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January
2022, 18(1): 375-396.
doi: 10.3934/jimo.2020158
A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project
| 1. | Department of Industrial Engineering, Yazd University, Yazd, Iran |
| 2. | Department of Industrial Engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran |
| 3. | Department of Project and ConstructionManagement, Tehran University, Tehran, Iran |
| 4. | Department of Project Management & Construction, Tarbiat Modarres University, Tehran, Iran, MAPNA Group, Oil & Gas Division, Tehran, Iran |
| 5. | Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran, Department of Industrial and Systems Engineering, Istinye University, Istanbul, Turkey |
| 6. | Poznan University of Technology, Faculty of Engineering, Management, Poznan, Poland, Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey |
Sustainable development requires scheduling and implementation of projects by considering cost, environment, energy, and quality factors. Using a robust approach, this study investigates the time-cost-quality-energy-environment problem in executing projects and practically indicates its implementation capability in the form of a case study of a bridge construction project in Tehran, Iran. This study aims to take into account the sustainability pillars in scheduling projects and uncertainties in modeling them. To model the study problem, robust nonlinear programming (NLP) involving the objectives of cost, quality, energy, and pollution level is applied with resource-constrained. According to the results, as time diminished, the cost, energy, and pollution initially decreased and then increased, witha reduction in quality. To make the model close to the real world by considering uncertainties, the cost and quality tangibly improved, and pollution and energy consumption declined. We applied the augmented $ \varepsilon $-constraint method to solve the proposed model. According to the result of the research, with regard to the time-cost, time-quality, time-energy, and time-pollution charts, as uncertainty increases, the cost and quality will improve, and pollution and energy will decrease.
The proposed model can be employed for all industrial projects, including roads, construction, and manufacturing.
Keywords:
Robust optimization,
Multi-objective optimization,
Time-Cost-Quality-Energy-Environment Trade-off,
Augmented $ \varepsilon $-Constraint Method.
Mathematics Subject Classification:
Primary: 90B36.
Citation:
Reza Lotfi, Zahra Yadegari, Seyed Hossein Hosseini, Amir Hossein Khameneh, Erfan Babaee Tirkolaee, Gerhard-Wilhelm Weber. A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project. Journal of Industrial and Management Optimization,
2022, 18
(1)
: 375-396.
doi: 10.3934/jimo.2020158
![]()
References:
| [1] |
A. Azaron, C. Perkgoz and M. Sakawa,
A genetic algorithm approach for the time-cost trade-off in PERT networks, Applied Mathematics and Computation, 168 (2005), 1317-1339.
doi: 10.1016/j.amc.2004.10.021. |
| [2] |
R. Abbasnia, A. Afshar and E. Eshtehardian,
Time-cost trade-off problem in construction project management, based on fuzzy logic, Journal of Applied Sciences, 8 (2008), 4159-4165.
|
| [3] |
H. N. Ahuja, S. Dozzi and S. M. AbouRizk, Project Management: Techniques in Planning and Controlling Construction Projects, John Wiley & Sons, 1994. |
| [4] |
A. J. G. Babu and N. Suresh,
Project management with time, cost, and quality considerations, European Journal of Operational Research, 88 (1996), 320-327.
doi: 10.1016/0377-2217(94)00202-9. |
| [5] |
A. Ben-Tal and A. Nemirovski,
Robust solutions of linear programming problems contaminated with uncertain data, Mathematical Programming, 88 (2000), 411-424.
doi: 10.1007/PL00011380. |
| [6] |
A.-P. Chang, Research on defining green road project management operating scope by application of PDRI. Advances in Civil, Architectural, Structural and Constructional Engineering, Proceedings of the International Conference on Civil, Architectural, Structural and Constructional Engineering, Dong-A University, Busan, South Korea, CRC Press, (2015-2016). |
| [7] |
I. Cohen, B. Golany and A. Shtub,
The stochastic timecost tradeoff problem: A robust optimization approach, Networks: An International Journal, 49 (2007), 175-188.
doi: 10.1002/net.20153. |
| [8] |
E. Demeulemeester, B. De Reyck, B. Foubert, W. Herroelen and and M. Vanhoucke,
New computational results on the discrete time/cost trade-off problem in project networks, Journal of the Operational Research Society, 49 (1998), 1153-1163.
|
| [9] |
G. Deǧirmenci and M. Azizoǧlu,
Branch and bound based solution algorithms for the budget constrained discrete time/cost trade-off problem, Journal of the Operational Research Society, 64 (2013), 1474-1484.
|
| [10] |
K. El-Rayes and A. Kandil,
Time-cost-quality trade-off analysis for highway construction, Journal of Construction Engineering and Management, 131 (2005), 477-486.
doi: 10.1061/(ASCE)0733-9364(2005)131:4(477). |
| [11] |
R. H. A. El Razek, A. M. Diab, S. M. Hafez and R. F. Aziz,
Time-cost-quality trade-off software by using simplified genetic algorithm for typical repetitive construction projects, World Academy of Science, Engineering and Technology, 37 (2010), 312-320.
|
| [12] |
C.-W. Feng, L. Liu and S. A. Burns,
Using genetic algorithms to solve construction time-cost trade-off problems, Journal of Computing in Civil Engineering, 11 (1997), 184-189.
doi: 10.1061/(ASCE)0887-3801(1997)11:3(184). |
| [13] |
C.-W. Feng and L. Liu,
Burns SA. Stochastic construction time-cost trade-off analysis, Journal of Computing in Civil Engineering, 14 (2000), 117-126.
|
| [14] |
M.-B. Fakhrzad and R. Lotfi,
Green vendor managed inventory with backorder in two echelon supply chain with epsilon-constraint and NSGA-Ⅱ approach, Journal of Industrial Engineering Research in Production Systems, 5 (2018), 193-209.
|
| [15] |
Ö. Hazir, E. Erel and Y. Günalay,
Robust optimization models for the discrete time/cost trade-off problem, International Journal of Production Economics, 130 (2011), 87-95.
doi: 10.1016/j.ijpe.2010.11.018. |
| [16] |
M. H. Haghighi, S. M. Mousavi, J. Antuchevičien$\dot{e}$ and V. Mohagheghi,
A new analytical methodology to handle time-cost trade-off problem with considering quality loss cost under interval-valued fuzzy uncertainty, Technological and Economic Development of Economy, 25 (2019), 277-299.
doi: 10.3846/tede.2019.8422. |
| [17] |
M. Hariga, A. Shamayleh and F. El-Wehedi,
Integrated timecost tradeoff and resources leveling problems with allowed activity splitting, International Transactions in Operational Research, 26 (2019), 80-99.
doi: 10.1111/itor.12329. |
| [18] |
A. Hafezalkotob, E. Hosseinpour, M. Moradi and K. Khalili-Damghani,
Multi-resource trade-off problem of the project contractors in a cooperative environment: Highway construction case study, International Journal of Management Science and Engineering Management, 13 (2018), 129-138.
doi: 10.1080/17509653.2017.1323240. |
| [19] |
E. Hemat and M. V. N Sivakumar,
An effective method for simultaneously considering time-cost trade-off and constraint resource scheduling using nonlinear integer framework, International Journal of Optimization in Civil Engineering, 7 (2017), 211-230.
