MATHEMATICAL MODELING AND VALIDATION OF PREDICTORS OF SCHEDULE DEVIATIONS IN TRUNK PIPELINE CONSTRUCTION BASED ON DAILY PRODUCTION DATA

ABSTRACT

This study is devoted to the development and verification of mathematical models designed to predict and minimize schedule deviations in the implementation of large-scale oil and gas projects, with particular attention to trunk pipeline construction in the Republic of Kazakhstan. The paper examines the factors contributing to construction schedule slippage and proposes a predictive analytics methodology based on the integration of daily production reports with linear scheduling algorithms and learning-curve models. The objective is to assess the effectiveness of moving from reactive management toward proactive modeling grounded in detailed productivity data. The methodological approach includes a systematic literature review, a comparison of statistical models, and a case study of the Future Growth Project (FGP) at the Tengiz field. The results obtained indicate that the application of multiple linear regression in combination with stochastic modeling increases the forecasting accuracy of the Schedule Performance Index (SPI) to 96–98%. In conclusion, the hypothesis is confirmed that early completion by up to 12 months is achievable provided that a system of daily monitoring is implemented and production constraints are eliminated at the operational-management level. The findings presented may be useful for senior construction project managers, project management office analysts, and executives of energy companies focused on capital cost optimization and strict schedule compliance under conditions of high uncertainty.

АННОТАЦИЯ

Исследование посвящено разработке и проверке математических моделей, предназначенных для прогнозирования и минимизации отклонений от графика при реализации крупномасштабных нефтегазовых проектов, с особым вниманием к строительству магистральных трубопроводов в Республике Казахстан. В работе рассматриваются факторы, способствующие задержкам в графике строительства, и предлагается методология прогнозной аналитики, основанная на интеграции ежедневных отчетов о производстве с линейными алгоритмами планирования и моделями кривых обучения. Цель состоит в оценке эффективности перехода от реактивного управления к проактивному моделированию, основанному на подробных данных о производительности. Методологический подход включает систематический обзор литературы, сравнение статистических моделей и тематическое исследование проекта «Будущий рост» (ПГР) на месторождении Тенгиз. Полученные результаты показывают, что применение множественной линейной регрессии в сочетании со стохастическим моделированием повышает точность прогнозирования Индекса выполнения графика (ИПГ) до 96–98%. В заключение подтверждается гипотеза о досрочном завершении работ на срок до 12 месяцев при условии внедрения системы ежедневного мониторинга и устранения производственных ограничений на уровне оперативного управления. Представленные результаты могут быть полезны для руководителей строительных проектов, аналитиков проектных бюро и руководителей энергетических компаний, занимающихся оптимизацией капитальных затрат и строгим соблюдением сроков в условиях высокой неопределенности.

Keywords: oil and gas industry, trunk pipelines, Future Growth Project, Tengiz field, mathematical modeling, predictive analytics, schedule planning, labor productivity, Republic of Kazakhstan, project management.

Ключевые слова: нефтегазовая отрасль, магистральные трубопроводы, проект «Будущий рост», месторождение Тенгиз, математическое моделирование, прогнозная аналитика, планирование графика работ, производительность труда, Республика Казахстан, управление проектами.

Introduction

In 2024, the global pipeline construction market entered a phase of active growth driven by rising worldwide demand for energy resources and by the need to modernize cross-border infrastructure. According to market research data, the size of this segment reached USD 52.49 billion in 2024, with projected growth to USD 55.32 billion in 2025 and a further increase to USD 84.26 billion by 2033 at a compound annual growth rate (CAGR) of 5.4–5.9% [1]. Within this context, the Republic of Kazakhstan functions as a strategic transit hub between Europe and Asia. The country’s oil and gas midstream sector, valued at USD 12.98 billion in 2024, is demonstrating a higher growth rate, with a CAGR of 3.26% during 2025–2030, which reflects a clear drive to expand export capacity and diversify transportation routes, including the development of the Trans-Caspian International Transport Route, or Middle Corridor [2].

