aviation and bus carriers, as well as adverse macroeconomic situation, which has led to a slowdown in economic growth and real disposable income.
It is known that passenger transportations are unprofitable traffic. Therefore, the development of the size of government subsidies necessary for the implementation of scheduled passenger transportation is one of the strategic management tasks. The proposed method includes the following steps:
- analysis of Campaign activity and identification using Ishikawa diagrams the impact on the income of all factors;
- building a Pareto chart to establish the main factors determining the largest contribution to the revenue;
- mathematical modeling of the dependency of income from the main factors;
- evaluation using the Fisher test of significance, mathematical models and rational choice based;
- prediction of yield on selected models and managerial decisions.
In the work was the analysis of the most significant causal relationships between the factors and the result indicator, which adopted the Company's revenue. It was built the Ishikawa diagram, also known as chart "Fish bones". Your graph has allowed to identify the key relationships between different factors and more accurately understand the study process. After identifying the main factors that have the most significant impact on the Company's revenue, was built Pareto chart presented in Fig.1. The analysis of the factors with the strongest impact on the revenue of the branch is established that the model must include a ticket service and repair.
To simulate the revenue branch of the Company was used a statistical database of key economic and performance indicators North West branch for the period 2010-2014.g. on a
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monthly basis. As a resulting indicator in this paper focused on the relative revenues of the Company and factors - the passenger traffic volume and the actual repair of rolling stock.
100%
90%
ч=80%
70%
82%
97%
15 70%
Ш 60%
ac 50%
ш
>40%
I—
< 30%
ш
20%
10%
0%
25%
55%
55%
25%
55%
Tickets sales through Tickets sales through its own offices its own offices plus e-tickets
Transportaion and repair
100%
15%
25%
55%
Transportaion and repair plus service
Fig. 1. The Pareto chart
To justify mathematical models of the dependence of the relative revenue of the North-West branch of JSC "FPC" from passenger traffic and volume of repair of rolling stock was applied regression analysis [5, 6]. As mathematical models are considered in this work linear and nonlinear regression function [7, 8]. Among the nonlinear models included type of model Alena and Cobb-Douglas. The construction was carried out using mean values of the result indicator and resources.
The linear model has the form:
Y = 0,62 - 0,002 • К + 0,0003 • L. Model type Cobb-Douglas has the form:
Y = —12,54 • K~°,89 •L1,67.
Model Alena has the form:
Y = 1,51 + 5,28£ - 08 • KL - 4,13E - 06 • K2 - 1,065£ -10- L2.
To select the most adequate models are needed to assess their quality. Quality assessment in the coefficient of determination revealed that the linear regression model has a higher coefficient of determination (0,67%). The calculation of the global error norms of the errors for the relevant production models confirmed the higher quality of the linear model among other models.
Estimating the error of approximation models also showed that for linear models there is the least error, which is equal to 18%. The calculation of the global error norms of the errors for the relevant production models confirmed the higher quality of the linear model among other models.
Evaluation of the models by the Fisher allowed for all production models reject the null hypothesis of random nature of the regression coefficient, and, consequently, to evaluate models, accept the alternative hypothesis of statistical significance of all regression equations. Based on performed calculations was recommended for further study and practical application of the linear model as the most simple and having higher quality metrics. In Fig. 2 presents the graphs of the revenue from passenger traffic at a fixed value of the volume of repairs.
The study showed that with an increase in passenger traffic is observed a reduction of revenue, if the ascertained value of the volume of repairs. Similarly, we investigated the dependence of revenue on the volume of repair when fixing the passenger (Fig.3). From Fig. 3 shows that the greater the volume of repair and maintenance, the more the Company's revenue. In Fig.4 shows the technical ability, i.e. graphs of passengers and the volume of repairs at a fixed value of revenue. From them it follows that the preservation of revenue requires the holding of a substantial amount of repair work. Thus, the contribution to the revenue volume of repair work is currently less significant, which confirms the Pareto chart.
