Time, cost and quality are the three factors that play a significant role in the planning and controlling of construction projects. The main barriers for their achievement are the changes in the project environment necessitating cost, time, and quality trade-offs. Literature has mainly focused on analyzing time and cost with little or no reported research focusing on models for optimizing construction time, cost, and quality jointly. Government agencies have recently started using new types of contracting methods which have placed an increasing pressure on decision makers in the construction industry to search for an optimal/near optimal resource utilization plan that minimizes construction cost and time while maximizing its quality. In this paper, a 0-1 Integer Programming model which enables meeting quality output standards and time and budget objectives respectively is developed. The clever use of binary variables allows us to solve many interesting and difficult problems and our ability to model complex problems increases tremendously when we use binary variables. A version of the model to minimize time meeting quality and cost objectives is applied to a road building project. Two alternatives versions of the model which enable to minimize cost meeting quality and time and to maximize quality meeting time and cost, are shown in an Appendix.