At the same time, the industry is confronting systemic problems associated with schedule deviations. Statistical evidence from 2024–2025 shows that up to 98% of major construction projects in North America and the Caspian region experience delays, the average overrun beyond planned duration reaches 37%, and budget overruns may amount to as much as 80% [4]. In the oil and gas sector, where the value of megaprojects such as the Future Growth Project (FGP) at the Tengiz field exceeds USD 45 billion, every week of delay produces substantial financial losses and social risks [3]. Among the key drivers of schedule disruption identified in 2024 are shortages of qualified personnel, with 92% of companies reporting hiring difficulties, volatility in steel prices, and the complexity of environmental permitting procedures [1].

Existing studies demonstrate the predominance of reactive control methods, such as the traditional Critical Path Method (CPM), which record deviations after they have already occurred but possess limited predictive capacity for managing dynamic changes under field conditions. The aim of this study is to develop and validate a mathematical framework that makes it possible to use daily production data, including weld-joint output and earthwork volumes, as leading indicators of schedule deviations.

The scientific novelty of the research lies in combining granular analysis of the daily output of welding and installation crews with stochastic modeling algorithms within the framework of linear scheduling methodology (LSM), thereby enabling dynamic adjustment of megaproject schedules in real time. The working hypothesis rests on the assumption that the use of predictive analytics based on daily production data and weekly verification walkdowns makes it possible not only to compensate for accumulated delay, but also to achieve early completion of critical work volumes through the early identification of institutional barriers to productivity.

Materials and Methods

The methodological foundation of the study was formed at the intersection of mathematical statistics, project management theory, and practical experience acquired in leading international consortia. The empirical base consists of implementation data from the Future Growth Project (FGP) at the Tengiz field, one of the deepest and most technologically complex oil fields in the world [7]. The project involved major global companies: Chevron (50%), ExxonMobil (25%), NC KazMunayGas JSC (20%), and Lukoil (5%) [8].

Several key approaches were applied in order to achieve the objective of the study. The case-study component and the practical analysis of management processes were grounded in experience gained through interaction with contracting organizations, including Bonatti (Italy), SICIM (Italy), GATE (Türkiye), and MCC (Kazakhstan). Within the author’s method of “non-standard monitoring,” daily productivity tables were compiled to record the actual volumes of completed work at the end of each shift, which made it possible to create a unique dataset for subsequent modeling.

The systematic literature review covered publications indexed in Scopus, Web of Science, IEEE, and Springer, with particular emphasis on the application of Machine Learning methods and neural networks in construction planning [10, 20, 27]. A comparative statistical analysis of multiple linear regression (MLR), artificial neural network (ANN), and decision tree (DT) models was carried out and showed that, for structured data from oil and gas construction projects, MLR provides forecasting accuracy above 96% [11].

To model learning curves, power-law and exponential models were used, describing the adaptation of welding crews to the specific requirements of working with CRA-clad pipes at Tengiz [12]. The Linear Scheduling Method (LSM) was applied to visualize the continuity of work processes and to identify space-time conflicts along the pipeline route [13].

The source base of the study included industry and governmental reports, such as data from the Ministry of Energy of the Republic of Kazakhstan and the 2024 annual report of NC KazMunayGas JSC [15, 16, 24]; technical documentation of the KPJV consortium (WorleyParsons, Fluor, KING, KGNT) for the FGP project [17]; as well as academic publications on predictive analytics in construction from Emerald, MDPI, and ASCE [19].

Results and Discussion

The Future Growth Project (FGP) at the Tengiz field constitutes a complex engineering undertaking marked by a set of highly unusual technological conditions. The reservoir lies at a depth of approximately 12,000 feet, while formation pressure reaches up to 800 bar in the presence of a high concentration of hydrogen sulfide, a combination that necessitates the use of corrosion-resistant alloys (CRA) and raw-gas injection technologies operating under ultra-high pressure [8].

The implementation of pipeline systems under such conditions requires strict compliance with welding standards and non-destructive examination (NDE) procedures capable of ensuring the long-term durability and operational reliability of the structures.

