Modelling the stochastic dependence underlying construction cost and duration
Abstract
Construction cost and duration are two critical project indicators. It is acknowledged that these two indicators are closely dependent and highly uncertain due to various common factors and limited data for explanatory model calibration. However, the stochastic dependence underlying construction cost and duration is usually ignored and the subsequent probabilistic analysis can be misleading. In response, this study develops a Nataf distribution model of building cost and duration, in which the uncertainties of total cost, unit cost, and duration are respectively quantified by univariate distribution fitting, while their stochastic dependence is inferred by maximum likelihood estimation. This method is applied to the costs and durations of 77 China residential building projects completed between 2011 and 2016. The goodness of fit test illustrates that the data conform well to the developed model. The conditional distributions of cost and duration are then derived and the corresponding conditional expectations and variances are given. The results provide the distribution of building costs for a desired duration and the expected duration given a budget. This, together with the ability to update probabilities when new project information is available, confirms the potential of the proposed model to benefit precontract decision making from a risk perspective.
Keyword : probabilistic modelling, cost-duration, stochastic dependence, Nataf distribution
How to Cite
Xiao, X., Wang, F., Li, H., & Skitmore, M. (2018). Modelling the stochastic dependence underlying construction cost and duration. Journal of Civil Engineering and Management, 24(6), 444-456. https://doi.org/10.3846/jcem.2018.5712
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Agdas, D.; Warne, D. J.; Osio-Norgaard, J.; Masters, F. J. 2017. Utility of genetic algorithms for solving large-scale construction time-cost trade-off problems, Journal of Computing in Civil Engineering 32(1): 04017072. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000718
Ahuja, H. N.; Nandakumar, V. 1985. Simulation model to forecast project completion time, Journal of Construction Engineering and Management 111(4): 325–342. https://doi.org/10.1061/(ASCE)0733-9364(1985)111:4(325)
Alavipour, S. R.; Arditi, D. 2018. Optimizing financing cost in construction projects with fixed project duration, Journal of Construction Engineering and Management 144(4): 04018012. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001451
Aminbakhsh, S.; Sonmez, R. 2016. Discrete particle swarm optimization method for the large-scale discrete time–cost trade-off problem, Expert Systems with Applications 51: 177–185. https://doi.org/10.1016/j.eswa.2015.12.041
Ballesteros-Pérez, P. 2017. M-PERT: Manual project-duration estimation technique for teaching scheduling basics, Journal of Construction Engineering and Management 143(9): 04017063. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001358
Bromilow, F. 1969. Contract time performance expectations and the reality. Paper presented at the Building Forum.
Chan, A. P. 1999. Modelling building durations in Hong Kong, Construction Management & Economics 17(2): 189–196. https://doi.org/10.1080/014461999371682
Chan, A. P. C.; Chan, A. P. L. 2004. Key performance indicators for measuring construction success, Benchmarking: An International Journal 11(2): 203–221. https://doi.org/10.1108/14635770410532624
Chen, C.; Wu, W.; Zhang, B.; Sun, H. 2015. Correlated probabilistic load flow using a point estimate method with Nataf transformation, International Journal of Electrical Power & Energy Systems 65: 325–333. https://doi.org/10.1016/j.ijepes.2014.10.035
D’Agostino, R. 2017. Goodness-of-fit-techniques. Routledge.
Dada, J. O.; Jagboro, G. 2007. An evaluation of the impact of risk on project cost overrun in the Nigerian construction industry, Journal of Financial Management of Property and Construction 12(1): 37–44. https://doi.org/10.1108/13664380780001092
Deckro, R. F.; Hebert, J. E.; Verdini, W. A.; Grimsrud, P. H.; Venkateshwar, S. 1995. Nonlinear time/cost tradeoff models in project management, Computers & Industrial Engineering 28(2): 219–229. https://doi.org/10.1016/0360-8352(94)00199-W
Erol, H.; Dikmen, I.; Birgonul, M. T. 2017. Measuring the impact of lean construction practices on project duration and variability: A simulation-based study on residential buildings, Journal of Civil Engineering and Management 23(2): 241–251. https://doi.org/10.3846/13923730.2015.1068846
Famiyeh, S.; Amoatey, C. T.; Adaku, E.; Agbenohevi, C. S. 2017. Major causes of construction time and cost overruns: A case of selected educational sector projects in Ghana, Journal of Engineering, Design and Technology 15(2): 181–198. https://doi.org/10.1108/JEDT-11-2015-0075
Farshchian, M. M.; Heravi, G.; AbouRizk, S. 2017. Optimizing the owner’s scenarios for budget allocation in a portfolio of projects using agent-based simulation, Journal of Construction Engineering and Management 143(7): 04017022. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001315
Fine, B.; Hackemer, G. 1970. Estimating and bidding strategy. Costaine, Operational Research Department.