|
| [20] |
B.-G. Hwang and J. S. Tan,
Green building project management: Obstacles and solutions for sustainable development, Sustainable Development, 20 (2012), 335-349.
doi: 10.1002/sd.492. |
| [21] |
B.-G. Hwang and W. J. Ng,
Project management knowledge and skills for green construction: Overcoming challenges, International Journal of Project Management, 31 (2013), 272-284.
|
| [22] |
A. Hand, J. Zuo, B. Xia, X. Jin and P. Wu, Are green project management practices applicable to traditional projects, Proceedings of the 19th International Symposium on Advancement of Construction Management and Real Estate, Springer, (2015). |
| [23] |
C. Hendrickson, C. T. Hendrickson and T. Au, Project Management for Construction: Fundamental Concepts for Owners, Engineers, Architects, and Builders, Chris Hendrickson, 1989. |
| [24] |
T. Hegazy,
Optimization of construction time-cost trade-off analysis using genetic algorithms, Canadian Journal of Civil Engineering, 26 (1999), 685-697.
doi: 10.1139/l99-031. |
| [25] |
H. Iranmanesh, M. Skandari and M. Allahverdiloo,
Finding Pareto optimal front for the multi-mode time, cost quality trade-off in project scheduling, World Academy of Science, Engineering and Technology, 40 (2008), 346-350.
|
| [26] |
D. B. Khang and Y. M. Myint,
Time cost and quality trade-off in project management: A case study, International Journal of Project Management, 17 (1999), 249-256.
doi: 10.1016/S0263-7863(98)00043-X. |
| [27] |
C. Li, Y. Liao, X. Wen, Y. Wang and F. Yang,
The development and countermeasures of household biogas in northwest grain for green project areas of China, Renewable and Sustainable Energy Reviews, 44 (2015), 835-846.
doi: 10.1016/j.rser.2015.01.027. |
| [28] |
H. Li and P. Love,
Using improved genetic algorithms to facilitate time-cost optimization, Journal of Construction Engineering and management, 123 (1997), 233-237.
doi: 10.1061/(ASCE)0733-9364(1997)123:3(233). |
| [29] |
X. Li, Z. He and N. Wang, Multi-mode time-cost-robustness trade-off project scheduling problem under uncertainty, 2019 International Conference on Industrial Engineering and Systems Management (IESM), IEEE, (2019), 1–5.
doi: 10.1109/IESM45758.2019.8948120. |
| [30] |
D. Liu, H. Li, H. Wang, C. Qi and T. Rose, Discrete symbiotic organisms search method for solving large-scale time-cost trade-off problem in construction scheduling, Expert Systems with Applications, 148 (2020), 113230.
doi: 10.1016/j.eswa.2020.113230. |
| [31] |
R. Lotfi, Y. Zare Mehrjerdi and M. S. Pishvaee, A robust optimization approach to Resilience and sustainable closed-loop supply chain network design under risk averse, in 15th Iran International Industrial Engineering Conference, Yazd university, (2019). |
| [32] |
R. Lotfi, M. A. Nayeri, S. M. Sajadifar and N. Mardani,
Determination of start times and ordering plans for two-period projects with interdependent demand in project-oriented organizations: A case study on molding industry, Journal of Project Management, 2 (2017), 119-142.
doi: 10.5267/j.jpm.2017.9.001. |
| [33] |
R. Lotfi, G.-W. Weber, S. M. Sajadifar and N. Mardani,
Interdependent demand in the two-period newsvendor problem, J. Ind. Manag. Optim., 16 (2020), 117-140.
doi: 10.3934/jimo.2018143. |
| [34] |
R. Lotfi, Y. Zare Mehrjerdi, M. S. Pishvaee, A. Sadeghieh and G.-W. Weber, A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk, Numerical Algebra, Control & Optimization.
doi: 10.3934/naco.2020023. |
| [35] |
R. Maltzman and D. Shirley, Green Project Management, CRC Press, 2010.
doi: 10.1201/EBK1439830017.
|
| [36] |
S. Mandal,
Supply chain resilience: A state-of-the-art review and research directions, International Journal of Disaster Resilience in the Built Environment, 5 (2014), 427-453.
|
| [37] |
G. Mavrotas,
Effective implementation of the $\varepsilon$-constraint method in multi-objective mathematical programming problems, Applied Mathematics and Computation, 213 (2009), 455-465.
doi: 10.1016/j.amc.2009.03.037. |
| [38] |
A. V. Moreira, Development of an optimization methodology for pavement management systems, 2018. |
| [39] |
O. Moselhi,
Schedule compression using the direct stiffness method, Canadian Journal of Civil Engineering, 20 (1993), 65-72.
doi: 10.1139/l93-007. |
| [40] |
A. Özmen, G. W. Weber, İ. Batmaz and E. Kropat,
RCMARS: Robustification of CMARS with different scenarios under polyhedral uncertainty set, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 4780-4787.
doi: 10.1016/j.cnsns.2011.04.001. |
| [41] |
A. Pagnoni, Project Engineering: Computer–Oriented Planning and Operational Decision Making, Springer Science & Business Media, 2012. |
| [42] |
J. H. Patterson and W. D. Huber,
A horizon-varying, zero-one approach to project scheduling, Management Science, 20 (1974), 903-1022.
doi: 10.1287/mnsc.20.6.990. |
| [43] |
W. Prager,
A structural method of computing project cost polygons, Management Science, 9 (1963), 351-515.
doi: 10.1287/mnsc.9.3.394. |
| [44] |
M. S. Pishvaee, M. Rabbani and S. A. Torabi,
A robust optimization approach to closed-loop supply chain network design under uncertainty, Applied Mathematical Modelling, 35 (2011), 637-649.
doi: 10.1016/j.apm.2010.07.013. |
| [45] |
Q.-K. Pan, L. Gao, L. Wang, J. Liang and X.-Y. Li,
Effective heuristics and metaheuristics to minimize total flowtime for the distributed permutation flowshop problem, Expert Systems with Applications, 124 (2019), 309-324.
doi: 10.1016/j.eswa.2019.01.062. |
| [46] |
R. Ruiz, Q.-K. Pan and B. Naderi,
Iterated Greedy methods for the distributed permutation flowshop scheduling problem, Omega, 83 (2019), 213-222.
doi: 10.1016/j.omega.2018.03.004. |
| [47] |
M. Rahimi and H. Iranmanesh,
Multi objective particle swarm optimization for a discrete time, cost and quality trade-off problem, World Applied Sciences Journal, 4 (2008), 270-276.
|
| [48] |
K. Roper and R. Payant, The Facility Management Handbook, Amacom, 2014. |
| [49] |
A. L. Soyster,
Convex programming with set-inclusive constraints and applications to inexact linear programming, Operations Research, 21 (1973), 1154-1157.
