The investment in the transportation system: analytical technologies as an important tool for key factors forecasting

. This paper takes a new look at the economic potential of investment decisions to optimize the transport system by minimizing the organizational and operational costs of cargo routing. We present a methodology of scenario forecasting based on statistical methods. Its application makes it possible to achieve a result using the optimal trend function. At the same time, correcting additive and multiplicative parameters allows gaining a given accuracy. The precision and the accuracy of the forecasting model were checked by both additional resulting indicators and the distribution of the model residuals. The simulated scenario forecast of freight turnover was used to formulate the conditions of the transport problem within a certain transport system, limited infrastructure, and the capabilities of a particular carrier. The solution to the transport problem with dynamic adjustment of restrictions determined the possibility of altering the number of routes for the transport work plan. Thus, the dynamics of transportation costs with a certain cargo turnover in various scenarios and an adjustable number of routes with changing restrictions on the throughput and carrying capacity of the transport system and a specific transport market entity will have a significant impact on the economic efficiency of the transportation. The findings of the study demonstrated a need for investment analysis of the possible removing some restrictions on throughput and carrying capacity in a certain economic situation, taking into account the development potential of both an entity and the transport system in general.


Introduction
The current economic rebound from the pandemic-induced recession is impossible without management decisions that force transport enterprises to stay competitive in the global economic marketplace.At the same time, the investment interaction of various economic entities comes to the fore, thus allowing transport systems of different levels to achieve optimal parameters.Making informed investment decisions is based on building a model that takes into account the basic factors and enables creating dynamic scenario forecasts [1], which are implemented in diverse conditions.Besides, the model becomes the basis of the transportation plan, whose development is grounded on the solution to the transport problem.
In the literature, there are many examples of methods for managing transport systems based on solving a transport problem both using ranking [2] and mathematical modeling of linear transport systems [3,4].However, few studies have been published on the economic and investment components of the abovementioned models.Though this is partially compensated by [5], the given work discusses the control of transport systems under monopoly.As stated by [6], pragmatics is a focus on solutions, so, in our opinion, the optimization of the transport system requires building a model that can predict freight volume and freight turnover, as well as develop a transportation work plan [7].This model must take into account both the optimal routing based on the solution to the transport problem and the limitations of the throughput/carrying capacity of the transport system as a whole and its individual entities.Besides, the model should provide primary data for assessing the feasibility and effectiveness of investments in removing existing restrictions.Thus, our study aimed to build a model that meets the aforementioned requirements using universal information systems.

Materials & methods
Making and optimizing the transportation plans of a transport company requires both statistical and economic analysis.In this case, optimization is not only a process of maximizing beneficial characteristics but also a description (model) of the problem area [8].
In this study, we used the following statistical methods moving average method, linear trend estimation, and index method.
To assess the trend and model adequacy, we applied the approximation reliability indicator, the standardized residual, and the distribution of residuals.
In an attempt to build a forecast in the model, we employed the residual variance, the standard deviation of the residuals, and the Student's t-distribution.
A wide array of methods, including the simplex method, the evolutionary method, and the generalized gradient method, were used to solve a transport problem with constraints.
The calculations were made using universal information systems.The data was analyzed by MS Excel spreadsheets.

