Cost Forecasting for Building Materials under Conditions of Uncertainty: Methodology and Practice

Abstract

Most large construction projects face the problem of cost overruns and failures to meet deadlines mainly due to changes in the cost of building materials. A lot of studies proved the high importance of the cost of building materials for the project budget and highlighted a number of factors that determine the cost of materials. However, modern unstable economic dynamics lead to the need not only to observe sufficient accuracy of quantity and cost calculations regarding primary building materials but also to carefully predict the cost, taking into account uncertainty factors (changes in the geopolitical situation, the impact of the pandemic, changes in the technological structure, etc.). This article proposes the use of a calculation and expert methodology for forecasting the cost of building materials on the example of building bars for two regions of the Russian Federation. This study includes a review of literature, which showed the dependence of the dynamics of the cost of construction on the prices of building materials, confirmed the impact of economic and noneconomic factors of the dynamics of prices of building materials and the impact of risk and uncertainty. Based on the literature review, it is also concluded that it is necessary to expertly adjust the results of the economic and mathematical modeling of the building materials’ price trend line under the influence of noneconomic factors of uncertainty. The statistics of the prices of building materials in Russia were analyzed, and the main causes of price dynamics (economic and noneconomic) were identified. The ARIMA model was selected to build a series of dynamics of prices of reinforcement steel, an expert adjustment of the forecast was made taking into account uncertainty factors. The method of calculation and expert forecasting of prices of building materials was proposed, and the forecast of prices of steel reinforcement in the regions of Russia was calculated on its basis. In conclusion, this study demonstrates the algorithm and practical results of forecasting the cost of building materials under the conditions of uncertainty, as well as recommendations for the implementation of predictive analytics tools in construction practice.

1. Introduction

In the scientific literature, construction is considered one of the main economic activities [1], the driver of the world economy, is characterized not only by a significant share in the gross world product [2,3] and job creation [4] but is also the basis for sustainable development through the creation of facilities for future generations [5]. According to [6], construction makes a very large contribution to the world economy (about 13% of the gross world product), and it is expected that it will increase by 2030 (construction volumes are expected to increase by 85%).

Large construction projects form a successful society and build up social reputation of each country through the implementation of social, production and economic requirements. Changes in the construction sector in one way or another influence the world economy. In recent decades, construction has been actively developing through technological improvement, innovative design solutions and digital technologies [7,8]. Despite the role of the driver of the world economy, it cannot be claimed that the construction sector is absolutely effective, since most construction megaprojects face the problem of meeting construction deadlines and cost overruns [9,10]. Disruption of construction deadlines and cost overruns related to the implementation of construction projects are a serious, almost global problem [11]. An increase in the cost of construction projects and extension of construction deadlines relative to the planned ones lead to both financial losses and the loss of opportunities for many participants and stakeholders of construction projects [11].

In [12], the cost is postulated as one of the main limitations in the implementation of construction projects, but the problem of cost overruns is highly prevalent—almost 90% of all cases [13]. The difference between the actual final cost of facility construction and the project budget before the start of its implementation varies from 20% to 55% [12,14,15]. Cost overruns lead to a large number of problems in the implementation of construction projects, which has a negative impact on the time parameters and cash flow of the project [12].

To complete projects on time and within the planned project budget, construction resources are needed. Primary resources include materials, equipment, labor and financial resources [16]. The availability, sufficiency and cost of these resources have a key impact on the cost and duration of facility construction. According to the study presented in [16], resources have the highest impact on the increased budgeted cost of construction projects. The calculation carried out by the researchers in [16] showed the range of variation from 40 to 59% of the cost of a construction project caused by the influence of the most significant resources.

In [12,17], materials and equipment are recognized as the primary resources affecting the implementation of construction projects. At the same time, actual construction costs in most cases exceed the project budget due to a change in the price of construction materials.

According to the conclusions presented in [17,18,19,20,21,22], priority should be given to the changes in the cost of material resources to ensure effective cost management during construction projects implementation.

A number of studies [23,24,25] confirmed that the cost of construction and the cost of building materials are influenced not only by inflation but also by a whole set of economic, political, legislative, design and other factors. The influence of noneconomic factors especially increases in the conditions of uncertainty, which can currently characterize the situation in the economy of Russia [26,27].

Accordingly, forecasting prices for building materials is a very important part of the construction project’s cost management system [28].

The result of the literature review showed the following:

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The problem of cost overruns and failures to meet deadlines in many construction projects;

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The increase in prices of building materials as the main reason for cost overruns and failures to meet deadlines in construction projects;

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The importance of reliable forecasting of prices of building materials in construction projects planning and management;

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The regional differentiation of prices of building materials under the influence of supply and transportation costs;

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The decreased reliability of price forecasting by the methods of economic and mathematical modeling under the influence of uncertainty factors and noneconomic price factors due to distortion of the trend line of price dynamics;

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The lack of practical research dedicated to the problem of forecasting the prices of building materials under the influence of uncertainty and noneconomic factors.

It can be assumed that it is relevant to build a methodology for forecasting the cost of building materials based on the methods of economic and mathematical modeling, which allows correcting the result of building the trend of price dynamics, taking into account uncertainty factors by the method of scenario analysis.

The purpose of this paper is to develop a calculation and expert methodology for forecasting the cost of building materials and to draw conclusions about the anticipated dynamics of the cost of primary building materials in the Russian Federation.