|
| [50] |
N. Siemens, A simple CPM time-cost tradeoff algorithm, Management Science, 17 (1971), B354–B363.
doi: 10.1287/mnsc.17.6.B354. |
| [51] |
A. K. Sangaiah, A. Goli, E. B. Tirkolaee, M. Ranjbar-Bourani, H. M. Pandey and W. Zhang,
Big data-driven cognitive computing system for optimization of social media analytics, IEEE Access, 8 (2020), 82215-82226.
doi: 10.1109/ACCESS.2020.2991394. |
| [52] |
R. Sonmez, M. A. Iranagh and F. Uysal, Critical sequence crashing heuristic for resource-constrained discrete timecost trade-off problem, Journal of Construction Engineering and Management, 142 (2016), 04015090. |
| [53] |
H. R. Tareghian and S. H. Taheri,
A solution procedure for the discrete time, cost and quality tradeoff problem using electromagnetic scatter search, Applied Mathematics and Computation, 190 (2007), 1136-1145.
doi: 10.1016/j.amc.2007.01.100. |
| [54] |
E. B. Tirkolaee, A. Goli, M. Hematian, A. K. Sangaiah and T. Han,
Multi-objective multi-mode resource constrained project scheduling problem using Pareto-based algorithms, Computing, 101 (2019), 547-570.
doi: 10.1007/s00607-018-00693-1. |
| [55] |
E. B. Tirkolaee, A. Goli and G. W. Weber, Fuzzy mathematical programming and self-adaptive artificial fish swarm algorithm for just-in-time energy-aware flow shop scheduling problem with outsourcing option, IEEE Transactions on Fuzzy Systems, (2020). |
| [56] |
M. Van Den Eeckhout, B. Maenhout and M. Vanhoucke,
A heuristic procedure to solve the project staffing problem with discrete time/resource trade-offs and personnel scheduling constraints, Computers & Operations Research, 101 (2019), 144-161.
doi: 10.1016/j.cor.2018.09.008. |
| [57] |
M. Vanhoucke and D. Debels,
The discrete time/cost trade-off problem: Extensions and heuristic procedures, Journal of Scheduling, 10 (2007), 311-326.
doi: 10.1007/s10951-007-0031-y. |
| [58] |
C. Vira and Y. Y. Haimes, Multiobjective decision making: Theory and methodology, North Holland Series in System Science and Engineering, North-Holland, (1983). |
| [59] |
W. Wang and Q. Feng, Multi-objective optimization in construction project based on a hierarchical subpopulation particle swarm optimization algorithm, in 2008 Second International Symposium on Intelligent Information Technology Application, IEEE, Shanghai, (2008), 746–750.
doi: 10.1109/IITA.2008.99. |
| [60] |
D. X. Zheng, S. T. Ng and M. M. Kumaraswamy,
Applying Pareto ranking and niche formation to genetic algorithm-based multiobjective timecost optimization, Journal of Construction Engineering and Management, 131 (2005), 81-91.
|
| [61] |
X. Zhao, B.-G. Hwang and Y. Gao,
A fuzzy synthetic evaluation approach for risk assessment: A case of Singapore's green projects, Journal of Cleaner Production, 115 (2016), 203-213.
doi: 10.1016/j.jclepro.2015.11.042. |
| [62] |
H. Zhang and H. Li,
Multi-objective particle swarm optimization for construction time-cost tradeoff problems, Construction Management and Economics, 28 (2010), 75-88.
doi: 10.1080/01446190903406170. |
| [63] |
H. Zhang, H. Li and C. Tam,
Particle swarm optimization for resource-constrained project scheduling, International Journal of Project Management, 24 (2006), 83-92.
doi: 10.1016/j.ijproman.2005.06.006. |
| [64] |
Y. Zare Mehrjerdi and R. Lotfi,
Development of a mathematical model for sustainable closed-loop supply chain with efficiency and resilience systematic framework, International Journal of Supply and Operations Management, 6 (2019), 360-388.
|
| [65] |
F. Zhao, F. Xue, Y. Zhang, W. Ma, C. Zhang and H. Song,
A hybrid algorithm based on self-adaptive gravitational search algorithm and differential evolution, Expert Systems with Applications, 113 (2018), 515-530.
doi: 10.1016/j.eswa.2018.07.008. |
| [66] |
F. Zhao, S. Qin, Y. Zhang, W. Ma, C. Zhang and H. Song,
A two-stage differential biogeography-based optimization algorithm and its performance analysis, Expert Systems with Applications, 115 (2019), 329-345.
doi: 10.1016/j.eswa.2018.08.012. |
| [67] |
J.-W. Zhang and H.-F. Shan, Multi-resource constrained discrete time/cost trade-off problem and its improved genetic algorithm, in 2010 International Conference on Management Science & Engineering, 17-th Annual Conference Proceedings, IEEE, (2010), 123–128.
doi: 10.1109/ICMSE.2010.5719794. |
show all references
References:
| [1] |
A. Azaron, C. Perkgoz and M. Sakawa,
A genetic algorithm approach for the time-cost trade-off in PERT networks, Applied Mathematics and Computation, 168 (2005), 1317-1339.
doi: 10.1016/j.amc.2004.10.021. |
| [2] |
R. Abbasnia, A. Afshar and E. Eshtehardian,
Time-cost trade-off problem in construction project management, based on fuzzy logic, Journal of Applied Sciences, 8 (2008), 4159-4165.
|
| [3] |
H. N. Ahuja, S. Dozzi and S. M. AbouRizk, Project Management: Techniques in Planning and Controlling Construction Projects, John Wiley & Sons, 1994. |
| [4] |
A. J. G. Babu and N. Suresh,
Project management with time, cost, and quality considerations, European Journal of Operational Research, 88 (1996), 320-327.
doi: 10.1016/0377-2217(94)00202-9. |
| [5] |
A. Ben-Tal and A. Nemirovski,
Robust solutions of linear programming problems contaminated with uncertain data, Mathematical Programming, 88 (2000), 411-424.
doi: 10.1007/PL00011380. |
| [6] |
A.-P. Chang, Research on defining green road project management operating scope by application of PDRI. Advances in Civil, Architectural, Structural and Constructional Engineering, Proceedings of the International Conference on Civil, Architectural, Structural and Constructional Engineering, Dong-A University, Busan, South Korea, CRC Press, (2015-2016). |
| [7] |
I. Cohen, B. Golany and A. Shtub,
The stochastic timecost tradeoff problem: A robust optimization approach, Networks: An International Journal, 49 (2007), 175-188.
doi: 10.1002/net.20153. |
| [8] |
E. Demeulemeester, B. De Reyck, B. Foubert, W. Herroelen and and M. Vanhoucke,
New computational results on the discrete time/cost trade-off problem in project networks, Journal of the Operational Research Society, 49 (1998), 1153-1163.
|
| [9] |
G. Deǧirmenci and M. Azizoǧlu,
Branch and bound based solution algorithms for the budget constrained discrete time/cost trade-off problem, Journal of the Operational Research Society, 64 (2013), 1474-1484.
|
| [10] |
K. El-Rayes and A. Kandil,
Time-cost-quality trade-off analysis for highway construction, Journal of Construction Engineering and Management, 131 (2005), 477-486.