Scenario statistical forecasting of cargo turnover and cargo flow of a transport company
The first stage implies determining the cargo turnover and cargo flows for various forecast scenarios.Then, based on the actual state of the transport system, it is necessary to build optimal plans for transportation work by combining the plans as they develop within the current scenario [9].
The scenario forecast is grounded on the analysis of the time series of the volume of transport work carried out by a transport company.The time series should contain a sufficient data array to build an adequate functional model.
It is practical to use the amount of cargo volume transported during regular periods (month, quarter, half-year, or year) as a data array.The period is chosen based on the depth of the available data and the forecast horizon.
The first phase includes developing a trend functional that makes it possible to assess the trend development.It is worth mentioning that the trend function adequacy is extremely important, for which it is advisable to use the approximation reliability value and several other indicators.
Fig. 1 exemplifies a transport company with some array data on the completed transportation work in previous periods.
For adaptation, we will use the smoothing of the time series by the moving average method, which, on the one hand, allows reducing the impact of random factors, and on the other, focusing on the seasonal component of the model [10].As can be seen, smoothing was carried out at three points.Actually, it is possible to use either an even or an odd number of intervals.If the value is odd, then the central levels of each smoothing interval are replaced with averages; otherwise, the middle of the smoothing interval falls between two levels located in the center of the interval.
Fig. 1   The primary analysis of the trend adequacy can be conducted by analyzing the accuracy value of the approximation.(Figure 2).As reported by [11], an optimal relationship should be sought between the adequacy of the model and its functional load.The given example combines the average values of the approximation reliability in the amount of 30% and a simplified universal linear trend line function.Taking into account the seasonal nature of some types of freight and passenger transportation, the use of seasonality indices in the forecast model of transportation work seems completely justified and expedient.
Seasonal indices are determined for each period.Then the calculation of average indices allows completing the building of a functional model (Figure 3).
The presented model makes it possible to predict the transport company's freight turnover in various scenarios of economic development.Predicting subsequent periods and assessing the model adequacy requires calculating the model residuals and calculating squared deviations (Figure 3).

Date
Freight  The adequacy assessment phase is split into two stages.
The first stage includes finding the standardized residual by the formula: Standardized residual = ∑ residuals / (√∑ residuals 2 / (n − 1) In our example, the standardized residual is 0.019271433, which means 99.52%-accuracy of the model.
The next stage implies estimating the distribution of the residuals using a histogram to confirm the model accuracy (Figure 4).The insignificant frequency of extreme deviations makes it possible to build a reasonable forecast in a given forecasting horizon.
Taking model data as a basis, we can develop a forecast for the optimistic, pessimistic, and baseline (model) scenarios (Figure 5).Therefore, statistical analysis allows developing an adequate forecast for the four forthcoming periods.However, it should be noted that this forecast does not take into account the possibilities of fundamental analysis, focusing on technical methods.
Next, the forecast is integrated into the framework of the transport system, thus forming the conditions of the transport problem.
In terms of transportation work, a transport company must form freight flows between points of departure and destination, which can be formulated as a transport problem, where the target function will determine the optimal freight turnover to maximize the profit.As a result, the optimal cargo turnover should correspond to the scenario forecast.A change in the scenario should lead to a change in the transportation plan, allowing the transport company to keep profits at maximum levels.

Investment potential of cargo routing within the transport system
This stage involves making a matrix of distances between points of departure and points of destination (Figure 6).It is noteworthy that the given problem has some limitations, in particular, the impossibility to change the transportation direction and organizing transit traffic.Further work needs to be done to remove the aforementioned restrictions.

Points of destination
At the end of this stage, we will determine the required freight flow, based on the average distance calculation, which in our example is 1,000 km.Taking the baseline scenario as grounds, we point out that the required freight volume will amount to 578,000 tons.This freight flow is distributed between points according to their needs and cargo stocks.
Next, we need to make a transportation plan for the transport company based on the solution to the transport problem.In this case, the transport problem is solved for each scenario in a year and a quarter-time interval.At the same time, we will pay special attention to the restrictions caused by the limited carrying and throughput capacity of the transport system and a particular transport company.We consider determining the amount of investment able to remove the existing restrictions, as well as defining their feasibility and effectiveness to one of the major tasks of the study.
We will solve the transport problem for 2021, excluding the quarterly division.At the same time, we set up certain restrictions without their differentiating into carrying or throughput capacity.Apparently, investments in their removal are financed from different sources and by different economic entities, but our task is to determine their volume and effectiveness.
First of all, we will make the transport problem for the calculated data and the distance matrix.