Flyvbjerg, B.; Skamris Holm, M. K.; Buhl, S. L. 2004. What causes cost overrun in transport infrastructure projects?, Transport Reviews 24(1): 3–18. https://doi.org/10.1080/0144164032000080494a
Friedman, L. 1956. A competitive-bidding strategy, Operations Research 4(1): 104–112. https://doi.org/10.1287/opre.4.1.104
Fulkerson, D. R. 1961. A network flow computation for project cost curves, Management Science 7(2): 167–178. https://doi.org/10.1287/mnsc.7.2.167
Grinyer, P. H.; Whittaker, J. D. 1973. Managerial judgement in a competitive bidding model, Journal of the Operational Research Society 24(2): 181–191. https://doi.org/10.1057/jors.1973.36
Higham, N. J. 2002. Accuracy and stability of numerical algorithms. Vol. 80. SIAM. https://doi.org/10.1137/1.9780898718027
Huo, T.; Ren, H.; Cai, W.; Shen, G. Q.; Liu, B.; Zhu, M.; Wu, H. 2018. Measurement and dependence analysis of cost overruns in megatransport infrastructure projects: Case study in Hong Kong, Journal of Construction Engineering and Management 144(3): 05018001. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001444
Irfan, M.; Khurshid, M. B.; Anastasopoulos, P.; Labi, S.; Moavenzadeh, F. 2011. Planning-stage estimation of highway project duration on the basis of anticipated project cost, project type, and contract type, International Journal of Project Management 29(1): 78–92. https://doi.org/10.1016/j.ijproman.2010.01.001
Isidore, L. J.; Back, W. E. 2002. Multiple simulation analysis for probabilistic cost and schedule integration, Journal of Construction Engineering and Management 128(3): 211–219. https://doi.org/10.1061/(ASCE)0733-9364(2002)128:3(211)
Ismail, I.; Memon, A. H.; Rahman, I. A. 2014. Expert opinion on risk level for factors affecting time and cost overrun along the project lifecycle in Malaysian construction projects, International Journal of Construction Technology and Management 1(2): 10–15.
Kaka, A.; Price, A. D. 1991. Relationship between value and duration of construction projects, Construction Management and Economics 9(4): 383–400. https://doi.org/10.1080/01446199100000030
Karabulut, M. 2017. Application of Monte Carlo simulation and PERT/CPM techniques in planning of construction projects: A case study, Periodicals of Engineering and Natural Sciences (PEN) 5(3). https://doi.org/10.21533/pen.v5i3.152
Kim, B.-C.; Reinschmidt, K. F. 2009. Probabilistic forecasting of project duration using Bayesian inference and the beta distribution, Journal of Construction Engineering and Management 135(3): 178–186. https://doi.org/10.1061/(ASCE)0733-9364(2009)135:3(178)
Kim, S.-Y.; Tuan, K. N.; Lee, J. D.; Pham, H.; Luu, V. T. 2018. Cost overrun factor analysis for hospital projects in Vietnam, KSCE Journal of Civil Engineering 22(1): 1–11. https://doi.org/10.1007/s12205-017-0947-5
Koo, C.; Hong, T.; Hyun, C.; Koo, K. 2010. A CBR-based hybrid model for predicting a construction duration and cost based on project characteristics in multi-family housing projects, Canadian Journal of Civil Engineering 37(5): 739–752. https://doi.org/10.1139/L10-007
Koo, C.; Hong, T.; Kim, S. 2015. An integrated multi-objective optimization model for solving the construction time-cost trade-off problem, Journal of Civil Engineering and Management 21(3): 323–333. https://doi.org/10.3846/13923730.2013.802733
Larsen, J. K.; Shen, G. Q.; Lindhard, S. M.; Brunoe, T. D. 2015. Factors affecting schedule delay, cost overrun, and quality level in public construction projects, Journal of Management in Engineering 32(1): 04015032. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000391
