# American Institute of Mathematical Sciences

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

* Corresponding author: Reza Lotfi (Reza.lotfi.ieng@gmail.com, Rezalotfi@stu.yazd.ac.ir)

Received  December 2019 Revised  July 2020 Published  November 2020

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.

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 & Management Optimization, doi: 10.3934/jimo.2020158
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Schematic of time parameters
Schematic performance of the $\varepsilon$-constraint algorithm [38]
the underpass bridge in Tehran
Network Graph of the bridge construction project
Time-cost, Time-quality, Time-Energy and Time-Pollution Charts
Effects of uncertainty changes on Cost, Quality, Energy and Pollution
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 $\varepsilon$-constraint method NSGA-Ⅱ MOSA 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 $\varepsilon$-constraint method Nesting GA NE - [30] MMDTCTP One Discrete symbiotic organisms search NE - This research RRCTCQEPTP Multi GAMS Augmented $\varepsilon$-constraint 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 $\varepsilon$-constraint method NSGA-Ⅱ MOSA 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 $\varepsilon$-constraint method Nesting GA NE - [30] MMDTCTP One Discrete symbiotic organisms search NE - This research RRCTCQEPTP Multi GAMS Augmented $\varepsilon$-constraint 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
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) $CO_2$ Pollution(Ton) Time (day) Cost (Million Toman) Quality (%) Energy (KJ) $CO_2$ Pollution (Ton) Men (Person/day) Machine (per day) $\bar{t_i}$ $\bar{c_i}$ $\bar{q_i}$ $\bar{e_i}$ $\bar{p_i}$ $\bar{t_i}'$ $\bar{c_i}'$ $\bar{q_i}'$ $\bar{e_i}'$ $\bar{p_i}'$ $\bar{d_i1}'$ $\bar{d_i2}'$ 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) $CO_2$ Pollution(Ton) Time (day) Cost (Million Toman) Quality (%) Energy (KJ) $CO_2$ Pollution (Ton) Men (Person/day) Machine (per day) $\bar{t_i}$ $\bar{c_i}$ $\bar{q_i}$ $\bar{e_i}$ $\bar{p_i}$ $\bar{t_i}'$ $\bar{c_i}'$ $\bar{q_i}'$ $\bar{e_i}'$ $\bar{p_i}'$ $\bar{d_i1}'$ $\bar{d_i2}'$ 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
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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