Recently, the benefits of employing philosophical principles to optimize supply chains in the construction sector have been delved into by many researchers. This comprises three key segments: customers or employers, design, and construction. To address challenges and enhance the viability and competitiveness of the construction sector, the adoption of supply chain management has been proposed. This study develops a multi-objective mathematical model to design a construction supply chain, which includes a primary supplier and multiple customer projects. The primary goal is to ensure that the necessary materials are delivered at different intervals, considering each product's specific technical requirements and life cycles. It is crucial to prevent late deliveries, as they can lead to product wastage and substantially impact management decisions. Additionally, it is important to highlight that this study addresses the uncertainty in the supply chain, which further complicates the planning and decision-making processes. Accordingly, some related sensitivity analyses were done to reveal the profound influence of uncertainty on the proposed model, and its important uncertain parameters were specified. Next, the study employs the robust programming approach introduced by Bertsimas and Sim to tackle the uncertainty. To validate the proposed approach, it is implemented in a real-world case study. For small-size problems, the modified weighted Chebyshev method is used for solving the model. Then, the best-worst multi-criteria decision-making technique assesses the suggested model's ability to solve various problems in larger sizes. Subsequently, the study applies meta-heuristic algorithms like MOGA-II, MORDA, and MOSA to solve large-size problems. According to the outputs analysis, the MORDA algorithm executed better than the others. Ultimately, the study derives managerial insights based on the findings from the sensitivity analysis.