Lee, H.-s.; Shin, J.-w.; Park, M.; Ryu, H.-G. 2009. Probabilistic duration estimation model for high-rise structural work, Journal of Construction Engineering and Management 135(12): 1289–1298. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000105
Lo, T. Y.; Fung, I. W.; Tung, K. C. 2006. Construction delays in Hong Kong civil engineering projects, Journal of Construction Engineering and Management 132(6): 636–649. https://doi.org/10.1061/(ASCE)0733-9364(2006)132:6(636)
Love, P. E.; Edwards, D. J.; Irani, Z. 2012. Moving beyond optimism bias and strategic misrepresentation: An explanation for social infrastructure project cost overruns, IEEE Transactions on Engineering Management 59(4): 560–571. https://doi.org/10.1109/TEM.2011.2163628
Moret, Y.; Einstein, H. H. 2016. Construction cost and duration uncertainty model: application to high-speed rail line project, Journal of Construction Engineering and Management 142(10): 05016010. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001161
Mulla, S. S.; Waghmare, A. P. 2015. A study of factors caused for time & cost overruns in construction project & their remedial measures, International Journal of Engineering Research and Applications 5(1): 48–53.
Nassar, K. M.; Gunnarsson, H. G.; Hegab, M. Y. 2005. Using Weibull analysis for evaluation of cost and schedule performance, Journal of Construction Engineering and Management 131(12): 1257–1262. https://doi.org/10.1061/(ASCE)0733-9364(2005)131:12(1257)
Ng, S. T., Mak, M. M. Y.; Skitmore, R. M.; Lam, K. C.; Varnam, M. 2001. The predictive ability of Bromilow’s timecost model, Construction Management and Economics 19(2): 165–173. https://doi.org/10.1080/01446190150505090
Ogunsemi, D. R.; Jagboro, G. O. 2006. Time-cost model for building projects in Nigeria, Construction Management and Economics 24(3): 253–258. https://doi.org/10.1080/01446190500521041
Pinto, J. K.; Morris, P. W. 2004. The Wiley guide to managing projects. Hoboken, NJ.: Wiley.
Rosenblatt, M. 1952. Remarks on a multivariate transformation, The Annals of Mathematical Statistics 23(3): 470–472. https://doi.org/10.1214/aoms/1177729394
Sanchez, O. P.; Terlizzi, M. A.; de Moraes, H. R. d. O. C. 2017. Cost and time project management success factors for information systems development projects, International Journal of Project Management 35(8): 1608–1626. https://doi.org/10.1016/j.ijproman.2017.09.007
Shehu, Z.; Endut, I. R.; Akintoye, A. 2014a. Factors contributing to project time and hence cost overrun in the Malaysian construction industry, Journal of Financial Management of Property and Construction 19(1): 55–75. https://doi.org/10.1108/JFMPC-04-2013-0009
Shehu, Z.; Endut, I. R.; Akintoye, A.; Holt, G. D. 2014b. Cost overrun in the Malaysian construction industry projects: A deeper insight, International Journal of Project Management 32(8): 1471–1480. https://doi.org/10.1016/j.ijproman.2014.04.004
Skitmore, M. 1991. The construction contract bidder homogeneity assumption: An empirical test, Construction Management and Economics 9(5): 403–429.
Skitmore, M. 2001. Raftery curves for tender price forecasting: Empirical probabilities and pooling, Financial Management of Property and Construction 6(3): 141–154.
Tran, D.-H.; Cheng, M.-Y.; Cao, M.-T. 2015. Hybrid multiple objective artificial bee colony with differential evolution for the time–cost–quality tradeoff problem, Knowledge-Based Systems 74: 176–186. https://doi.org/10.1016/j.knosys.2014.11.018
Van Cauwelaert, F.; Heynig, E. 1979. Correction of bidding errors: the Belgian solution, Journal of the Construction Division 105(1): 13–23.