Work performed with contracting organizations, including SICIM, covered the construction of high-pressure oil systems and metering station facilities, which rather clearly illustrates the complexity of process coordination and the need for precise planning of both resources and work schedules.

Table 1 summarizes the technical characteristics of SICIM’s initial pipeline scope in the FGP project. It should be noted, however, that SICIM’s final participation in the overall pipeline program later expanded due to the award of the separate P4 package (56 km) and the redistribution of part of the unfinished P2/P3 scope after Bonatti’s demobilization.

Table 1.

Technical characteristics and work volumes of SICIM’s initial pipeline scope in the FGP project (compiled by the author based on [22]).

The author’s experience, both in the role of client representative and in subcontracting practice, made it possible to identify a recurring problem: traditional managerial reports often fail to reflect the actual situation on site with sufficient objectivity. The introduction of weekly walkdowns across all work fronts, combined with direct conversations with crews regarding their plans for the following week, produced a more accurate picture of current project status than formalized reporting routines. This approach revealed that the principal obstacles were associated not with the productivity of the workforce itself, but with the absence of approved drawings, delays in obtaining permit documentation, and shortages of materials. That observation aligns with studies in which delays in drawing issuance are consistently identified among the five leading causes of schedule slippage [11].

To formalize the monitoring process, a model was developed that treats daily output as a predictor variable. In pipeline construction, welding remains the core critical process. For that reason, the indicators “joints per day” and “inch-dia” were selected as the key metrics for quantitative analysis [23]. The mathematical validation of the forecasts was based on learning-curve modeling. The exponential learning model demonstrated the best fit to the observed data, making it possible to detect regularities in productivity change as a function of accumulated work volume and crew experience. Not every shift, of course, follows a perfectly smooth pattern; still, the overall trajectory proved sufficiently stable to support robust predictive interpretation.

In addition, the analysis of time lags between material delivery and the start of welding operations showed that more than 40% of downtime is associated with logistics-related delays rather than with technical production difficulties. This makes it possible to identify bottlenecks with greater precision and, in practical terms, to optimize resource planning at construction sites in a more grounded way.

The use of quantitative models also revealed the significance of human-capital factors. Differences in productivity between crews working on structurally identical sections reached 15–20%, which confirms the need for systematic knowledge sharing and internal training mechanisms. Once these indicators are incorporated into forecasting models, completion dates can be assessed in a more realistic manner, and the risks of violating contractual obligations are reduced accordingly.

Beyond that, integration of the model with construction management information systems enables the automatic generation of warnings regarding possible deviations from plan. This creates the conditions for proactive intervention and allows schedules to be adjusted in a timely manner, resources to be redistributed where they are actually needed, and financial losses connected with downtime and material overruns to be reduced before they accumulate into larger systemic delays.

                                                    (1),

Where y is the time for the x-th operation,  is the time of the first operation, b is the learning rate, and c is the decay constant. A study based on a 29-day sample (842 joints) confirmed that the average productivity for the first 20 days of a project is a reliable indicator for estimating the completion date of an object with an error of less than 5%.

Hierarchical planning and barrier removal play a decisive role in the effective delivery of large-scale construction projects. Within the author’s proposed approach, a two-level planning system was introduced to ensure alignment between operational execution and strategic management. At the first level, supervisors prepare a detailed three-week plan, that is, a look-ahead schedule, which makes it possible to control the available work front and track daily productivity on a continuous basis. The second level, represented by superintendents, operates with planning horizons of up to 12 months and focuses on strategic matters such as equipment mobilization, material procurement, and workforce upskilling [9, 12, 21].

The practical implementation of this methodology demonstrated a high degree of effectiveness. In particular, SICIM was able to complete substantial volumes of work 12 months ahead of the contractual deadline, despite an initial delay of approximately 6 months. This outcome was achieved through continuous daily productivity monitoring, weekly field walkdowns, and the rapid escalation of constraints requiring management intervention. The key success factor was the rapid identification and escalation of all issues requiring resolution at the management level, something made possible through the author’s direct interaction with the top management of subcontracting organizations. This created the conditions for strategically significant decisions to be taken without delay and, just as importantly, for the continuity of the construction process to be preserved.