О
3
3
04
-1,00 w
Passenger traffic
■ L=20909 —|_=134470
■ L=67785 W L=33892,5
L=101677,5
Fig. 2. The dependence of the revenue from passenger traffic
K=503,70 9 K=830,15 —K=1156,60
K=1483,05 ^ K=1809,50
Fig. 3. The dependence of the revenue from volume of repairs
To assess the degree of influence of one factor on revenue while maintaining the values of the other factor made a study of the elasticity model. The obtained ratios of the elasticity of revenue passenger (Ек) and the elasticity of the revenue on the volume of repair and maintenance^):
dy К dK y(K)
= b *
К '
7ою;
dy L L
L dL y(i) y(i)
The calculation showed that when you change the passenger traffic on 1% revenue branch of the Company is reduced by 5.53 percent, and also that when you change the volume of repair and maintenance of rolling stock, 1% of the Company's revenue will increase by 0.08%.
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Intellectual Technologies on Transport. 2015. №2
The adequacy of the proposed models was established by comparing the actual data for the month of February 2015 and predicted values of revenue from operations based on the selected model. The real value of revenues was 1.97 and predicted point value of the relative revenue amounted to:
% = 0,62 - 0,002 • Kp + 0,0003 • Lp = 1,87.
Predicted point value of the Company's revenue matches actual - yxp = 1,97 (the error in the calculations - 4,69%), it also confirms the possibility of using linear models to predict the main production and economic indicators.
To determine the confidence interval of the relative forecast revenue needed to calculate the forecast error according to the formula [2]:
1 + + _ (kp~k)2 _ + _ (lp~l)2 _ ) =
100 (K1-K)2+- + (K100-K)^" (L1-L)2+-+(L100-L)V
0,36
The maximum forecast error, which with probability 0,95 is not exceeded, will be:
Дур=1;табл *m^ = 1,98 * 338205,40 = 0,70,
where 1табл - the tabular value of t-statistics t-test for the number of degrees of freedom n-2=98, and the significance level of 0.05.Then the limit values of the confidence interval of the forecast revenue of the branch as follows:
yPmin = 117;
Уртах =yp + Ayp= 2,58
Performed predictive interval calculation for linear regression models showed that, with sufficient reliability (probability of 0.95), the predicted value of the relative revenue yxp = 1,97 will be covered with a range (1,17; 2,58).
Card of isoquants
0,00
Fig. 4. The dependence from the volume of repairs
In conclusion, the estimated subsidy for making management decisions on scheduled passenger transportation. In the face of declining revenue forecast point value of the size of subsidies for 2016 is 25.7 billion rubles
In Fig. 5 shows the change in revenue and subsidy for the period from 2011 to 2016. As follows from the figure that since 2012 there has been a considerable reduction of state subsidies to passenger transportation long-distance when the significant-dimensional growth of the Company. The size of the predictive values of subsidies for 2016 equal to the relative size of the forecast revenue of the Branch.
The subsidy, bln. rub. ^^=Relative revenue
31,50 30,70
Fig. 5. The subsidy
The decrease in revenue and subsidy from 2014 due to declining passenger traffic, increasing competition among air and bus carriers, and macroeconomic situation in the country.
References
1. Panova Y., Korovyakovsky E., Bessolitsyn A. Rail passenger transport: Analysis and Prospects//Russian Journal of Logistics and Transport Managament/2014 №2 (1), pp. 3-17.
2. Bablutskaya E., Russian Trasport Infrastructure Devel-opment.//Russian Journal of Logistics and Transport Management. 2014.№2 (1), pp.21-30.
3. Gerasimenko V.P. Analysis of the dynamics of freight turnover of railway transport in Ukraine and in the CIS countries in pre-crisis and crisis period. Proceedings of the VI International scientific-practical conference "Problems and prospects of development of transport systems"[^nalis dinamiki gruzooborota zheleznodoroznogo transporta v Ukraine I v stranah SNG v predkrixisniy i krizisniy period], Kyiv: DETOT, 2013, pp. 56-57.
4. A study of the impact of the global crisis on structural changes in the dynamics of the turnover of JSC "RZD" [Issle-dovanie vliayniya mirovogo krizisa na structurnie ismeneniya dinamiki gruzooborota RZD]. Proceedings of the IV International scientific-practical conference "Modern financial markets: development strategy". SPb.: Publishing house of St. Petersburg state economic University, 2013, pp. 18-20.