The objectives of this study are as follows:

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A review of literature dedicated to the impact of the cost of building materials on the indicators of construction projects, the factors of environmental uncertainty and taking into account its impact on the cost of materials, the factors of the dynamics of the cost of materials, the analysis of the statistics of prices of building materials in Russia, the determination of price dynamics factors and the methods of cost forecasting;

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Forecasting the price of building materials by the methods of economic and mathematical modeling with further expert adjustment of the price forecast and a plan–fact analysis to take into account the uncertainty caused by the influence of noneconomic factors;

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A formulation algorithm for the calculation and expert forecasting of prices for building materials and a forecast of prices for steel reinforcement in the regions of Russia.

In accordance with the purpose and objectives of this study, its hypothesis was developed, its logical sequence was established, and the methodology was determined.

Hypothesis and Sequence of This Study

The hypothesis and the process of proof that represents the logical structure or methodology of this study were developed based on the study relevance and objectives.

The hypothesis of this study represents the following assumption. When drawing up the project budget, it is necessary to take into account the forecast of the cost of primary price-forming building materials (that comprise the maximum share in the structure of project costs) made under the conditions of uncertainty, using the calculation and expert method based on economic and mathematical modeling of statistical data to ensure the successful implementation of construction projects with minimal deviations from the plan in terms of timing and cost.

Based on the study objectives and hypothesis, the following structure of this paper is proposed.

Section 1 includes an analytical review of modern opinions regarding the dynamics of the cost of building materials and their determining factors. Section 2 is devoted to the methods and models of cost forecasting for building materials under the conditions of uncertainty: a comprehensive analysis of the literature sources, a price statistics analysis based on the publicly available data, the determination of the regional specifics of the cost of materials, the mathematical and expert methods of forecasting. Section 2 also provides empirical data for forecasting. Section 3 presents a plan–fact analysis of the cost of primary building materials on the example of steel reinforcement by two regions of Russia, using the methodology of calculation and expert forecast with a confidence interval we proposed. Section 4 deals with the discussion of forecast results, effectiveness of the proposed methodology of calculation and expert forecasting of the cost of building materials, results of forecasting the cost of steel reinforcement for two different regions of Russia and promising management actions. Section 5 presents the main conclusions and recommendations based on the results of this research, as well as promising areas for its further development.

The content of this study and its main issues are summarized in Figure 1.

We chose steel reinforcement as a price-forming building material to be the object of this empirical research (according to the results presented in [22]). This research was conducted in the Russian Federation (as it is a country characterized by high uncertainty according to a number of research studies [26,27]) for the Moscow region and the city of Yekaterinburg (Ural Federal District).

2. Materials and Methods

2.1. Review of the Literature Dedicated to the Problems of Forecasting the Cost of Building Materials

2.1.1. Impact of Changes in the Cost of Building Materials on the Indicators of Construction Projects

The problem of assessing the impact of the cost of building materials on the indicators of investment and construction projects and construction facilities is well covered in the scientific literature.

It is also emphasized in [12] that building materials are the main component of each construction project, and changes in their price indicators affect the entire project. Moreover, changes in prices for building materials affect budget overruns irrespective of whether innovative technologies have been introduced or not. Management of material resources in construction is the most important and key activity that ensures the completion of a construction project within the planned timeframe and budget, as well as ensures the rhythm and continuity of investment project implementation [18].

Construction industry is the largest consumer of materials. Two-fifths of all materials and energy in the world economy, as well as about 40% of raw materials worldwide account for construction [19]. These facts confirm that an increase in construction volumes and successful implementation of construction projects depend on the stability of prices for building materials.

Investors, such as other participants of construction projects, may be affected by changes in prices for building materials [20]. Building materials and their cost have an enormous impact on the indicators of ongoing and planned construction projects due to their high share in the structure of resources for construction. Studies [12,21] revealed a high degree of dependence between prices for building materials and the rate of inflation. Changes in the inflation rate affect the price for building materials, accordingly, it will lead to a deviation from the planned project budget.

An important task is to determine the trend of prices for building materials caused by changes in inflation, which can further lead to construction budget overruns. According to [12,13,17,21], the initial budget of a construction project can differ from the final budget by five to ten percent due to changes in prices for building materials caused by inflation. Despite multiple studies in the field of cost engineering dedicated to overcoming the problem of budget overruns in construction projects, many projects face cost overruns caused mainly by prices for building materials, which are affected by the inflation rate [12]. According to the report presented in [22], the share of the cost of building materials in the total budget of a construction project on average exceeds 70%, and the primary materials are eight building materials used in almost all projects—steel reinforcement, ready-mixed concrete, bricks, sand, cement, glass, paint and plywood. Each type of building materials is produced by the relevant industry, so it can be concluded that inflation and a number of other factors affect these industries.

The researchers in [29] note that the cost of building materials exceeds 50% of the total cost of capital construction, so the cost of building materials, their availability and quality characteristics have a direct impact on the efficiency of construction projects and the quality of construction and installation work.

At the same time, materials are one of the key factors causing a delay in the implementation of construction projects in various countries [30,31,32,33,34]. Particular emphasis needs to be placed on the fact that the dependence of the construction project duration on the supply and price for materials is relevant for both developing countries and highly developed countries [31].

Various studies reveal various reasons for delays in project implementation as compared to the planned timing. Thus, the recently conducted research [23] based on the study of 97 sources revealed a total of 149 reasons for delays in the planned schedule of project implementation. Ten most important reasons were financial problems of the organization and the lack of building materials. The study presented in [35] revealed that the inflation of prices for materials and exchange rates, along with the project’s poor quality, is the main reason for delays in the planned schedule of project implementation and cost overruns. The researchers in [35] conclude that the development of a competent plan for the purchase of materials, along with a clear idea of their cost at the time of construction, can reduce the negative impact of inflation. Other studies, such as [36,37], also postulate poor quality of materials, delays in the delivery of ordered materials and higher prices for building materials as the main reasons for delays in the implementation of construction projects and cost overruns. Flexible planning, constant monitoring of prices, training of personnel in risk management and construction quality management are proposed as measures that can help to reduce the negative impact of the above factors. It is also noted in [35] that careful project planning considering the time and cost criteria, as well as clear contractual relations and communication between project participants can effectively influence the identified causes of the actual deviation in time and cost when implementing construction projects.