Fig. 7. Transport problem statement
We will solve this problem in the baseline scenario; the cargo turnover will amount to 578 million ton-kilometers.It is should be mentioned that there are no transport systems without any restrictions.Investments in both infrastructure and rolling stock allow modifying the potential of the transport system, in general, and its individual aspects.The considered transportation plan has a limited throughput/carrying capacity of 50,000 tons for each of the existing routes.We will specify how the change in the scenario will affect the routing organization.Finally, we will analyze how the increased capacity of the transportation system affects the transportation plan.When solving the given transport problem, we can make a transportation work plan with 19 routes.It should be noted that such a system has a minimum of 8 routes.The degenerate solution to the problem includes from 8 to 10 routes, while a non-degenerate solution with extreme conditions contains 11 routes.
We will calculate the number of routes in other scenarios to consider which of the scenarios contains the maximum number of routes and determine the transport company's potential in organizing transportation work.Fig. 9 illustrates the calculated pessimistic scenario for a freight turnover of 520 mln.tonkilometers.Fig. 9. Solution to the transport problem with a 50,000-ton limit for the pessimistic scenario The figure above shows that a reduction in freight turnover does not always lead to a reduction in the number of routes.For instance, the proposed plan contains 20 routes.
We will calculate the optimistic scenario for a 635-tkm cargo turnover.Fig. 10.Solution to the transport problem with a 50,000-ton limit for the optimistic scenario Both the optimistic and pessimistic scenarios increase the number of routes by one compared to the baseline, while fluctuations in both positive and negative directions up to 10% can be considered insignificant since the transport company's potential dampens such changes without any additional costs.
Hence, the organization of traffic in all scenarios of our forecast will not require additional financial investments, if we assume that the existing transport company's potential allows implementing the baseline scenario.
Taking the organization of a route as a unit of account, we can determine the costs of the transportation process by summing up the costs for individual routes, if, to simplify and universalize the calculation, we assume that the costs of organizing an additional route are identical.At the same time, the reduction in the number of routes also leads to extra costs for moving rolling stock to other routes, since the total freight volume and freight turnover remain constant, while fixed and variable costs remain the same.The level of conditionally fixed costs for route organizing organizations will vary depending on their number [12].That is, investments in removing restrictions on throughput/carrying capacity in the transport problem are based on determining the effectiveness of investments, reducing the cost of organizing and maintaining additional routes.
Besides, we find it necessary to examine the influence of risks and the time factor.As stated by [13], investments in transport infrastructure are always long-term, and the investment stage of the project itself can be implemented over a long time interval [14].However, in the overwhelming majority, investments in rolling stock are medium-term ones [15].Thus, we strongly believe the use of discounted estimates (NPV, PI, IRR, and DPP) to be the most appropriate.Our study is not aimed at determining a specific indicator.On the contrary, we strive to demonstrate the possibility to maximize the transport company's profit with a constant optimal or given cargo flow that appears when organizing the transportation process, optimizing routing and investing in the transport system's potential, and removing the restrictions.
As for our example, we will adjust the restrictions from 50,000 to 70,000 tons for a route and solve the transport problem for the baseline scenario.Solving the transport problem with a 70,000-ton throughput/carrying capacity limitation allows drawing up a transportation plan with 14 routes.In other words, the 20,000-ton limitation reduces the number of routes by 5. A further calculation of the investment efficiency in removing restrictions can be carried out using the transport company's savings in the organization of additional routes, i.e. if investments in expanding the throughput/carrying capacity by 20,000 tons in the estimated time interval by reducing the conditionally fixed costs for 5 additional routes allows gaining additional profit, it means that they are effective and expedient.Besides, it should be noted that with infrastructure investments, taking into account their capital intensity, it is necessary to consider the possibility of their point application for single routes, but this issue requires further research.
Thus, we can conclude that investments in the transport system, both at the individual entities and infrastructure level, in expanding their transportation capacity result in increasing and maximizing the transport company's profit.In this case, it is advisable to use dynamic indicators of economic efficiency in the calculations, using the wide possibilities of statistics to forecast the quantitative indicators of the transport company's work.Planning the route based on the solution to the transport problem allows optimizing the number of necessary routes and calculating the economic efficiency of the management decisions made to organize the transportation process.