In addition, the systematization of planning contributed to the identification of hidden bottlenecks and barriers, including logistics-related problems, shortcomings in subcontractor coordination, and delays in the approval of design documentation. The application of multi-level control made it possible to forecast potential downtime and to redistribute resources in advance, thereby reducing the risks of schedule disruption.

It should also be noted that the methodology is integrated with modern construction management information systems, which ensures transparency of plans, automatic report generation, and the possibility of scenario modeling. This makes it possible not only to optimize ongoing operations, but also to formulate strategic recommendations aimed at process improvement, thereby increasing the overall reliability and predictability of project execution.

A comparison of the production indicators of NC KazMunayGas JSC for 2023–2024 is presented in Table 2.

Table 2.

Comparison of production indicators of NC KazMunayGas JSC for 2023–2024 (compiled by the author based on [24-28]).

An analysis of the data presented shows that maintaining stable production even at mature fields such as Tengiz and Kashagan depends directly on the timely completion of construction and maintenance operations. Any deviation from schedule, as occurred at Tengiz in 2024 because of the need for deep infrastructure modernization, demonstrates the critical importance of precise calendar planning and coordinated action by all project participants. Regular monitoring and prompt response to deviations make it possible to minimize production losses and ensure the reliable functioning of the facilities.

To improve risk controllability, a predictive model was developed that relies on the daily collection of data and makes it possible to visualize the logic of managerial decision-making (Figure 1). The model captures the entire process, from the recording of productivity indicators and facility conditions to deviation analysis and proactive intervention. Such an approach enables the early detection of potential bottlenecks and the prevention of downtime, thereby forming the basis for strategically sound planning and operational resource allocation.

In addition, the use of predictive instruments makes it possible to integrate quantitative indicators with qualitative factors, such as the level of personnel training, the condition of equipment, and the availability of approved design solutions. This provides a more comprehensive assessment of risks and allows corrective measures to be developed that are aimed at maintaining production pace and meeting established deadlines. The practical implementation of the model contributes to the formation of a culture of systemic control and transparency in management processes, which is critically important for facilities characterized by high technological complexity and substantial capital expenditures.

Figure 1. Management workflow for controlling deviations based on daily production data (Management Workflow)

Within the proposed model, an SPI < 0.9 value, that is, a Schedule Performance Index below 0.9, is treated as a signal requiring an immediate site visit for a Field Walkthrough. This approach differs from standard coordination meetings, where the causes of delay are often distorted or understated, because direct presence in the field makes it possible to document the actual circumstances on the ground: the absence of required equipment, delays in material deliveries, or downtime caused by waiting for a quality inspector. The regular application of this methodology ensures an objective identification of bottlenecks and makes it possible to implement corrective measures before deviations result in substantial losses of time and resources.

To verify the proposed model, a systematic assessment of the accuracy of different forecasting methods was carried out. Data from academic review studies published in 2024–2025 were used, in which machine-learning methods were compared with traditional statistical calculations. The analysis showed that the integration of quantitative algorithms with expert judgment provides greater forecast reliability and makes it possible to account both for historical productivity indicators and for the influence of managerial and external factors on the schedule of work execution.

In addition, the findings of the study revealed that the use of learning curves and exponential performance-prediction models ensures forecast stability even in the presence of instability in resources and external conditions. This confirms that an integrated approach combining mathematical modeling, operational on-site control, and regular data validation constitutes the most effective instrument for managing construction risks and increases the reliability of planning in large infrastructure projects.

The comparative accuracy of mathematical models for forecasting schedule deviations is demonstrated in Table 3.

Table 3.

Comparative accuracy of mathematical models for forecasting schedule deviations (compiled by the author based on [5, 9, 11, 14]).

The results of the validation performed demonstrate that the logistic learning model has the highest accuracy when forecasting repetitive operations such as pipeline joint welding. It allows the probabilistic distribution of the successful completion of each operation to be taken into account and adapts to changing site conditions. The multiple linear regression (MLR) model retains high effectiveness because of its simplicity and the possibility of implementation in standard spreadsheet processors, which ensures the prompt application of forecasting tools directly at the construction site without the need for complex computing resources.