It is emphasized in [12] that cost overruns occur under the influence of many factors, but one of the most correlating factors is the rate of inflation, which has a direct impact on the change in prices for building materials during the project life cycle. Accordingly, the dynamics of prices for building materials and their correlation with the inflation rate were studied in [12].

The authors of [38] studied the dependence of the cost of housing projects on the cost of building materials. The importance of understanding the relationship between the change in the cost of building materials and the completion of housing construction projects in accordance with the planned building construction program were highlighted. The authors of [39] indicated that the cost of building materials is actually half of the total cost of all construction projects. The cost of building materials itself depends on the supply and demand, on the quality and quantity of materials, as well as on the time and place of purchase and sale, and on the characteristics of buyers and sellers in the process of construction operations [40]. Moreover, the cost of materials is influenced by the exchange rate, bills of materials, the inflation rate and the availability of new, including innovative, materials in the country or region [38].

In addition to the cost of materials, the quality of use and storage of materials at the construction site affects the total cost of housing construction projects according to [37]. In [23], the reasons for the delay in the implementation of construction projects and failures to meet the planned deadlines were studied. The study showed that the climatic conditions for project implementation, inefficient communication between project participants, lack of project coordination and conflicts between stakeholders, errors in planning, shortcomings in project management, lack of necessary experience, labor resources, financial problems, lack of equipment and materials are among ten most important reasons.

A number of researchers in [38,41] believe that building materials play a crucial role in the development of a construction project. It is noted that constantly increasing prices for building materials is a very serious problem for productivity in construction when implementing projects of proper quality within the established timeframe. Fluctuations in the cost of building materials presuppose high risks in construction project implementation for all its participants [38].

We agree with [38,41] that the demand for housing of all types, along with an increase in the inflation rate and a shortage of money, creates a challenge for the formation of prices for building materials. We believe that this statement of the problem is also relevant for Russia due to similar conditions in construction. To ensure sustainable commissioning of housing within the established timeframes, within the project budget, to ensure its proper quality, as well as to meet the requirements of stakeholders, it is necessary to forecast and take into account the dynamics of the cost of building materials, as well as to manage this cost. We also agree with [38] that reducing the cost of construction is necessary to achieve the goal of sustainable development, and since building materials account for almost half of the expense part of the construction project budget, it is necessary to take into account and manage the factors that will minimize the excess value of building materials.

The findings of the study presented in [38] show that an increase in the cost of building materials has a negative impact and impedes the progressive development of construction due to the impact on the fluctuations in the cost of construction, the increase in the cost of maintenance of buildings and structures due to poor quality of construction and the corresponding increase in the cost of repairs due to the use of low-quality or inappropriate materials. The expert survey conducted in the study presented in [41] showed that fluctuations in the cost of building materials have the maximum impact on changes in the cost of construction. Consumers and contractors of construction projects face serious problems related to ensuring the stability of the construction cost forecast. Accordingly, monitoring the forecast of expenditures for construction materials during construction is a key factor ensuring project effectiveness [42]. We agree with the opinion provided in [38]—to prevent excessive deviations in the cost of construction relative to the planned budget, its participants should have a well-thought-out plan of expenditures for materials to reduce negative consequences of an increase in prices for building materials due to changing market conditions. Thorough planning and scheduling of work at the initial stages of construction, including optimal planning of stocks, are important to reduce the risk of cost overruns, conflicts. It will increase the speed of construction, ensure timely commissioning of residential real estate in accordance with the planned project budget. Similar conclusions are presented in [33]. Based on the statistical data, three most frequent and significant reasons for the discrepancy between the planned and actual cost and duration of construction project implementation are errors in the design and contract documentation, as well as incorrect assessment and overestimation of material costs. We agree with the conclusion made in [33] that participants and stakeholders of construction projects should improve methods for assessing the cost of materials, as well as take into account inflationary changes in the cost of materials and fluctuations in the cost when preparing price quotations.

Summarizing the analysis of scientific papers dedicated to the impact of the cost of materials on the efficiency, timeliness of construction project implementation and compliance with the planned budget, we can conclude that it is necessary to forecast the cost of building materials with high reliability, to draw up a project budget, taking into account the forecasted cost, as well as to improve the efficiency of material resources management in construction, which in the economic aspect can also be achieved through competent planning and forecasting of cost indicators.

2.1.2. Noneconomic Factors

The uncertainty of the modern environment in which construction projects are implemented is caused by the impact of key challenges of modern economic reality [43], which include the impact of the COVID-19 pandemic, import substitution, changes in the geopolitical situation [44] and development trends, which include changes in the technological order and Industry 4.0 and 5.0, digital economy formation and development and sustainable development [45,46,47,48,49].

That is, the cost of building materials and, accordingly, construction projects, are affected by both economic factors of demand, supply and risk, as well as a number of noneconomic factors.