doi: 10.1061/(ASCE)0733-9364(2005)131:4(477). |
| [11] |
R. H. A. El Razek, A. M. Diab, S. M. Hafez and R. F. Aziz,
Time-cost-quality trade-off software by using simplified genetic algorithm for typical repetitive construction projects, World Academy of Science, Engineering and Technology, 37 (2010), 312-320.
|
| [12] |
C.-W. Feng, L. Liu and S. A. Burns,
Using genetic algorithms to solve construction time-cost trade-off problems, Journal of Computing in Civil Engineering, 11 (1997), 184-189.
doi: 10.1061/(ASCE)0887-3801(1997)11:3(184). |
| [13] |
C.-W. Feng and L. Liu,
Burns SA. Stochastic construction time-cost trade-off analysis, Journal of Computing in Civil Engineering, 14 (2000), 117-126.
|
| [14] |
M.-B. Fakhrzad and R. Lotfi,
Green vendor managed inventory with backorder in two echelon supply chain with epsilon-constraint and NSGA-Ⅱ approach, Journal of Industrial Engineering Research in Production Systems, 5 (2018), 193-209.
|
| [15] |
Ö. Hazir, E. Erel and Y. Günalay,
Robust optimization models for the discrete time/cost trade-off problem, International Journal of Production Economics, 130 (2011), 87-95.
doi: 10.1016/j.ijpe.2010.11.018. |
| [16] |
M. H. Haghighi, S. M. Mousavi, J. Antuchevičien$\dot{e}$ and V. Mohagheghi,
A new analytical methodology to handle time-cost trade-off problem with considering quality loss cost under interval-valued fuzzy uncertainty, Technological and Economic Development of Economy, 25 (2019), 277-299.
doi: 10.3846/tede.2019.8422. |
| [17] |
M. Hariga, A. Shamayleh and F. El-Wehedi,
Integrated timecost tradeoff and resources leveling problems with allowed activity splitting, International Transactions in Operational Research, 26 (2019), 80-99.
doi: 10.1111/itor.12329. |
| [18] |
A. Hafezalkotob, E. Hosseinpour, M. Moradi and K. Khalili-Damghani,
Multi-resource trade-off problem of the project contractors in a cooperative environment: Highway construction case study, International Journal of Management Science and Engineering Management, 13 (2018), 129-138.
doi: 10.1080/17509653.2017.1323240. |
| [19] |
E. Hemat and M. V. N Sivakumar,
An effective method for simultaneously considering time-cost trade-off and constraint resource scheduling using nonlinear integer framework, International Journal of Optimization in Civil Engineering, 7 (2017), 211-230.
|
| [20] |
B.-G. Hwang and J. S. Tan,
Green building project management: Obstacles and solutions for sustainable development, Sustainable Development, 20 (2012), 335-349.
doi: 10.1002/sd.492. |
| [21] |
B.-G. Hwang and W. J. Ng,
Project management knowledge and skills for green construction: Overcoming challenges, International Journal of Project Management, 31 (2013), 272-284.
|
| [22] |
A. Hand, J. Zuo, B. Xia, X. Jin and P. Wu, Are green project management practices applicable to traditional projects, Proceedings of the 19th International Symposium on Advancement of Construction Management and Real Estate, Springer, (2015). |
| [23] |
C. Hendrickson, C. T. Hendrickson and T. Au, Project Management for Construction: Fundamental Concepts for Owners, Engineers, Architects, and Builders, Chris Hendrickson, 1989. |
| [24] |
T. Hegazy,
Optimization of construction time-cost trade-off analysis using genetic algorithms, Canadian Journal of Civil Engineering, 26 (1999), 685-697.
doi: 10.1139/l99-031. |
| [25] |
H. Iranmanesh, M. Skandari and M. Allahverdiloo,
Finding Pareto optimal front for the multi-mode time, cost quality trade-off in project scheduling, World Academy of Science, Engineering and Technology, 40 (2008), 346-350.
|
| [26] |
D. B. Khang and Y. M. Myint,
Time cost and quality trade-off in project management: A case study, International Journal of Project Management, 17 (1999), 249-256.
doi: 10.1016/S0263-7863(98)00043-X. |
| [27] |
C. Li, Y. Liao, X. Wen, Y. Wang and F. Yang,
The development and countermeasures of household biogas in northwest grain for green project areas of China, Renewable and Sustainable Energy Reviews, 44 (2015), 835-846.
doi: 10.1016/j.rser.2015.01.027. |
| [28] |
H. Li and P. Love,
Using improved genetic algorithms to facilitate time-cost optimization, Journal of Construction Engineering and management, 123 (1997), 233-237.
doi: 10.1061/(ASCE)0733-9364(1997)123:3(233). |
| [29] |
X. Li, Z. He and N. Wang, Multi-mode time-cost-robustness trade-off project scheduling problem under uncertainty, 2019 International Conference on Industrial Engineering and Systems Management (IESM), IEEE, (2019), 1–5.
doi: 10.1109/IESM45758.2019.8948120. |
| [30] |
D. Liu, H. Li, H. Wang, C. Qi and T. Rose, Discrete symbiotic organisms search method for solving large-scale time-cost trade-off problem in construction scheduling, Expert Systems with Applications, 148 (2020), 113230.
doi: 10.1016/j.eswa.2020.113230. |
| [31] |
R. Lotfi, Y. Zare Mehrjerdi and M. S. Pishvaee, A robust optimization approach to Resilience and sustainable closed-loop supply chain network design under risk averse, in 15th Iran International Industrial Engineering Conference, Yazd university, (2019). |
| [32] |
R. Lotfi, M. A. Nayeri, S. M. Sajadifar and N. Mardani,
Determination of start times and ordering plans for two-period projects with interdependent demand in project-oriented organizations: A case study on molding industry, Journal of Project Management, 2 (2017), 119-142.
doi: 10.5267/j.jpm.2017.9.001. |
| [33] |
R. Lotfi, G.-W. Weber, S. M. Sajadifar and N. Mardani,
Interdependent demand in the two-period newsvendor problem, J. Ind. Manag. Optim., 16 (2020), 117-140.
doi: 10.3934/jimo.2018143. |
| [34] |
R. Lotfi, Y. Zare Mehrjerdi, M. S. Pishvaee, A. Sadeghieh and G.-W. Weber, A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk, Numerical Algebra, Control & Optimization.
doi: 10.3934/naco.2020023. |
| [35] |
R. Maltzman and D. Shirley, Green Project Management, CRC Press, 2010.
doi: 10.1201/EBK1439830017.
|
| [36] |
S. Mandal,
Supply chain resilience: A state-of-the-art review and research directions, International Journal of Disaster Resilience in the Built Environment, 5 (2014), 427-453.
|
| [37] |
G. Mavrotas,
Effective implementation of the $\varepsilon$-constraint method in multi-objective mathematical programming problems, Applied Mathematics and Computation, 213 (2009), 455-465.
doi: 10.1016/j.amc.2009.03.037. |
| [38] |
A. V. Moreira, Development of an optimization methodology for pavement management systems, 2018. |
| [39] |
O. Moselhi,
Schedule compression using the direct stiffness method, Canadian Journal of Civil Engineering, 20 (1993), 65-72.
