Impact of activity time stochasticity on critical paths and their completion probabilities in construction projects

Saurabh  Gupta; Riya Catherine  George; Deepu  Philip; Syam  Nair

doi:10.59400/be1703

Impact of activity time stochasticity on critical paths and their completion probabilities in construction projects

Saurabh Gupta Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Riya Catherine George Department of Civil and Environmental Engineering, Hiroshima University, Hiroshima 739-8511, Japan
Deepu Philip Department of Industrial and Management Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Syam Nair Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

Article ID: 1703

Keywords: activity delays; advanced simulation tool; construction project; critical path; project planning; PERT; robust schedules

Abstract

Accurate planning and project control activities are essential in ensuring the timely completion of construction projects. Even though the classical scheduling techniques like Gantt charts, critical path method (CPM), program evaluation and review technique (PERT), etc., are well-designed and can effectively support construction scheduling functions, they do not account for the variability in activity times arising out of the random/stochastic nature of the activities involved. The study utilizes a simulation-based approach to identify the impact of variability in activity time durations on critical paths and on the probability of timely completion of construction projects. The effectiveness of four different probability distribution functions, namely uniform, triangular, bound exponential, and unbound exponential, in capturing the stochasticity of activity times in construction projects was also evaluated as part of the study. A MATLAB-based simulation framework was developed to sample random durations of project activities and compute various project scheduling parameters based on PERT assumptions. Activity time variability was introduced in the network by extending pessimistic time (t_p) by up to 50%. Observation in the study suggests that for projects that experience delays during execution, allocating additional resources to the preassigned critical path may not always be effective in addressing these delays. Instead, dynamic corrective measures (time extensions, resource allocation, etc.) that consider all possible scenarios of project completion and can account for any possible changes in critical path due to the incurred delay may be adopted to ensure a higher probability of project completion within the revised schedule. Exponential bounded distribution was found to provide a more realistic estimate of project completion time with a high probability of timely completion of construction projects. The study also suggests exponential unbound distribution to be effective in simulating worst-case scenarios encountered in construction projects. Future research could validate this approach on real projects and use machine learning to automate scheduling adjustments for delays.

References

[1]Rose KH. A Guide to the Project Management Body of Knowledge (PMBOK Guide) Fifth Edition. Project Management Journal. 2013; 44(3). doi: 10.1002/pmj.21345

[2]Kerzner H. Project Management: A systems approach to planning, scheduling and control, 10th Ed. Industrial Engineering/Project Management; 2010.

[3]Lester EIA. Project Management. Project Management, Planning and Control. Butterworth-Heinemann; 2014.

[4]Nicholas JM, Steyn H. Project Management for Engineering, Business and Technology. Routledge; 2020.

[5]González-Cruz M-C, Ballesteros-Pérez P, Lucko G, et al. Critical Duration Index: Anticipating Project Delays from Deterministic Schedule Information. Journal of Construction Engineering and Management. 2022; 148(11). doi: 10.1061/(ASCE)CO.1943-7862.0002387

[6]Khamooshi H, Cioffi DF. Uncertainty in Task Duration and Cost Estimates: Fusion of Probabilistic Forecasts and Deterministic Scheduling. Journal of Construction Engineering and Management. 2013; 139(5): 488-497. doi: 10.1061/(ASCE)CO.1943-7862.0000616

[7]Zhang S, Song X, Shen L, et al. Complicated Time-Constrained Project Scheduling Problems in Water Conservancy Construction. Processes. 2023; 11(4): 1110. doi: 10.3390/pr11041110

[8]Olawale YA, Sun M. Cost and time control of construction projects: inhibiting factors and mitigating measures in practice. Construction Management and Economics. 2010; 28(5): 509-526. doi: 10.1080/01446191003674519

[9]Gupta S, George RC, Philip D, et al. Activity Time Variations and Its Influence on Realization of Different Critical Paths in a PERT Network: An Empirical Study Using Simulations. In: Proceedings of the 2nd International Civil Engineering and Architecture Conference; 11-14 March 2022; Singapore.

