Mathematical relations between supplier capacities, the resulting material supply shortages, together with the impact of material delays on construction projects are not well defined. In response to this, this paper presents a novel multi-objective mixed integer linear programming model that considers the selection of suitable suppliers, inventory management practices, order quantities and the possibility of splitting a material order as integrated decisions to be optimised. The trade-off between the overall procurement cost and the weighted lateness, a measure of material delay impacts, is optimised. Material prices, supplier capacities, and resulting delays are treated as fuzzy scenario-based parameters. The proposed model is tested on a numerical example and computation experiments validate the model performance. An extensive sensitivity analysis is carried out and results suggest that by considering high variations in uncertain supplier capacities, the model would generate lower procurement cost and show less significant delay impacts. Whereas greater variations in uncertain material prices cause the total procurement cost to grow 55%; greater variations in uncertain delay durations also drastically increase the weighted lateness by over 70%. This highlights the importance of having high quality estimates for uncertain parameters. Additionally, the analysis also indicates that a minimum overall satisfaction level of 0.9338 can be achieved depending on the model user's strategies, and the proposed scenario-adjusted problem outperforms problems modelled under deterministic market conditions. The major contribution of this paper lies in the development of a fuzzy scenario-based model to solve the supplier selection and material purchasing problem in construction supply chains.