doi: 10.1139/l93-007. |
| [40] |
A. Özmen, G. W. Weber, İ. Batmaz and E. Kropat,
RCMARS: Robustification of CMARS with different scenarios under polyhedral uncertainty set, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 4780-4787.
doi: 10.1016/j.cnsns.2011.04.001. |
| [41] |
A. Pagnoni, Project Engineering: Computer–Oriented Planning and Operational Decision Making, Springer Science & Business Media, 2012. |
| [42] |
J. H. Patterson and W. D. Huber,
A horizon-varying, zero-one approach to project scheduling, Management Science, 20 (1974), 903-1022.
doi: 10.1287/mnsc.20.6.990. |
| [43] |
W. Prager,
A structural method of computing project cost polygons, Management Science, 9 (1963), 351-515.
doi: 10.1287/mnsc.9.3.394. |
| [44] |
M. S. Pishvaee, M. Rabbani and S. A. Torabi,
A robust optimization approach to closed-loop supply chain network design under uncertainty, Applied Mathematical Modelling, 35 (2011), 637-649.
doi: 10.1016/j.apm.2010.07.013. |
| [45] |
Q.-K. Pan, L. Gao, L. Wang, J. Liang and X.-Y. Li,
Effective heuristics and metaheuristics to minimize total flowtime for the distributed permutation flowshop problem, Expert Systems with Applications, 124 (2019), 309-324.
doi: 10.1016/j.eswa.2019.01.062. |
| [46] |
R. Ruiz, Q.-K. Pan and B. Naderi,
Iterated Greedy methods for the distributed permutation flowshop scheduling problem, Omega, 83 (2019), 213-222.
doi: 10.1016/j.omega.2018.03.004. |
| [47] |
M. Rahimi and H. Iranmanesh,
Multi objective particle swarm optimization for a discrete time, cost and quality trade-off problem, World Applied Sciences Journal, 4 (2008), 270-276.
|
| [48] |
K. Roper and R. Payant, The Facility Management Handbook, Amacom, 2014. |
| [49] |
A. L. Soyster,
Convex programming with set-inclusive constraints and applications to inexact linear programming, Operations Research, 21 (1973), 1154-1157.
|
| [50] |
N. Siemens, A simple CPM time-cost tradeoff algorithm, Management Science, 17 (1971), B354–B363.
doi: 10.1287/mnsc.17.6.B354. |
| [51] |
A. K. Sangaiah, A. Goli, E. B. Tirkolaee, M. Ranjbar-Bourani, H. M. Pandey and W. Zhang,
Big data-driven cognitive computing system for optimization of social media analytics, IEEE Access, 8 (2020), 82215-82226.
doi: 10.1109/ACCESS.2020.2991394. |
| [52] |
R. Sonmez, M. A. Iranagh and F. Uysal, Critical sequence crashing heuristic for resource-constrained discrete timecost trade-off problem, Journal of Construction Engineering and Management, 142 (2016), 04015090. |
| [53] |
H. R. Tareghian and S. H. Taheri,
A solution procedure for the discrete time, cost and quality tradeoff problem using electromagnetic scatter search, Applied Mathematics and Computation, 190 (2007), 1136-1145.
doi: 10.1016/j.amc.2007.01.100. |
| [54] |
E. B. Tirkolaee, A. Goli, M. Hematian, A. K. Sangaiah and T. Han,
Multi-objective multi-mode resource constrained project scheduling problem using Pareto-based algorithms, Computing, 101 (2019), 547-570.
doi: 10.1007/s00607-018-00693-1. |
| [55] |
E. B. Tirkolaee, A. Goli and G. W. Weber, Fuzzy mathematical programming and self-adaptive artificial fish swarm algorithm for just-in-time energy-aware flow shop scheduling problem with outsourcing option, IEEE Transactions on Fuzzy Systems, (2020). |
| [56] |
M. Van Den Eeckhout, B. Maenhout and M. Vanhoucke,
A heuristic procedure to solve the project staffing problem with discrete time/resource trade-offs and personnel scheduling constraints, Computers & Operations Research, 101 (2019), 144-161.
doi: 10.1016/j.cor.2018.09.008. |
| [57] |
M. Vanhoucke and D. Debels,
The discrete time/cost trade-off problem: Extensions and heuristic procedures, Journal of Scheduling, 10 (2007), 311-326.
doi: 10.1007/s10951-007-0031-y. |
| [58] |
C. Vira and Y. Y. Haimes, Multiobjective decision making: Theory and methodology, North Holland Series in System Science and Engineering, North-Holland, (1983). |
| [59] |
W. Wang and Q. Feng, Multi-objective optimization in construction project based on a hierarchical subpopulation particle swarm optimization algorithm, in 2008 Second International Symposium on Intelligent Information Technology Application, IEEE, Shanghai, (2008), 746–750.
doi: 10.1109/IITA.2008.99. |
| [60] |
D. X. Zheng, S. T. Ng and M. M. Kumaraswamy,
Applying Pareto ranking and niche formation to genetic algorithm-based multiobjective timecost optimization, Journal of Construction Engineering and Management, 131 (2005), 81-91.
|
| [61] |
X. Zhao, B.-G. Hwang and Y. Gao,
A fuzzy synthetic evaluation approach for risk assessment: A case of Singapore's green projects, Journal of Cleaner Production, 115 (2016), 203-213.
doi: 10.1016/j.jclepro.2015.11.042. |
| [62] |
H. Zhang and H. Li,
Multi-objective particle swarm optimization for construction time-cost tradeoff problems, Construction Management and Economics, 28 (2010), 75-88.
doi: 10.1080/01446190903406170. |
| [63] |
H. Zhang, H. Li and C. Tam,
Particle swarm optimization for resource-constrained project scheduling, International Journal of Project Management, 24 (2006), 83-92.
doi: 10.1016/j.ijproman.2005.06.006. |
| [64] |
Y. Zare Mehrjerdi and R. Lotfi,
Development of a mathematical model for sustainable closed-loop supply chain with efficiency and resilience systematic framework, International Journal of Supply and Operations Management, 6 (2019), 360-388.
|
| [65] |
F. Zhao, F. Xue, Y. Zhang, W. Ma, C. Zhang and H. Song,
A hybrid algorithm based on self-adaptive gravitational search algorithm and differential evolution, Expert Systems with Applications, 113 (2018), 515-530.
doi: 10.1016/j.eswa.2018.07.008. |
| [66] |
F. Zhao, S. Qin, Y. Zhang, W. Ma, C. Zhang and H. Song,
A two-stage differential biogeography-based optimization algorithm and its performance analysis, Expert Systems with Applications, 115 (2019), 329-345.
doi: 10.1016/j.eswa.2018.08.012. |
| [67] |
J.-W. Zhang and H.-F. Shan, Multi-resource constrained discrete time/cost trade-off problem and its improved genetic algorithm, in 2010 International Conference on Management Science & Engineering, 17-th Annual Conference Proceedings, IEEE, (2010), 123–128.
doi: 10.1109/ICMSE.2010.5719794. |
Figure 3.
the underpass bridge in Tehran
Figure 4.