[10]Malcolm DG, Roseboom JH, Clark CE, et al. Application of a Technique for Research and Development Program Evaluation. Operations Research. 1959; 7(5): 646-669. doi: 10.1287/opre.7.5.646

[11]Sculli D. A historical note on PERT times. Omega. 1989; 17(2):195-196. doi: 10.1016/0305-0483(89)90011-X

[12]Dodin B. Approximating the distribution functions in stochastic networks. Computers & Operations Research. 1985; 12(3): 251-264. doi: 10.1016/0305-0548(85)90024-3

[13]Dodin B, Sirvanci M. Stochastic networks and the extreme value distribution. Computers & Operations Research. 1990; 17(4): 397-409. doi: 10.1016/0305-0548(90)90018-3

[14]Tesfaye E, Girma K, Berhan E, et al. A simulation of project completion probability using different probability distribution functions. Advances in Intelligent Systems and Computing. 2015; 334: 133–145. doi: 10.1007/978-3-319-13572-4_11

[15]Thompson RC, Lucko G, Su Y. Reconsidering an Appropriate Probability Distribution Function for Construction Simulations. Construction Research Congress 2016; 2016.

[16]Hahn ED, Martin MDML. Robust project management with the tilted beta distribution. Maryland Shared Open Access Repository; 2015.

[17]Lau HS, Somarajan C. A proposal on improved procedures for estimating task-time distributions in PERT. European Journal of Operational Research. 1995; 85(1): 39-52. doi: 10.1016/0377-2217(93)E0213-H

[18]Premachandra IM. An approximation of the activity duration distribution in PERT. Computers & Operations Research. 2001; 28(5): 443-452. doi: 10.1016/S0305-0548(99)00129-X

[19]Badiru AB. A simulation approach to PERT network analysis. SIMULATION. 1991; 57(4): 245-255. doi: 10.1177/003754979105700409

[20]Lee DE, Arditi D, Son CB. The probability distribution of project completion times in simulation-based scheduling. KSCE Journal of Civil Engineering. 2013; 17(4): 638-645. doi: 10.1007/s12205-013-0147-x

[21]Salas-Morera L, Arauzo-Azofra A, García-Hernández L, et al. New Approach to the Distribution of Project Completion Time in PERT Networks. Journal of Construction Engineering and Management. 2018; 144(10). doi: 10.1061/(ASCE)CO.1943-7862.0001552

[22]Williams FE. PERT Completion Times Revisited. INFORMS Transactions on Education. 2005; 6(1): 21-34. doi: 10.1287/ited.6.1.21

[23]Yao MJ, Chu WM. A new approximation algorithm for obtaining the probability distribution function for project completion time. Computers & Mathematics with Applications. 2007; 54(2): 282-295. doi: 10.1016/j.camwa.2007.01.036

[24]Mohan S, Gopalakrishnan M, Balasubramanian H, et al. A lognormal approximation of activity duration in PERT using two time estimates. Journal of the Operational Research Society. 2007; 58(6): 827-831. doi: 10.1057/palgrave.jors.2602204

[25]Hajdu M, Bokor O. The Effects of Different Activity Distributions on Project Duration in PERT Networks. Procedia - Social and Behavioral Sciences. 2014; 119: 766-775. doi: 10.1016/j.sbspro.2014.03.086

[26]Khan IA, Bickel JE, Hammond RK. Determining the Accuracy of the Triangular and PERT Distributions. Decision Analysis. 2023; 20(2): 151-165. doi: 10.1287/deca.2022.0464

[27]Parks WH, Ramsing KD. The Use of the Compound Poisson in Pert. Management Science. 1969; 15(8): B-397-B-402. doi: 10.1287/mnsc.15.8.b397

[28]Abdelkader YH. Evaluating project completion times when activity times are Weibull distributed. European Journal of Operational Research. 2004; 157(3): 704-715. doi: 10.1016/S0377-2217(03)00269-8

[29]Hahn ED. Mixture densities for project management activity times: A robust approach to PERT. European Journal of Operational Research. 2008; 188(2): 450-459. doi: 10.1016/j.ejor.2007.04.032