For the effective management of information flows in contemporary pipeline construction projects, a digital architecture based on a Directed Acyclic Graph (DAG) was proposed. The DAG concept makes it possible to formalize the movement of data from field sensors and execution units to managerial decisions (Figure 3). Such a structure ensures transparency in the logic of data processing, traceability of dependencies between events, and the possibility of automatically generating signals indicating the need for intervention, thereby reducing the risk of errors caused by inconsistency or loss of information.

In addition, the application of a DAG facilitates the integration of heterogeneous data sources, including productivity indicators, logistics reports, quality-control results, and weather conditions. This makes it possible to build comprehensive analytical models, identify correlations, and forecast possible deviations in the work schedule with high accuracy. Taken together, the digital data architecture and the mathematical forecasting models form a reliable instrument for the systemic management of construction risks and for improving the efficiency of the implementation of large-scale infrastructure projects (see Figure 2).

Figure 2. Data integration architecture (Construction Data Integration DAG) (author’s development)

This architecture makes it possible to integrate Building Information Modeling (BIM) data effectively with actual on-site productivity. For example, if the three-dimensional model indicates a complex tie-in node, while daily output on the corresponding section begins to decline, the system automatically generates a signal indicating the need to allocate additional resources or adjust the sequence of work [18]. Such a mechanism ensures a prompt response to local problems and contributes to the minimization of downtime, which is particularly critical for high-technology operations in pipeline projects.

At the same time, the implementation of predictive modeling based on daily data is associated with a number of systemic risks. First, the quality of the input data directly determines the accuracy of the forecasts, since unreliable reporting from subcontractors can produce erroneous conclusions [31]. Second, possible resistance from personnel, especially line managers, is shaped by the perception of detailed daily control as an instrument of pressure rather than as a means of optimization. A third factor consists in the logistical and climatic constraints characteristic of Western Kazakhstan: dust storms, extreme temperatures, and other external conditions introduce stochastic noise into the data, making filtration by standard methods more difficult [33, 34, 35]. Finally, the shortage of qualified planning engineers capable of working with machine-learning algorithms remains a critical constraint for projects in 2025 [6]. To reduce these risks, a Responsible AI system was implemented on the FGP project, ensuring the mandatory review of automated forecasts by senior construction managers [30, 32]. This approach preserves a balance between technological capability and practical experience, thereby supporting the reliability of managerial decisions.

The economic effectiveness of applying the described methodology on the Tengiz FGP megaproject became visible in the substantial leveling of the work schedule and in the reduction of costs associated with equipment rental, the maintenance of temporary rotational camps, and non-productive downtime. Since the cost of a single day of delay on a project of this scale is measured in millions of dollars, the early completion of work by 12 months generated a massive economic effect. For the Republic of Kazakhstan, the development of such competencies is directly linked to the country’s energy security: at the end of 2024, oil exports through the CPC pipeline amounted to 54.9 million tonnes [16]. Predictive modeling creates the possibility of ensuring the timely commissioning of new capacities, such as the Third-Generation Plant (3GP) at Tengiz, reducing the risks of downtime and strengthening the strategic resilience of the oil and gas sector [36].

In addition, the deployment of such systems contributes to the formation of a corporate culture of proactive management, in which decisions are made on the basis of factual data rather than intuition or outdated reporting. This makes it possible not only to optimize current processes, but also to accumulate knowledge for subsequent projects, increasing the overall professional competence of participants and creating the basis for scaling successful practices to other major infrastructure facilities in the country.

Another significant effect is the increase in transparency and accountability at all levels of management. The integration of digital data architecture with predictive models makes it possible to generate timely reports for all stakeholders, reducing the likelihood of conflict and ensuring alignment among contractors, subcontractors, and regulators. This is especially important for projects involving complex technological chains and multiple points at which the interests of different participants intersect [29].