Wang, W.-C. 2005. Impact of soft logic on the probabilistic duration of construction projects, International Journal of Project Management 23(8): 600–610. https://doi.org/10.1016/j.ijproman.2005.05.008
Yeong, C. M. 1994. Time and cost performance of building contracts in Australia and Malaysia. University of South Australia.
Zheng, D. X.; Ng, S. T.; Kumaraswamy, M. M. 2004. Applying a genetic algorithm-based multiobjective approach for time-cost optimization, Journal of Construction Engineering and Management 130(2): 168–176. https://doi.org/10.1061/(ASCE)0733-9364(2004)130:2(168)
Žujo, V.; Car-Pušić, D.; Žileska-Pančovska, V.; Ćećez, M. 2017. Time and cost interdependence in water supply system construction projects, Technological and Economic Development of Economy 23(6): 895–914. https://doi.org/10.3846/20294913.2015.1071292
Ahuja, H. N.; Nandakumar, V. 1985. Simulation model to forecast project completion time, Journal of Construction Engineering and Management 111(4): 325–342. https://doi.org/10.1061/(ASCE)0733-9364(1985)111:4(325)
Alavipour, S. R.; Arditi, D. 2018. Optimizing financing cost in construction projects with fixed project duration, Journal of Construction Engineering and Management 144(4): 04018012. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001451
Aminbakhsh, S.; Sonmez, R. 2016. Discrete particle swarm optimization method for the large-scale discrete time–cost trade-off problem, Expert Systems with Applications 51: 177–185. https://doi.org/10.1016/j.eswa.2015.12.041
Ballesteros-Pérez, P. 2017. M-PERT: Manual project-duration estimation technique for teaching scheduling basics, Journal of Construction Engineering and Management 143(9): 04017063. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001358
Bromilow, F. 1969. Contract time performance expectations and the reality. Paper presented at the Building Forum.
Chan, A. P. 1999. Modelling building durations in Hong Kong, Construction Management & Economics 17(2): 189–196. https://doi.org/10.1080/014461999371682
Chan, A. P. C.; Chan, A. P. L. 2004. Key performance indicators for measuring construction success, Benchmarking: An International Journal 11(2): 203–221. https://doi.org/10.1108/14635770410532624
Chen, C.; Wu, W.; Zhang, B.; Sun, H. 2015. Correlated probabilistic load flow using a point estimate method with Nataf transformation, International Journal of Electrical Power & Energy Systems 65: 325–333. https://doi.org/10.1016/j.ijepes.2014.10.035
D’Agostino, R. 2017. Goodness-of-fit-techniques. Routledge.
Dada, J. O.; Jagboro, G. 2007. An evaluation of the impact of risk on project cost overrun in the Nigerian construction industry, Journal of Financial Management of Property and Construction 12(1): 37–44. https://doi.org/10.1108/13664380780001092
Deckro, R. F.; Hebert, J. E.; Verdini, W. A.; Grimsrud, P. H.; Venkateshwar, S. 1995. Nonlinear time/cost tradeoff models in project management, Computers & Industrial Engineering 28(2): 219–229. https://doi.org/10.1016/0360-8352(94)00199-W
Erol, H.; Dikmen, I.; Birgonul, M. T. 2017. Measuring the impact of lean construction practices on project duration and variability: A simulation-based study on residential buildings, Journal of Civil Engineering and Management 23(2): 241–251. https://doi.org/10.3846/13923730.2015.1068846
Famiyeh, S.; Amoatey, C. T.; Adaku, E.; Agbenohevi, C. S. 2017. Major causes of construction time and cost overruns: A case of selected educational sector projects in Ghana, Journal of Engineering, Design and Technology 15(2): 181–198. https://doi.org/10.1108/JEDT-11-2015-0075
Farshchian, M. M.; Heravi, G.; AbouRizk, S. 2017. Optimizing the owner’s scenarios for budget allocation in a portfolio of projects using agent-based simulation, Journal of Construction Engineering and Management 143(7): 04017022. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001315
Fine, B.; Hackemer, G. 1970. Estimating and bidding strategy. Costaine, Operational Research Department.