Network Graph of the bridge construction project
Figure 5.
Time-cost, Time-quality, Time-Energy and Time-Pollution Charts
Figure 6.
Effects of uncertainty changes on Cost, Quality, Energy and Pollution
Table 1.
Survey on related works
| Reference | Problem | Objective | Algorithms | Case Study | Uncertainty |
| [43] | TCTP | One | Heuristic algorithm | NE | - |
| [50] | TCTP | One | Heuristic algorithm | NE | - |
| [39] | TCTP | One | Heuristic algorithm | NE | - |
| [4] | TCQTP | Multi | Unknown Solver | NE | - |
| [42] | RCTCTP | One | Min and Max Bound | NE | - |
| [12] | TCTP | One | GA | NE | - |
| [28] | TCTP | One | GA | Household biogas | - |
| [8] | RCDTCTP | One | Branch-and-bound | NE | - |
| [24] | TCTP | One | GA | Construction | - |
| [26] | TCQTP | Multi | LINDO | Cement factory | - |
| [60] | TCTP | Multi | GA | NE | - |
| [10] | RCDTCQTP | Multi | GA | Highway construction | - |
| [47] | TCQTP | Multi | PSO | NE | - |
| [53] | DTCQTP | Multi | Electromagnetism algorithm | NE | - |
| [2] | FTCTP | One | ACO | Construction | Fuzzy logic |
| [25] | MMTCTP | One | FAST PGA Pareto optimal front | NE | - |
| [59] | TCTP | One | Hierarchical PSO | NE | - |
| [11] | TCQTP | Multi | Simplified GA | Construction | - |
| [7] | RTCTP | One | GAMS | NE | Robust optimization |
| [15] | RMMDTCTP | One | Benders Decomposition and Tabu search | NE | Robust optimization |
| [9] | MMDTCTP | One | Branch and bound and heuristic algorithms | NE | - |
| [16] | FTCQTP | Multi | GAMS | NE | Interval-valued fuzzy |
| [54] | MMRCPSP | Multi | NE | - | |
| [17] | MMRCTCTP | One | Cplex-Soler | NE | - |
| [56] | RCTCTP | One | Heuristic procedure | NE | - |
| [18] | CRCTCTP | One | LINGO | Highway | - |
| [19] | RCDTCTP | Multi | Microsoft Excel and project | NE | - |
| [52] | MMRCTCTP | One | Heuristic method | NE | - |
| [57] | RCDTCTP | One | Hybrid heuristic method | NE | - |
| [67] | MMRCTCTP | One | GA | NE | - |
| [29] | MMRCTCTP | Multi | NE | - | |
| [30] | MMDTCTP | One | Discrete symbiotic organisms search | NE | - |
| This research | RRCTCQEPTP | Multi | GAMS Augmented |
Bridge Construction | Robust optimization |
|
● NE: Numerical Example.
● NSGA-Ⅱ: Non-dominated Sorting Genetic Algorithm Ⅱ. MOSA: Multi-Objective Simulated Annealing Algorithm ● TCTP: Time-cost Trade-off Problem ● FTCTP: Fuzzy Time-cost Trade-off Problem ● RTCTP: Robust Time-cost Trade-off Problem ● RMMDTCTP: Robust Multi-mode Discrete Time-cost Trade-off Problem ● MMTCTP: Multi-mode Time-cost Trade-off Problem ● MMDTCTP: Multi-mode Discrete Time-cost Trade-off Problem ● TCQTP: Time-Cost- Quality Trade-Off Problem ● FTCQTP: Fuzzy Time-Cost- Quality Trade-Off Problem ● RCTCTP: Resource Constraint Time-cost Trade-off Problem ● DTCQTP: Discrete Time-Cost- Quality Trade-Off Problem ● RCDTCTP: Resource Constraint Discrete Time-Cost- Quality Trade-Off Problem ● MMRCSP: Multi-mode Resource Constraint Scheduling Problem ● MMRCTCTP: Multi-mode Resource Constraint Time-cost Trade-off Problem ● CRCTCTP: Cooperation Resource Constraint Time-cost Trade-off Problem ● RRCTCQEPTP: Robust Resource Constraint Time-Cost- Quality-Energy-Pollution Trade-off Problem | |||||
| Reference | Problem | Objective | Algorithms | Case Study | Uncertainty |
| [43] | TCTP | One | Heuristic algorithm | NE | - |
| [50] | TCTP | One | Heuristic algorithm | NE | - |
| [39] | TCTP | One | Heuristic algorithm | NE | - |
| [4] | TCQTP | Multi | Unknown Solver | NE | - |
| [42] | RCTCTP | One | Min and Max Bound | NE | - |
| [12] | TCTP | One | GA | NE | - |
| [28] | TCTP | One | GA | Household biogas | - |
| [8] | RCDTCTP | One | Branch-and-bound | NE | - |
| [24] | TCTP | One | GA | Construction | - |
| [26] | TCQTP | Multi | LINDO | Cement factory | - |
| [60] | TCTP | Multi | GA | NE | - |
| [10] | RCDTCQTP | Multi | GA | Highway construction | - |
| [47] | TCQTP | Multi | PSO | NE | - |
| [53] | DTCQTP | Multi | Electromagnetism algorithm | NE | - |
| [2] | FTCTP | One | ACO | Construction | Fuzzy logic |
| [25] | MMTCTP | One | FAST PGA Pareto optimal front | NE | - |
| [59] | TCTP | One | Hierarchical PSO | NE | - |
| [11] | TCQTP | Multi | Simplified GA | Construction | - |
| [7] | RTCTP | One | GAMS | NE | Robust optimization |
| [15] | RMMDTCTP | One | Benders Decomposition and Tabu search | NE | Robust optimization |
| [9] | MMDTCTP | One | Branch and bound and heuristic algorithms | NE | - |
| [16] | FTCQTP | Multi | GAMS | NE | Interval-valued fuzzy |
| [54] | MMRCPSP | Multi | NE | - | |
| [17] | MMRCTCTP | One | Cplex-Soler | NE | - |
| [56] | RCTCTP | One | Heuristic procedure | NE | - |
| [18] | CRCTCTP | One | LINGO | Highway | - |
| [19] | RCDTCTP | Multi | Microsoft Excel and project | NE | - |
| [52] | MMRCTCTP | One | Heuristic method | NE | - |
| [57] | RCDTCTP | One | Hybrid heuristic method | NE | - |
| [67] | MMRCTCTP | One | GA | NE | - |
| [29] | MMRCTCTP | Multi | NE | - | |
| [30] | MMDTCTP | One | Discrete symbiotic organisms search | NE | - |
| This research | RRCTCQEPTP | Multi | GAMS Augmented |
Bridge Construction | Robust optimization |
|
● NE: Numerical Example.