Finally, the experience of implementing predictive modeling at Tengiz demonstrates that a systemic approach to construction risk management contributes not only to the reduction of costs and timelines, but also to the strengthening of the institutional resilience of the industry. The establishment of digital monitoring standards, the training of personnel, and the introduction of forecasting algorithms create the conditions for the long-term reliability of infrastructure projects, which is of strategic importance for the energy security and economic stability of the region (see Figure 3).

Figure 3. Risk prioritization matrix for delay factors in pipeline construction (Risk Heatmap Logic)

An analysis of the matrix (Figure 4) shows that the parameter “Daily Welding Output” is characterized by high predictability and a substantial impact on overall project performance, which makes it a primary candidate for predictive modeling. The regular recording of this indicator makes it possible to track crew productivity, identify deviations from the planned schedule, and adjust resources or the sequence of operations in a timely manner, thereby minimizing the risks of downtime and schedule slippage.

At the same time, “Design Changes” demonstrate a high impact on the overall outcome while remaining low in predictability.

Their management requires a different set of approaches, including flexible escalation mechanisms, coordination with the project office, and continuous interaction between engineers and contractors. A timely response to design changes makes it possible to reduce their negative effect on schedule and budget; however, it is not possible to eliminate uncertainty in this parameter completely.

The integration of such classifications into a predictive modeling system ensures priority attention to parameters that are both highly significant and highly predictable, while at the same time distinguishing separate processes that require strategic decisions and additional managerial resources. Such a differentiated approach makes it possible to optimize the allocation of attention and effort, thereby ensuring more effective management of complex construction projects characterized by multiple interdependent factors.

Conclusion

As a result of the research conducted, a comprehensive mathematical substantiation and practical validation were carried out regarding the use of daily production data for forecasting schedule deviations in trunk pipeline construction. The results achieved fully correspond to the objectives stated in the abstract and demonstrate the high applicability of the proposed methods under real conditions of large-project implementation.

The key findings of the study emphasize the insufficient effectiveness of traditional planning methods, such as the Critical Path Method (CPM), for managing megaprojects in 2024–2025, whereas multiple linear regression (MLR) models and learning-curve approaches provide forecast accuracy exceeding 96%.

The integration of daily work-volume monitoring with weekly verification walkdowns makes it possible to identify productivity bottlenecks at an early stage, which not only prevents delays but also contributes to project completion ahead of schedule by as much as 12 months.

The experience of managing international consortia at the Tengiz field confirmed that project success depends on the client’s ability to bring all divisions together within a unified information environment and to resolve issues promptly at the level of subcontractor leadership.

This requires the implementation of a transparent data-sharing system, the timely escalation of problems, and support for a common approach to decision-making, all of which improve coordination and reduce the risk of downtime.

The digitalization of construction processes through the introduction of data architectures based on Directed Acyclic Graphs (DAGs) and their integration with BIM technologies constitutes a key condition for the development of Kazakhstan’s oil and gas sector and for ensuring its competitiveness in the international market. Such an architecture makes it possible not only to forecast deviations, but also to establish a system of proactive management in which managerial problem-solving is grounded in objective data and analytical models.

The practical significance of the study is expressed in the developed algorithm of “non-standard monitoring,” which is capable of being scaled to any linear construction project. The application of this approach opens opportunities for increasing operational excellence, shortening timelines, and optimizing costs, which will be especially valuable for senior executives and project-control specialists seeking to improve the efficiency and reliability of large infrastructure delivery in the oil and gas industry.

In addition, the implementation of the proposed models and digital tools contributes to the formation of a resilient organizational culture of proactive management, in which data and forecasts become the basis for decision-making.

This creates long-term advantages in risk management, increases process transparency, and makes it possible to accumulate knowledge systematically for subsequent projects, thereby strengthening company capabilities and enhancing the strategic resilience of the industry as a whole.

Finally, the combination of mathematical modeling, daily monitoring, and digital integration forms a universal methodology capable of adapting to projects of different scales and levels of complexity, which makes the proposed approach a key instrument for ensuring the timely execution and sustainable operation of critically important oil and gas infrastructure assets.

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