[30]Pérez JG, Martín M del ML, García CG, et al. Project management under uncertainty beyond beta: The generalized bicubic distribution. Operations Research Perspectives. 2016; 3: 67-76. doi: 10.1016/j.orp.2016.09.001

[31]Lee D-E. Stochastic Project Scheduling Simulation System (SPSS III). Korean Journal of Construction Engineering and Management. 2005; 6: 73-79

[32]Lee D-E, Yi C-Y, Lim T-K, et al. Integrated Simulation System for Construction Operation and Project Scheduling. Journal of Computing in Civil Engineering. 2010; 24(6): 557-569. doi: 10.1061/(ASCE)CP.1943-5487.0000061

[33]Golenko-Ginzburg D. On the Distribution of Activity Time in PERT. Journal of the Operational Research Society. 1988; 39(8): 767-771. doi: 10.1057/jors.1988.132

[34]Alagheband A. An efficient algorithm for calculating the exact overall time distribution function of a project with uncertain task durations. Indian Journal of Science and Technology. 2012; 5(9): 1-7. doi: 10.17485/ijst/2012/v5i9.20

[35]Kleindorfer GB. Bounding Distributions for a Stochastic Acyclic Network. Operations Research. 1971; 19(7): 1586-1601. doi: 10.1287/opre.19.7.1586

[36]Mehrotra K, Chai J, Pillutla S. A study of approximating the moments of the job completion time in PERT networks. Journal of Operations Management. 1996; 14: 277-289. doi: 10.1016/0272-6963(96)00002-2

[37]Soroush HM. The Most Critical Path in a PERT Network. Journal of the Operational Research Society. 1994; 45(3): 287-300. doi: 10.1057/jors.1994.42

[38]Soroush HM. The most critical path in a PERT network: A heuristic approach. European Journal of Operational Research. 1994; 78(1): 93-105. doi: 10.1016/0377-2217(94)90124-4

[39]Lee D-E. Probability of Project Completion Using Stochastic Project Scheduling Simulation. Journal of Construction Engineering and Management. 2004; 131(3): 310-318. doi: 10.1061/(ASCE)0733-9364(2005)131:3(310)

[40]Lee DE, Bae TH, Arditi D. Advanced Stochastic Schedule Simulation System. Civil Engineering and Environmental Systems; 2011.

[41]Ahuja HN, Dozzi SP, AbouRizk SM. Project management: techniques in planning and controlling construction projects. Wiley India; 1994.

[42]Hillier FS, Lieberman GJ. Introduction to operations research, ELEVENTH. McGraw Hill; 2021.

[43]Pinedo ML. Planning and Scheduling in Manufacturing and Services, 2nd ed. Springer-Verlag New York; 2000.

[44]Winston WL. Operations Research: Applications and Algorithms. Cengage Learning; 2022.

[45]Hajdu M. Effects of the application of activity calendars on the distribution of project duration in PERT networks. Automation in Construction. 2013; 1(35): 397-404.

[46]Zohrehvandi S. A Project-Scheduling and Resource Management Heuristic Algorithm in the Construction of Combined Cycle Power Plant Projects. Computers. 2022; 11(2): 23. doi: 10.3390/computers11020023

[47]Hajdu M, Bokor O. Sensitivity analysis in PERT networks: Does activity duration distribution matter? Automation in Construction. 2016; 65: 1-8. doi: 10.1016/j.autcon.2016.01.003

[48]Mályusz L, Vattai Z. Project scheduling algorithms for construction projects with stretchable activities. IOP Conference Series: Materials Science and Engineering. 2022; 1218(1): 012043. doi: 10.1088/1757-899x/1218/1/012043

[49]Wang J, Liu H, Wang Z. Stochastic Project Scheduling Optimization for Multi-stage Prefabricated Building Construction with Reliability Application. KSCE Journal of Civil Engineering. 2023; 27(6): 2356-2371. doi: 10.1007/s12205-023-2164-8

[50]Ansar A, Flyvbjerg B, Budzier A, et al. Does infrastructure investment lead to economic growth or economic fragility? Evidence from China. Oxford Review of Economic Policy. 2016; 32(3): 360-390. doi: 10.1093/oxrep/grw022

[51]Cantarelli CC, Flyvbjerg B, Molin EJE, et al. Cost Overruns in Large-scale Transportation Infrastructure Projects: Explanations and Their Theoretical Embeddedness. European Journal of Transport and Infrastructure Research; 2010.