In [50], the researchers studied the impact of the crisis that began in 2020 on the dynamics of market prices and consumption of materials in the construction sector of the economies of developing countries. As a result, it was revealed that the socioeconomic changes initiated by the COVID-19 pandemic had a significant impact on both the construction market and the building materials market in developing countries and also affected consumer preferences. The findings presented in [50] indicate a decrease in the correlation between the price of building materials and their quality, a change in the price–quality ratio during the crisis period and a disproportionate increase in prices in the construction industry and construction.

The analysis of empirical data given by the manufacturers of building materials shows a sharp increase in expenditures starting from 2020 [50]. Despite the rather large number of factors of such price dynamics, the key ones are the closure of borders associated with the COVID-19 pandemic and the corresponding delays in the supply of raw materials necessary for production. All this led to a significant increase in the price for raw materials [51]. The increase in the volume of online purchases caused by the COVID-19 pandemic led to an increase in the price of packaging by 20%, as well as in subsequent years there was an increase in the prices for electricity and fuel, which led to an increase in production expenditures [50]. In the absence of wage dynamics, inflation began in 2020, which, along with an increase in real estate investment volumes, led to an increase in the price of one square meter of residential buildings.

The escalation of inflation contributed to an increase in the cost of building materials, subsequently leading to negative deviations in financial planning and the speed of construction project implementation, which prevents from utilizing cost budgets on time and maintaining the planned rate of profit of construction project participants. Economic theory indicates the need to implement state monetary policy measures to curb the inflation rate [52]. However, the results of the study presented in [52] indicate that monetary policy did not have an impact on the dynamics of prices for building materials; therefore, it cannot be an effective tool for stabilizing the price dynamics in the building materials market. Based on the foregoing, the need in planning and forecasting the price dynamics of building materials in the context of instability is identified. This will help to improve the efficiency of management of material costs in construction and construction projects as a whole, is taken into account in the project budget.

In Russia, the current conditions of economic instability [26], which are a consequence of a rather sharp change in the foreign policy situation, characterized by a change in the key rate of the Central Bank, imposed sanctions and foreign trade restrictions, a change in logistics conditions [48], fluctuations in exchange rates and other related and derivative factors [44], led to a rather sharp increase in the cost of building and finishing materials [26,48].

The somewhat chaotic dynamics of the cost of building materials, including some decrease in market prices for a number of items, are largely due to government intervention and a decrease in demand, along with the need to provide a certain amount of products for manufacturers. Various studies postulate an increase in the cost of building materials from 10 to 50% [26,48,49], and the production of a number of building materials is import-dependent.

The current conditions in which the construction industry operates and investment projects are implemented in Russia are characterized by a high degree of uncertainty and risk as a result of geopolitical changes and subsequent sanctions, external restrictions that led to a short-term panic in the raw materials and commodity markets in the spring of 2022 and roaring demand [26].

In this case, the use of only the regression analysis when constructing a trend may have many “outliers” that distort the real forecast trend due to the influence of subjective changes in the price of building materials caused by the influence of noneconomic factors of risk and uncertainty [26].

It is necessary to forecast the price dynamics of building materials using both judgmental adjustments and plan–fact comparisons in order to assess the reliability of the selected trend line [26]. The influence of inflation is taken into account when developing a forecast of the material price dynamics (regression analysis and constructing a trend line), while noneconomic factors of uncertainty and risk are difficult to take into account when constructing a trend line, which requires additional judgmental adjustments, including on the basis of scenario analysis [53].

The literature analysis shows that the problem of forecasting the cost of building materials in the conditions of uncertainty is not sufficiently covered in publications. This study dedicated to the methodology of forecasting prices for building materials, taking into account the effect of uncertainty, as well as the compilation of forecast dynamics of prices for building materials, fills this gap and allows determining material costs in construction project budgets more accurately and reliably.

2.1.3. Economic Factors That Form the Trend of Construction Materials’ Cost Dynamics

The main factors that form the trend in the dynamics of the cost of building materials are the economic factors that determine the demand for materials (depending on the volume of construction) and the supply of building materials.

Based on the analysis of publications [12,21,28,29,49,54,55], it can be concluded that the main factor influencing the trend in the price dynamics of building materials is the general economic situation in the entire world economy. Thus, papers [54,56,57] indicate that developed countries have been experiencing a problem of rising prices for building materials in recent years, and there is a clearly upward trend in the price dynamics. The situation is similar in developing countries—there is an increase in prices for building materials [21,57]. Accordingly, the dynamics of the cost of construction and housing prices are similar to the dynamics of prices for building materials [21]. Moreover, in a number of countries, there is an overspending of the budget of construction projects due to an increase in the prices for building materials [12,21,30,31], especially the main price-forming ones: steel reinforcement, cement, sand.

The study presented in [58,59] also confirms the importance for the investor to monitor the fluctuations of prices for building materials and implement management decisions that are adequate for the price dynamics, including through cost control, cost management and changes in the price of construction objects.

Import costs [21,60], inflation and other financial factors [38,41,50], international and country market conditions [58] and a number of other factors are identified as the main factors affecting the dynamics of prices for building materials in different sources.

One of the most important factors, which is noted in many studies, is the regional specificity of the construction site. In [56], the differentiation of prices for building materials is explained by various location factors, including transport costs, interregional competition, labor costs, the level of income of construction products consumers, as well as development, and supply chains. It is substantiated that the existing supply chains and the level of competition in the region contribute to the formation of the building materials market within the region that establishes the appropriate price for building materials. According to Weber’s theory of industrial location [59], there are two main reasons for the regional differentiation of prices for building materials, namely transportation costs and labor costs. The authors of [56] substantiated the notion that prices for building materials vary depending on the region in most countries of the world. A similar regional specificity of the level of prices for building materials is in Russia [26,49]. These specifics reflect the impact of building materials supply.

