Time, cost, and quality (TCQ) as a triple constraint of construction projects have dependent and conflicting objectives. Considering the limited resources, estimation of the approximate TCQ is a complex and dynamic problem. In addition, the uncertain nature of construction projects and highly variable alternatives make the decision making process a complicated issue. In order to overcome these difficulties, many researchers in the related academic literature introduced different mathematical models on the TCQ trade-off problem so far. In these models, two different approaches were used to estimate TCQ-related data. In the continues approach, it was assumed that the relationship among these three components could be expressed by continuous functions. In the discrete approach, it was accepted that (i) the construction method, (ii) the crew formation, and (iii) the crew overtime policy have some impacts on the project TCQ and that the relationships among these three components become discrete. However, in previous studies, construction materials that have a significant impact on TCQ of construction activities and projects were not taken into account completely during the data formation process. As an exception, El Rayes and Kandil [1] considered different strengths of concrete as material alternatives in a highway construction project. In fact, all the studies focused on proving the applicability of different optimization techniques instead of optimizing TCQ of a real construction project. In this context, some simple projects including a limited number of activities were used to evaluate the applicability of the developed models. Therefore, in the present study, it is aimed to outline a new two-step methodology, including the alternative construction material utilization, for TCQ trade-off problems, especially for building projects which enable the utilization of the high variety of construction materials. For this purpose, the impact of construction materials on TCQ of a project was explained in a detailed manner. (C) 2016 The Authors. Published by Elsevier Ltd.