[52]Ellis RD, Thomas HR. The root causes of delays in highway construction. In: Proceedings of the 82nd Annual Meeting of the Transportation Research Board; 2002; Washington, D.C.

[53]Salhab D, Lindhard SM, Hamzeh F. Simulation-Based Approximation of the Gain from Applying Overlapping Activities. Journal of Construction Engineering and Management. 2024; 150(4). doi: 10.1061/jcemd4.coeng-14166

[54]Révész P. The laws of large numbers. Academic Press; 1968.

[55]Salhab D, Møller DE, Lindhard SM, et al. Accounting for Variability: Identifying Critical Activities as a Supplement to the Critical Path. Journal of Construction Engineering and Management. 2022; 148(5). doi: 10.1061/(ASCE)CO.1943-7862.0002266

[56]MoSPI G of I. FLASH REPORT ON (Rs. 150 crore and above). Government of India Ministry of Statistics and Programme Implementation Infrastructure and Project Monitoring Division; 2020.

[57]Gupta S, George RC, Philip D, et al. Data-Driven Decision Framework for Modeling and Quantification of Uncertainty and Variability in Construction Project Scheduling. Journal of Structural Design and Construction Practice ASCE. 2024. doi: 10.1061/JSDCCC/SCENG-1817

Published

2025-04-09

How to Cite

Gupta, S., George, R. C., Philip, D., & Nair, S. (2025). Impact of activity time stochasticity on critical paths and their completion probabilities in construction projects. Building Engineering, 3(2), 1703. https://doi.org/10.59400/be1703

Download Citation

Issue

Vol. 3 No. 2 (2025)

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

Editor-in-Chief

Prof. Scholz Miklas
University of Johannesburg, South Africa

eISSN

3029-2670

Publication Frequency

Quarterly (since 2025)

About the Publisher

Academic Publishing insists on taking academic exchange and publication as the main line, carrying out comprehensive management based on science and technology, and fully exploring excellent international publishing resources. Within 5 years, it will form a strategic framework and scale with science (S), technology (T), medicine (M), education (E), and humanities and arts (H) as the main publishing fields. Academic Publishing is headquartered in Singapore and based in Malaysia, with the United States and China providing the main scientific and academic resources. At the same time, it has established long-term good cooperative relations with other publishing companies, scientific research communities, and academic organizations in more than a dozen countries and regions. Academic Publishing uses English and Chinese as its main publishing languages, mainly publishing books, journals, and conference papers in print and online. The vast majority of publications follow the international open access policy, providing stable and long-term quality and professional publications. With the joint efforts of the expert team and our professional editorial team, our publications will gradually be indexed by international databases in stages to provide convenient and professional retrieval for various scholars. At the same time, manuscripts we accept will be subject to the peer review principle, and cutting-edge and innovative research articles will be preferentially accepted for peer reference and discussion. All kinds of our publications are welcome for peer to contribute, access, and download.

more

Volume Arrangement

2025

2024

2023

Featured Articles

Effect of natural pozzolana, pozzolanic sand, and basalt on thermal and mechanical properties of green concrete