An important factor in price dynamics, especially recently in Russia, is the density of competition [61] and possible monopoly collusions. These facts influence the purchase price of materials and should be taken into account when developing measures of state antimonopoly regulation.

So, the main economic price factors are supply and demand factors determined both by the situation and price dynamics in the world and country markets and by the specifics of the region, as well as by antimonopoly policy.

2.2. Analysis of Price Statistics for Primary Building Materials in Russia

The process of planning future costs is impossible without scientifically based approaches to forecasting the cost of resources based on market monitoring of their current value [62]. Constant monitoring of prices for materials is carried out in each region, as a rule, by regional authorities responsible for pricing in construction.

Prices for building materials in Russia are monitored at various levels. Monthly monitoring reports of the Federal State Statistics Service are prepared in the context of average prices for the primary materials purchased by construction organizations [63]. Monitoring of the main factors of pricing in construction, including monitoring of prices for construction materials, products, structures and equipment in the Moscow region is carried out by Scientific Research Analytic Center State Autonomous Institution, which is a subordinate department of the Moscow City Committee on Pricing Policy in Construction and State Expertise of Projects. Monthly monitoring reports are prepared in the context of average selling prices for representative materials [64]. Then, prices of suppliers of building materials are analyzed in each region and city with an appropriate averaging.

An analysis of market prices for the main price-forming building material chosen for this study—steel reinforcement—was conducted.

The dynamics of average prices for D12 A500C steel reinforcement in the Moscow region according to mcena.ru are shown in Figure 2.

The dynamics of prices for steel reinforcement, similar to most building materials, correspond to the dynamics of demand, i.e., the volume of construction work, taking into account seasonal dynamics. As can be seen from the data presented in the figure above, the price increase in March 2022, which occurred for geopolitical reasons, was later replaced by price stabilization with a slight jump due to the influence of the seasonal factor. There is also a decrease in prices for steel reinforcement caused by the agreement of steel reinforcement manufacturers with traders to limit the maximum markup for the sale of steel reinforcement at the level of twelve percent in the second quarter of this year. Compared to the markup applied in 2021, this figure is two times lower. This empirical result of the statistics analysis is consistent with the data of researchers on the relationship of prices for building materials with the density of competition [58,61] and factors of uncertainty of the external environment [44,48,50,51].

The correlation analysis of factors influencing the dynamics of the cost of building materials carried out by us according to the data of Scientific Research Analytic Center State Autonomous Institution (

Table 1. Expert assessment of the individual significance of communication problems faced by project stakeholders, points.

	Reinforcement Blanks	USD Exchange Rate	Alloy Steel
Reinforcement blanks	1.00
USD exchange rate	0.29	1.00
Alloy steel	0.94	0.21	1.00

) by the method of calculating the pair correlation coefficient [65,66] showed a direct relationship between the level of prices for steel reinforcement and prices for steel and no correlation with the dynamics of the US dollar exchange rate.

The low correlation of the level of prices for the building materials under consideration with the dynamics of the US dollar exchange rate is explained by production of these materials from local raw materials. The need for technological upgrading of foreign-made equipment characterizes the existing level of interrelation of factor features.

Let us consider regional determinants of the cost of steel reinforcement.

To determine regional determinants, statistical data on the cost of steel reinforcement for the Moscow region (Central Federal District) and the city of Yekaterinburg (Ural Federal District), in which metal processing is developed, were selected (Figure 3).

The dynamics of prices for steel reinforcement after a sharp price increase in the summer of 2021 as a result of cartel agreement of rolled metal suppliers [26] decreased due to the inspections of metal traders conducted by the Federal Antimonopoly Service in all regions. The leap in prices in March 2022 was due to geopolitical changes.

The correlation analysis of prices for building materials in the regional context revealed a very high level of correlation of prices for steel reinforcement by regions (the value of the coefficient of pair correlation of prices for steel reinforcement in the Central and Ural Federal Districts is R = 0.93), which indicates the commonality of trends in the dynamics of prices for this material (according to [66]). The lower level of prices in the Ural Federal District is caused by the presence of metallurgical industry in the Ural Federal District, in particular, in the Sverdlovsk region. Accordingly, an empirical analysis of statistics on the dynamics of prices for steel reinforcement in the regions of Russia confirmed the conclusions contained in papers [49,56,59] about the regional differentiation of prices depending on the transport component and availability of manufacturers of building materials in the region. At the same time, the high level of the pair correlation coefficient of prices for steel reinforcement in different regions indicates the greater importance of general market trends and other factors in the country and the world, which was also identified by the researchers earlier [12,21,28,54,55,57].

2.3. Forecasting the Cost of Primary Building Materials, Using the Methods of Economic and Mathematical Modeling

Based on the conclusions obtained in the previous paragraphs and sections of this study, actual prices for the studied regions according to the data of regional departments and centers of pricing in construction were selected to develop the time series and the forecast trend. The feasibility of applying them for the purposes of forecasting was proved by the correlation analysis and justification of the high level of correlation with the data of Scientific Research Analytic Center State Autonomous Institution and official statistics of Federal State Statistics Service. The data on the dynamics of prices for D12 A500C steel reinforcement in the Moscow region are given in Appendix A.

When choosing forecasting methods, we were guided by the following calculations. There are a number of interesting developments in the field of forecasting the cost of building materials. Thus, in [62], it is proposed to use the method of neural networks to make a forecast. Despite all the advantages of this method, there is a difficulty in interpreting the results, and a limited number of factors affecting the result of the forecast are selected [62,67]. As we noted in Section 2.1 considering a comprehensive analysis of the literature, there are many factors affecting the cost of building materials, and their composition and strength vary depending on the region and conditions, especially in the conditions of instability. In [28], the use of the GM model based on Grey system theory is proposed, but it is shown that this model is applicable for short-term forecasting.

