Application of three metaheuristic algorithms to time-cost-quality trade-off project scheduling problem for construction projects considering time value of money

Time, cost, and quality have been known as the project iron triangles and substantial factors in construction projects. Several studies have been conducted on time-cost-quality trade-off problems so far, however, none of them has considered the time value of money. In this paper, a multi-objective mathematical programming model is developed for time-cost-quality trade-off scheduling problems in construction projects considering the time value of money, since the time value of money, which is decreased during a long period of time, is a very important matter. Three objective functions of time, cost, and quality are taken into consideration. The cost objective function includes holding cost and negative cash flows. In this model, the net present value (NPV) of negative cash flow is calculated considering the costs of non-renewable (consumable) and renewable resources in each time period of executing activities, which can be mentioned as the other contribution of this study. Then, three metaheuristic algorithms including multi-objective grey wolf optimizer (MOGWO), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective particle swarm optimization (MOPSO) are applied, and their performance is evaluated using six metrics introduced in the literature. Finally, a bridge construction project is considered as a real case study. The findings show that considering the time value of money can prevent cost overrun in projects. Additionally, the results indicate that the MOGWO algorithm outperforms the NSGA-II and MOPSO algorithms.