A Mathematical Model for Optimizing NPV and Greenhouse Gases for Construction Projects Under Carbon Emissions Constraints

Traditionally, projects have been scheduled with a primary focus on optimizing economic bene-fits, often at the expense of environmental considerations. However, in today's context, there is an increasing societal demand for organizations to incorporate sustainability practices into their project management policies. This research aims to address this pressing issue by developing a comprehensive mathematical model that takes into account two crucial objectives: project net present value (NPV) and greenhouse gas (GHG) emissions. This model introduces carbon emission constraints on a per-period basis, alongside the usual precedence and resource constraints. the problem represented by this model is proven to be NP-hard, which adds complexity to its solution. To tackle this challenge, two multi-objective metaheuristic algorithms, specifically the Modified Grey Wolf Optimizer (MGWO) and the Strength Pareto Evolutionary Algorithm 2 (SPEA2), have been employed to solve the model. Extensive comparative analyses of these me-ta heuristics across various multi-objective performance measures indicate that MGWO consistently outperforms SPEA2 in most scenarios. To illustrate the practical applicability of the pro-posed model, a real-world case study has been utilized. The results of this case study offer compelling insights, showing that project NPV can be significantly improved with only a marginal increase in GHG emissions. This finding highlights the model's potential to provide pragmatic solutions and valuable trade-off options for project planners and practitioners striving to balance economic objectives with environmental sustainability.