Results & discussion
The most remarkable result to emerge from our study is that the trend functional model demonstrated an upward trend with seasonal variations.The model trend function is adequate to the set goal with an initial value of the approximation reliability of 30%, which is explained by the choice of a linear trend function.So there is a question: higher approximation reliability naturally complicates the functional component, while it is possible to use an exponential, logarithmic, polynomial, or power function, depending on the cargo turnover dynamics.In our opinion, it is necessary to keep a balance between the complexity of the model and the required calculation accuracy.Furthermore, additive and multiplicative additions, including seasonal indices, allow adapting the model accuracy to the problem.In our case, the solution to the problem was confirmed by a standardized residual and an analysis of the residual distribution.The use of an adequate model proves the relevance of the forecast scenario, which determines the freight turnover dynamics of a transport company in the forthcoming periods.At the same time, it is still possible to adjust the transportation plan in each scenario or their combinations following the current economic situation.Unfortunately, we were unable to analyze the combination of scenarios in this work, but our investigations into this area are in progress.
The next step was to build a transport problem, taking into account the limitations of the transport system's throughput and carrying capacity, as well as a number of assumptions.For instance, we did not consider the possibilities of transit transportations and transportations in the opposite direction.The complication of the model will make it possible to level these assumptions, which will become one of the major goals in our further studies.The solution to the transport problem allows making the transportation plan based on the transportation routing between a consignor and consignee.It is noteworthy that the number of routes is a key factor in assessing the investment potential of removing restrictions.Since the problem is solved for a constant cargo turnover, possible investments in removing restrictions can be directly related to changes in the enterprise's routing costs.
Creating a model showed a significant reduction in the required routes when changing the limitations in the transport problem.The efficiency of investments with further linking of routing and limitations of the transport problem remains a debatable issue.The findings of the study have strengthened our confidence that risks, the profitability of transportation, and costs for its organization, time horizons are the key factors of the analysis.To further our research, we intend to study the specific indicators of investment efficiency in removing the limitations of the transport problem.

Conclusion
Our research has highlighted the importance of statistical methods and several other ones for solving the transport problem.We have obtained comprehensive results proving the following.
First, in the current economic situation, scenario forecasting appeared to be a powerful tool, since it allows taking into account numerous directions of economic situation development.Besides, it makes it possible to alter the transportation plan in real-time.
Secondly, using the method of solving transport problems to build a transport plan ensures the planning accuracy we need.On the other hand, there are a certain number of restrictions.At the same time, the restrictions are concentrated both in the methodology for solving the transport problem and in the transport system's limitations, within which the transportation work is carried out.Since the removal of the first type of restrictions is based on the methodology, thus we did not pay special attention to it.The second type of restrictions and their adjustment has significant investment potential in the routing.The calculation showed the possibility of transportation with a given constant cargo turnover with a different number of routes while differentiating the limitations in the transport system's throughput and the particular entity's carrying capacity.Therefore, by combining these facts, we can deduce that it is necessary to determine the investment potential of management decisions to remove the transport system's restrictions, taking into account the specific situation and the potential of its development dynamics.

Fig. 1 .
Fig. 1.Trend model of the transport company's freight volume

Fig. 3 .
Fig. 3. Model of a transport company's freight turnover

Fig. 4 .
Fig. 4. Histogram of the residual distribution in the model

Fig. 8 .
Fig. 8. Solution to the transport problem with a 50,000-ton limit for the route

Fig. 11 .
Fig. 11.Solution to the problem with a 70,000-ton limit for the baseline scenario presents a trend based on a smoothed time series of freight volumes.