5. Johnston J. and Di Nardo J. Econometric Methods, 4th edition. - Mc Graw-Hill, 1997. 531 p.
6. Applied statistics. The basics of econometrics: Textbook for university, in 2 volumes, 2 edition, Ayvazyan S.A. Fundamentals econometrical. -M.UNITY-DANA.2001.
7. Gerasimenko V.P. Method of modeling risk in predicting investment results of the production activity of the enterprise [Metod modelirovaniya riska pri prognozirovanii re-sultatov investirovaniya proizvodstevennoy deyatelnosty predpriatiya]. News of St. Petersburg University of means of communication. 2012. № 2 (31), pp. 142-147.
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8. Gerasimenko V.P., Stasishina A.E. Simulation of production and economic activity of the branch of JSC "Federal passenger company" [Modelirovanie proizvodstvenno-
economicheskoy deyatelnosti filiala AO Federalnaya Pas-
sagirskaya Companiya]. Materials of VII International scientific-practical conference "the State and business. Modern problems of the economy. Volume 1". Ranepa. 2015 St Petersburg, pp. 111-116.
Прогнозирование размера субсудий на пассажирские перевозки железнодорожным
транспортом
Герасименко П.В.
Петербургский государственный университет путей сообщения Императора Александра I Санкт-Петербург, Россия pv39@mail.ru
Аннотация. Предложен алгоритм прогнозирования объема субсидий на пассажирские перевозки. В основу алгоритма положено построение на основе статистических данных Северо-Западного филиала математической модели и обоснование производственно-экономической деятельности филиала АО «Федеральная пассажирская компания». Обоснование выполнено по оценке качества трех типов регрессионных моделей: линейной, типа Кобба-Дугласа и Алена. По выбранной из трех моделей произведено прогнозирование и оценивание погрешности. Установлен уровень потерь выручки филиала при увеличении объема пассажирских перевозок и прогноз субсидий.
Ключевые слова: пассажирские перевозки; ремонт и эксплуатация; выручка; регрессионные модели; коэффициент детерминации; критерий Фишера.
Литература
1. Panova Y., Korovyakovsky E., Bessolitsyn A. Rail passenger transport: Analysis and Prospects//Russian Journal of Logistics and Transport Managament/2014 №2 (1) c. 3-17.
2. Bablutskaya E., Russian Trasport Infrastructure De-velopment.//Russian Journal of Logistics and Transport Management. 2014.№2 (1). C.21-30.
3. Герасименко П.В. Анализ динамики грузооборота железнодорожного транспорта в Украине и в странах СНГ в предкризисный и кризисный период. Материалы
Стасишина А. Е.
Петербургский государственный университет путей сообщения Императора Александра I Санкт-Петербург, Россия stasishinanastya@gmail.com
VI Международной научно-практической конференции «Проблемы и перспективы развития транспортных систем». Киев: ДЕТУТ, 2013. - С. 56-57.
4. Исследование влияния мирового кризиса на структурные изменения динамики грузооборота ОАО «РЖД». Сборник материалов IV Международной научно-практической конференции «Современные финансовые ринки: стратегии развития». СПб.: Изд-во СПбГЭУ, 2013. - С. 18-20.
5. Johnston J. and Di Nardo J. Econometric Methods, 4th edition. - Mc Graw-Hill, 1997. - 531 c.
6. Applied statistics. The basics of econometrics: Textbook for university, in 2 volumes, 2 edition, Ayvazyan S.A. Fundamentals econometrical. -M.UNITY-DANA. 2001.
7. Герасименко П.В. Методика моделирования риска при прогнозировании результатов инвестирования производственной деятельности предприятия. Известия Петербургского университета путей сообщения. 2012. № 2 (31). - С. 142-147.
8. Герасименко П.В., Стасишина А.Е. Моделирование производственно-экономической деятельности филиала АО "Федеральная пассажирская компания". Материалы VII Международной научно-практической конференции "Государство и бизнес. Современные проблемы экономики. Том 1". РАНХиГС. 2015 г. Санкт-Петербург. - С. 111-116.
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