Non-linear time-cost trade-off models of activity crashing: Application to construction scheduling and project compression with fast-tracking

When shortening a project's duration, activity crashing, fast-tracking and substitution are the three most commonly employed compression techniques. Crashing generally involves allocating extra resources to an activity with the intention of reducing its duration. To date, the activity time-cost relationship has for the most part been assumed to be linear, however, a few studies have suggested that this is not necessarily the case in practice. This paper proposes two non-linear theoretical models which assume either collaborative or non-collaborative resources. These models closely depict the two most common situations occurring during construction projects. The advantages of these models are that they allow for both discrete and continuous, as well as deterministic and stochastic configurations. Additionally, the quantity of resources required for crashing the activity can be quantified. Comparisons between the models and another recent fast-tracking model from the literature are discussed, and a Genetic Algorithm is implemented for a fictitious application example involving both compression techniques. •Almost all time-cost trade-off models are wrongly assumed to be linear or discrete.•Two new non-linear theoretical models are proposed for construction projects.•They allow discrete/continuous, and deterministic/stochastic configurations.•Comparison of crashing and fast-tracking is mathematically analysed.