Green concrete, also known as sustainable concrete, is a building material that aims to reduce environmental impact by using natural, recycled, or sustainable materials in its production. One way to achieve sustainability in concrete is to replace cement with pozzolanic materials, which not only reduces the carbon footprint but also improves the performance of concrete and reduces its cost. This study aims to use natural materials that can partially or completely replace cement and conventional aggregates in concrete mixes. pozzolanic gravel (GPoz) replaced coarse aggregate, basaltic sand (SBas) and pozzolanic (SPoz) replaced fine aggregate, while ground pozzolana (PN) replaced cement. This work focuses on the experimentation and simulation of concrete mixes using the four abovementioned materials. 36 cubes were cast to conduct the thermal conductivity test by direct exposure of concrete samples, where an insulated thermal chamber was designed from thermal bricks, equipped with a heat source from the bottom and an empty space for the tested sample from the top, and then the resistance test on simple pressure was conducted for the cubic samples at the age of 28 days. Pozzolanic aggregate, when used in combination with basalt sand, showed greater thermal resistance compared to conventional concrete. Even with the replacement of 50% of the cement with ground pozzolana, we notice an increase in resistance of more than 11%, but with the replacement of basalt sand with pozzolana sand, we notice an increase in thermal resistance of more than 53%. As for the mechanical properties represented by resistance on simple pressure, we notice an acceptable decrease in resistance when replacing cement with pozzolana, with the exception of mixtures containing aggregates and pozzolana sand together, where replacing 50% of the cement with pozzolana increases the resistance on simple pressure by more than 46.4%.

Fulfilling the potentials of residential solar energy in Egypt

Energy plays a very important role in Egypt’s economic development, but the country has a gap between its produced energy and the demand of its growing population. Utilization of solar power systems in Egypt could help the country to close this gap and fulfil its national and international obligations. However, since 1980, the focus in Egypt has been on large-scale industrial solar projects. Limited attention is given to smaller systems for typical residential buildings. The aim of this research, therefore, is to highlight the potential of small residential solar systems (SRSS) in Egypt. With the huge number of residential buildings accommodating more than 115 million Egyptians, SRSS could be the unearthed gem of a sustainable source of energy in Egypt. The geographical location of Egypt and climate were used to generate solar data using the Global Solar Atlas application. The amounts of monthly and annual solar irradiations were calculated and analysed to decide the best orientation of the system (facing east, west, north, and south), identify the optimum tilt angle of the system, and determine the size of the solar panels. A case study was used to illustrate the procedures of designing SRSS for a typical residential building in Egypt. The results showed that a 26 kWp SRSS oriented facing the east with an optimum tilt angle between 15° and 30° could produce an annual total output of electricity more than the annual demand of the occupants of the studied residential building. Such a system would fit easily on the roof of the building. It was concluded that the installation of SRSS in Egypt could help the country meet the demand of its ever-increasing population if properly regulated, financed, and managed. It is recommended that Egypt develop and implement policies to make installations of SRSS an attractive choice among homeowners and investors by introducing encouraging incentives and creating a competitive market with affordable SRSS.

Fighting for collusive bidding in the construction industry: A text mining-enabled approach

Policy measures are crucial for regulating collusive bidding and are integral to effective governance. However, current research lacks a comparative exploration of strategies to combat collusive bidding through policy. Therefore, this study aims to identify more effective countermeasures by examining policy variations between regions with low and high incidences of collusive bidding. Using Latent Dirichlet Allocation (LDA) topic modeling, the study extracts key themes from these policies, while qualitative analysis highlights differences in approaches. It underscores that integrating electronic and information technology into bidding systems significantly reduces collusive practices. While increasing penalties can deter collusive bidding, achieving desired impacts requires thorough investigation and vigilant oversight. Additionally, strengthening external supervision enhances control over such activities. This study identifies critical governance strategies for addressing collusive bidding and advocates further research into more effective methods within the construction sector.