For the purposes of forecasting, the authors of [65,68,69] use the tools of the regression analysis and modeling of time series, which became widespread and well-tested. Some researchers [68,69] supplement and expand the regression analysis tools by finding optimal methods for a certain forecasting task. In the study presented in [26], we proposed an approach to forecasting based on the regression analysis. In this study, we propose a refined and improved forecasting model.

Taking into account the results of [68], the autoregressive integrated moving average (ARIMA) was chosen for forecasting. A regression model was built. It includes a certain number and type of terms, and the data are prepared by the degree of difference to make it stationary, that is, to remove the trend and seasonal structures that negatively affect the regression model.

The adoption of the ARIMA model for the time series presupposes that the basic process that performed the observations is the ARIMA process. This may seem obvious, but it helps to motivate the need to confirm the assumptions of the model in unprocessed observations and in the residual errors of the forecasts from the model [68]. For the correct application of the model [68], a study of the developed time series for the presence of autocorrelation was carried out (Figure 4).

Similarly, a study of the time series for partial autocorrelation [68] was carried out to find the order of the autoregressive model of the series (Figure 5).

The formal definition of the model obtained in Python is as follows:

The ARIMA model (p, d, q) for the nonstationary time series X_i is as follows:

$${∆}^d{X}_t=c+\sum _{i=1}^p{a}_i{∆}^d{X}_{t-1}+\sum _{j=1}^q{b}_j{∆}^d{\epsilon }_{t-1}+{\epsilon }_t$$

(1)

where ${\epsilon }_t$ is the stationary time series; c, a_i, b_j are model parameters; ${∆}^d$ is the operator of the difference in the time series of order d (sequential taking d times the differences in the first order—first from the time series, then from the obtained differences in the first order, then from the second order, etc.).

The formal definition of the model meets the requirements of the regression analysis and time series modeling [66,68,69].

The resulting diagram of the time series and the forecast of the dynamics of the price for D12 A500C steel reinforcement in the Moscow region is shown in the figure below (Figure 6).

According to the results of the forecast, it is expected that the dynamics of prices for steel reinforcement will become stable and slightly increase in the future (without taking into account the influence of uncertainty factors).

2.4. Expert Assessment and Adjustment of Building Materials’ Cost Dynamics

Judgmental adjustments are necessary in the conditions of a high degree of uncertainty and influence of noneconomic factors, which complicates the practical application of economic-mathematical and econometric models. In this situation, an expert assessment of trends and main scenarios of price changes is possible.

The forecast of the impact of all the environmental uncertainty factors specified in Section 2.1.2 of this study was adjusted on the basis of an expert assessment [21,43], which united 20 leading specialists in the construction sector and construction industry (including estimators, heads of contractors, customers, professors of Moscow State University of Civil Engineering (National Research University), experts of state and non-state examination of design documentation, specialists of enterprises producing reinforced concrete products and steel structures). An example of questions included in the questionnaire, which combined studies not only of the price for steel reinforcement but also of a number of basic price-forming building materials, is given in Appendix B.

The quantitative results of the survey can be analyzed in terms of statistics and consistency. Average scores by points, simple percent, standard deviation, coefficient of variation were used for data analysis [43,53,70]. As a result of the expert survey, the following estimates of possible options for the dynamics of prices for steel reinforcement and concrete mixes were obtained, and an appropriate estimated adjustment of price indicators was made (

Table 2. Results of an expert assessment of possible dynamics of prices for building materials (on the example of steel reinforcement).

Increase in the Cost of Materials	Average Value	Maximum Value	Minimum Value	Variance	Standard Deviation	Coefficient of Variation	Forecast of the Cost, RUB
Steel reinforcement	+15%	+20%	+5%	10.24	3.20	0.273	59,651
Concrete	…	…	…	…	…	…	…

).

The calculation of the standard deviation and the coefficient of variation of the estimates indicates the consistency of experts in terms of the value of the change in the cost of steel reinforcement. Moreover, the consistency was assessed using Kendall’s coefficient of concordance W = 0.76. Kendall’s W ranges from 0 (no concordance) to 1 (complete concordance), and any value above 0.7 proves a high level of concordance [70,71]. The consistency of the respondents’ responses is high.

Next, it is necessary to integrate the calculation and expert approaches to forecasting and to develop a new methodology for forecasting the cost of building materials in the conditions of uncertainty.

3. Research Results

3.1. Forecasting the Cost of Building Materials by the Method of Economic and Mathematical Modeling with Expert Adjustment in Conditions of Uncertainty

The comprehensive review of the literature conducted in Section 2.1 of this study made it possible to determine the upward trend in the dynamics of prices for building materials both in the world economy and in the Russian economy from a theoretical perspective. The literature review presented in Section 2.1.2 also showed the uncertainty of the situation related to the socioeconomic development in Russia and in the world, which active formation started in the days of the COVID-19 pandemic and continued under the influence of geopolitical factors [43,44,50,52]. Based on the literature analysis presented in Section 2.1, we identified the need to create a methodology that will help to forecast prices for building materials, taking into account the influence of uncertainty factors. Moreover, the literature review allowed us to identify the ultimate goal of forecasting the cost of building materials, namely, more accurate and reliable determination of material costs in the construction project budget, ensuring the compliance of project implementation deadlines with the planned ones and minimizing the difference between the actual cost of project implementation and the planned budget of the construction project, which will ultimately increase the efficiency of project implementation and have a positive impact on investment activities both in Russia and in the world economy (Section 2.1.1 of this study).

