The construction Supply Chain (SC) suffers from very low productivity due to the temporary nature of projects, the complexity and extent of communication between actors, and high logistics costs. Therefore, leveraging synergy and interaction, along with the presence of an integrator, can help mitigate these challenges. Fourth-party logistics is one of the drivers that can be considered an integrator in the construction industry, given its successful implementation in other industries. This study presents a mathematical model to investigate the effect of synergy in the construction industry by taking advantage of the integrative potential of a 4PL. It also considers the interaction between contractors and 4PL, pricing for the supply of raw materials, and the choice of transportation method, thereby bringing the problem closer to reality. To validate and demonstrate the efficiency of the proposed model, GAMS, a commercial software package, is used to conduct sensitivity analyses of key variables. The results show that creating a synergistic framework between contractors and leveraging the integrative capabilities of a fourth-party logistics enterprise can significantly reduce project delivery costs and delays, suggesting the proposed model's higher efficiency than those available in the literature on the subject.