Comprehensive seismic loss model of Tehran, Iran in the case of Mosha fault seismic scenario using stochastic finite-fault method

This paper presents the results of a study caried out to assess probable seismic loss, in term of damage to the residential buildings and the number of fatalities, in the case of Mosha Fault seismic scenario in Tehran, Iran. Accordingly, seismic risk components (including seismic hazard, exposure model and fragility curves) are evaluated. The stochastic finite-fault method with dynamic corner frequency is applied for quantifying ground motion values. The results shows that PGA on the soil surface could range between 0.1 g to 0.45 g. Then, a reliable model of building exposure by analyzing census data from Tehran is compiled. This model included 19 different classes of buildings and is used to evaluate the potential damage to buildings from seismic scenario. The results indicate that the median of damage ratio from 100,000 iterations for the whole of the city is about 6% ± 1.54%. The study found that the central and eastern parts of Tehran are the most vulnerable areas, with an estimated 15,952 residents at risk of losing their lives in this scenario. This is equivalent to 0.2 percent of total population of Tehran. The finding from this study can be used by local authorities to provide appropriate emergency-response and preparedness plans in the case of Mosha Fault seismic scenario.

Digital transformation of quality management in the construction industry during the execution phase by integration of building information modeling (BIM) and cloud computing

The quality of construction projects significantly impacts social and economic development. However, low quality and project failure often result from factors such as lack of quality procedures, poor communication, task coordination, and inefficient progress monitoring. This research aims to improve the efficiency of the construction phase by creating quality control checklists for processes and enhancing quality management through a collaborative digital environment integrating building information modeling (BIM) and cloud computing. Expert constructive interviews were first conducted to define a construction process quality control procedure to be linked to the 3DBIM model and then transition to a collaborative cloud environment (Autodesk Construction Cloud). An actual instance in Latakia City (Syria) demonstrated that the proposed methodology improves the efficiency and effectiveness of quality management during the implementation phase. It does so by offering a robust database, enhancing on-site quality information extraction from BIM models using smartphones, documenting defects and entering inspection data directly into a shared digital environment, and making it easier to track corrective actions and feedback. This facilitates constant and organized access to current data, reducing errors and rework, saving money and time, and enhancing decision-making speed and effectiveness. The search recommends the necessity of strict laws to adhere to quality procedures and the importance of providing infrastructure for digital transformation in quality management.

Net zero energy analysis and energy conversion of sustainable residential building in Muscat, Oman

The building sector is the predominant consumer of primary energy globally. The building sector accounts for around 40% of global energy production.Net Zero Energy Buildings (NZEBs) are highly suggested by energy experts as an effective option to alleviate the strain on primary energy sources caused by the building sector. The disparity between energy performance predictions provided during the design phase and the actual energy performance of residential buildings is mostly attributed to a limited comprehension of the components that influence energy consumption and the constraints of whole building simulation software. The objective of this research was to perform a comparison analysis of the expected and actual energy consumption of a prototype net-zero energy house built at the University of Technology and Applied Sciences in Muscat. The Hourly Analysis Programme (HAP V4.2) was utilised to forecast the energy consumption of a Net Zero Energy Building (NZEB) at HCT, taking into account the availability of an Energy Recovery Ventilator (ERV) and the absence of an ERV. The newly built house underwent a one-month testing phase to fulfil many duties according to competition regulations. One of the main goals was to generate on-site energy through photovoltaic panels, producing an amount proportional to the energy consumed by the house. Upon comparing the actual energy consumption data with the simulated result, it was noticed that the actual energy demand of the house was around 20% lower than the prediction made by the simulation tool.

Architecting sustainability performances and enablers for grid-interactive efficient buildings

Today, grid-interactive efficient buildings are gaining popularity due to their potential sustainability performances through their ability to learn, adapt, and evolve at different scales to improve the quality of life of their users while optimizing resource usage and service availability. This is realized through various practices such as management and control measures enabled by smart grid technologies, interoperability, and human-cyber-physical security. However, despite their great potential, the research of those technologies still faces various challenges. These include a lack of communication and control infrastructure to address interpretability, security, cost barriers, and difficulties balancing occupant needs with grid benefits. Initially, system modelling and simulation are promising approaches to address those challenges ahead of time. It involves the consideration of complex systems made up of components from various research domains. This paper addresses the above practices, highlighting the value of integrating technology and intelligence in the planning and operation of buildings, both new and old. It provides a way to educate architects and engineers about this emerging field and demonstrates how these practices can help in creating efficient, resilient, and secure buildings that contribute to occupant comfort and decarbonization.