A new framework for project time–cost–environmental trade-off problem with hybrid Fermatean fuzzy–grey information

One of the commitments held out by the project managers is to make sure that the project will end on time, within the stated funding, and with the highest standard. Environmental pollution is an impact of implementing construction projects. Therefore, environmental impact has recently been taken into account to judge project success. In this paper, a new framework is offered that concentrates on project scheduling from the standpoint of duration, expenditure, and environmental trade-off by viewing quality loss expense. To be more precise, the methodology has four steps. First grey critical path (GCP) analysis is carried out. In the second step, activities' environmental impacts on each execution mode under Fermatean fuzzy sets (FFSs) uncertainty are calculated utilizing a multi-criteria decision-making (MCDM) approach. Third, a new mathematical model under grey uncertainty is developed with crashing and overlapping strategies to minimize project duration, expense, quality loss expense, and environmental influences. At last, the fourth step is presented to categorize the activities into three groups based on their criticality level. A case study in the construction field is implemented to validate the methodology. Also, through sensitivity analysis, the methodology is confirmed.