● NSGA-Ⅱ: Non-dominated Sorting Genetic Algorithm Ⅱ. MOSA: Multi-Objective Simulated Annealing Algorithm ● TCTP: Time-cost Trade-off Problem ● FTCTP: Fuzzy Time-cost Trade-off Problem ● RTCTP: Robust Time-cost Trade-off Problem ● RMMDTCTP: Robust Multi-mode Discrete Time-cost Trade-off Problem ● MMTCTP: Multi-mode Time-cost Trade-off Problem ● MMDTCTP: Multi-mode Discrete Time-cost Trade-off Problem ● TCQTP: Time-Cost- Quality Trade-Off Problem ● FTCQTP: Fuzzy Time-Cost- Quality Trade-Off Problem ● RCTCTP: Resource Constraint Time-cost Trade-off Problem ● DTCQTP: Discrete Time-Cost- Quality Trade-Off Problem ● RCDTCTP: Resource Constraint Discrete Time-Cost- Quality Trade-Off Problem ● MMRCSP: Multi-mode Resource Constraint Scheduling Problem ● MMRCTCTP: Multi-mode Resource Constraint Time-cost Trade-off Problem ● CRCTCTP: Cooperation Resource Constraint Time-cost Trade-off Problem ● RRCTCQEPTP: Robust Resource Constraint Time-Cost- Quality-Energy-Pollution Trade-off Problem | |||||
Table 2.
Cost, Quality, Energy, and Pollution Information for the bridge
| ID-Code | Activity | Predecessor | Nominal Normal | Nominal Compacted | Resource | |||||||||
| Time (day) | Cost (Million Toman) | Quality (%) | Energy (KJ) | Time (day) | Cost (Million Toman) | Quality (%) | Energy (KJ) | Men (Person/day) | Machine (per day) | |||||
| 1 | Workplace equipment | 12 | 100 | 100 | 900 | 300 | 10 | 110 | 96 | 932 | 370 | 7 | 10 | |
| 2 | Foundation pile | 1FS | 40 | 40 | 100 | 400 | 400 | 37 | 60 | 98 | 406 | 572 | 8 | 12 |
| 3 | Foundation | 2FS | 7 | 40 | 100 | 500 | 100 | 5 | 48 | 96 | 535 | 162 | 5 | 7 |
| 4 | Column | 3FS | 5 | 40 | 100 | 600 | 300 | 3 | 44 | 97 | 608 | 438 | 6 | 5 |
| 5 | Girder construction | 1FS | 80 | 200 | 100 | 400 | 200 | 73 | 300 | 98 | 413 | 329 | 7 | 9 |
| 6 | Bearings installation | 4.5FS | 5 | 5 | 100 | 200 | 400 | 2 | 6 | 98 | 213 | 677 | 10 | 7 |
| 7 | Girder installation | 6FS | 30 | 20 | 100 | 300 | 500 | 28 | 22 | 100 | 312 | 820 | 11 | 8 |
| 8 | Bolting | 7FS | 10 | 5 | 100 | 450 | 600 | 8 | 7.5 | 100 | 450 | 962 | 15 | 5 |
| 9 | Welding | 8FS | 10 | 40 | 100 | 300 | 400 | 8 | 48 | 97 | 300 | 614 | 20 | 6 |
| 10 | Slab form working | 9FS | 30 | 50 | 100 | 200 | 200 | 28 | 55 | 99 | 215 | 220 | 10 | 7 |
| 11 | Cantilever form working | 10FS | 20 | 40 | 100 | 300 | 300 | 18 | 60 | 98 | 322 | 450 | 14 | 10 |
| 12 | Reinforcement | 11FS | 48 | 60 | 100 | 700 | 450 | 46 | 72 | 99 | 740 | 750 | 7 | 11 |
| 13 | Concreting | 12FS | 6 | 45 | 100 | 300 | 300 | 4 | 49.5 | 99 | 310 | 355 | 8 | 7 |
| 14 | Cantilever coffrage | 13FS | 3 | 20 | 100 | 100 | 200 | 2 | 30 | 99 | 108 | 289 | 9 | 8 |
| 15 | Bituminizing | 14FS | 4 | 60 | 100 | 200 | 300 | 3 | 72 | 100 | 210 | 506 | 10 | 9 |
| 16 | East all | 15FS | 24 | 50 | 100 | 300 | 700 | 22 | 55 | 96 | 320 | 868 | 5 | 6 |
| 17 | East ramp | 16FS | 10 | 40 | 100 | 600 | 300 | 7 | 60 | 98 | 639 | 348 | 6 | 7 |
| 18 | Ramp and deck guard rail installation | 17.2 | 7 | 100 | 100 | 300 | 60 | 6 | 150 | 99 | 307 | 76 | 8 | 8 |
| FS | ||||||||||||||
| 19 | West wall | 15FS | 24 | 50 | 100 | 400 | 60 | 23 | 60 | 97 | 434 | 100 | 7 | 9 |
| 20 | West ramp | 19FS | 10 | 40 | 100 | 200 | 100 | 7 | 66 | 97 | 218 | 150 | 8 | 10 |
| 21 | Ramp and desk curb installation | 18FS | 5 | 60 | 100 | 450 | 40 | 4 | 72 | 95 | 458 | 51 | 9 | 5 |
| 22 | Ramp and deck side walk implementation | 21FS | 10 | 40 | 100 | 300 | 60 | 6 | 44 | 99 | 323 | 77 | 5 | 6 |
| 23 | Ramp and deck (asphalt) | 22FS | 4 | 60 | 100 | 200 | 40 | 3 | 90 | 99 | 217 | 59 | 2 | 8 |
| 24 | Take workshop down | 23FS | 10 | 40 | 100 | 300 | 200 | 9 | 48 | 95 | 313 | 251 | 1 | 1 |
| Resource need in all project | 3387 | 3532 | ||||||||||||
| ID-Code | Activity | Predecessor | Nominal Normal | Nominal Compacted | Resource | |||||||||
| Time (day) | Cost (Million Toman) | Quality (%) | Energy (KJ) | Time (day) | Cost (Million Toman) | Quality (%) | Energy (KJ) | Men (Person/day) | Machine (per day) | |||||
| 1 | Workplace equipment | 12 | 100 | 100 | 900 | 300 | 10 | 110 | 96 | 932 | 370 | 7 | 10 | |
| 2 | Foundation pile | 1FS | 40 | 40 | 100 | 400 | 400 | 37 | 60 | 98 | 406 | 572 | 8 | 12 |
| 3 | Foundation | 2FS | 7 | 40 | 100 | 500 | 100 | 5 | 48 | 96 | 535 | 162 | 5 | 7 |
| 4 | Column | 3FS | 5 | 40 | 100 | 600 | 300 | 3 | 44 | 97 | 608 | 438 | 6 | 5 |
| 5 | Girder construction | 1FS | 80 | 200 | 100 | 400 | 200 | 73 | 300 | 98 | 413 | 329 | 7 | 9 |