The analysis of statistics of prices for primary building materials in Russia showed that the trend line is formed not only by objective factors of supply and demand but also by subjective factors of uncertainty and risk, including noneconomic ones (Section 2.2 of this study).

Forecasting the price of building materials on the example of steel reinforcement made it possible to determine the construction of an economic and mathematical model of autoregression with an integrated moving average as a trend line for the dynamics of prices for building materials reflecting the influence of objective economic factors (Section 3.1 of this study).

However, trend construction by regression methods does not allow taking into account the influence of noneconomic factors and other subjective factors of uncertainty. Therefore, the expediency of expert adjustment of the forecast is substantiated (Section 3.2 of this study).

As a result, the algorithm for forecasting the cost of building materials under uncertainty was proposed. It is based on the initial construction of the trend line of the price of building materials by the methods of economic and mathematical modeling with subsequent expert adjustment. It is presented in Figure 7.

The proposed algorithm for forecasting the cost of building materials in the conditions of uncertainty involves, firstly, identifying the main factors of changes in the cost based on the literature review. Moreover, the main price-forming building materials are selected on the basis of the study of statistical data and the literature review. The cost of such materials will be forecasted according to the methodology. After that, it is necessary to analyze the possibility and feasibility of import substitution of certain building materials in accordance with their quality and price characteristics, taking into account the conclusions of many studies (Section 2.1.3). Then, regional determinants of the cost of building materials are assessed. The main regional determinants are the availability and proximity of the manufacturers of this building material, transport costs and labor resources (Section 2.1.3). Regional specifics determination leads to the need to forecast the cost of building materials in each region separately. Nevertheless, the general trends in the dynamics of prices for primary building materials in the world economy and the economies of individual countries revealed as a result of the literature analysis (Section 2.1.3) allow the economic and statistical modeling of the series of price dynamics for primary building materials on the basis of data provided by the country’s statistics services and portals of manufacturers of building materials (Section 2.2).

It is proposed to carry out forecasting by the regression analysis methods, namely, by choosing the ARIMA model in the conditions of existing trends of changes in the cost of primary building materials and the factors affecting them (Section 3.1 and Section 2.1.3). Since only the trend values of the time series of prices for building materials can be forecasted by the methods of the regression analysis and modeling of time series, and the trends are not only formed under the influence of objective factors in the conditions of uncertainty but also taking into account the influence of subjective factors of uncertainty, the proposed methodology assumes an expert assessment and a corresponding scenario adjustment of the forecast obtained as a result of a regression analysis. Accordingly, the projected value and the most likely confidence interval of the forecast are formed. It also includes best-case and worst-case scenarios of the expert forecast as the minimum and maximum price values, taking into account the expert assessment.

Since in the conditions of uncertainty, there are sharp abrupt price fluctuations under the influence of subjective factors and conditions, it is necessary to constantly monitor actual values of prices for building materials, compare them with the projected values and carry out the corresponding plan–fact analysis, on the basis of which the projected values are adjusted.

3.2. Calculation and Expert Forecast and Plan–Fact Analysis of the Cost of Building Materials in Russia on the Example of Steel Reinforcement

The proposed methodology was tested on the example of the forecast of the cost of D12 A500C steel reinforcement in the Moscow region and in the city of Yekaterinburg.

Based on the results of forecasting and expert assessment adjustment, it can be concluded that in the near future prices for building materials (steel reinforcement) are not expected to decrease. If we consider the most optimistic scenario, the price growth will slow down to 5–7%. However, the base-case scenario presupposes that prices will rise by 12–15% in aggregate. The worst-case scenario provides for an even greater increase in prices—by 20–25%.

The resulting final forecast of the price for steel reinforcement in the Moscow region and Yekaterinburg for the forecast period of 3, 6 and 9 months is given in the table below (

Table 3. Forecasted values of prices for steel reinforcement for the forecast period of 3, 6 and 9 months.

Forecast Period	Price per Tonne of Steel Reinforcement in the Moscow Region, RUB	Price per Tonne of Steel Reinforcement in Yekaterinburg, RUB
3 months	70,553.31	49,342.59
6 months	72,503.56	53,400.78
9 months	72,655.44	57,131.65

).

To compare the forecast and actual values of the price for steel reinforcement, an analysis of prices for D12 A500C steel reinforcement in the Moscow region and Yekaterinburg according to the data available at mcena.ru for 2022 was conducted. A forecast was made based on these data. In general, it is noted that the actual values of the price for steel reinforcement in the above regions are within the confidence interval of the forecast and reflect the trend of price changes determined earlier in the process of forecasting.

The dynamics of the price for steel reinforcement in the Moscow region (Appendix C) are within the confidence interval and characterize the general tendency of the trend line (Figure 8).

However, it should be noted that in the three-month forecasting timeframe, the downward deviation of actual prices from the forecasted ones is in the range of 11 to 14%, which generally characterizes the forecast as reliable.

In the regions that produce steel reinforcement, the actual dynamics also tend to decrease (Figure 9).

The lower level of prices for steel reinforcement in Yekaterinburg compared to the Moscow region revealed by the results of forecasting is a consequence of industry specialization in metallurgical production in Yekaterinburg and the Sverdlovsk region [26].