Flyvbjerg, B.; Skamris Holm, M. K.; Buhl, S. L. 2004. What causes cost overrun in transport infrastructure projects?, Transport Reviews 24(1): 3–18. https://doi.org/10.1080/0144164032000080494a
Friedman, L. 1956. A competitive-bidding strategy, Operations Research 4(1): 104–112. https://doi.org/10.1287/opre.4.1.104
Fulkerson, D. R. 1961. A network flow computation for project cost curves, Management Science 7(2): 167–178. https://doi.org/10.1287/mnsc.7.2.167
Grinyer, P. H.; Whittaker, J. D. 1973. Managerial judgement in a competitive bidding model, Journal of the Operational Research Society 24(2): 181–191. https://doi.org/10.1057/jors.1973.36
Higham, N. J. 2002. Accuracy and stability of numerical algorithms. Vol. 80. SIAM. https://doi.org/10.1137/1.9780898718027
Huo, T.; Ren, H.; Cai, W.; Shen, G. Q.; Liu, B.; Zhu, M.; Wu, H. 2018. Measurement and dependence analysis of cost overruns in megatransport infrastructure projects: Case study in Hong Kong, Journal of Construction Engineering and Management 144(3): 05018001. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001444
Irfan, M.; Khurshid, M. B.; Anastasopoulos, P.; Labi, S.; Moavenzadeh, F. 2011. Planning-stage estimation of highway project duration on the basis of anticipated project cost, project type, and contract type, International Journal of Project Management 29(1): 78–92. https://doi.org/10.1016/j.ijproman.2010.01.001
Isidore, L. J.; Back, W. E. 2002. Multiple simulation analysis for probabilistic cost and schedule integration, Journal of Construction Engineering and Management 128(3): 211–219. https://doi.org/10.1061/(ASCE)0733-9364(2002)128:3(211)
Ismail, I.; Memon, A. H.; Rahman, I. A. 2014. Expert opinion on risk level for factors affecting time and cost overrun along the project lifecycle in Malaysian construction projects, International Journal of Construction Technology and Management 1(2): 10–15.
Kaka, A.; Price, A. D. 1991. Relationship between value and duration of construction projects, Construction Management and Economics 9(4): 383–400. https://doi.org/10.1080/01446199100000030
Karabulut, M. 2017. Application of Monte Carlo simulation and PERT/CPM techniques in planning of construction projects: A case study, Periodicals of Engineering and Natural Sciences (PEN) 5(3). https://doi.org/10.21533/pen.v5i3.152
Kim, B.-C.; Reinschmidt, K. F. 2009. Probabilistic forecasting of project duration using Bayesian inference and the beta distribution, Journal of Construction Engineering and Management 135(3): 178–186. https://doi.org/10.1061/(ASCE)0733-9364(2009)135:3(178)
Kim, S.-Y.; Tuan, K. N.; Lee, J. D.; Pham, H.; Luu, V. T. 2018. Cost overrun factor analysis for hospital projects in Vietnam, KSCE Journal of Civil Engineering 22(1): 1–11. https://doi.org/10.1007/s12205-017-0947-5
Koo, C.; Hong, T.; Hyun, C.; Koo, K. 2010. A CBR-based hybrid model for predicting a construction duration and cost based on project characteristics in multi-family housing projects, Canadian Journal of Civil Engineering 37(5): 739–752. https://doi.org/10.1139/L10-007
Koo, C.; Hong, T.; Kim, S. 2015. An integrated multi-objective optimization model for solving the construction time-cost trade-off problem, Journal of Civil Engineering and Management 21(3): 323–333. https://doi.org/10.3846/13923730.2013.802733
Larsen, J. K.; Shen, G. Q.; Lindhard, S. M.; Brunoe, T. D. 2015. Factors affecting schedule delay, cost overrun, and quality level in public construction projects, Journal of Management in Engineering 32(1): 04015032. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000391
Lee, H.-s.; Shin, J.-w.; Park, M.; Ryu, H.-G. 2009. Probabilistic duration estimation model for high-rise structural work, Journal of Construction Engineering and Management 135(12): 1289–1298. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000105
Lo, T. Y.; Fung, I. W.; Tung, K. C. 2006. Construction delays in Hong Kong civil engineering projects, Journal of Construction Engineering and Management 132(6): 636–649. https://doi.org/10.1061/(ASCE)0733-9364(2006)132:6(636)
Love, P. E.; Edwards, D. J.; Irani, Z. 2012. Moving beyond optimism bias and strategic misrepresentation: An explanation for social infrastructure project cost overruns, IEEE Transactions on Engineering Management 59(4): 560–571. https://doi.org/10.1109/TEM.2011.2163628
Moret, Y.; Einstein, H. H. 2016. Construction cost and duration uncertainty model: application to high-speed rail line project, Journal of Construction Engineering and Management 142(10): 05016010. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001161
Mulla, S. S.; Waghmare, A. P. 2015. A study of factors caused for time & cost overruns in construction project & their remedial measures, International Journal of Engineering Research and Applications 5(1): 48–53.