| 6 | Bearings installation | 4.5FS | 5 | 5 | 100 | 200 | 400 | 2 | 6 | 98 | 213 | 677 | 10 | 7 |
| 7 | Girder installation | 6FS | 30 | 20 | 100 | 300 | 500 | 28 | 22 | 100 | 312 | 820 | 11 | 8 |
| 8 | Bolting | 7FS | 10 | 5 | 100 | 450 | 600 | 8 | 7.5 | 100 | 450 | 962 | 15 | 5 |
| 9 | Welding | 8FS | 10 | 40 | 100 | 300 | 400 | 8 | 48 | 97 | 300 | 614 | 20 | 6 |
| 10 | Slab form working | 9FS | 30 | 50 | 100 | 200 | 200 | 28 | 55 | 99 | 215 | 220 | 10 | 7 |
| 11 | Cantilever form working | 10FS | 20 | 40 | 100 | 300 | 300 | 18 | 60 | 98 | 322 | 450 | 14 | 10 |
| 12 | Reinforcement | 11FS | 48 | 60 | 100 | 700 | 450 | 46 | 72 | 99 | 740 | 750 | 7 | 11 |
| 13 | Concreting | 12FS | 6 | 45 | 100 | 300 | 300 | 4 | 49.5 | 99 | 310 | 355 | 8 | 7 |
| 14 | Cantilever coffrage | 13FS | 3 | 20 | 100 | 100 | 200 | 2 | 30 | 99 | 108 | 289 | 9 | 8 |
| 15 | Bituminizing | 14FS | 4 | 60 | 100 | 200 | 300 | 3 | 72 | 100 | 210 | 506 | 10 | 9 |
| 16 | East all | 15FS | 24 | 50 | 100 | 300 | 700 | 22 | 55 | 96 | 320 | 868 | 5 | 6 |
| 17 | East ramp | 16FS | 10 | 40 | 100 | 600 | 300 | 7 | 60 | 98 | 639 | 348 | 6 | 7 |
| 18 | Ramp and deck guard rail installation | 17.2 | 7 | 100 | 100 | 300 | 60 | 6 | 150 | 99 | 307 | 76 | 8 | 8 |
| FS | ||||||||||||||
| 19 | West wall | 15FS | 24 | 50 | 100 | 400 | 60 | 23 | 60 | 97 | 434 | 100 | 7 | 9 |
| 20 | West ramp | 19FS | 10 | 40 | 100 | 200 | 100 | 7 | 66 | 97 | 218 | 150 | 8 | 10 |
| 21 | Ramp and desk curb installation | 18FS | 5 | 60 | 100 | 450 | 40 | 4 | 72 | 95 | 458 | 51 | 9 | 5 |
| 22 | Ramp and deck side walk implementation | 21FS | 10 | 40 | 100 | 300 | 60 | 6 | 44 | 99 | 323 | 77 | 5 | 6 |
| 23 | Ramp and deck (asphalt) | 22FS | 4 | 60 | 100 | 200 | 40 | 3 | 90 | 99 | 217 | 59 | 2 | 8 |
| 24 | Take workshop down | 23FS | 10 | 40 | 100 | 300 | 200 | 9 | 48 | 95 | 313 | 251 | 1 | 1 |
| Resource need in all project | 3387 | 3532 | ||||||||||||
Table 3.
Augmented $ \varepsilon $ -constraint method results for RRCTCQEPTP
| Time (day) |
Cost (Million Toman) |
Quality (%) |
Energy (KJ) |
CO2 Pollution (Ton) |
Time (day) |
Cost (Million Toman) |
Quality (%) |
Energy (KJ) |
CO2 Pollution (Ton) |
| 328 | 4525 | 92 | 10540 | 8150 | 305 | 4362 | 90 | 10596 | 9828 |
| 328 | 4525 | 92 | 10540 | 8150 | 305 | 4461 | 91 | 10554 | 9445 |
| 328 | 4533 | 92 | 10540 | 8590 | 305 | 4464 | 91 | 10504 | 9427 |
| 328 | 4525 | 92 | 10540 | 8150 | 305 | 4556 | 91 | 10610 | 8488 |
| 328 | 4802 | 89 | 10816 | 10249 | 305 | 4610 | 89 | 10745 | 10474 |
| 320 | 4453 | 92 | 10542 | 8653 | 297 | 4378 | 89 | 10626 | 10378 |
| 320 | 4557 | 92 | 10522 | 8405 | 297 | 4483 | 91 | 10608 | 10016 |
| 320 | 4512 | 92 | 10508 | 8757 | 297 | 4454 | 90 | 10541 | 9927 |
| 320 | 4508 | 92 | 10553 | 8172 | 297 | 4518 | 90 | 10622 | 9124 |
| 320 | 4741 | 89 | 10794 | 10344 | 297 | 4554 | 89 | 10730 | 10596 |
| 312 | 4390 | 91 | 10535 | 9187 | 289 | 4430 | 89 | 10679 | 10535 |
| 312 | 4488 | 92 | 10527 | 8892 | 289 | 4472 | 89 | 10645 | 10359 |
| 312 | 4484 | 91 | 10496 | 9098 | 289 | 4464 | 89 | 10639 | 10495 |
| 312 | 4558 | 91 | 10538 | 8276 | 289 | 4473 | 89 | 10679 | 10277 |
| 312 | 4672 | 89 | 10768 | 10397 | 289 | 450 | 88 | 10718 | 10734 |
| Time (day) |
Cost (Million Toman) |
Quality (%) |
Energy (KJ) |
CO2 Pollution (Ton) |
Time (day) |
Cost (Million Toman) |
Quality (%) |
Energy (KJ) |
CO2 Pollution (Ton) |
| 328 | 4525 | 92 | 10540 | 8150 | 305 | 4362 | 90 | 10596 | 9828 |
| 328 | 4525 | 92 | 10540 | 8150 | 305 | 4461 | 91 | 10554 | 9445 |
| 328 | 4533 | 92 | 10540 | 8590 | 305 | 4464 | 91 | 10504 | 9427 |
| 328 | 4525 | 92 | 10540 | 8150 | 305 | 4556 | 91 | 10610 | 8488 |
| 328 | 4802 | 89 | 10816 | 10249 | 305 | 4610 | 89 | 10745 | 10474 |
| 320 | 4453 | 92 | 10542 | 8653 | 297 | 4378 | 89 | 10626 | 10378 |
| 320 | 4557 | 92 | 10522 | 8405 | 297 | 4483 | 91 | 10608 | 10016 |
| 320 | 4512 | 92 | 10508 | 8757 | 297 | 4454 | 90 | 10541 | 9927 |
| 320 | 4508 | 92 | 10553 | 8172 | 297 | 4518 | 90 | 10622 | 9124 |
| 320 | 4741 | 89 | 10794 | 10344 | 297 | 4554 | 89 | 10730 | 10596 |
| 312 | 4390 | 91 | 10535 | 9187 | 289 | 4430 | 89 | 10679 | 10535 |
| 312 | 4488 | 92 | 10527 | 8892 | 289 | 4472 | 89 | 10645 | 10359 |
| 312 | 4484 | 91 | 10496 | 9098 | 289 | 4464 | 89 | 10639 | 10495 |
| 312 | 4558 | 91 | 10538 | 8276 | 289 | 4473 | 89 | 10679 | 10277 |
| 312 | 4672 | 89 | 10768 | 10397 | 289 | 450 | 88 | 10718 | 10734 |
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