4. Discussion of Study Results

The proposed algorithm for forecasting the cost of building materials in the conditions of uncertainty was applied in the construction and planning of project budgets of large construction company “DSK”. The company’s need for steel reinforcement for the implementation of construction projects in 2022 in the Moscow region was estimated at about 12,000 tonnes, in Yekaterinburg—at about 9000 tonnes. Forecasting was made starting from May 2022. Every three months, monitoring was performed, and forecasts were adjusted [26].

To compare forecasted and actual values of prices for steel reinforcement, an analysis of prices for D12 A500C steel reinforcement in the Moscow region and Yekaterinburg for 2022 was conducted. The forecast was made based on these data. In general, it is noted that the actual values of prices for steel reinforcement in the above regions are within the confidence interval of the forecast but reflect the price tendency determined earlier in the process of forecasting with a significant deviation. The greater reliability of the forecast for Yekaterinburg is based on the lower impact of the logistics component on the price of steel reinforcement, since there is metallurgical production and processing of ferrous scrap in the region, which characterizes the lower average price compared to the Moscow region [43].

A fragment of the plan–fact cost analysis taking into account the forecast of prices for steel reinforcement in the Moscow region is given in Appendix B.

It should be noted that in the three-month forecasting timeframe, actual prices differed from the forecasted ones by about 24% downwards for three months, which generally characterizes the forecast as quite reliable (

Table 4. Comparison of average forecast and actual prices for steel reinforcement in the Moscow region within the forecast interval of 3 months.

Reporting Period	Actual Price, RUB	Simulated Price, RUB	Difference between the Actual Price and the Forecast One
1 October 2022–17 December 2022	45,390.00	59,592.45	24%

).

The dynamics of prices for steel reinforcement in Yekaterinburg are at the lower limit of the confidence interval of the forecast made in the second quarter of 2022, and they characterize the general tendency of the trend line, however, not taking into account the impact of changes in the price structure and growth in the logistics component due to geopolitical reasons. In this case, the forecasted trend line should be adjusted taking into account all the reasons for the dynamics of prices for steel reinforcement, taking into account today’s factor values and dynamics by expert evaluation methods, which corresponds to the methodology proposed by us.

It is also worth considering that the key reason for the increase in the price of steel reinforcement starting from 2021 was a cartel price collusion, which negatively affected the accuracy of the time series simulation [68]. Confirming the conclusions made in [72], a fair distribution is necessary. This will increase the manufacturer’s profits and make the supply chain more stable.

We can take into account the conclusions made in [73] regarding the collection of statistical information on the actual prices for building materials with the help of a special search robot as promising management actions that positively affect the accuracy of material cost forecast. This will increase the accuracy of calculating the initial actual data and the cost forecast by 50%.

Moreover, an effective tool for management digitalization aimed at improving the efficiency of building materials management with a negative cost forecast can be the model of materials procurement and storage optimization proposed in [74], which will lead to cost savings and reduce the impact of the shortage of primary price-forming materials.

5. Conclusions

Based on the review of the literature, this study allowed us to identify the problem of cost overruns and failures to meet deadlines in the implementation of many construction projects due to an increase in the price of primary price-forming building materials, substantiate the importance of reliable forecasting of prices of building materials in calculating the project budget and project management, confirm the impact of economic factors on the ratio of supply and demand of building materials and, accordingly, their price, as well as the influence of noneconomic and subjective factors of uncertainty. The review of the literature and the analysis of the statistics of prices of building materials in Russia showed that the trend line of the dynamics of prices for building materials built by the methods of economic and mathematical modeling can be distorted under the influence of a large number of noneconomic factors or a high level of uncertainty. Therefore, it is proposed to adjust such a forecast through expert assessment by the method of scenario analysis.

In this study, we proposed and tested a new methodology for forecasting the cost of building materials under uncertainty based on expert adjustment of the price forecast obtained by the methods of modeling.

The literature review, statistics analysis and calculations performed applying this methodology confirmed the reliability of the study hypothesis adopted in Section 2.1.

The comparison of planned and forecasted values showed a high reliability of the forecast, which indicates the fairness and practical applicability of the proposed forecasting methodology.

Based on the assessment of using the forecast of the cost of steel reinforcement by the construction company “DSK”, the head of the financial department concluded that the accuracy of planning project budgets was increased by 20%, and the delay in the planned work schedule was reduced by 10% due to improved financial planning.

This study recommends that construction companies should include the forecasted level of prices for materials in the project budget, as well as use forecasted and actual values when conducting a plan–fact analysis of construction projects, which will help to establish reliably the reason for the failure to meet deadlines, as well as the reason for cost overruns.

However, this study did not calculate the company’s losses incurred due to an increase in prices for construction materials, the effect of applying the methodology for forecasting prices for building materials and did not develop a tool for introducing the forecast into the budget planning and control system. We consider this to be the most important area for the development of this study.

Moreover, further development of this research topic should take into account the calculation of the effect of increasing the accuracy of the cost of building materials if they are included in the project budget, using digital tools.

Based on the forecasted values, it is possible not only to plan more carefully the purchase of building materials but also to implement lean construction methods, taking into account the forecasted dynamics of the cost of building materials (namely, pull planning and other planning methods within lean construction) [43,75]. We believe this area should become a promising area of development of this study.

This study has limitations. Firstly, it considered the forecast of the cost of steel reinforcement in whole, without considering the supply chain specifics and price structure, in two regions of Russia, which differ in terms of local production. We believe that further areas of research should include forecasting of locally produced aggregates, as well as cement, which is specific due to the transport component of the price. Secondly, in this study, the expert analysis took into account all the components of uncertainty, according to the experts’ opinion, while further development of the research topic should include more objective determination of main factors for the risk of a price increase and taking into account each of them in forecasting when analyzing the sensitivity.