Nassar, K. M.; Gunnarsson, H. G.; Hegab, M. Y. 2005. Using Weibull analysis for evaluation of cost and schedule performance, Journal of Construction Engineering and Management 131(12): 1257–1262. https://doi.org/10.1061/(ASCE)0733-9364(2005)131:12(1257)
Ng, S. T., Mak, M. M. Y.; Skitmore, R. M.; Lam, K. C.; Varnam, M. 2001. The predictive ability of Bromilow’s timecost model, Construction Management and Economics 19(2): 165–173. https://doi.org/10.1080/01446190150505090
Ogunsemi, D. R.; Jagboro, G. O. 2006. Time-cost model for building projects in Nigeria, Construction Management and Economics 24(3): 253–258. https://doi.org/10.1080/01446190500521041
Pinto, J. K.; Morris, P. W. 2004. The Wiley guide to managing projects. Hoboken, NJ.: Wiley.
Rosenblatt, M. 1952. Remarks on a multivariate transformation, The Annals of Mathematical Statistics 23(3): 470–472. https://doi.org/10.1214/aoms/1177729394
Sanchez, O. P.; Terlizzi, M. A.; de Moraes, H. R. d. O. C. 2017. Cost and time project management success factors for information systems development projects, International Journal of Project Management 35(8): 1608–1626. https://doi.org/10.1016/j.ijproman.2017.09.007
Shehu, Z.; Endut, I. R.; Akintoye, A. 2014a. Factors contributing to project time and hence cost overrun in the Malaysian construction industry, Journal of Financial Management of Property and Construction 19(1): 55–75. https://doi.org/10.1108/JFMPC-04-2013-0009
Shehu, Z.; Endut, I. R.; Akintoye, A.; Holt, G. D. 2014b. Cost overrun in the Malaysian construction industry projects: A deeper insight, International Journal of Project Management 32(8): 1471–1480. https://doi.org/10.1016/j.ijproman.2014.04.004
Skitmore, M. 1991. The construction contract bidder homogeneity assumption: An empirical test, Construction Management and Economics 9(5): 403–429.
Skitmore, M. 2001. Raftery curves for tender price forecasting: Empirical probabilities and pooling, Financial Management of Property and Construction 6(3): 141–154.
Tran, D.-H.; Cheng, M.-Y.; Cao, M.-T. 2015. Hybrid multiple objective artificial bee colony with differential evolution for the time–cost–quality tradeoff problem, Knowledge-Based Systems 74: 176–186. https://doi.org/10.1016/j.knosys.2014.11.018
Van Cauwelaert, F.; Heynig, E. 1979. Correction of bidding errors: the Belgian solution, Journal of the Construction Division 105(1): 13–23.
Wang, W.-C. 2005. Impact of soft logic on the probabilistic duration of construction projects, International Journal of Project Management 23(8): 600–610. https://doi.org/10.1016/j.ijproman.2005.05.008
Yeong, C. M. 1994. Time and cost performance of building contracts in Australia and Malaysia. University of South Australia.
Zheng, D. X.; Ng, S. T.; Kumaraswamy, M. M. 2004. Applying a genetic algorithm-based multiobjective approach for time-cost optimization, Journal of Construction Engineering and Management 130(2): 168–176. https://doi.org/10.1061/(ASCE)0733-9364(2004)130:2(168)
Žujo, V.; Car-Pušić, D.; Žileska-Pančovska, V.; Ćećez, M. 2017. Time and cost interdependence in water supply system construction projects, Technological and Economic Development of Economy 23(6): 895–914. https://doi.org/10.3846/20294913.2015.1071292