Time-cost trade-off is a decision making problem in construction management Numerous optimization models have been developed to solve this problem most all of them are not applicable for even small-sized projects, because of the unmanageable required number of variables and constraints. The proper sequence (logic) of activities can be maintained by allowing for one constraint for each possible path, In practice, only small number of paths are dominant, while the others are redundant. In this paper, an efficient time-cost optimization model, which minimizes project cost, is developed depending on eliminating redundant paths. Precise activity time-cost relationship is used and overlapping between consecutive activities is permitted. The model is formulated in the form of zero-one programming. The model constraints include zero one constrains and network logic constraints. In formulating network logic constraints, only dominant paths are considered. Redundant paths are eliminated and consequently unnecessary decision variables are excluded. The model guarantees the optimal solution. The model is entirely formulated by interface with computer subroutine. The model requires as input: precedence relationship between activities, overlap values, and discrete utility data for project activities. The model efficiently reduces the problem size and can be used for large-sized project networks.