A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project

Reza Lotfi; Zahra Yadegari; Seyed Hossein Hosseini; Amir Hossein Khameneh; Erfan Babaee Tirkolaee; Gerhard-Wilhelm Weber

doi:10.3934/jimo.2020158

Article Contents

2022, Volume 18, Issue 1: 375-396. Doi: 10.3934/jimo.2020158

This issue Previous Article Optimality results for a specific fractional problem Next Article Research on cascading failure modes and attack strategies of multimodal transport network

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

Received: November 30, 2019

Revised: June 30, 2020

Early access: November 2020

Published: January 2022

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Abstract

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:

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Figure 1. Schematic of time parameters

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Figure 2. Schematic performance of the $ \varepsilon $-constraint algorithm [38]

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Figure 3. the underpass bridge in Tehran

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Figure 4. Network Graph of the bridge construction project

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Figure 5. Time-cost, Time-quality, Time-Energy and Time-Pollution Charts

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Figure 6. Effects of uncertainty changes on Cost, Quality, Energy and Pollution

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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	$ \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

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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)	$ 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
18	Ramp and deck guard rail installation	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

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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

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