Mathematical modelling as an element of planning rail transport strategies

Effective planning and optimization of rail transport operations depends on effective and reliable forecasting of demand. The results of transport performance forecasts usually differ from measured values because the mathematical models used are inadequate. In response to this applicative need, we report the results of a study whose goal was to develop, on the basis of historical data, an effective mathematical model of rail passenger transport performance that would allow to make reliable forecasts of future demand for this service. Several models dedicated to this type of empirical data were proposed and selection criteria were established. The models used in the study are: the seasonal naive model, the Exponential Smoothing (ETS) model, the exponential smoothing state space model with Box–Cox transformation, ARMA errors, trigonometric trend and seasonal components (TBATS) model, and the AutoRegressive Integrated Moving Average (ARIMA) model. The proposed time series identification and forecasting methods are dedicated to the processing of time series data with trend and seasonality. Then, the best model was identified and its accuracy and effectiveness were assessed. It was noticed that investigated time series is characterized by strong seasonality and an upward trend. This information is important for planning a development strategy for rail passenger transport, because it shows that additional investments and engagement in the development of both transport infrastructure and superstructure are required to meet the existing demand. Finally, a forecast of transport performance in sequential periods of time was presented. Such forecast may significantly improve the system of scheduling train journeys and determining the level of demand for rolling stock depending on the season and the annual rise in passenger numbers, increasing the effectiveness of management of rail transport

Metoda oceny zadań transportowych w wojsku z wykorzystaniem modelowania matematycznego

The article analyzes military transport operating within the Armed Forces logistics system. The proprietary method of its evaluation was presented. The technical subsystem has been characterized with the specification of the requirements it is faced with. General criteria for the assessment of the technical subsystem were identified, distinguishing the equipment, personnel, technical material resources, training and experience of soldiers, as well as their combat readiness and flexibility. The essential part of the discussion is devoted to empirical evaluation. It was made through the analysis of completed transport tasks. The research conducted with respect to the mileages of motor vehicles allows to ascertain whether the system is sufficient to meet the current needs. The mathematical model proposed allows to estimate the development tendency, based on which it is possible to formulate improvement proposals.W artykule dokonano analizy transportu wojskowego, funkcjonującego w ramach systemu logistycznego Sił Zbrojnych. Przedstawiono autorską metodę jego oceny. Dokonano charakterystyki podsystemu technicznego z wyszczególnieniem stawianych mu wymagań. Zidentyfikowano ogólne kryteria oceny podsystemu technicznego, wyróżniając ukompletowanie w sprzęt, ludzi, techniczne środki materiałowe, wyszkolenie i doświadczenie żołnierzy a także ich gotowość bojową i elastyczność. Zasadniczą cześć rozważań poświęcono empirycznej ocenie. Dokonano jej poprzez analizę zrealizowanych zadań transportowych. Badania przeprowadzone w zakresie przebiegów pojazdów samochodowych pozwalają stwierdzić, czy system jest wystarczający do zaspokojenia realizowanych potrzeb. Zaproponowany model matematyczny pozwala oszacować tendencję rozwojową, na bazie której możliwe jest sformułowanie propozycji usprawnień